Detection of spin- and valley-polarized states in van der Waals materials via thermoelectric and non-reciprocal transport
Pith reviewed 2026-05-13 20:35 UTC · model grok-4.3
The pith
Thermoelectric and rectification effects detect valley-polarized states in van der Waals junctions.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
We predict thermoelectric and current rectification effects in hybrid junctions formed by Ising superconductors and materials hosting valley-polarized states. Both effects originate from the interplay of intrinsic Ising spin-orbit coupling, spin-splitting from an exchange or Zeeman field, and valley polarization. The resulting transport signatures provide experimentally accessible probes of valley-polarized states in van der Waals heterostructures, such as junctions of few-layer transition metal dichalcogenides and twisted bilayer or rhombohedral graphene.
What carries the argument
Hybrid junctions of an Ising superconductor with a valley-polarized van der Waals material, in which Ising spin-orbit coupling, exchange or Zeeman spin-splitting, and valley polarization together generate thermoelectric and rectification responses.
If this is right
- Valley-polarized states produce distinct thermoelectric voltages in the junctions.
- Non-reciprocal transport and current rectification emerge from the combined spin and valley effects.
- These signatures enable electrical detection in junctions of few-layer transition metal dichalcogenides and twisted bilayer or rhombohedral graphene.
- Standard thermoelectric and I-V measurements suffice to observe the effects.
Where Pith is reading between the lines
- The rectification property could support valleytronic devices that convert valley information into directed current.
- Varying junction cleanliness would test how robust the signatures remain against realistic scattering.
- Analogous thermoelectric probes might apply to other 2D systems that combine strong spin-orbit coupling with valley degrees of freedom.
Load-bearing premise
The interplay of Ising spin-orbit coupling, magnetic spin-splitting, and valley polarization produces dominant measurable thermoelectric and rectification effects that survive disorder and interface scattering in real devices.
What would settle it
Fabricating an Ising superconductor–TMDC junction and measuring zero thermoelectric voltage together with symmetric current-voltage curves under applied fields would falsify the predicted signatures.
Figures
read the original abstract
We predict thermoelectric and current rectification effects in hybrid junctions formed by Ising superconductors and materials hosting valley-polarized states. Both effects originate from the interplay of intrinsic Ising spin-orbit coupling, spin-splitting from an exchange or Zeeman field, and valley polarization. The resulting transport signatures provide experimentally accessible probes of valley-polarized states in van der Waals heterostructures, such as junctions of few-layer transition metal dichalcogenides and twisted bilayer or rhombohedral graphene.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript predicts thermoelectric and current rectification effects in hybrid junctions formed by Ising superconductors and materials hosting valley-polarized states. These effects originate from the interplay of intrinsic Ising spin-orbit coupling, spin-splitting from an exchange or Zeeman field, and valley polarization. The resulting transport signatures are proposed as experimentally accessible probes of valley-polarized states in van der Waals heterostructures, such as junctions of few-layer transition metal dichalcogenides and twisted bilayer or rhombohedral graphene.
Significance. If the predicted signatures prove robust, the work supplies a concrete electrical-transport route to detect valley polarization in vdW systems, complementing optical probes and potentially aiding device characterization. The prediction is constructed from standard, parameter-free ingredients (Ising SOC, Zeeman/exchange splitting, valley polarization) rather than fitted quantities, which is a positive feature for falsifiability.
major comments (1)
- [Transport model and results] The central claim that the thermoelectric and rectification effects remain dominant and measurable rests on the assumption that they are not washed out by disorder, interface scattering, or other mechanisms. No quantitative estimates (e.g., comparison of mean free path to junction length or scattering-rate thresholds) are provided to support this, leaving the accessibility of the signatures unsubstantiated.
minor comments (1)
- [Abstract] The abstract would be strengthened by a single sentence indicating the expected magnitude of the thermoelectric coefficient or rectification ratio relative to typical experimental noise floors.
Simulated Author's Rebuttal
We thank the referee for their thorough review and constructive feedback on our manuscript. We have carefully considered the major comment and provide our response below, along with revisions to the manuscript.
read point-by-point responses
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Referee: [Transport model and results] The central claim that the thermoelectric and rectification effects remain dominant and measurable rests on the assumption that they are not washed out by disorder, interface scattering, or other mechanisms. No quantitative estimates (e.g., comparison of mean free path to junction length or scattering-rate thresholds) are provided to support this, leaving the accessibility of the signatures unsubstantiated.
Authors: We agree with the referee that the manuscript would benefit from a discussion of disorder effects to better support the experimental accessibility of the predicted signatures. Our theoretical model assumes a clean system to isolate the intrinsic contributions from Ising SOC, Zeeman splitting, and valley polarization. In the revised version, we have included a new subsection discussing the robustness against disorder. Specifically, we provide estimates drawing from experimental data on van der Waals materials: mean free paths in high-mobility samples of graphene and TMDs often reach hundreds of nanometers, exceeding typical junction lengths of tens of nanometers used in transport experiments. We also outline that for scattering rates much smaller than the superconducting gap or the energy scales of the spin and valley splittings, the effects should persist. While a comprehensive numerical study of interface scattering is beyond the present scope, these arguments indicate that the signatures are measurable in current high-quality heterostructures. We have updated the abstract and conclusions to reflect this discussion. revision: yes
Circularity Check
No significant circularity; derivation is self-contained forward prediction
full rationale
The paper derives thermoelectric and rectification signatures from the standard interplay of Ising SOC, Zeeman/exchange splitting, and valley polarization in hybrid junctions. These are established physical ingredients modeled via standard transport theory (e.g., nonequilibrium Green's functions or Boltzmann approaches implied by the context). No quantity is defined in terms of the predicted effect itself, no fitted parameters are relabeled as predictions, and no self-citation chain is invoked to justify uniqueness or force the result. The central claim remains a testable prediction rather than a tautology, consistent with the reader's assessment of low circularity.
Axiom & Free-Parameter Ledger
axioms (2)
- domain assumption Ising spin-orbit coupling is intrinsic and dominant in the superconducting layer
- domain assumption Valley polarization can be independently controlled or present in the van der Waals layer
Reference graph
Works this paper leans on
-
[1]
K. S. Novoselov, A. Mishchenko, A. Carvalho, and A. Castro Neto, 2d materials and van der Waals het- erostructures, Science353, aac9439 (2016)
work page 2016
- [2]
-
[3]
J. R. Schaibley, H. Yu, G. Clark, P. Rivera, J. S. Ross, K. L. Seyler, W. Yao, and X. Xu, Valleytronics in 2d materials, Nat. Rev. Mater.1, 16055 (2016)
work page 2016
-
[4]
Z. Y. Zhu, Y. C. Cheng, and U. Schwingenschl¨ ogl, Gi- ant spin-orbit-induced spin splitting in two-dimensional transition-metal dichalcogenide semiconductors, Phys. Rev. B84, 153402 (2011)
work page 2011
-
[5]
D. Xiao, G.-B. Liu, W. Feng, X. Xu, and W. Yao, Cou- pled spin and valley physics in monolayers of MoS 2 and other group-VI dichalcogenides, Phys. Rev. Lett.108, 196802 (2012)
work page 2012
-
[6]
A. Korm´ anyos, G. Burkard, M. Gmitra, J. Fabian, V. Z´ olyomi, N. D. Drummond, and V. Fal’ko,k·pthe- ory for two-dimensional transition metal dichalcogenide semiconductors, 2D Mater.2, 022001 (2015)
work page 2015
-
[7]
J. Lu, O. Zheliuk, I. Leermakers, N. F. Yuan, U. Zeitler, K. T. Law, and J. Ye, Evidence for two-dimensional Ising superconductivity in gated MoS2, Science350, 1353 (2015)
work page 2015
- [8]
-
[9]
X. Xi, Z. Wang, W. Zhao, J.-H. Park, K. T. Law, H. Berger, L. Forr´ o, J. Shan, and K. F. Mak, Ising pair- ing in superconducting NbSe 2 atomic layers, Nat. Phys. 12, 139 (2016)
work page 2016
-
[10]
Y. Xing, K. Zhao, P. Shan, F. Zheng, Y. Zhang, H. Fu, Y. Liu, M. Tian, C. Xi, H. Liu, J. Feng, X. Lin, S. Ji, X. Chen, Q.-K. Xue, and J. Wang, Ising superconduc- tivity and quantum phase transition in macro-size mono- layer NbSe2, Nano Lett.17, 6802 (2017)
work page 2017
-
[11]
J. Lu, O. Zheliuk, Q. Chen, I. Leermakers, N. E. Hussey, U. Zeitler, and J. Ye, Full superconducting dome of strong Ising protection in gated monolayer WS 2, Proc. Nat. Acad. Sci.115, 3551 (2018)
work page 2018
-
[12]
S. C. De la Barrera, M. R. Sinko, D. P. Gopalan, N. Sivadas, K. L. Seyler, K. Watanabe, T. Taniguchi, A. W. Tsen, X. Xu, D. Xiao, and M. B. Hunt, Tun- ing Ising superconductivity with layer and spin–orbit coupling in two-dimensional transition-metal dichalco- genides, Nat. Commun.9, 1427 (2018)
work page 2018
-
[13]
Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional super- conductivity in magic-angle graphene superlattices, Na- ture556, 43 (2018)
work page 2018
-
[14]
Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo- Herrero, Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature556, 80 (2018)
work page 2018
-
[15]
H. C. Po, L. Zou, A. Vishwanath, and T. Senthil, Ori- 6 gin of Mott insulating behavior and superconductivity in twisted bilayer graphene, Phys. Rev. X8, 031089 (2018)
work page 2018
-
[16]
T. J. Peltonen, R. Ojaj¨ arvi, and T. T. Heikkil¨ a, Mean- field theory for superconductivity in twisted bilayer graphene, Phys. Rev. B98, 220504 (2018)
work page 2018
-
[17]
M. Yankowitz, S. Chen, H. Polshyn, Y. Zhang, K. Watan- abe, T. Taniguchi, D. Graf, A. F. Young, and C. R. Dean, Tuning superconductivity in twisted bilayer graphene, Science363, 1059 (2019)
work page 2019
-
[18]
A. L. Sharpe, E. J. Fox, A. W. Barnard, J. Finney, K. Watanabe, T. Taniguchi, M. Kastner, and D. Goldhaber-Gordon, Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene, Science365, 605 (2019)
work page 2019
- [19]
-
[20]
K. P. Nuckolls, M. Oh, D. Wong, B. Lian, K. Watanabe, T. Taniguchi, B. A. Bernevig, and A. Yazdani, Strongly correlated Chern insulators in magic-angle twisted bi- layer graphene, Nature588, 610 (2020)
work page 2020
-
[21]
N. Bultinck, S. Chatterjee, and M. P. Zaletel, Mecha- nism for anomalous hall ferromagnetism in twisted bi- layer graphene, Phys. Rev. Lett.124, 166601 (2020)
work page 2020
- [22]
-
[23]
H. Zhou, T. Xie, T. Taniguchi, K. Watanabe, and A. F. Young, Superconductivity in rhombohedral trilayer graphene, Nature598, 434 (2021)
work page 2021
-
[24]
H. Zhou, T. Xie, A. Ghazaryan, T. Holder, J. R. Ehrets, E. M. Spanton, T. Taniguchi, K. Watanabe, E. Berg, M. Serbyn, and A. F. Young, Half-and quarter-metals in rhombohedral trilayer graphene, Nature598, 429 (2021)
work page 2021
-
[25]
S. Chatterjee, T. Wang, E. Berg, and M. P. Zaletel, Inter- valley coherent order and isospin fluctuation mediated superconductivity in rhombohedral trilayer graphene, Nat. Commun.13, 6013 (2022)
work page 2022
-
[26]
E. Pangburn, L. Haurie, A. Cr´ epieux, O. A. Awoga, A. M. Black-Schaffer, C. P´ epin, and C. Bena, Supercon- ductivity in monolayer and few-layer graphene: I. Review of possible pairing symmetries and basic electronic prop- erties, Phys. Rev. B108, 134514 (2023)
work page 2023
-
[27]
T. Arp, O. Sheekey, H. Zhou, C. Tschirhart, C. L. Patter- son, H. Yoo, L. Holleis, E. Redekop, G. Babikyan, T. Xie, J. Xiao, Y. Vituri, T. Holder, T. Taniguchi, K. Watan- abe, M. E. Huber, E. Berg, and A. F. Young, Intervalley coherence and intrinsic spin–orbit coupling in rhombohe- dral trilayer graphene, Nat. Phys.20, 1413 (2024)
work page 2024
-
[28]
R. Bistritzer and A. H. MacDonald, Moir´ e bands in twisted double-layer graphene, Proc. Nat. Acad. Sci.108, 12233 (2011)
work page 2011
- [29]
-
[30]
N. B. Kopnin, M. Ij¨ as, A. Harju, and T. T. Heikkil¨ a, High-temperature surface superconductivity in rhombo- hedral graphite, Phys. Rev. B87, 140503 (2013)
work page 2013
-
[31]
O. A. Awoga, T. L¨ othman, and A. M. Black-Schaffer, Superconductivity and magnetism in the surface states of abc-stacked multilayer graphene, Phys. Rev. B108, 144504 (2023)
work page 2023
-
[32]
K. F. Mak, K. He, J. Shan, and T. F. Heinz, Control of valley polarization in monolayer MoS2 by optical helicity, Nat. Nanotechnol.7, 494 (2012)
work page 2012
-
[33]
H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, Valley po- larization in MoS2 monolayers by optical pumping, Nat. Nanotechnol.7, 490 (2012)
work page 2012
-
[34]
T. Cao, G. Wang, W. Han, H. Ye, C. Zhu, J. Shi, Q. Niu, P. Tan, E. Wang, B. Liu, and J. Feng, Valley-selective circular dichroism of monolayer molybdenum disulphide, Nat. Commun.3, 887 (2012)
work page 2012
-
[35]
B. E. Feldman, J. Martin, and A. Yacoby, Broken- symmetry states and divergent resistance in suspended bilayer graphene, Nat. Phys.5, 889 (2009)
work page 2009
-
[36]
X. Du, I. Skachko, F. Duerr, A. Luican, and E. Y. Andrei, Fractional quantum Hall effect and insulating phase of Dirac electrons in graphene, Nature462, 192 (2009)
work page 2009
-
[37]
A. F. Young, C. R. Dean, L. Wang, H. Ren, P. Cadden- Zimansky, K. Watanabe, T. Taniguchi, J. Hone, K. L. Shepard, and P. Kim, Spin and valley quantum hall fer- romagnetism in graphene, Nat. Phys.8, 550 (2012)
work page 2012
-
[38]
R. Gorbachev, J. Song, G. Yu, A. Kretinin, F. Withers, Y. Cao, A. Mishchenko, I. Grigorieva, K. S. Novoselov, L. Levitov,et al., Detecting topological currents in graphene superlattices, Science346, 448 (2014)
work page 2014
-
[39]
M. Sui, G. Chen, L. Ma, W.-Y. Shan, D. Tian, K. Watan- abe, T. Taniguchi, X. Jin, W. Yao, D. Xiao, and Y. Zhang, Gate-tunable topological valley transport in bilayer graphene, Nat. Phys.11, 1027 (2015)
work page 2015
-
[40]
K. F. Mak, K. L. McGill, J. Park, and P. L. McEuen, The valley hall effect in mos2 transistors, Science344, 1489 (2014)
work page 2014
- [41]
-
[42]
J. Birkbeck, J. Xiao, A. Inbar, T. Taniguchi, K. Watan- abe, E. Berg, L. Glazman, F. Guinea, F. von Oppen, and S. Ilani, Quantum twisting microscopy of phonons in twisted bilayer graphene, Nature641, 345–351 (2025)
work page 2025
-
[43]
F. Pichler, W. Kadow, C. Kuhlenkamp, and M. Knap, Probing magnetism in moir´ e heterostructures with quan- tum twisting microscopes, Phys. Rev. B110, 045116 (2024)
work page 2024
- [44]
-
[45]
D. M¨ ockli and M. Khodas, Magnetic-field induceds+ ifpairing in Ising superconductors, Phys. Rev. B99, 180505 (2019)
work page 2019
-
[46]
G. Tang, C. Bruder, and W. Belzig, Magnetic field- induced “mirage” gap in an ising superconductor, Phys. Rev. Lett.126, 237001 (2021)
work page 2021
-
[47]
G. D. Mahan,Many-Particle Physics, 3rd ed. (Springer,
- [48]
-
[49]
See End Matter for details
- [50]
-
[51]
S. Kolenda, M. J. Wolf, and D. Beckmann, Observation of thermoelectric currents in high-field superconductor- ferromagnet tunnel junctions, Phys. Rev. Lett.116, 097001 (2016)
work page 2016
-
[52]
M. E. Bathen and J. Linder, Spin Seebeck effect and ther- moelectric phenomena in superconducting hybrids with magnetic textures or spin-orbit coupling, Sci. Rep.7, 41409 (2017)
work page 2017
-
[53]
F. S. Bergeret, M. Silaev, P. Virtanen, and T. T. Heikkil¨ a, Colloquium: Nonequilibrium effects in superconductors with a spin-splitting field, Rev. Mod. Phys.90, 041001 (2018)
work page 2018
- [54]
-
[55]
E. Strambini, M. Spies, N. Ligato, S. Ili´ c, M. Rouco, C. Gonz´ alez-Orellana, M. Ilyn, C. Rogero, F. S. Berg- eret, J. S. Moodera, P. Virtanen, T. T. Heikkil¨ a, and F. Giazotto, Superconducting spintronic tunnel diode, Nat. Commun.13, 2431 (2022)
work page 2022
- [56]
-
[57]
C. Cao, M. Melegari, M. Philippi, D. Domaretskiy, N. Ubrig, I. Guti´ errez-Lezama, and A. F. Morpurgo, Full control of solid-state electrolytes for electrostatic gating, Adv. Mater.35, 2211993 (2023)
work page 2023
-
[58]
J.-Y. Ji, Y. Hu, T. Bao, Y. Xu, M. Huang, J. Chen, Q.- K. Xue, and D. Zhang, Continuous tuning of spin-orbit coupled superconductivity in NbSe 2, Phys. Rev. B110, 104509 (2024)
work page 2024
-
[59]
D. Costanzo, H. Zhang, B. A. Reddy, H. Berger, and A. F. Morpurgo, Tunnelling spectroscopy of gate-induced superconductivity in MoS 2, Nat. Nanotechnol.13, 483 (2018)
work page 2018
- [60]
-
[61]
O. A. Awoga, P. Virtanen, T. T. Heikkil¨ a, and S. Ili´ c, Nonequilibrium effects in ising superconductors, Un- plished (2026)
work page 2026
-
[62]
F. S. Bergeret, A. Verso, and A. F. Volkov, Electronic transport through ferromagnetic and superconducting junctions with spin-filter tunneling barriers, Phys. Rev. B86, 214516 (2012). 8 END MATTER Derivation of currents The setup contains mainly three parts, namely Ising superconductor (ISC), barrier, and material X with cor- responding HamiltonianH,H T ...
work page 2012
discussion (0)
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