Strain and Twist Engineering of Interfacial Thermal Transport in Homo- and Hetero-Interfaces of Graphene and Hexagonal Boron Nitride

Huasong Qin; Michael Urbakh; Oded Hod; Wengen Ouyang; Wenwu Jiang; Yilun Liu

arxiv: 2604.26300 · v1 · submitted 2026-04-29 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Strain and Twist Engineering of Interfacial Thermal Transport in Homo- and Hetero-Interfaces of Graphene and Hexagonal Boron Nitride

Wenwu Jiang , Huasong Qin , Yilun Liu , Wengen Ouyang , Oded Hod , Michael Urbakh This is my paper

Pith reviewed 2026-05-07 13:07 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.mtrl-sci

keywords graphenehexagonal boron nitrideinterfacial thermal transportstraintwistphonon modes2D interfaces

0 comments

The pith

Homogeneous graphene and h-BN interfaces reduce vertical heat flow under strain or twist while heterogeneous ones respond only to strain.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper predicts a clear split in behavior: stacks of two graphene sheets or two h-BN sheets lose vertical thermal conductance when the layers are strained in-plane or twisted relative to each other. Mixed graphene-on-h-BN stacks stay insensitive to twist but gain conductance under compression and lose it under tension. These outcomes are traced to changes in vertical phonons and the local stacking pattern between layers. A simple model that tracks only the interlayer distance and stacking arrangement reproduces the full set of simulation results. The distinction matters for any device that must move heat across atomically thin interfaces.

Core claim

Vertical thermal conductance at homogeneous interfaces decreases strongly for both in-plane strain and interfacial twist, while at heterogeneous graphene/h-BN interfaces it remains insensitive to twist yet increases under compressive strain and decreases under tensile strain. Atomistic simulations, Fermi's golden rule analysis, and phonon density-of-modes calculations show that vertical phonons together with local stacking configurations govern the transport. A phenomenological model built on interlayer distance and stacking reproduces the observed dependence on both strain and twist.

What carries the argument

Phenomenological model based on local interlayer distance and stacking configurations that reproduces the strain and twist dependence of vertical thermal conductance.

If this is right

Compressive strain can raise vertical heat flow across graphene/h-BN junctions while tensile strain lowers it.
Twist angle can suppress conductance at graphene-graphene or h-BN/h-BN interfaces without affecting graphene/h-BN ones.
Vertical phonons and local stacking patterns determine how deformations change interlayer heat transport.
A minimal model using only interlayer spacing and stacking type captures the full mechanical response.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The selective sensitivity could let designers create thermal switches that respond to one mechanical variable but ignore another.
The same strain-twist contrast may appear in other van der Waals bilayers once comparable simulations are run.
Controlled fabrication of strained or twisted hetero-stacks would provide a direct experimental test of the predicted conductance changes.

Load-bearing premise

The atomistic simulations, Fermi's golden rule analysis, and phonon density-of-modes calculations accurately capture real interlayer heat transport under strain and twist without major artifacts from model choices or parameters.

What would settle it

Direct measurement of vertical thermal conductance in a compressed graphene/h-BN interface that shows no increase relative to the unstrained case.

read the original abstract

A dramatic difference between the vertical thermal conductance response of homogeneous and heterogeneous graphene/h-BN interfaces to external mechanical perturbations, is predicted. Homogeneous graphene and h-BN interfaces exhibit strong conductance reduction for both in-plane strain and interfacial twist. Conversely, the vertical thermal conductance of the heterogeneous graphene/h-BN junction is insensitive to twist deformations but shows significant increase or decrease under compressive or tensile strains, respectively. Our atomistic simulations predictions are rationalized by Fermi's golden rule and density of phonon modes analyses, indicating that vertical phonons and local stacking configurations have a central role in the interlayer heat transport behavior. A simple phenomenological model, based on local interlayer distance and stacking, captures well the dependence of vertical heat conductance on strain and twist deformations.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper finds that twist strongly suppresses vertical thermal conductance at homo-interfaces of graphene or hBN but leaves it nearly unchanged at the graphene/hBN hetero-interface, while strain tunes the hetero case in the opposite direction.

read the letter

The main takeaway is the reported contrast: homogeneous interfaces drop in conductance under both twist and strain, but the mixed graphene/hBN interface stays flat with twist and rises or falls with compression or tension. That difference, plus the simple model tying it to local spacing and stacking, is the actual new piece here. Prior work has looked at twist or strain separately in these materials, but the side-by-side homo-versus-hetero comparison under both perturbations is not in the cited literature. The Fermi golden-rule plus phonon-density analysis gives a clean rationalization for why vertical modes and registry matter, and the phenomenological model reproduces the trends without extra fitting parameters. That combination is useful and worth having on record. The soft spot is the reliance on empirical interlayer potentials and finite supercells for the twisted cases. Those potentials are usually fit at equilibrium, so they can misrepresent force changes when spacing shifts or when moiré patterns create varying local stacks. If the supercells are not large enough or not checked for convergence, the claimed twist-insensitivity in the hetero case could be an artifact. The abstract does not show error bars or potential-variation tests, so that needs checking in the full methods. This is the kind of work that belongs in a specialized journal on 2D materials or nanoscale heat transport. Readers who run or interpret molecular-dynamics thermal calculations will get the most out of it, and experimental groups looking for mechanical knobs on interfacial conductance could use the predictions as starting points. It is solid enough on its own terms to deserve referee time rather than a desk reject. I would send it out for review with the expectation that the authors add convergence data and potential-sensitivity checks.

Referee Report

0 major / 3 minor

Summary. The manuscript predicts a dramatic difference in the response of vertical thermal conductance to in-plane strain and interfacial twist between homogeneous interfaces (graphene-graphene or h-BN-h-BN) and the heterogeneous graphene/h-BN interface. Homogeneous interfaces exhibit strong conductance reduction under both perturbations, whereas the hetero-interface remains insensitive to twist but shows a significant increase under compressive strain and decrease under tensile strain. These atomistic simulation results are rationalized via Fermi's golden rule and phonon density of modes analyses, which highlight the central role of vertical phonons and local stacking configurations; a simple phenomenological model based on local interlayer distance and stacking is shown to capture the observed dependence.

Significance. If the predictions hold, the work would be significant for the field of interfacial thermal transport in van der Waals materials, as it identifies distinct mechanical tunability routes for homo- versus hetero-interfaces and provides mechanistic insight through combined simulation and analytical approaches. The emphasis on local stacking and the development of a phenomenological model based on interlayer distance are particular strengths that could inform device design for thermal management in 2D heterostructures.

minor comments (3)

The first sentence of the abstract contains an extraneous comma before 'is predicted,' which should be removed for grammatical clarity.
Ensure consistent capitalization and hyphenation of 'graphene' and 'hexagonal boron nitride' (or 'h-BN') throughout the text, figures, and captions.
Figure captions should explicitly state the supercell sizes and k-point sampling used for twisted configurations to allow readers to assess the sampling of moiré patterns.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive evaluation of our manuscript and the recommendation for minor revision. The referee's summary accurately captures the central prediction of distinct mechanical tunability between homogeneous and heterogeneous interfaces, along with the supporting analyses via Fermi's golden rule, phonon density of states, and the phenomenological model.

Circularity Check

0 steps flagged

No circularity: predictions arise from independent atomistic simulations and standard phonon analysis

full rationale

The paper derives its central claims (dramatic homo/hetero differences in strain/twist response of vertical thermal conductance) directly from atomistic simulations, which are then rationalized via Fermi's golden rule transition rates and phonon density-of-modes calculations. These steps are standard, externally verifiable techniques applied to the interfaces; the phenomenological model based on local interlayer distance and stacking is presented only as a post-hoc capture of the observed dependence, not as the source of the predictions. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear in the derivation chain. The work remains self-contained against external benchmarks such as established interatomic potentials and phonon transport formalisms.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard phonon transport theory and atomistic simulation methods without introducing new free parameters or invented entities in the abstract.

axioms (2)

standard math Phonon-mediated interlayer heat transport can be analyzed via Fermi's golden rule and density of phonon modes
Invoked to rationalize the simulation predictions.
domain assumption Vertical phonons and local stacking configurations dominate interfacial thermal conductance
Central to explaining the strain and twist dependence.

pith-pipeline@v0.9.0 · 5454 in / 1397 out tokens · 90885 ms · 2026-05-07T13:07:26.385908+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

88 extracted references · 88 canonical work pages

[1]

Ouyang, O

W. Ouyang, O. Hod, and M. Urbakh, Phys. Rev. Lett. 126, 216101 (2021)

work page 2021
[2]

Mandelli, W

D. Mandelli, W. Ouyang, M. Urbakh, and O. Hod, ACS Nano 13, 7603 (2019)

work page 2019
[3]

Hunt et al., Science 340, 1427 (2013)

B. Hunt et al., Science 340, 1427 (2013)

work page 2013
[4]

C. R. Dean et al., Nature 497, 598 (2013)

work page 2013
[5]

Lyu et al., Nature 628, 758 (2024)

B. Lyu et al., Nature 628, 758 (2024)

work page 2024
[6]

H. Wang, S. Wang, S. Zhang, M. Zhu, W. Ouyang, and Q. Li, Natl. Sci. Rev. 10, nwad175 (2023)

work page 2023
[7]

G. J. Slotman, M. M. van Wijk, P.-L. Zhao, A. Fasolino, M. I. Katsnelson, and S. Yuan, Phys. Rev. Lett. 115, 186801 (2015)

work page 2015
[8]

C. R. Woods et al., Nat. Phys. 10, 451 (2014)

work page 2014
[9]

Yankowitz, Q

M. Yankowitz, Q. Ma, P. Jarillo-Herrero, and B. J. LeRoy, Nat. Rev. Phys. 1, 112 (2019)

work page 2019
[10]

Ouyang, D

W. Ouyang, D. Mandelli, M. Urbakh, and O. Hod, Nano Lett. 18, 6009 (2018)

work page 2018
[11]

Y . Song, D. Mandelli, O. Hod, M. Urbakh, M. Ma, and Q. Zheng, Nat. Mater. 17, 894 (2018)

work page 2018
[12]

Mandelli, W

D. Mandelli, W. Ouyang, O. Hod, and M. Urbakh, Phys. Rev. Lett. 122, 076102 (2019)

work page 2019
[13]

Huang, H

K. Huang, H. Qin, S. Zhang, Q. Li, W. Ouyang, and Y . Liu, Adv. Funct. Mater. 32, 2204209 (2022)

work page 2022
[14]

Wu and Q

X. Wu and Q. Han, ACS Appl. Mater. Interfaces 13, 32564 (2021)

work page 2021
[15]

A. J. Pak and G. S. Hwang, Phys. Rev. Appl. 6, 034015 (2016)

work page 2016
[16]

X. Liu, G. Zhang, and Y .-W. Zhang, Nano Lett. 16, 4954 (2016)

work page 2016
[17]

X.-K. Chen, M. Pang, T. Chen, D. Du, and K. -Q. Chen, ACS Appl. Mater. Interfaces 12, 15517 (2020)

work page 2020
[18]

Z. Yan, L. Chen, M. Yoon, and S. Kumar, Nanoscale 8, 4037 (2016)

work page 2016
[19]

Zhang, Y

J. Zhang, Y . Hong, and Y . Yue, J. Appl. Phys. 117, 134307 (2015)

work page 2015
[20]

W. Ren, S. Lu, C. Yu, J. He, Z. Zhang, J. Chen, and G. Zhang, Appl. Phys. Rev. 10, 041404 (2023)

work page 2023
[21]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009)

work page 2009
[22]

Koren, I

E. Koren, I. Leven, E. Lörtscher, A. Knoll, O. Hod, and U. Duerig, Nat. Nanotechnol. 11, 752 (2016)

work page 2016
[23]

K. S. Novoselov, A. K. Geim, S. V . Morozov, D. Jiang, M. I. Katsnelson, I. V . Grigorieva, S. V . Dubonos, and A. A. Firsov, Nature 438, 197 (2005)

work page 2005
[24]

K. S. Novoselov, A. K. Geim, S. V . Morozov, D. Jiang, Y . Zhang, S. V . Dubonos, I. V . Grigorieva, and A. A. Firsov, Science 306, 666 (2004)

work page 2004
[25]

Zhang, Y .-W

Y . Zhang, Y .-W. Tan, H. L. Stormer, and P. Kim, Nature 438, 201 (2005)

work page 2005
[26]

C. R. Dean et al., Nat. Nanotechnol. 5, 722 (2010)

work page 2010
[27]

A. K. Geim and I. V . Grigorieva, Nature 499, 419 (2013)

work page 2013
[28]

Li et al., Nature 579, 368 (2020)

J. Li et al., Nature 579, 368 (2020)

work page 2020
[29]

K. S. Novoselov, A. Mishchenko, A. Carvalho, and A. H. Castro Neto, Science 353, aac9439 (2016)

work page 2016
[30]

Wang et al., Science 342, 614 (2013)

L. Wang et al., Science 342, 614 (2013)

work page 2013
[31]

Z.-G. Chen, Z. Shi, W. Yang, X. Lu, Y . Lai, H. Yan, F. Wang, G. Zhang, and Z. Li, Nat. Commun. 5, 4461 (2014)

work page 2014
[32]

Y . Yang, J. Ma, J. Yang, and Y . Zhang, ACS Appl. Mater. Interfaces 14, 45742 (2022)

work page 2022
[33]

Lyu et al., Adv

B. Lyu et al., Adv. Mater. 34, 2200956 (2022)

work page 2022
[34]

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, Nano Lett. 8, 902 (2008)

work page 2008
[35]

Ghosh, I

S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L. Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, Appl. Phys. Lett. 92, 151911 (2008)

work page 2008
[36]

Jiang, X

P. Jiang, X. Qian, R. Yang, and L. Lindsay, Phys. Rev. Mater. 2, 064005 (2018)

work page 2018
[37]

E. K. Sichel, R. E. Miller, M. S. Abrahams, and C. J. Buiocchi, Phys. Rev. B 13, 4607 (1976)

work page 1976
[38]

Xu et al., Nat

X. Xu et al., Nat. Commun. 5, 3689 (2014)

work page 2014
[39]

Liu et al., Sci

Y . Liu et al., Sci. Rep. 7, 43886 (2017). 10

work page 2017
[40]

D. B. Brown, T. L. Bougher, X. Zhang, P. M. Ajayan, B. A. Cola, and S. Kumar , Phys. Status Solidi A 216, 1900446 (2019)

work page 2019
[41]

C.-C. Chen, Z. Li, L. Shi, and S. B. Cronin, Appl. Phys. Lett. 104, 081908 (2014)

work page 2014
[42]

Ouyang, H

W. Ouyang, H. Qin, M. Urbakh, and O. Hod, Nano Lett. 20, 7513 (2020)

work page 2020
[43]

W. Ren, Y . Ouyang, P. Jiang, C. Yu, J. He, and J. Chen, Nano Lett. 21, 2634 (2021)

work page 2021
[44]

Lin et al., ACS Nano 12, 8770 (2018)

M.-L. Lin et al., ACS Nano 12, 8770 (2018)

work page 2018
[45]

Li, J.-M

Z. Li, J.-M. Lai, and J. Zhang, J. Semicond. 44, 011902 (2023)

work page 2023
[46]

Y . Xiao, J. Liu, and L. Fu, Matter 3, 1142 (2020)

work page 2020
[47]

Zhang, Y

L. Zhang, Y . Zhong, X. Li, J. H. Park, Q. Song, L. Li, L. Guo, J. Kong, and G. Chen, Nano Lett. 23, 7790 (2023)

work page 2023
[48]

S. E. Kim et al., Nature 597, 660 (2021)

work page 2021
[49]

Jiang, T

W. Jiang, T. Liang, J. Xu, and W. Ouyang, Int. J. Heat Mass Transf. 217, 124662 (2023)

work page 2023
[50]

Cheng, Z

Y . Cheng, Z. Fan, T. Zhang, M. Nomura, S. V olz, G. Zhu, B. Li, and S. Xiong, Mater. Today Phys. 35, 101093 (2023)

work page 2023
[51]

Z. Qin, L. Dai, M. Li, S. Li, H. Wu, K. E. White, G. Gani, P. S. Weiss, and Y . Hu, Adv. Mater. 36, 2312176 (2024)

work page 2024
[52]

Eriksson, E

F. Eriksson, E. Fransson, C. Linderälv, Z. Fan, and P. Erhart, ACS Nano 17, 25565 (2023)

work page 2023
[53]

Jiang, T

W. Jiang, T. Liang, H. Bu, J. Xu, and W. Ouyang, ACS Nano 19, 16287 (2025)

work page 2025
[54]

N. Wei, Y . Zhang, Y . Chen, and Y . Zhang, Int. J. Smart Nano Mater. 11, 310 (2020)

work page 2020
[55]

Yang et al., Phys

F. Yang et al., Phys. Rev. Lett. 134, 146302 (2025)

work page 2025
[56]

Liang, W

T. Liang, W. Jiang, K. Xu, H. Bu, Z. Fan, W. Ouyang, and J. Xu, J. Appl. Phys. 138, 075101 (2025)

work page 2025
[57]

B. Xu, M. An, S. Masubuchi, Y . Li, R. Guo, T. Machida, and J. Shiomi, Adv. Funct. Mater. 35, 2422761 (2025)

work page 2025
[58]

H. Bu, W. Jiang, P. Ying, T. Liang, Z. Fan, and W. Ouyang, J. Mech. Phys. Solids 210, 106540 (2026)

work page 2026
[59]

W. Yuan, K. Ueji, T. Yagi, T. Endo, H. E. Lim, Y . Miyata, Y . Yomogida, and K. Yanagi, ACS Nano 15, 15902 (2021)

work page 2021
[60]

Ouyang, O

W. Ouyang, O. Hod, and R. Guerra, J. Chem. Theory Comput. 17, 7215 (2021)

work page 2021
[61]

Ouyang, R

W. Ouyang, R. Sofer, X. Gao, J. Hermann, A. Tkatchenko, L. Kronik, M. Urbakh, and O. Hod, J. Chem. Theory Comput. 17, 7237 (2021)

work page 2021
[62]

Z. Feng, Y . Yao, J. Liu, B. Wu, Z. Liu, and W. Ouyang, J. Phys. Chem. C 127, 8704 (2023)

work page 2023
[63]

Y . Yao, B. Wu, Z. Liu, and W. Ouyang, J. Phys. Chem. C 128, 6836 (2024)

work page 2024
[64]

Z. Feng, Z. Lei, Y . Yao, J. Liu, B. Wu, and W. Ouyang, Langmuir 39, 18198 (2023)

work page 2023
[65]

Jiang, R

W. Jiang, R. Sofer, X. Gao, A. Tkatchenko, L. K ronik, W. Ouyang, M. Urbakh, and O. Hod, J. Phys. Chem. A 127, 9820 (2023)

work page 2023
[66]

Jiang, R

W. Jiang, R. Sofer, X. Gao, L. Kronik, O. Hod, M. Urbakh, and W. Ouyang, J. Phys. Chem. C 129, 1417 (2025)

work page 2025
[67]

Liang, W

Q. Liang, W. Jiang, Y . Liu, and W. Ouyang, J. Phys. Chem. C 127, 18641 (2023)

work page 2023
[68]

Ouyang, I

W. Ouyang, I. Azuri, D. Mandelli, A. Tkatchenko, L. Kronik, M. Urbakh, and O. Hod, J. Chem. Theory Comput. 16, 666 (2020)

work page 2020
[69]

X. Gao, W. Ouyang, L. Kronik, M. Urbakh, and O. Hod, J. Chem. Phys. 163, 041001 (2025)

work page 2025
[70]

Xu et al., Mater

K. Xu et al., Mater. Genome Eng. Adv. 3, e70028 (2025)

work page 2025
[71]

D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni, and S. B. Sinnott, J. Phys.: Condens. Matter 14, 783 (2002)

work page 2002
[72]

Kınacı, J

A. Kınacı, J. B. Haskins, C. Sevik, and T. Çağın, Phys. Rev. B 86, 115410 (2012)

work page 2012
[73]

Y . Chen, J. Wan, Y . Chen, H. Qin, Y . Liu, Q.-X. Pei, and Y .-W. Zhang, Int. J. Therm. Sci. 183, 107871 (2023)

work page 2023
[74]

Qin and W

H. Qin and W. Jiang, J. Phys. D: Appl. Phys. 57, 105303 (2024)

work page 2024
[75]

Jiang, T

W. Jiang, T. Liang, J. Xu, and W. Ouyang, ACS Appl. Mater. Interfaces 17, 34833 (2025). 11

work page 2025
[76]

W. Yan, J. Liu, W. Ouyang, and Z. Liu, Interdiscip. Mater. 3, 343 (2024)

work page 2024
[77]

A. P. Thompson et al., Comput. Phys. Commun. 271, 108171 (2022)

work page 2022
[78]

The Supplemental Material includes Refs

See Supplemental Material for methodology, calculation of vertical thermal conductivity, twist - angle-dependent vertical thermal conductivity of homogeneous graphene and h-BN stacks, harmonic phonon -phonon couplings across van der Waals interfaces, spectral heat current decomposition, vertical heat transport in different stacking modes, definition of ve...

work page
[79]

Liang et al., npj Comput

T. Liang et al., npj Comput. Mater. 12, 11 (2026)

work page 2026
[80]

G. L. Pollack, Rev. Mod. Phys. 41, 48 (1969)

work page 1969

Showing first 80 references.

[1] [1]

Ouyang, O

W. Ouyang, O. Hod, and M. Urbakh, Phys. Rev. Lett. 126, 216101 (2021)

work page 2021

[2] [2]

Mandelli, W

D. Mandelli, W. Ouyang, M. Urbakh, and O. Hod, ACS Nano 13, 7603 (2019)

work page 2019

[3] [3]

Hunt et al., Science 340, 1427 (2013)

B. Hunt et al., Science 340, 1427 (2013)

work page 2013

[4] [4]

C. R. Dean et al., Nature 497, 598 (2013)

work page 2013

[5] [5]

Lyu et al., Nature 628, 758 (2024)

B. Lyu et al., Nature 628, 758 (2024)

work page 2024

[6] [6]

H. Wang, S. Wang, S. Zhang, M. Zhu, W. Ouyang, and Q. Li, Natl. Sci. Rev. 10, nwad175 (2023)

work page 2023

[7] [7]

G. J. Slotman, M. M. van Wijk, P.-L. Zhao, A. Fasolino, M. I. Katsnelson, and S. Yuan, Phys. Rev. Lett. 115, 186801 (2015)

work page 2015

[8] [8]

C. R. Woods et al., Nat. Phys. 10, 451 (2014)

work page 2014

[9] [9]

Yankowitz, Q

M. Yankowitz, Q. Ma, P. Jarillo-Herrero, and B. J. LeRoy, Nat. Rev. Phys. 1, 112 (2019)

work page 2019

[10] [10]

Ouyang, D

W. Ouyang, D. Mandelli, M. Urbakh, and O. Hod, Nano Lett. 18, 6009 (2018)

work page 2018

[11] [11]

Y . Song, D. Mandelli, O. Hod, M. Urbakh, M. Ma, and Q. Zheng, Nat. Mater. 17, 894 (2018)

work page 2018

[12] [12]

Mandelli, W

D. Mandelli, W. Ouyang, O. Hod, and M. Urbakh, Phys. Rev. Lett. 122, 076102 (2019)

work page 2019

[13] [13]

Huang, H

K. Huang, H. Qin, S. Zhang, Q. Li, W. Ouyang, and Y . Liu, Adv. Funct. Mater. 32, 2204209 (2022)

work page 2022

[14] [14]

Wu and Q

X. Wu and Q. Han, ACS Appl. Mater. Interfaces 13, 32564 (2021)

work page 2021

[15] [15]

A. J. Pak and G. S. Hwang, Phys. Rev. Appl. 6, 034015 (2016)

work page 2016

[16] [16]

X. Liu, G. Zhang, and Y .-W. Zhang, Nano Lett. 16, 4954 (2016)

work page 2016

[17] [17]

X.-K. Chen, M. Pang, T. Chen, D. Du, and K. -Q. Chen, ACS Appl. Mater. Interfaces 12, 15517 (2020)

work page 2020

[18] [18]

Z. Yan, L. Chen, M. Yoon, and S. Kumar, Nanoscale 8, 4037 (2016)

work page 2016

[19] [19]

Zhang, Y

J. Zhang, Y . Hong, and Y . Yue, J. Appl. Phys. 117, 134307 (2015)

work page 2015

[20] [20]

W. Ren, S. Lu, C. Yu, J. He, Z. Zhang, J. Chen, and G. Zhang, Appl. Phys. Rev. 10, 041404 (2023)

work page 2023

[21] [21]

A. H. Castro Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov, and A. K. Geim, Rev. Mod. Phys. 81, 109 (2009)

work page 2009

[22] [22]

Koren, I

E. Koren, I. Leven, E. Lörtscher, A. Knoll, O. Hod, and U. Duerig, Nat. Nanotechnol. 11, 752 (2016)

work page 2016

[23] [23]

K. S. Novoselov, A. K. Geim, S. V . Morozov, D. Jiang, M. I. Katsnelson, I. V . Grigorieva, S. V . Dubonos, and A. A. Firsov, Nature 438, 197 (2005)

work page 2005

[24] [24]

K. S. Novoselov, A. K. Geim, S. V . Morozov, D. Jiang, Y . Zhang, S. V . Dubonos, I. V . Grigorieva, and A. A. Firsov, Science 306, 666 (2004)

work page 2004

[25] [25]

Zhang, Y .-W

Y . Zhang, Y .-W. Tan, H. L. Stormer, and P. Kim, Nature 438, 201 (2005)

work page 2005

[26] [26]

C. R. Dean et al., Nat. Nanotechnol. 5, 722 (2010)

work page 2010

[27] [27]

A. K. Geim and I. V . Grigorieva, Nature 499, 419 (2013)

work page 2013

[28] [28]

Li et al., Nature 579, 368 (2020)

J. Li et al., Nature 579, 368 (2020)

work page 2020

[29] [29]

K. S. Novoselov, A. Mishchenko, A. Carvalho, and A. H. Castro Neto, Science 353, aac9439 (2016)

work page 2016

[30] [30]

Wang et al., Science 342, 614 (2013)

L. Wang et al., Science 342, 614 (2013)

work page 2013

[31] [31]

Z.-G. Chen, Z. Shi, W. Yang, X. Lu, Y . Lai, H. Yan, F. Wang, G. Zhang, and Z. Li, Nat. Commun. 5, 4461 (2014)

work page 2014

[32] [32]

Y . Yang, J. Ma, J. Yang, and Y . Zhang, ACS Appl. Mater. Interfaces 14, 45742 (2022)

work page 2022

[33] [33]

Lyu et al., Adv

B. Lyu et al., Adv. Mater. 34, 2200956 (2022)

work page 2022

[34] [34]

A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Teweldebrhan, F. Miao, and C. N. Lau, Nano Lett. 8, 902 (2008)

work page 2008

[35] [35]

Ghosh, I

S. Ghosh, I. Calizo, D. Teweldebrhan, E. P. Pokatilov, D. L. Nika, A. A. Balandin, W. Bao, F. Miao, and C. N. Lau, Appl. Phys. Lett. 92, 151911 (2008)

work page 2008

[36] [36]

Jiang, X

P. Jiang, X. Qian, R. Yang, and L. Lindsay, Phys. Rev. Mater. 2, 064005 (2018)

work page 2018

[37] [37]

E. K. Sichel, R. E. Miller, M. S. Abrahams, and C. J. Buiocchi, Phys. Rev. B 13, 4607 (1976)

work page 1976

[38] [38]

Xu et al., Nat

X. Xu et al., Nat. Commun. 5, 3689 (2014)

work page 2014

[39] [39]

Liu et al., Sci

Y . Liu et al., Sci. Rep. 7, 43886 (2017). 10

work page 2017

[40] [40]

D. B. Brown, T. L. Bougher, X. Zhang, P. M. Ajayan, B. A. Cola, and S. Kumar , Phys. Status Solidi A 216, 1900446 (2019)

work page 2019

[41] [41]

C.-C. Chen, Z. Li, L. Shi, and S. B. Cronin, Appl. Phys. Lett. 104, 081908 (2014)

work page 2014

[42] [42]

Ouyang, H

W. Ouyang, H. Qin, M. Urbakh, and O. Hod, Nano Lett. 20, 7513 (2020)

work page 2020

[43] [43]

W. Ren, Y . Ouyang, P. Jiang, C. Yu, J. He, and J. Chen, Nano Lett. 21, 2634 (2021)

work page 2021

[44] [44]

Lin et al., ACS Nano 12, 8770 (2018)

M.-L. Lin et al., ACS Nano 12, 8770 (2018)

work page 2018

[45] [45]

Li, J.-M

Z. Li, J.-M. Lai, and J. Zhang, J. Semicond. 44, 011902 (2023)

work page 2023

[46] [46]

Y . Xiao, J. Liu, and L. Fu, Matter 3, 1142 (2020)

work page 2020

[47] [47]

Zhang, Y

L. Zhang, Y . Zhong, X. Li, J. H. Park, Q. Song, L. Li, L. Guo, J. Kong, and G. Chen, Nano Lett. 23, 7790 (2023)

work page 2023

[48] [48]

S. E. Kim et al., Nature 597, 660 (2021)

work page 2021

[49] [49]

Jiang, T

W. Jiang, T. Liang, J. Xu, and W. Ouyang, Int. J. Heat Mass Transf. 217, 124662 (2023)

work page 2023

[50] [50]

Cheng, Z

Y . Cheng, Z. Fan, T. Zhang, M. Nomura, S. V olz, G. Zhu, B. Li, and S. Xiong, Mater. Today Phys. 35, 101093 (2023)

work page 2023

[51] [51]

Z. Qin, L. Dai, M. Li, S. Li, H. Wu, K. E. White, G. Gani, P. S. Weiss, and Y . Hu, Adv. Mater. 36, 2312176 (2024)

work page 2024

[52] [52]

Eriksson, E

F. Eriksson, E. Fransson, C. Linderälv, Z. Fan, and P. Erhart, ACS Nano 17, 25565 (2023)

work page 2023

[53] [53]

Jiang, T

W. Jiang, T. Liang, H. Bu, J. Xu, and W. Ouyang, ACS Nano 19, 16287 (2025)

work page 2025

[54] [54]

N. Wei, Y . Zhang, Y . Chen, and Y . Zhang, Int. J. Smart Nano Mater. 11, 310 (2020)

work page 2020

[55] [55]

Yang et al., Phys

F. Yang et al., Phys. Rev. Lett. 134, 146302 (2025)

work page 2025

[56] [56]

Liang, W

T. Liang, W. Jiang, K. Xu, H. Bu, Z. Fan, W. Ouyang, and J. Xu, J. Appl. Phys. 138, 075101 (2025)

work page 2025

[57] [57]

B. Xu, M. An, S. Masubuchi, Y . Li, R. Guo, T. Machida, and J. Shiomi, Adv. Funct. Mater. 35, 2422761 (2025)

work page 2025

[58] [58]

H. Bu, W. Jiang, P. Ying, T. Liang, Z. Fan, and W. Ouyang, J. Mech. Phys. Solids 210, 106540 (2026)

work page 2026

[59] [59]

W. Yuan, K. Ueji, T. Yagi, T. Endo, H. E. Lim, Y . Miyata, Y . Yomogida, and K. Yanagi, ACS Nano 15, 15902 (2021)

work page 2021

[60] [60]

Ouyang, O

W. Ouyang, O. Hod, and R. Guerra, J. Chem. Theory Comput. 17, 7215 (2021)

work page 2021

[61] [61]

Ouyang, R

W. Ouyang, R. Sofer, X. Gao, J. Hermann, A. Tkatchenko, L. Kronik, M. Urbakh, and O. Hod, J. Chem. Theory Comput. 17, 7237 (2021)

work page 2021

[62] [62]

Z. Feng, Y . Yao, J. Liu, B. Wu, Z. Liu, and W. Ouyang, J. Phys. Chem. C 127, 8704 (2023)

work page 2023

[63] [63]

Y . Yao, B. Wu, Z. Liu, and W. Ouyang, J. Phys. Chem. C 128, 6836 (2024)

work page 2024

[64] [64]

Z. Feng, Z. Lei, Y . Yao, J. Liu, B. Wu, and W. Ouyang, Langmuir 39, 18198 (2023)

work page 2023

[65] [65]

Jiang, R

W. Jiang, R. Sofer, X. Gao, A. Tkatchenko, L. K ronik, W. Ouyang, M. Urbakh, and O. Hod, J. Phys. Chem. A 127, 9820 (2023)

work page 2023

[66] [66]

Jiang, R

W. Jiang, R. Sofer, X. Gao, L. Kronik, O. Hod, M. Urbakh, and W. Ouyang, J. Phys. Chem. C 129, 1417 (2025)

work page 2025

[67] [67]

Liang, W

Q. Liang, W. Jiang, Y . Liu, and W. Ouyang, J. Phys. Chem. C 127, 18641 (2023)

work page 2023

[68] [68]

Ouyang, I

W. Ouyang, I. Azuri, D. Mandelli, A. Tkatchenko, L. Kronik, M. Urbakh, and O. Hod, J. Chem. Theory Comput. 16, 666 (2020)

work page 2020

[69] [69]

X. Gao, W. Ouyang, L. Kronik, M. Urbakh, and O. Hod, J. Chem. Phys. 163, 041001 (2025)

work page 2025

[70] [70]

Xu et al., Mater

K. Xu et al., Mater. Genome Eng. Adv. 3, e70028 (2025)

work page 2025

[71] [71]

D. W. Brenner, O. A. Shenderova, J. A. Harrison, S. J. Stuart, B. Ni, and S. B. Sinnott, J. Phys.: Condens. Matter 14, 783 (2002)

work page 2002

[72] [72]

Kınacı, J

A. Kınacı, J. B. Haskins, C. Sevik, and T. Çağın, Phys. Rev. B 86, 115410 (2012)

work page 2012

[73] [73]

Y . Chen, J. Wan, Y . Chen, H. Qin, Y . Liu, Q.-X. Pei, and Y .-W. Zhang, Int. J. Therm. Sci. 183, 107871 (2023)

work page 2023

[74] [74]

Qin and W

H. Qin and W. Jiang, J. Phys. D: Appl. Phys. 57, 105303 (2024)

work page 2024

[75] [75]

Jiang, T

W. Jiang, T. Liang, J. Xu, and W. Ouyang, ACS Appl. Mater. Interfaces 17, 34833 (2025). 11

work page 2025

[76] [76]

W. Yan, J. Liu, W. Ouyang, and Z. Liu, Interdiscip. Mater. 3, 343 (2024)

work page 2024

[77] [77]

A. P. Thompson et al., Comput. Phys. Commun. 271, 108171 (2022)

work page 2022

[78] [78]

The Supplemental Material includes Refs

See Supplemental Material for methodology, calculation of vertical thermal conductivity, twist - angle-dependent vertical thermal conductivity of homogeneous graphene and h-BN stacks, harmonic phonon -phonon couplings across van der Waals interfaces, spectral heat current decomposition, vertical heat transport in different stacking modes, definition of ve...

work page

[79] [79]

Liang et al., npj Comput

T. Liang et al., npj Comput. Mater. 12, 11 (2026)

work page 2026

[80] [80]

G. L. Pollack, Rev. Mod. Phys. 41, 48 (1969)

work page 1969