1. Introduction

Active control of heat flow at the nanoscale is of both fundamental and applied interest in diverse fields including nanoscale thermometry^[1,2], heat-assisted high-density data storage^[3,4], thermal management of microelectronics^[5,6], and advanced energy conversion technology^[7,8]. For example, with the continued miniaturization and ever-increasing power density of electronic chips^[9,10], thermal dissipation has become a primary bottleneck limiting performance, reliability, and lifespan^[11,12]. Conventional thermal modulation relies on static material engineering, such as chemical doping^[13], defect control^[14-17], isotope enrichment^[18-21], strain regulation^[22-24], and fabrication of phononic crystals and metamaterials^[25-28]. While these approaches have achieved considerable success, their dependence on permanent structural or compositional modifications inherently restricts dynamic tunability, post-fabrication reconfigurability, and operational adaptability.

Microscopically, thermal transport is mediated by a variety of elementary energy carriers such as electrons and phonons for heat conduction and photons for thermal radiation. The dynamics and interactions of these energy carriers are therefore of fundamental importance, as they are ultimately dictated by lattice geometry, atomic potentials, and band structures. Any mechanism capable of reconfiguring these attributes provides a powerful avenue for engineering thermal transport at the nanoscale. Recently, graphene^[29] and diverse other layered van der Waals (vdW) materials^[30-34] have emerged as an ideal platform, which readily enable atomic-level control via stacking configurations. In particular, the rise of twistronics has driven a paradigm shift by leveraging rotations between adjacent atomic layers as a new degree of freedom to tune various physical properties. The introduction of a twist angle yields periodic moiré superlattices, which reshape the Brillouin zone and atomic potential landscape while preserving the chemical composition of the constituent materials^[35-38]. This geometric manipulation, first popularized by the magic-angle twisted bilayer graphene (TBG) with flat electronic bands and strongly correlated electron phenomena^[39,40], has rapidly established twist engineering as a highly effective knob for thermal modulation beyond conventional static approaches. Furthermore, state-of-the-art microdevices such as micro-electromechanical systems (MEMS)-based in-situ rotation platforms have enabled precise and continuous twist tuning^[41], paving the way for dynamic, reversible, and on-demand thermal manipulation in vdW heterostructures.

Here, we provide a timely review of recent advances in the twist engineering of nanoscale thermal transport (Figure 1). We start by introducing the basic principles of twist engineering in Section 2, including the formation of moiré superlattices and subsequent modulation of various energy carriers, together with a brief summary of state-of-the-art experimental techniques to obtain twisted vdW structures. In Section 3, we discuss the twist engineering of heat conduction, including both the experimental and computational advances across diverse materials. After outlining the inherent challenges in investigating these systems, we describe in detail the observed transport phenomena along both the out-of-plane and in-plane directions. In Section 4, we shift our focus from phonons to photons, and categorize the current efforts in twist engineering of thermal radiation into two primary strategies: tuning the intrinsic optical responses and modulating the extrinsic couplings. Finally, we conclude by highlighting the remaining challenges and promising directions for future research in this field.

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Figure 1. Twist engineering of nanoscale thermal transport.

2. Basic Principles of Twist Engineering

2.1 Formation of moiré superlattice

When two crystalline layers are stacked with a relative twist angle, the local stacking configuration varies gradually across the interface, giving rise to a long-wavelength moiré pattern (Figure 2a)^[37,42]. At zero twist or at certain discrete twist angles, the two lattices can share an exact common atomic supercell; such structures are referred to as commensurate. For most twist angles, however, the two lattices do not repeat exactly at the atomic scale and are therefore incommensurate. Commensurability provides the geometric basis for viewing a twisted bilayer as a single artificial crystal with an exact moiré supercell, thereby enabling conventional Bloch band theory descriptions. For incommensurate twist angles, this exact atomic periodicity is absent, but a well-defined moiré length, L, and nearly periodic modulation of local stacking remain, allowing the system to be described effectively as a moiré superlattice.

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Figure 2. Basic principles of twist engineering. (a) Formation of moiré superlattices in a twisted bilayer MoS₂/WS₂ heterostructure (θ = 9.2°), as characterized by the HAADF-STEM image, together with the corresponding SAED and fast Fourier transform patterns. Reproduced with permission from reference^[42]. Copyright © 2026 National Academy of Sciences; (b) Topographic and corrugation profiles of graphene layers. The upper panels show the fully relaxed out-of-plane z-displacement (corrugation) relative to the midinterface plane, while the lower panels depict the corrugation profile along the indicated dashed lines. Reproduced with permission from reference^[45]. Copyright © 2024 American Physical Society; (c) Reciprocal space representation showing the folding of the Brillouin zones (red and gray hexagons) into the moiré Brillouin zone (dashed black hexagon) due to lattice rotation. Reproduced with permission from reference^[150]. Copyright © 2021 American Physical Society; (d) Electronic band structure of TBG at the magic angle (θ = 1.1°), exhibiting flat bands near the Fermi level. Reproduced from reference^[40]. CC BY 4.0; (e) Evolution of interfacial friction as a function of θ, showing the transition from incommensurate to commensurate phases as predicted by the MD simulation (red) and the analytical model (blue). Reproduced with permission from reference^[45]. Copyright © 2024 American Physical Society; (f) Integration platform for precision twist-angle control. Left: Exploded schematic of the MEMS device architecture. Right: Cross-sectional view of the assembled device, where the 2D materials are integrated at the base of the central Si pillar (circled with red dashed lines and magnified in the inset). One layer is anchored on the pyramid-etched bottom of the Si pillar, while the other is placed on the substrate. Reproduced with permission from reference^[41]. Copyright © 2024 Springer Nature. MEMS: micro-electromechanical systems; TBG: twisted bilayer graphene; MD: molecular dynamics; HAADF-STEM: high-angle annular dark-field scanning transmission electron microscopy; SAED: selective area electron diffraction.

For an ideal rigid homobilayer with lattice constant a, the moiré period can be approximated by L = a/[2sin(θ/2)]^[43], where θ is the interlayer twist angle. As θ decreases, the moiré period grows rapidly, giving the lattice more space to deform within each moiré cell. At small twist angles, the rigid-lattice picture becomes less complete. In this regime, the system can lower its total energy by enlarging favorable stacking regions and reducing unfavorable ones, a process commonly described as lattice relaxation^[44,45]. In twisted bilayer graphene, for example, small-angle reconstruction reduces the area of high-energy AA stacking and expands AB/BA stacking domains, producing a triangular domain pattern separated by narrow boundaries. As shown in Figure 2b, the morphology of this relaxed interface depends strongly on the twist angle. At large twist angles, the corrugation tends to be very weak and approximately sinusoidal. As the twist angle decreases, the corrugation grows moderately and the profile deviates from a sinusoidal form^[37,45].

2.2 Effects of twist angle on energy carriers

The ability of twist angle to regulate heat flow originates from its impact on the elementary energy carriers. Conceptually, interlayer twist leads to the formation of a moiré superlattice, which alters the overall potential landscape and may also induce local atomic relaxations. As a result, the band structures of electrons and phonons and their self- and mutual interactions can be substantially or even fundamentally modified. Meanwhile, variations in the electronic and phononic properties inevitably impact the photonic responses. Altogether, this forms a unified picture for twist engineering of heat conduction and thermal radiation.

Historically, investigations of twist effects were first established for electrons, where the modulation of electronic structure serves as the primary starting point. In momentum space, the spatial twist manifests as a relative shift between the original electronic bands (such as the Dirac cones in bilayer graphene). This shift vector subsequently defines a new, smaller moiré Brillouin zone, as shown in Figure 2c. Within this restricted zone, the periodic moiré potential induces strong interlayer coupling and band hybridization, substantially altering the pristine band structure^[35,36]. Notably, at specific magic angles such as θ = 1.1°, this results in the emergence of flat bands and a drastically enhanced electronic density of states (DOS) (Figure 2d), giving rise to a variety of exotic phenomena including correlated insulators and unconventional superconductivity^[39,40]. In addition, lattice relaxation strongly modifies the band structure of TBG with small twisted angles, opening a low-energy gap near the Brillouin zone center. Away from these magic angles, the moiré superlattice can also enable substantial tuning of electronic properties such as bandgaps, effective masses, and mobilities^[37,46-48].

Closely tied to this electronic band reconstruction is the remarkable control of optical properties. The twist-dependent modification of the dielectric function and optical response enables active control over light-matter interactions, including absorption, emission, and scattering processes^[49-54]. These tunable optical characteristics provide the foundation for twist-engineered thermal radiation.

Beyond the electronic effects, the moiré potential also imposes a complex modulation on lattice vibrations^[55]. Analogous to the band reconstruction in electronic structures, the folded Brillouin zone induces hybridized vibrational modes^[56,57], including the low-frequency phason modes in an incommensurate moiré lattice^[58,59]. In parallel, twist-driven commensurate-incommensurate transitions drastically suppress interlayer friction, yielding structural superlubricity that further modulates the lattice dynamics of twisted systems^[60-62] (Figure 2e). This alters the coupling between atomic vibrations in the two layers, thereby reducing the transmission coefficients of phonons across the interface. Collectively, these modulations lead to flat phonon bands^[62,63], phonon localization^[64], and enhanced anharmonicity^[65], which in turn have a notable impact on heat conduction.

2.3 Techniques for preparing twisted structures

The fabrication of twisted vdW structures has been extensively reviewed elsewhere^[37,66]. Here, we briefly summarize the major fabrication routes. Existing approaches can be broadly categorized as mechanical assembly, direct growth, and, more recently, dynamic in-situ rotation.

To date, mechanical assembly remains the most widely adopted strategy due to its unparalleled flexibility in creating arbitrary twist angles^[67]. This top-down approach usually relies on polymer-assisted pick-up and transfer techniques (e.g., using viscoelastic polymer stamps) to sequentially stack exfoliated flakes or those grown by chemical vapor deposition (CVD). When coupled with customized nano-alignment stages, the twist-angle accuracy of this method typically reaches below 1°, with state-of-the-art implementations achieving sub-0.1° precision^[66,68,69]. However, such methods often introduce interfacial contamination and trapped blisters, while being limited to small sample areas and low processing efficiency.

Direct bottom-up growth approaches, such as CVD and molecular beam epitaxy, are therefore highly desirable for producing macroscale, and residue-free vdW interfaces. However, precise thermodynamic control over the twist angle during growth remains inherently challenging. To overcome this, advanced epitaxial strategies have been engineered^[70-73]; for instance, by sandwiching two pre-rotated single-crystal copper foils, the robust metal–layer interaction uniquely dictates the orientation of each epitaxially grown monolayer, successfully locking in customizable, highly consistent twist angles over large areas^[74].

Both direct growth and mechanical assembly typically produce statically twisted structures, with the twist angle permanently fixed once the device is fabricated. Recent technological advancements have driven the field towards dynamic in-situ control. Early dynamic approaches utilized micro-manipulators or atomic force microscopy (AFM) probes to mechanically shear and slide predefined 2D micro-mesas^[75-77]. To achieve higher precision and integration, on-chip MEMS platforms have recently been developed^[41,78]. The device architecture features a layered stack with a central silicon (Si) pillar supporting the top 2D material layer, while the bottom layer is anchored to the substrate (Figure 2f, left). Electrostatic actuation between the top and bottom layers enables precise rotational alignment. The cross-sectional view highlights the integration of 2D materials at the base of the Si pillar: one layer is fixed on the pyramid-etched bottom, and the other is placed on the substrate (Figure 2f, right). This design supports continuous tuning over the full 0–180° range with high angular resolution (0.33°). Such dynamic approaches have opened new frontiers for real-time characterization and the development of reconfigurable electronic, photonic, and thermal devices.

3. Heat Conduction

Among the three basic modes of thermal transport, heat conduction has so far received the most attention in terms of twist engineering. In twisted vdW materials, heat is primarily carried by phonons, making lattice vibrations the key to understanding twist effects^[79,80]. In this section, we first discuss the experimental and computational challenges associated with research on phonon-mediated heat conduction in twisted systems. We then summarize recent progress in twist-controlled out-of-plane and in-plane heat conduction, covering both homo- and heterostructures. We conclude this section with a brief discussion of ultrahigh and widely tunable thermal anisotropy.

3.1 Challenges in thermal measurement

Compared with electrical and optical measurements, thermal characterization of twisted vdW structures remains less developed, as reflected by the limited number of experimental studies. Although various micro/nanoscale thermal measurement techniques have already been comprehensively reviewed^[12,81,82], their application to twisted systems is far from straightforward. To minimize redundancy, here we only focus on the specific challenges in quantifying heat conduction in twisted systems.

For in-plane transport, optothermal Raman spectroscopy is most frequently employed^[83,84], which relies primarily on laser-induced local heating and temperature-dependent Raman peak shifts. However, this method generally suffers from large measurement uncertainties, since the extraction of thermal conductivity depends critically on the precise calibration of the Raman temperature coefficient and laser absorption efficiency. This makes it rather difficult to resolve subtle twist-dependent thermal effects.

For out-of-plane transport, the laser pump-probe techniques of time-domain thermoreflectance (TDTR) and frequency-domain thermoreflectance (FDTR) are often used^{[62,63,85-87]}. These methods provide non-contact measurements of the out-of-plane thermal conductivity and interfacial thermal conductance^[88-92]. Despite their higher accuracy, the characterization of twisted vdW systems remains a great challenge due to several inherent limitations. The primary obstacle arises from the intrinsically low sensitivity of these methods to the thermal signatures of samples with atomic thicknesses. Furthermore, the extraction of the intrinsic thermal properties is profoundly complicated by the presence of other thermal resistances in series. In particular, the boundary thermal resistances between the sample and the metal transducer or the substrate often overshadow the minute thermal resistance variation of the vdW twisted interface itself, making accurate data decoupling exceedingly difficult.

Of equal importance is the sample preparation process, which imposes another major bottleneck. Resolving twist-dependent thermal properties often demands multiple samples with a set of carefully selected twist angles. However, this requirement inevitably introduces deleterious sample-to-sample inconsistencies during the transfer process, such as random interfacial contamination, trapped nanoscale bubbles, varying degrees of structural reconstruction, and heterogeneous strain fields, which can substantially modify thermal transport properties. These extrinsic factors can severely obscure intrinsic twist effects and complicate the interpretation of experimental data.

3.2 Challenges in atomistic simulation

Theoretical modeling of thermal transport in twisted vdW systems is also inherently challenging because moiré superlattices introduce large length scales and complex structural relaxation. As a result, no single computational framework is currently able to simultaneously deliver atomistic fidelity, mode-level insight, and direct access to experimentally relevant system sizes.

The phonon Boltzmann transport equation (BTE), when combined with density functional theory (DFT) or machine-learned potentials (MLPs), provides a rigorous route to mode-resolved thermal transport calculations^[93-95]. In principle, this framework can capture twist-induced changes in phonon dispersion, group velocity, and phonon–phonon scattering. Such capabilities are especially valuable for identifying microscopic mechanisms such as band folding, mode softening, and lifetime suppression in twisted structures. However, the computational cost associated with constructing large moiré supercells has so far restricted first-principles BTE studies to relatively large twist angles and small systems^[65,96].

For larger systems beyond the applicability of BTE, molecular dynamics (MD) simulations remain the most widely used tool. Both equilibrium methods based on the Green–Kubo formalism^[97,98] and non-equilibrium methods have been employed to evaluate thermal conductivity and interfacial thermal conductance^[99]. A key advantage of MD is that anharmonicity is treated nonperturbatively, making it well suited for disordered, reconstructed, and twisted interfaces^[100]. Although simulations to date are mostly limited to the use of inaccurate empirical potentials, the rapid development and wide deployment of MLPs^[101,102] have made it possible to approach first-principles accuracy at a much lower cost. Nevertheless, several intrinsic limitations remain. First, classical MD neglects nuclear quantum statistics, which can be significant for high-frequency phonons and thermal transport at low temperatures. Further, mode-resolved transport information is missing by default and can only be extracted via additional spectral analysis. Moreover, force errors in MLPs can lead to notable underestimations of thermal conductivity^[103,104].

3.3 Manipulation of out-of-plane heat conduction

Out-of-plane transport has emerged as the primary focus among studies of twist-engineered heat conduction. In this geometry, heat must traverse the structurally modulated vdW gap, rendering thermal transport highly sensitive to twist-induced variations in interlayer coupling. To date, most theoretical studies have relied on MD simulations. Experimentally, TDTR and FDTR have been the primary techniques used to probe out-of-plane heat conduction. Representative results are summarized in Table 1.

Over the past few years, experimental investigations of graphite, bilayer graphene, and molybdenum disulfide (MoS₂) have broadly indicated that introducing a twist angle generally suppresses the out-of-plane interfacial thermal conductance, G^{[62,63,85,105]}. At the same time, this trend has been reproduced by simulations for a wide range of homostructures. However, these experiments and simulations also exhibit notable quantitative inconsistencies. Taking graphene as an example, MD studies of multilayer graphene reveal a monotonic but strongly nonlinear dependence of G on twist angle (Figure 3a)^[106]. Specifically, G drops steeply at small θ, typically within the first few degrees, and then plateaus at larger θ above roughly 15°^[106]. In contrast, experiments on TBG show a distinct trend. As demonstrated in Figure 3b, the measured G continues to decrease with increasing θ from about 3.2° to 27.2°^[85]. A similar discrepancy is observed in MoS₂. Although twist is also predicted to suppress out-of-plane heat transport in this material^[63,107], experiments indicate that G is nearly independent of θ^[108], as shown in Figure 3c. These discrepancies between theoretical calculations and experimental measurements primarily arise from their inherent limitations as detailed in earlier sections. In particular, on the theoretical side, the limited accuracy of empirical potentials, the neglect of nuclear quantum effects^[109], and the specific parameters used to model vdW layer thickness all contribute. On the experimental side, the results also suffer from multiple sources of inaccuracies and uncertainties, such as possible sample wrinkling and contamination, complications due to the substrate and various contact resistances, and inherently low sensitivity for atomically thin layers and buried interfaces.

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Figure 3. Twist engineering of out-of-plane heat conduction. (a) Calculated G for two kinds of twisted multilayer graphene as a function of θ. Reproduced with permission from reference^[106]. Copyright © 2020 American Physical Society; (b) Experimentally measured G as a function of θ in TBG. Reproduced with permission from reference^[85]. Copyright © 2024 Wiley; (c) Experimentally measured G as a function of θ in twisted bilayer MoS₂. Reproduced from reference^[108]. CC BY 4.0; (d) Measured κ_o (left) of HOPG and EG micro mesas and the extracted G (right) of the twisted superlubric interface as a function of temperature. Reproduced with permission from reference^[62]. Copyright © 2025 American Physical Society. Inset: Schematic of the mesa-based FDTR measurement; (e) Thermal resistance (left) and effective κ_o (right) of stacked monolayer amorphous carbon as a function of thickness (1L to 16L). Reproduced with permission from reference^[110]. Copyright © 2025 American Physical Society; (f) Measured and calculated G as a function of θ in twisted bilayer MoS₂/WS₂. Reproduced with permission from reference^[42]. Copyright © 2026 National Academy of Sciences; (g) X-shaped sensors together with a trilayer MoS₂/MoSSe/WSe₂ heterostructure and measured G under J⁺ (from MoS₂ to WSe₂, top profile) and J^- (from WSe₂ to MoS₂, bottom profile) heat flow conditions. Reproduced with permission from reference^[117]. Copyright © 2026 Springer Nature. TBG: twisted bilayer graphene; FDTR: frequency-domain thermoreflectance; HOPG: highly oriented pyrolytic graphite; EG: epitaxial graphite.

Although current efforts mainly focus on comparing different samples with fixed twist angles, in-situ interlayer rotations have also been implemented to directly examine twist-dependent thermal transport in graphite^[62]. By integrating microfabricated mesa structures with in-situ mechanical manipulation and FDTR thermal characterization (inset of Figure 3d), imperfections at the twisted interface are essentially eliminated, signal sensitivity to the buried interface is substantially amplified, and the twist angle truly stands as the sole independent variable. Consequently, the evolution of G can be resolved with unprecedented reliability. When the interface evolves from a superlubric state into a commensurate locked state, the signal difference reveals that the thermal conductance of a superlubric twisted graphite interface is ultrahigh at approximately 600 MWm^-2 K^-1[62]. Notably, such an observation is also corroborated by another independent methodology that comparatively measures the thermal transport across highly oriented pyrolytic graphite (HOPG) and single-crystal epitaxial graphite (EG) mesas (Figure 3d). Although this value is suppressed by roughly 30-fold compared to the locked state, it remains nearly an order of magnitude higher than the G values of most artificially stacked vdW heterostructures.

Beyond a single twisted interface, several studies have explored more complex stacking architectures, including randomly stacked^[63,110-112] and continuously twisted multilayer structures^[113]. These systems establish the stacking sequence as an extra degree of freedom that can influence thermal transport. For example, the out-of-plane thermal conductivity κ_o in randomly stacked MoS₂, graphene, and hexagonal boron nitride (hBN) can be suppressed by about two orders of magnitude to the one-dimensional glassy transport limit^[63,114]. This is because twist-induced disorder scattering of phonons overwhelms intrinsic phonon-phonon scattering, which reduces the phonon mean free paths to around the interlayer spacing. In addition, κ_obarely varies across a broad temperature range since disorder scattering is temperature insensitive. More recently, Wang et al. extend the concept of disordered stacking from crystalline to amorphous systems by vertically assembling monolayer amorphous carbon, and report an ultralow κ_o of ~0.08 W m^-1 K^-1 (Figure 3e)^[110]. A different behavior is observed in continuously twisted multilayer graphene (CTMG), which exhibits a more bulk-like transport character and a higher κ_o compared to stacked structures with the same number of layers but only a single twisted interface^[113]. Furthermore, although interfacial thermal conductance generally increases with temperature^[42,99], the bulk-like nature of CTMG leads to a smaller G at higher temperatures^[113].

More recent advancements are concerned with twisted heterostructures, which can exhibit thermal transport behaviors that differ from those of homostructures. While the thermal conductance in homostructures typically decreases with increasing θ, the measured G at θ = 38° in MoS₂/tungsten disulfide (WS₂) bilayers is higher than that of the commensurate 0° configuration (Figure 3f)^[42]. However, this behavior is not universal, since other twisted heterostructures, such as graphene/hBN^[114], graphene/MoS₂^[116], and molybdenum diselenide (MoSe₂)/tungsten diselenide (WSe₂)^[117], still exhibit a decrease in G with increasing θ. These results suggest that a general criterion to predict whether twist suppresses or enhances interfacial thermal transport in heterostructures has yet to be established. Beyond modulation of G, it has also been reported that twist engineering can be used to tune asymmetric thermal transport in a MoS₂/molybdenum sulfide selenide (MoSSe)/WSe₂ heterostructure^[117]. For example, by varying the twist angles at the two interfaces, the thermal rectification ratio increases from 23% to 104% (Figure 3g).

While a unified understanding is still missing, several physical mechanisms have been proposed to explain various twist-dependent heat conduction phenomena. In homostructures, the reduction of κ_o or G is widely attributed to the suppression of low-frequency acoustic phonons^{[107,108,118]} (Figure 4a), which serve as the dominant heat carriers. Recent studies based on both MD simulations and first-principles lattice dynamics reveal that the twist angle can induce the collapse of the transverse acoustic (TA) vibrational branches^[62,63,114] (Figure 4b), thereby reducing the group velocities. Moreover, the lifetimes of the heat carriers also tend to decrease due to increased scattering. Together, these factors strongly suppress thermal transport.

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Figure 4. Mechanism of twist-engineered out-of-plane heat conduction. (a) Spectral interfacial thermal conductance G at different twist angles from MD simulations. Inset: Schematic of twisted graphite. Reproduced with permission from reference^[62]. Copyright © 2025 American Physical Society; (b) Effect of twist on the phonon dispersion of graphite along the A-Γ direction. The orange lines represent the AB-stacked phase, while the blue lines represent the twisted configuration. Reproduced with permission from reference^[62]. Copyright © 2025 American Physical Society; (c) Schematic illustration of phonon transmission across locked (top) and slippery (bottom) interfaces. Reproduced with permission from reference^[62]. Copyright © 2025 American Physical Society; (d) MD calculated G for various twisted materials compared with the analytical predictions. Reproduced with permission from reference^[118]. Copyright © 2025 American Physical Society; (e) Average temperature of phonon modes at both sides of the untwisted and twisted bilayer MoS₂/WS₂ interface. Reproduced with permission from reference^[42]. Copyright © 2026 National Academy of Sciences; (f) SHC decomposition of the interfacial G of the MoSSe/WSe₂ heterointerface. η refers to the asymmetric property of heat transfer. Reproduced with permission from reference^[117]. Copyright © 2026 Springer Nature. MD: molecular dynamics; SHC: spectral heat current; TA: transverse acoustic.

To provide an intuitive understanding of the relationship between twist angle and interfacial thermal transport, a force-heat correlation picture has been proposed^[62]. As illustrated in Figure 4c, the twist modulation of thermal transport can be understood from the same interfacial-force perspective used to describe structural superlubricity. When the two layers are well aligned, the periodic interfacial potential remains highly correlated across the contact, and the restoring forces associated with atomic vibrations add constructively. As a result, the vibrational motion of atoms in the upper layer can efficiently drive the response of atoms in the lower layer, which promotes phonon transmission across the interface. By contrast, once the layers are twisted away from the locked state, the loss of registry makes the interfacial forces increasingly inhomogeneous and mutually compensating. This force cancellation not only leads to interfacial superlubricity as manifested by the sharply reduced lateral shear force (Figure 2e), but also reduces the ability of the lower layer to respond to the vibrational excitation of the upper layer, thereby hindering phonon-mediated heat flow. This intuitive picture moves beyond conventional spectral analysis in the reciprocal space and offers a direct real-space perspective.

Building upon the softening of acoustic phonons, an analytical model has been proposed to capture the relationship between G and θ as $G\left(\theta \right)/G_0={\lambda }^{e^{-\sqrt{\theta }}-1}$, where G₀ denotes the thermal conductance at θ = 0°, and λ is a parameter associated with the binding energies within the moiré superlattice^[118]. This formula agrees well with non-equilibrium molecular dynamics (NEMD) simulations for graphene, hBN, and TMDs (Figure 4d). However, it should be noted that the applicability is primarily limited to twist angles from 0° to 25°. Considering the intrinsic rotational symmetry of the underlying crystals, a natural extension can be made by incorporating the corresponding periodicity in θ. Beyond this mechanism, other twist-induced effects such as localized phonon modes in twisted multilayer graphene (TMG)^[119] and overdamped phonon dynamics in twisted graphene/MoS₂^[120] have also been identified as important factors that suppress thermal transport.

To understand the twist-induced enhancement of thermal conductance observed in some heterostructures (Figure 3f), inelastic phonon scattering at the interface has been considered. Briefly, interlayer twisting reconstructs the nonequilibrium interfacial phonon population and reverses the modal thermal hierarchy, such that high-energy optical modes on the hot side become more effectively coupled to low-energy acoustic modes on the cold side (Figure 4e). This twist-enabled optical-to-acoustic conversion opens additional inelastic transport pathways, which alleviates the intrinsic phonon mismatch and therefore induces an anomalous conductance enhancement^[42].

Finally, the thermal rectification in trilayer MoS₂/MoSSe/WSe₂ has been attributed to the structural asymmetry introduced by the Janus MoSSe layer, which creates two distinct heterointerfaces with different spectral heat current (SHC) characteristics. At the MoS₂/MoSSe interface, G is dominated by high-frequency phonons, whereas at the MoSSe/WSe₂ interface, low-frequency phonons contribute comparably to high-frequency ones (Figure 4f). This leads to unequal thermal resistance under forward and reverse heat fluxes, while the twist angle further tunes the rectification by modifying the moiré pattern and phonon coupling.

3.4 Manipulation of in-plane heat conduction

The influence of interlayer twist is not confined to the out-of-plane direction. Twist engineering can also affect in-plane phonon transport, even though the in-plane covalent bonds remain nearly unchanged. Experimental studies of in-plane thermal transport in twisted structures are relatively limited, primarily because accurate measurement of in-plane thermal conductivity κ_i in suspended thin samples remains technically challenging. A summary of available studies is presented in Table 2.

To date, only a few studies have managed to extract twist-dependent in-plane thermal properties. By employing the optothermal Raman method, it has been first demonstrated that TBG at θ = 34° exhibits a lower κ_i than monolayer graphene and Bernal-stacked bilayer graphene (Figure 5a)^[83]. Subsequently, an asymmetric V-shaped variation of κ_i is observed as θ increases from 0° to 30° (W-shaped for 0° to 60°), with a minimum κ_i near 11° (Figure 5b)^[84]. More recently, a suspended H-type gold nanosensor was used to simultaneously measure the in-plane thermal and electrical properties of suspended MoSe₂/WSe₂ heterostructures (Figure 5c)^[121]. As θ increases from 0° to 30°, the thermal rectification ratio decreases from 65% to 30%, whereas the electrical rectification ratio rises from 100% to 200%. It has been suggested that reducing the moiré period suppresses thermal asymmetry through stronger interlayer coupling. Meanwhile, it also amplifies electrical rectification by enhancing electronic DOS asymmetry.

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Figure 5. Twist engineering of in-plane heat conduction. (a) Optothermal Raman measurement of thermal conductivity in TBG. Reproduced with permission from reference^[83]. Copyright © 2014 American Chemical Society; (b) Measured thermal conductivity of TBG as a function of θ. Reproduced with permission from reference^[84]. Copyright © 2021 American Institute of Physics; (c) Thermal rectification of MoSe₂/WSe₂ heterostructures. Reproduced with permission from reference^[121]. Copyright © 2025 American Chemical Society; (d) W-shape for calculated thermal conductivity in twisted graphene. Reproduced from reference^[122]. CC BY 4.0; (e) Cumulative thermal conductivity of TBG as a function of phonon frequency. Reproduced with permission from reference^[65]. Copyright © 2023 American Chemical Society; (f) Normalized thermal conductivity by the corresponding untwisted one as a function of θ, and spatial distribution of in-plane atomic vibrational amplitude (θ = 1.1° and 5.0°) in TBG. Reproduced from reference^[124]. CC BY 4.0. TBG: twisted bilayer graphene; SG: single-layer graphene; AB-BG: AB-stacked bilayer graphene; MGTA: Multilayer graphene with twist angle.

In comparison to the limited experiments, theoretical studies have enabled broader observations. For example, MD simulations have reported a minimum in κ_i near 15°^[84] or 20°^[122], or a nearly constant plateau between 10° and 20° (Figure 5d)^[123-125]. Despite the subtle discrepancies, these studies attribute the reduction in κ_i to twist-induced modifications of phonon dispersions, reconstruction of the scattering phase space, and enhanced anharmonicity (particularly for the flexural modes)^[65,126] (Figure 5e). In this way, twist acts as a non-destructive geometrical perturbation that reshapes in-plane heat-carrying channels indirectly through interlayer coupling. One interesting concept emerging from recent simulations is the so-called thermal magic angle^[124]. Specifically, at the electronic magic angle of 1.08°, TBG exhibits a pronounced local minimum in κ_i (Figure 5f). This specific reduction arises from the delicate competition between two opposing effects: the increasing density of phonon scattering sites and homogenization of atomic vibrations and local stresses^[124] (right panels of Figure 5f). To date, this thermal magic angle has only been computationally predicted in TBG. Future simulations of other vdW materials, combined with direct experimental measurements, will be essential for exploring this phenomenon.

3.5 Manipulation of highly anisotropic heat conduction

Twist engineering can be employed not only to tune the individual components of thermal conductivity, but also to reshape the anisotropic character of heat conduction. Remarkable effects emerge when in-plane and cross-plane transport are considered together. A representative example is randomly stacked MoS₂ (Figure 6a), in which the thermal conductivity anisotropy ratio reaches as high as 900 at room temperature^[63] (Figure 6b,c). This exceptionally large value highlights the effectiveness of rotational disorder and stacking control in redirecting heat flow into preferred pathways. More broadly, these results suggest that twist engineering is not merely a way to suppress or enhance thermal conductivity, but a versatile route to tailor the full tensorial character of heat transport^{[107,114,127]}.

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Figure 6. Twist engineering of anisotropic heat conduction. (a) Schematic of thermal transport engineering in randomly stacked MoS₂; (b) Experimental and MD calculated in-plane (κ_i) and out-of-plane (κ_o) thermal conductivity in MoS₂ and randomly stacked MoS₂; (c) Comparison of the thermal anisotropy ratio (ρ) for different materials as a function of the slow-axis thermal conductivity (κ_s). Reproduced from reference^[63]. CC BY 4.0. MD: molecular dynamics; PG: pyrolytic graphite.

4. Thermal Radiation

While the primary focus of twist engineering has been on phonon-mediated heat conduction, its influence on electronic and optical properties has also opened up new avenues for controlling thermal radiation. In the far-field regime, the radiative heat flux is bounded by the Stefan-Boltzmann law for a blackbody, whereas at sub-wavelength gaps, near-field radiative heat transfer (NFRHT) can exceed the blackbody limit by orders of magnitude^[128-130] through the tunneling of evanescent waves, especially when the materials support highly localized surface electromagnetic modes such as surface plasmon polaritons (SPPs) and surface phonon polaritons (SPhPs)^[131-136]. Introducing a twist can reshape the surface modes and also the coupling between them without requiring complex nanostructuring or chemical modification of the materials. As a result, twist engineering provides a reversible and geometry-based knob for actively regulating radiative heat flow, with implications for advanced thermal management^[137], nanoscale energy harvesting^[138-141], and thermal logic circuitry^[142-144]. In general, twist engineering of thermal radiation can be realized either by modifying the intrinsic optical responses of materials or by controlling the extrinsic coupling between materials of fixed properties.

Despite the conceptual promise of twist-engineered thermal radiation, significant challenges remain in both experimental and theoretical studies, especially in the near-field regime. Experimentally, measuring NFRHT is notoriously difficult, especially in planar configurations^{[133-136,145]}. The need to incorporate twisted materials or configurational twists further complicates the setup, thus making precise and robust experiments extremely elusive. Understandably, no twist angle-resolved NFRHT experiment has been reported to date. Simulating thermal radiation of twisted materials within existing frameworks also poses additional challenges because their optical conductivities or dielectric functions are often unknown, and must be calculated using first-principles or tight-binding models over broad frequency ranges^[146,147].

4.1 Modulating heat flow via intrinsic optical response

Graphene is widely studied in NFRHT due to its electrically and chemically tunable SPPs in the terahertz and midinfrared range, which originate from its characteristic Dirac-cone electronic band structure^{[142,148,149]}. The introduction of interlayer rotation in bilayer graphene can effectively modulate the electronic bands and optical responses, making TBG attractive for twist control of thermal radiation. Yang et al.^[150,151] perform a systematic theoretical investigation of the NFRHT between two identical TBG sheets separated by a vacuum gap, as shown in Figure 7a. They find that the radiative heat flux can be strongly modulated by the twist angle through changes in the Drude weight (D) of the TBG, which governs the strength of intraband SPPs (Figure 7b). At relatively large twist angles (θ > 1.5°) and high chemical potentials, the heat flux can vary by more than 10-fold over only a few degrees of twist around some special angles dictated by D.

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Figure 7. Modulation of thermal radiation via intrinsic optical response. (a) Schematic of thermal radiation between two twisted graphene sheets separated by a vacuum gap d. Reproduced with permission from reference^[150]. Copyright © 2021 American Chemical Society; (b) Heat transfer coefficient h as a function of the twist angle at T = 300 K and a chemical potential of μ = 0.25 eV for d = 10 nm and 1 μm, together with the Drude weight in arbitrary units. Reproduced with permission from reference^[150]. Copyright © 2021 American Chemical Society; (c) Strong suppression near the magic angle. The left axis shows h as a function of gap size at T = 50 K and μ = 0.05 eV with an electron scattering rate of Γ = 0.7 meV, and the right axis shows the ratio of h at 10° to that at 1.05°. Reproduced with permission from reference^[151]. Copyright © 2022 Elsevier; (d) Spectral heat transfer coefficient across a 10 nm gap at T = 300 K and μ = 0. Reproduced with permission from reference^[151]. Copyright © 2022 Elsevier; (e) Far-field radiation spectrum of TBG with different twist angles as a function of photon energy at T = 300 K. Reproduced from reference^[153]. CC BY 4.0. TBG: twisted bilayer graphene.

More dramatic variations emerge near the magic angle of θ = 1.1° and at a low chemical potential (close to the charge neutrality point). In this regime, the emergence of flat bands leads to a reduced D, enabling more than 100-fold modulation of the radiative heat flow within 0.25° at 50 K. Further, over 10,000-fold suppression could be achieved as the electron scattering rate Γ reduces to 0.7 meV, as shown in Figure 7c (right axis). Meanwhile, the near-field thermal radiation spectra are also distinct from those of untwisted graphene, where the interband transitions lead to a multiband thermal transport phenomenon (Figure 7d). Finally, the impact of lattice relaxation on NFRHT is also investigated in terms of the interlayer coupling energy, which is considered important for θ below 2°^[152]. The results reveal that a stronger coupling leads to reduced modulation but more prominent multiband features in the radiation spectrum.

The unique electronic structure of flat bands also governs far-field thermal emission of a single body, albeit with a different manifestation (Figure 7e). As demonstrated by Zhang et al.^[153], TBG exhibits highly controllable far-field thermal radiation spectra. When θ approaches the magic angle, the radiation spectrum of TBG becomes highly concentrated with a narrow full width at half maximum (0.05-0.08 eV), due to the emergence of highly enhanced DOS peaks known as van Hove singularities. Because these specific wavelengths can be tuned away from the atmospheric windows, such a mechanism provides a promising platform for infrared invisibility and advanced thermal insulation.

4.2 Modulating heat flow via extrinsic coupling

Distinct from the interlayer twist that changes the band structure and optical properties of a material, another approach involves changing the relative orientations between radiating objects to modulate their couplings while keeping the intrinsic physical properties unchanged. Early traces of this idea date back more than a decade^[130,154]. Initial trials relied on the geometric asymmetry of the surfaces or objects, such as the NFRHT between two gratings.

Recently, intrinsically anisotropic materials have gained growing attention, which can support directional polaritons and therefore provide a pattern-free route to regulate NFRHT. By changing the relative orientation of two anisotropic objects, the mode-resolved overlap between the thermal emitter and receiver varies, which further modulates the photon transmission probability and radiative heat flux (Figure 8a). This idea has been explored in 2D systems including multilayers of black phosphorus where twists reshape the hybridization of multiple anisotropic plasmon branches^[155], and also in polar crystals in which optical-axis rotation redistributes the contributions of elliptic and hyperbolic phonon polaritons^[156]. In materials with broken time-reversal symmetry, including Weyl semimetals and ferromagnetic insulators with an external magnetic field, the same geometric principle is enriched by nonreciprocity, so that twisting directional plasmon or magnon polaritons can produce switch-like, and sometimes nonmonotonic, modulation of near-field heat flux^[157-159].

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Figure 8. Modulation of thermal radiation via extrinsic coupling. (a) Schematic of NFRHT between two semi-infinite uniaxial polar crystals with a relative rotation angle φ between their OAs. Reproduced with permission from reference^[156]. Copyright © 2025 American Chemical Society; (b) Effective temperature ratio ξ for two nanostructures rotating with different angular frequencies Ω₁ and Ω₂, where θ₂ denotes the thermal frequency. The dashed lines indicate the corresponding frequencies for which ξ is equal to 1. Reproduced with permission from reference^[160]. Copyright © 2025 American Chemical Society; (c) Schematic of the NFRHT system composed of three graphene gratings. Reproduced with permission from reference^[161]. Copyright © 2021 Elsevier; (d) Schematic of an idealized bilayer system consisting of a lossless quarter-wave plate stacked on a lossy dichroic emitter with a perfect electric conductor as the substrate (upper). The two layers are twisted with respect to each other by an angle. Microscope image of a twisted bilayer α-MoO₃ sample (lower). Reproduced from reference^[163]. CC BY 4.0. NFRHT: near-field radiative heat transfer; OAs: optical axes.

Beyond static two-body configurations, twist control has also been extended to various other ways of regulating radiative coupling. For example, NFRHT between a pair of rotating nanostructures can be increased, decreased, or even reversed when compared to the case of no rotation, as shown in Figure 8b^[160]. Further, the introduction of a third body offers an extra degree of freedom, where the middle layer serves as a tunable mediator between the emitter and receiver (Figure 8c). By rotating this layer, the coupling of the surface modes can be either enhanced or suppressed, which effectively opens or blocks select channels for heat flow^[161,162]. Finally, internal twist has also been employed to modulate the emission of a single body by controlling the mode coupling within it. For instance, twisting anisotropic vdW layers such as molybdenum trioxide (α-MoO₃) can break inversion-rotation symmetry and has been experimentally demonstrated to generate intrinsic chiral mid-infrared emission in the far field without using complex 3D metamaterials^[163]. In the configuration shown in Figure 8d, the bottom α-MoO₃ layer acts as a dichroic emitter while the top layer serves as a quarter-wave plate.

5. Conclusion and Outlook

Twist engineering has advanced rapidly over the past decade, achieving remarkable success in the exploration of electronic and optical properties. However, research on twist-modulated thermal transport lags far behind, despite its unique potential to control nanoscale heat flow via phonons and photons for novel energy conversion and thermal management applications. In our view, this is primarily due to nontrivial challenges in accurately measuring and simulating thermal transport in moiré superlattices. Encouragingly, several intriguing experimental and theoretical studies have recently emerged both in heat conduction and thermal radiation, paving the way for future exploration.

Looking forward, the full realization of in-situ and dynamic twist control is expected to enable unique experimental observations. So far, most studies have focused on statically twisted systems, while future real-time techniques may allow continuous measurement of heat flow in rotating vdW homo- and heterostructures, opening new possibilities for studying transient evolutions of heat carriers in moving systems. As an example, we anticipate the seamless integration of precise positioning platforms with advanced laser pump-probe techniques, such as TDTR or FDTR, to be crucial. In addition, establishing accurate measurements of in-plane heat conduction in free-standing twisted vdW structures will potentially reveal emergent phenomena such as the thermal magic angle. Moreover, advancements in atomistic computations particularly through the incorporation of machine-learned potentials may enable deeper and broader physical insights into twist engineering, as efficient simulations of ever-larger systems at quantum-mechanical accuracy become accessible.

Scientific questions of interest may include coherent and hydrodynamic phonon transport in twisted materials, twist engineering of the coupling among diverse energy carriers such as phonons, electrons, and photons, as well as multiphysics control of thermal transport in twisted systems via external fields. In particular, the impact of the strong electronic band reconstruction and the associated quantum phases on phonon dynamics and thermal transport remains a compelling open question. In addition, experimental observation of twist-controlled thermal radiation would be of great interest. In the near field, this requires integrating high-precision in-situ rotational control into existing platforms alongside advanced material transfer techniques that eliminate sample non-idealities and enable the formation of nanometer gaps.

Apart from fundamental research, twist engineering could also facilitate technological applications. First, twisted structures can enable highly anisotropic heat transport, offering new opportunities for thermal management in nanoelectronics and quantum devices. Beyond passive heat dissipation, dynamic interlayer rotation may support active thermal switching and rectification, and foster the development of reconfigurable and moving devices such as twistronics and slidetronics. To this end, low-friction metal/vdW interfaces and twisted TMD heterostructures may be among the leading candidates. Finally, twist engineering also holds promise for energy conversion by decoupling electron and phonon transport, thereby improving thermoelectric performance^[164,165], and by tailoring the radiation spectra for high-efficiency thermophotovoltaics.

Acknowledgements

We appreciate the High-performance Computing Platform of Peking University for supporting our simulations.

Authors contribution

Zhou W, Yang F, Wu S: Investigation, writing-original draft, writing-review & editing.

Song B: Writing-review & editing, funding acquisition, supervision.

Conflicts of interest

Bai Song is an Editorial Board Member of Thermo-X. The other authors declare no conflicts of interest.

Ethical approval

Not applicable.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

Availability of data and materials

Not applicable.

Funding

This work was financially supported by the National Key R & D Program of China (No. 2024YFA1207900), the Science Fund for Creative Research Groups from the National Natural Science Foundation of China (No. 52521007), and the Scientific Research Innovation Capability Support Project for Young Faculty (ZYGXQNJSKYCXNLZCXM-E1) from the Ministry of Education of China. W.Z. acknowledges support from the National Natural Science Foundation of China (No. 525B2087) and China Association for Science and Technology. B.S. acknowledges support from the New Cornerstone Science Foundation through the XPLORER PRIZE (This program does not have a grant number).

Copyright

© The Author(s) 2026.