pith. sign in

arxiv: 2604.23111 · v1 · submitted 2026-04-25 · ❄️ cond-mat.mes-hall

Spin Seebeck Effect in Normal-Metal--Chiral-Insulator Heterostructure

Jiayan Zhang , Gaoyang Li , Gaomin Tang , Yanxia Xing This is my paper

Pith reviewed 2026-05-08 07:41 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall
keywords spin Seebeck effectchiral phononsheterostructurenegative differential effectspin rectificationnonlinear spin transportphonon angular momentum
0
0 comments X

The pith

Chiral phonons in an insulator convert their angular momentum to electron spins at a metal interface, producing a temperature-driven spin current with negative differential response and rectification.

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

The paper develops a nonequilibrium Green's function theory for spin current across a normal-metal chiral-insulator boundary where phonons with circular atomic motion supply angular momentum that transfers to electron spin. This mechanism yields two nonlinear effects: the spin current decreases with increasing temperature difference once thermal excitation of electrons overtakes the bias drive, and the current flows preferentially in one direction, resembling a diode. These behaviors depend on the chemical potential in the metal and the spectral properties at the interface. If the conversion process holds, the results suggest a route to control spin flow purely by temperature gradients without external magnetic fields or charge currents.

Core claim

The authors establish that phonon angular momentum carried by circularly polarized atomic vibrations in the chiral insulator converts to electron spin angular momentum at the normal-metal interface, generating a spin Seebeck effect whose magnitude and direction respond nonlinearly to thermal bias. The negative differential spin Seebeck effect arises specifically from the competition between the applied thermal gradient and the increase in thermally excited electron density. The same framework produces spin-current rectification, indicating that a temperature bias can be used to enforce unidirectional spin flow.

What carries the argument

Phonon angular momentum conversion at the NM-CI interface, tracked through an effective interfacial spectral density within the nonequilibrium Green's function formalism.

If this is right

  • Spin current varies with thermal bias, chemical potential in the normal metal, and presence of an extra interfacial layer.
  • Negative differential spin Seebeck effect occurs when thermal excitation of electrons competes with the temperature gradient drive.
  • Spin-current rectification enables a thermally controlled spin diode without charge or magnetic bias.
  • All spin transport features tie directly to the shape of the effective interfacial spectral density.

Where Pith is reading between the lines

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

  • The same interface could be engineered to filter spin currents by temperature alone in layered devices.
  • Varying the chiral insulator thickness or phonon spectrum would test how angular momentum transfer scales with interface properties.
  • Connection to other temperature-gradient spin effects could appear if phonon chirality is preserved across different material classes.

Load-bearing premise

Phonons carry net angular momentum through circular polarization of atomic motion and this angular momentum transfers directly into electron spin at the interface.

What would settle it

Absence of a region where spin current decreases with increasing temperature difference across the junction, while the chemical potential and interface remain fixed, would contradict the negative differential mechanism.

Figures

Figures reproduced from arXiv: 2604.23111 by Gaomin Tang, Gaoyang Li, Jiayan Zhang, Yanxia Xing.

Figure 1
Figure 1. Figure 1: FIG. 1. (a) Schematic of the experimental device. The view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Effective spectral density view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. (a) Rectification ratio view at source ↗
read the original abstract

Phonons can carry angular momentum and exhibit chirality through the circular polarization of atomic motion. This enables a phonon-mediated spin Seebeck effect (SSE) via the conversion of phonon angular momentum into electron spin angular momentum. In this Letter, we develop a theoretical framework for calculating the spin current in a normal-metal (NM)-chiral-insulator (CI) heterostructure within the nonequilibrium Green's function formalism. We discuss the influence of (i) the thermal bias across the NM-CI interface, (ii) the chemical potential of the NM, and (iii) the insertion of an additional interfacial layer, on the spin transport properties. We identify two remarkable nonlinear spin transport phenomena: negative differential SSE and spin-current rectification. The negative differential SSE arises from the competition between the thermal bias and the thermally excited electron density. The spin-current rectification suggests the possibility of realizing a thermally controlled spin diode. We also find that the spin transport behavior is closely associated with an effective interfacial spectral density. This work provides a novel route toward thermally controlled spintronic devices using chiral phonons.

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.

Referee Report

1 major / 0 minor

Summary. The manuscript develops a nonequilibrium Green's function (NEGF) framework to compute spin current across a normal-metal--chiral-insulator (NM-CI) interface mediated by chiral phonons. It examines the dependence of spin transport on thermal bias, NM chemical potential, and an inserted interfacial layer, and reports two nonlinear phenomena: negative differential spin Seebeck effect (SSE) arising from competition between thermal bias and thermally excited electron density, plus spin-current rectification that could enable a thermally controlled spin diode. The transport is tied to an effective interfacial spectral density.

Significance. If the central mapping from circularly polarized phonons to net spin current is robust, the work identifies potentially useful nonlinear spin-transport effects and a new route to thermally driven spintronic devices. The explicit connection between spectral density shape and the reported negative differential SSE and rectification provides concrete, falsifiable predictions that could be tested experimentally.

major comments (1)
  1. [NEGF model and interfacial spectral density] The interfacial coupling that converts phonon angular momentum (circular atomic motion) into electron spin current is introduced via an effective spectral density without derivation from a microscopic electron-phonon Hamiltonian that incorporates phonon polarization vectors. This assumption is load-bearing for the negative differential SSE and rectification claims, as both phenomena are shown to follow from the chosen spectral-density form and the thermal-bias/electron-density competition. A concrete microscopic derivation or explicit justification of the spin-dependent self-energy term is required to establish that the nonlinear effects are not artifacts of the model construction.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We are grateful to the referee for the thorough review and the valuable feedback on our manuscript. The positive assessment of the potential significance is encouraging. We address the major comment in detail below.

read point-by-point responses

  1. Referee: [NEGF model and interfacial spectral density] The interfacial coupling that converts phonon angular momentum (circular atomic motion) into electron spin current is introduced via an effective spectral density without derivation from a microscopic electron-phonon Hamiltonian that incorporates phonon polarization vectors. This assumption is load-bearing for the negative differential SSE and rectification claims, as both phenomena are shown to follow from the chosen spectral-density form and the thermal-bias/electron-density competition. A concrete microscopic derivation or explicit justification of the spin-dependent self-energy term is required to establish that the nonlinear effects are not artifacts of the model construction.

    Authors: We thank the referee for highlighting this important point. The effective interfacial spectral density is indeed central to our framework, as it encapsulates the spin-angular momentum conversion at the NM-CI interface. While a full microscopic derivation starting from an electron-phonon Hamiltonian including explicit phonon polarization vectors would provide additional rigor, such a derivation is technically involved and lies beyond the scope of the present Letter, which focuses on the transport phenomenology. Instead, our model is constructed based on symmetry considerations: the chiral phonons carry angular momentum due to their circular polarization, and the coupling to electrons is chosen to conserve total angular momentum, leading to a spin-dependent self-energy. The specific form of the spectral density is chosen to reflect the frequency-dependent coupling strength typical for phonon-mediated processes. We will revise the manuscript to include an expanded discussion in the methods or supplementary material justifying the effective model through symmetry arguments and referencing related works on chiral phonon-spin coupling. This will help demonstrate that the negative differential SSE and rectification arise from the general competition between thermal bias and electron density, modulated by the chiral nature of the spectral density, rather than being artifacts of an arbitrary choice. revision: partial

Circularity Check

0 steps flagged

No circularity: model outputs are independent of inputs

full rationale

The paper constructs a NEGF framework for spin current across the NM-CI interface and computes nonlinear effects (negative differential SSE, rectification) as functions of thermal bias, chemical potential, and an effective interfacial spectral density. These quantities are not fitted to the target phenomena nor defined in terms of them; the competition between thermal bias and electron density is an explicit dynamical outcome of the transport equations rather than a tautology. No self-citation chain or ansatz is invoked to force the reported results. The derivation remains self-contained against the model's stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests primarily on the domain assumption of phonon chirality and angular momentum transfer to electrons. No free parameters or invented entities are explicitly introduced or fitted in the abstract.

axioms (1)
  • domain assumption Phonons can carry angular momentum and exhibit chirality through the circular polarization of atomic motion.
    Invoked in the opening of the abstract as the basis for the phonon-mediated SSE.

pith-pipeline@v0.9.0 · 5498 in / 1246 out tokens · 64017 ms · 2026-05-08T07:41:47.277501+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

77 extracted references

  1. [1]

    The results show that theηcan be enhanced (diminished) forε d >0 (ε d <0), demonstrating the effect of the interlayer in regulating the rectification efficiency

    Figure 4(b) gives the rectification ratio for different εd atT 0 = 90 K andµ L = 1 meV. The results show that theηcan be enhanced (diminished) forε d >0 (ε d <0), demonstrating the effect of the interlayer in regulating the rectification efficiency. Conclusion—In summary, we propose the realization of the spin Seebeck effect by utilizing the angular mo- m...

  2. [2]

    ˇZuti´ c, J

    I. ˇZuti´ c, J. Fabian, and S. Das Sarma, Spintronics: Fun- damentals and applications, Rev. Mod. Phys.76, 323 (2004)

    2004

  3. [3]

    Bader and S

    S. Bader and S. Parkin, Spintronics, Annu. Rev. Con- dens. Matter Phys.1, 71 (2010)

    2010

  4. [4]

    Bandyopadhyay and M

    S. Bandyopadhyay and M. Cahay,Introduction to spin- tronics(CRC press, 2008)

    2008

  5. [5]

    Kajiwara, K

    Y. Kajiwara, K. Harii, S. Takahashi, J.-i. Ohe, K. Uchida, M. Mizuguchi, H. Umezawa, H. Kawai, K. Ando, K. Takanashi,et al., Transmission of electrical signals by spin-wave interconversion in a magnetic insulator, Nature 464, 262 (2010)

    2010

  6. [6]

    L. J. Cornelissen, J. Liu, R. A. Duine, J. B. Youssef, and B. J. van Wees, Long-distance transport of magnon spin information in a magnetic insulator at room temperature, Nat. Phys.11, 1022 (2015)

    2015

  7. [7]

    Heinrich, C

    B. Heinrich, C. Burrowes, E. Montoya, B. Kardasz, E. Girt, Y.-Y. Song, Y. Sun, and M. Wu, Spin Pump- ing at the Magnetic Insulator (YIG)/Normal Metal (Au) Interfaces, Phys. Rev. Lett.107, 066604 (2011)

    2011

  8. [8]

    Matsuo, Y

    M. Matsuo, Y. Ohnuma, T. Kato, and S. Maekawa, Spin Current Noise of the Spin Seebeck Effect and Spin Pump- ing, Phys. Rev. Lett.120, 037201 (2018)

    2018

  9. [9]

    Ominato, M

    Y. Ominato, M. Yama, A. Yamakage, M. Matsuo, and T. Kato, Spin pumping into two-dimensional systems, J. Phys.: Condens. Matter37, 433001 (2025)

    2025

  10. [10]

    Adachi, K.-i

    H. Adachi, K.-i. Uchida, E. Saitoh, and S. Maekawa, Theory of the spin Seebeck effect, Rep. Prog. Phys.76, 036501 (2013)

    2013

  11. [11]

    Uchida, S

    K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa, and E. Saitoh, Observation of the spin Seebeck effect, Nature455, 778 (2008)

    2008

  12. [12]

    Uchida, S

    K. Uchida, S. Takahashi, J. Ieda, K. Harii, K. Ikeda, W. Koshibae, S. Maekawa, and E. Saitoh, Phenomeno- logical analysis for spin-Seebeck effect in metallic mag- nets, J. Appl. Phys.105, 07C908 (2009)

    2009

  13. [13]

    Uchida, J

    K. Uchida, J. Xiao, H. Adachi, J. Ohe, S. Takahashi, J. Ieda, T. Ota, Y. Kajiwara, H. Umezawa, H. Kawai, G. E. W. Bauer, S. Maekawa, and E. Saitoh, Spin Seebeck insulator, Nat. Mater.9, 894 (2010)

    2010

  14. [14]

    Saitoh, M

    E. Saitoh, M. Ueda, H. Miyajima, and G. Tatara, Con- version of spin current into charge current at room tem- perature: Inverse spin-Hall effect, Appl. Phys. Lett.88, 182509 (2006)

    2006

  15. [15]

    S. O. Valenzuela and M. Tinkham, Direct electronic mea- surement of the spin Hall effect, Nature442, 176 (2006)

    2006

  16. [16]

    Kimura, Y

    T. Kimura, Y. Otani, T. Sato, S. Takahashi, and S. Maekawa, Room-Temperature Reversible Spin Hall Ef- fect, Phys. Rev. Lett.98, 156601 (2007)

    2007

  17. [17]

    Mahfouzi and B

    F. Mahfouzi and B. K. Nikoli´ c, Signatures of electron- magnon interaction in charge and spin currents through magnetic tunnel junctions: A nonequilibrium many-body perturbation theory approach, Phys. Rev. B90, 045115 (2014)

    2014

  18. [18]

    G. Li, H. Jin, Y. Wei, and J. Wang, Giant effec- tive electron-magnon coupling in a nonmagnetic metal– ferromagnetic insulator heterostructure, Phys. Rev. B 106, 205303 (2022)

    2022

  19. [19]

    Li and J

    G. Li and J. Wang, Spin transport study in a disordered- metal/ferromagnetic-insulator heterostructure based on full counting statistics within the coherent potential ap- proximation, Phys. Rev. B109, 125403 (2024)

    2024

  20. [20]

    G. Tang, X. Chen, J. Ren, and J. Wang, Rectifying full- counting statistics in a spin Seebeck engine, Phys. Rev. B97, 081407 (2018)

    2018

  21. [21]

    Zheng, S

    J. Zheng, S. Bender, J. Armaitis, R. E. Troncoso, and R. A. Duine, Green’s function formalism for spin trans- port in metal-insulator-metal heterostructures, Phys. Rev. B96, 174422 (2017)

    2017

  22. [22]

    Y. H. Shen, X. S. Wang, and X. R. Wang, Thermal spin current and spin accumulation at ferromagnetic in- sulator/nonmagnetic metal interface, Phys. Rev. B94, 014403 (2016)

    2016

  23. [23]

    T. Kato, Y. Ohnuma, M. Matsuo, J. Rech, T. Jonck- heere, and T. Martin, Microscopic theory of spin trans- port at the interface between a superconductor and a ferromagnetic insulator, Phys. Rev. B99, 144411 (2019)

    2019

  24. [24]

    L. G. Johnsen, H. T. Simensen, A. Brataas, and J. Lin- der, Magnon Spin Current Induced by Triplet Cooper Pair Supercurrents, Phys. Rev. Lett.127, 207001 (2021)

    2021

  25. [25]

    M. A. Silaev, Finite-frequency spin susceptibility and spin pumping in superconductors with spin-orbit relax- ation, Phys. Rev. B102, 144521 (2020)

    2020

  26. [26]

    S. Seki, T. Ideue, M. Kubota, Y. Kozuka, R. Takagi, M. Nakamura, Y. Kaneko, M. Kawasaki, and Y. Tokura, Thermal Generation of Spin Current in an Antiferromag- net, Phys. Rev. Lett.115, 266601 (2015)

    2015

  27. [27]

    S. M. Rezende, R. L. Rodr´ ıguez-Su´ arez, and A. Azevedo, Theory of the spin Seebeck effect in antiferromagnets, Phys. Rev. B93, 014425 (2016)

    2016

  28. [28]

    Ohnuma, H

    Y. Ohnuma, H. Adachi, E. Saitoh, and S. Maekawa, Spin Seebeck effect in antiferromagnets and compensated fer- rimagnets, Phys. Rev. B87, 014423 (2013)

    2013

  29. [29]

    Q. Cui, B. Zeng, P. Cui, T. Yu, and H. Yang, Efficient spin Seebeck and spin Nernst effects of magnons in alter- magnets, Phys. Rev. B108, L180401 (2023)

    2023

  30. [30]

    E. W. Hodt and J. Linder, Spin pumping in an altermagnet/normal-metal bilayer, Phys. Rev. B109, 174438 (2024)

    2024

  31. [31]

    Sun and J

    C. Sun and J. Linder, Spin pumping from a ferromagnetic insulator into an altermagnet, Phys. Rev. B108, L140408 (2023)

    2023

  32. [32]

    Bardeen, L

    J. Bardeen, L. N. Cooper, and J. R. Schrieffer, Theory of Superconductivity, Phys. Rev.108, 1175 (1957)

    1957

  33. [33]

    N. Li, J. Ren, L. Wang, G. Zhang, P. H¨ anggi, and B. Li, Colloquium: Phononics: Manipulating heat flow with electronic analogs and beyond, Rev. Mod. Phys.84, 1045 (2012)

    2012

  34. [34]

    Yamamoto and K

    T. Yamamoto and K. Watanabe, Nonequilibrium Green’s Function Approach to Phonon Transport in Defective Carbon Nanotubes, Phys. Rev. Lett.96, 255503 (2006)

    2006

  35. [35]

    J.-S. Wang, J. Wang, and N. Zeng, Nonequilibrium Green’s function approach to mesoscopic thermal trans- port, Phys. Rev. B74, 033408 (2006)

    2006

  36. [36]

    Strohm, G

    C. Strohm, G. L. J. A. Rikken, and P. Wyder, Phe- nomenological Evidence for the Phonon Hall Effect, Phys. Rev. Lett.95, 155901 (2005)

    2005

  37. [37]

    Sheng, D

    L. Sheng, D. N. Sheng, and C. S. Ting, Theory of the Phonon Hall Effect in Paramagnetic Dielectrics, Phys. Rev. Lett.96, 155901 (2006)

    2006

  38. [38]

    S. Dai, Z. Fei, Q. Ma, A. S. Rodin, M. Wagner, A. S. McLeod, M. K. Liu, W. Gannett, W. Regan, K. Watan- abe, T. Taniguchi, M. Thiemens, G. Dominguez, A. H. C. 6 Neto, A. Zettl, F. Keilmann, P. Jarillo-Herrero, M. M. Fogler, and D. N. Basov, Tunable Phonon Polaritons in Atomically Thin van der Waals Crystals of Boron Nitride, Science343, 1125 (2014)

    2014

  39. [39]

    X. G. Xu, B. G. Ghamsari, J.-H. Jiang, L. Gilburd, G. O. Andreev, C. Zhi, Y. Bando, D. Golberg, P. Berini, and G. C. Walker, One-dimensional surface phonon polari- tons in boron nitride nanotubes, Nat. Commun.5, 4782 (2014)

    2014

  40. [40]

    Rivera, T

    N. Rivera, T. Christensen, and P. Narang, Phonon Po- laritonics in Two-Dimensional Materials, Nano Lett.19, 2653 (2019)

    2019

  41. [41]

    Zhang and Q

    L. Zhang and Q. Niu, Angular Momentum of Phonons and the Einstein–de Haas Effect, Phys. Rev. Lett.112, 085503 (2014)

    2014

  42. [42]

    Zhang and Q

    L. Zhang and Q. Niu, Chiral Phonons at High-Symmetry Points in Monolayer Hexagonal Lattices, Phys. Rev. Lett. 115, 115502 (2015)

    2015

  43. [43]

    H. Ueda, M. Garc´ ıa-Fern´ andez, S. Agrestini, C. P. Ro- mao, J. van den Brink, N. A. Spaldin, K.-J. Zhou, and U. Staub, Chiral phonons in quartz probed by X-rays, Nature618, 946 (2023)

    2023

  44. [44]

    Zhang, N

    H. Zhang, N. Peshcherenko, F. Yang, T. Z. Ward, P. Raghuvanshi, L. Lindsay, C. Felser, Y. Zhang, J.-Q. Yan, and H. Miao, Measurement of phonon angular mo- mentum, Nat. Phys.21, 1387 (2025)

    2025

  45. [45]

    H. Zhu, J. Yi, M.-Y. Li, J. Xiao, L. Zhang, C.-W. Yang, R. A. Kaindl, L.-J. Li, Y. Wang, and X. Zhang, Obser- vation of chiral phonons, Science359, 579 (2018)

    2018

  46. [46]

    Ishito, H

    K. Ishito, H. Mao, Y. Kousaka, Y. Togawa, S. Iwasaki, T. Zhang, S. Murakami, J.-i. Kishine, and T. Satoh, Truly chiral phonons inα-HgS, Nat. Phys.19, 35 (2023)

    2023

  47. [47]

    D. M. Juraschek, R. M. Geilhufe, H. Zhu, M. Basini, P. Baum, A. Baydin, S. Chaudhary, M. Fechner, B. Fle- bus, G. Grissonnanche, A. I. Kirilyuk, M. Lemeshko, S. F. Maehrlein, M. Mignolet, S. Murakami, Q. Niu, U. Nowak, C. P. Romao, H. Rostami, T. Satoh, N. A. Spaldin, H. Ueda, and L. Zhang, Chiral phonons, Nat. Phys.21, 1532 (2025)

    2025

  48. [48]

    D. M. Juraschek and N. A. Spaldin, Orbital magnetic mo- ments of phonons, Phys. Rev. Mater.3, 064405 (2019)

    2019

  49. [49]

    K. Ohe, H. Shishido, M. Kato, S. Utsumi, H. Matsuura, and Y. Togawa, Chirality-Induced Selectivity of Phonon Angular Momenta in Chiral Quartz Crystals, Phys. Rev. Lett.132, 056302 (2024)

    2024

  50. [50]

    Nabei, C

    Y. Nabei, C. Yang, H. Sun, H. Jones, T. Mai, T. Wang, R. Bodin, B. Pandey, Z. Wang, Y. Xiong, A. H. Comstock, B. Ewing, J. Bingen, R. Sun, D. Smirnov, W. Zhang, A. Hoffmann, R. Rao, M. Hu, Z. V. Vardeny, B. Yan, X. Li, J. Zhou, J. Liu, and D. Sun, Orbital See- beck effect induced by chiral phonons, Nat. Phys.22, 245 (2026)

    2026

  51. [51]

    Ishito, H

    K. Ishito, H. Mao, K. Kobayashi, Y. Kousaka, Y. Togawa, H. Kusunose, J.-i. Kishine, and T. Satoh, Chiral phonons: circularly polarized Raman spectroscopy and ab initio calculations in a chiral crystal tellurium, Chirality35, 338 (2023)

    2023

  52. [52]

    M. Che, J. Liang, Y. Cui, H. Li, B. Lu, W. Sang, X. Li, X. Dong, L. Zhao, S. Zhang, T. Sun, W. Jiang, E. Liu, F. Jin, T. Zhang, and L. Yang, Magnetic Or- der Induced Chiral Phonons in a Ferromagnetic Weyl Semimetal, Phys. Rev. Lett.134, 196906 (2025)

    2025

  53. [53]

    Yokoyama, Phonon Edelstein effect in chiral metals, Phys

    T. Yokoyama, Phonon Edelstein effect in chiral metals, Phys. Rev. B112, L020406 (2025)

    2025

  54. [54]

    Kishine, A

    J. Kishine, A. S. Ovchinnikov, and A. A. Tereshchenko, Chirality-Induced Phonon Dispersion in a Noncen- trosymmetric Micropolar Crystal, Phys. Rev. Lett.125, 245302 (2020)

    2020

  55. [55]

    Funato, M

    T. Funato, M. Matsuo, and T. Kato, Chirality-Induced Phonon-Spin Conversion at an Interface, Phys. Rev. Lett. 132, 236201 (2024)

    2024

  56. [56]

    Haug and A

    H. Haug and A. P. Jauho,Quantum kinetics in trans- port and optics of semiconductors(Quantum Kinetics in Transport & Optics of Semiconductors, 2008)

    2008

  57. [57]

    Stefanucci and R

    G. Stefanucci and R. van Leeuwen,Nonequilibrium Many-Body Theory of Quantum Systems: A Modern In- troduction, 2nd ed. (Cambridge University Press, 2025)

    2025

  58. [58]

    R. A. Jishi,Feynman Diagram Techniques in Condensed Matter Physics(Cambridge University Press, 2013)

    2013

  59. [59]

    Meir and N

    Y. Meir and N. S. Wingreen, Landauer formula for the current through an interacting electron region, Phys. Rev. Lett.68, 2512 (1992)

    1992

  60. [60]

    M. P. L. Sancho, J. M. L. Sancho, and J. Rubio, Quick iterative scheme for the calculation of transfer matrices: application to Mo (100), J. Phys. F: Met. Phys.14, 1205 (1984)

    1984

  61. [61]

    M. P. L. Sancho, J. M. L. Sancho, J. M. L. Sancho, and J. Rubio, Highly convergent schemes for the calculation of bulk and surface Green functions, J. Phys. F: Met. Phys.15, 851 (1985)

    1985

  62. [62]

    [54, 55, 59, 60, 62–64]

    See Supplemental Material at XXX for the derivation of the expression of left-lead spin current, Green’s func- tion of the central region, the expression of right-lead phonon angular momentum current, the verification of current conservation, the lattice Hamiltonian of normal metal, and the spin current for different system dimen- sion, which includes Ref...

  63. [63]

    Weiss,Quantum Dissipative Systems(WORLD SCI- ENTIFIC, 2008)

    U. Weiss,Quantum Dissipative Systems(WORLD SCI- ENTIFIC, 2008)

    2008

  64. [64]

    Thorwart, J

    M. Thorwart, J. Eckel, and E. R. Mucciolo, Non- Markovian dynamics of double quantum dot charge qubits due to acoustic phonons, Phys. Rev. B72, 235320 (2005)

    2005

  65. [65]

    Q.-S. Tan, W. Wu, L. Xu, J. Liu, and L.-M. Kuang, Quantum sensing of supersensitivity for the Ohmic quan- tum reservoir, Phys. Rev. A106, 032602 (2022)

    2022

  66. [66]

    H. Wang, C. Du, P. C. Hammel, and F. Yang, Antiferro- magnonic Spin Transport from Y3Fe5O12 into NiO, Phys. Rev. Lett.113, 097202 (2014)

    2014

  67. [67]

    W. Lin, K. Chen, S. Zhang, and C. L. Chien, Enhance- ment of Thermally Injected Spin Current through an An- tiferromagnetic Insulator, Phys. Rev. Lett.116, 186601 (2016)

    2016

  68. [68]

    Lee, N.-W

    W.-Y. Lee, N.-W. Park, G.-S. Kim, M.-S. Kang, J. W. Choi, K.-Y. Choi, H. W. Jang, E. Saitoh, and S.-K. Lee, Enhanced Spin Seebeck Thermopower in Pt/Holey MoS2/Y3Fe5O12 Hybrid Structure , Nano Lett.21, 189 (2021)

    2021

  69. [69]

    B. Li, L. Wang, and G. Casati, Thermal Diode: Rectifi- cation of Heat Flux, Phys. Rev. Lett.93, 184301 (2004)

    2004

  70. [70]

    Ren, Predicted rectification and negative differential spin Seebeck effect at magnetic interfaces, Phys

    J. Ren, Predicted rectification and negative differential spin Seebeck effect at magnetic interfaces, Phys. Rev. B 88, 220406 (2013)

    2013

  71. [71]

    Datta,Electronic Transport in Mesoscopic Systems (Cambridge University Press, 1995)

    S. Datta,Electronic Transport in Mesoscopic Systems (Cambridge University Press, 1995)

    1995

  72. [72]

    Sergueev, Q.-f

    N. Sergueev, Q.-f. Sun, H. Guo, B. G. Wang, and J. Wang, Spin-polarized transport through a quantum dot: Anderson model with on-site Coulomb repulsion, 7 Phys. Rev. B65, 165303 (2002)

    2002

  73. [73]

    Ren and J.-X

    J. Ren and J.-X. Zhu, Theory of asymmetric and neg- ative differential magnon tunneling under temperature bias: Towards a spin Seebeck diode and transistor, Phys. Rev. B88, 094427 (2013)

    2013

  74. [74]

    Ren and J.-X

    J. Ren and J.-X. Zhu, Heat diode effect and negative differential thermal conductance across nanoscale metal- dielectric interfaces, Phys. Rev. B87, 241412 (2013)

    2013

  75. [75]

    Cheng, D

    R. Cheng, D. Li, H. Zhou, C. Wang, A. Yin, S. Jiang, Y. Liu, Y. Chen, Y. Huang, and X. Duan, Electrolumi- nescence and Photocurrent Generation from Atomically Sharp WSe 2/MoS2 Heterojunctionp-nDiodes, Nano Lett.14, 5590 (2014)

    2014

  76. [76]

    Z. Li, K. Yuan, and Y. Ye, High rectification ratio metal- insulator-semiconductor tunnel diode based on single- layer MoS2, Nanotechnology31, 075202 (2019)

    2019

  77. [77]

    Iovan, S

    A. Iovan, S. Andersson, Y. G. Naidyuk, A. Vedyaev, B. Dieny, and V. Korenivski, Spin Diode Based on Fe/MgO Double Tunnel Junction, Nano Lett.8, 805 (2008)

    2008