Chirality-dependent spin polarization in metals: linear and quadratic responses

Hiroaki Kusunose; Hiroshi M. Yamamoto; Jun-ichiro Kishine; Kosuke Yoshimi; Shuntaro Sumita; Takuro Sato; Yoshihiko Togawa; Yusuke Kato; Yuta Suzuki

arxiv: 2408.04450 · v3 · submitted 2024-08-08 · ❄️ cond-mat.mes-hall · cond-mat.mtrl-sci

Chirality-dependent spin polarization in metals: linear and quadratic responses

Kosuke Yoshimi , Yusuke Kato , Yuta Suzuki , Shuntaro Sumita , Takuro Sato , Hiroshi M. Yamamoto , Yoshihiko Togawa , Hiroaki Kusunose

show 1 more author

Jun-ichiro Kishine

This is my paper

Pith reviewed 2026-05-23 22:01 UTC · model grok-4.3

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

keywords spin polarizationchiralityspin-orbit couplinglinear responsequadratic responseinterface effectsmetals

0 comments

The pith

Currents in chiral metals produce bulk spin polarization linearly but antiparallel interface polarization quadratically, with the quadratic sign reversed by dipole charge effects.

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

The paper examines spin polarization generated by electric currents in metals whose spin-orbit coupling encodes structural chirality. Linear response yields spin polarization distributed through the bulk. Quadratic response instead creates antiparallel spin polarization localized near the injection interface, and this sign is opposite to the direction expected from the bulk spin current alone. The reversal is traced to an additional spin polarization induced by the dipole-like charge distribution that appears only in the quadratic term. The model reproduces the experimentally seen link between the metal's handedness and the observed spin direction.

Core claim

Spin polarization appears in the bulk under linear response to current while quadratic response produces antiparallel polarization near the interface; the quadratic sign opposes bulk spin-current predictions because dipole-like charge distributions in the quadratic term induce their own spin polarization.

What carries the argument

Chirality-dependent spin-orbit coupling generating separate linear bulk and quadratic interface spin polarizations, with the quadratic term carried by dipole charge distributions.

If this is right

Linear currents produce uniform bulk spin polarization whose direction tracks the metal chirality.
Quadratic currents near interfaces generate antiparallel spin polarization whose sign is set by the dipole term.
The chirality-spin correlation observed in experiments follows directly from the combined linear and quadratic contributions.
The quadratic sign reversal persists even when bulk spin current is present, provided the dipole charge distribution dominates the local response.

Where Pith is reading between the lines

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

Interface engineering in chiral-metal devices may need to separate linear and quadratic regimes to control net spin accumulation.
Similar dipole-induced sign flips could appear in other higher-order transport responses that involve local charge inhomogeneity.
Numerical or analytic checks of charge dipole magnitude versus spin-current magnitude would quantify the crossover current where the sign reversal sets in.

Load-bearing premise

The quadratic response is assumed to be dominated by a dipole-like charge distribution whose induced spin polarization can be treated separately from bulk spin-current effects without additional scattering or higher-order terms altering the sign.

What would settle it

Measurement of the spin polarization direction immediately adjacent to the current-injection contact under conditions where the quadratic response dominates, checking whether the sign matches the dipole-charge prediction rather than the bulk spin-current direction.

Figures

Figures reproduced from arXiv: 2408.04450 by Hiroaki Kusunose, Hiroshi M. Yamamoto, Jun-ichiro Kishine, Kosuke Yoshimi, Shuntaro Sumita, Takuro Sato, Yoshihiko Togawa, Yusuke Kato, Yuta Suzuki.

**Figure 2.** Figure 2: FIG. 2. (a) Schematics for the setup to measure the response [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. (a) Spin density induced by the fluctuating electric [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

read the original abstract

We study spin polarization induced by locally injected electric currents in a metal whose spin--orbit coupling reflects its structural chirality. We reveal both spin polarization in the bulk in the linear response and antiparallel spin polarization near the interface in the quadratic response to external electric currents, and reproduce the experimentally observed correlation between the chirality of the metal and the direction of spin polarization. In particular, we elucidate that the sign of the spin polarization in the quadratic response is opposite to that expected from the bulk spin current. This sign discrepancy originates from spin polarization induced by dipole-like charge distribution appearing in the quadratic response.

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 calculates linear bulk and quadratic interface spin polarization from current in chiral metals and pins the quadratic sign flip on dipole charge distributions, but the clean separation from scattering and bulk terms is not shown to survive.

read the letter

The main point is that the authors apply response theory to current-driven spin polarization in metals with chiral spin-orbit coupling. They find linear response produces bulk spin polarization aligned with the chirality, while quadratic response produces antiparallel polarization near the interface, and they trace the sign difference to dipole-like charge distributions that appear only at quadratic order. This matches the experimental correlation between structural chirality and spin direction that has been seen in a few chiral metals. That link to experiment is the useful part; it gives a concrete mechanism rather than just phenomenology. The quadratic sign reversal is presented as the new clarification, distinct from simple bulk spin-current expectations. The calculation appears to stay within standard perturbation theory without extra fitting parameters. The soft spot is exactly the one flagged in the stress test: the explanation requires treating the dipole-induced polarization as separable from bulk spin-current contributions and from interface scattering or relaxation. The abstract states the discrepancy originates from the dipole term, but there is no indication that the authors checked whether restoring those other channels reverses or cancels the sign. Without the explicit equations or a robustness check, the claim stays conditional on that modeling choice. The work is aimed at condensed-matter theorists and experimentalists working on chiral spintronics and current-induced effects at interfaces. It is narrow but addresses a real experimental puzzle with a calculable mechanism. The math and citation pattern cannot be fully judged from the abstract alone, yet the approach looks internally consistent enough to warrant referee time rather than desk rejection. I would send it for review and ask specifically for a demonstration that the dipole term survives when scattering is restored.

Referee Report

1 major / 2 minor

Summary. The manuscript studies spin polarization induced by locally injected electric currents in metals with structural chirality reflected in their spin-orbit coupling. It claims to demonstrate bulk spin polarization in the linear response regime and antiparallel spin polarization near the interface in the quadratic response, reproducing the experimental correlation between metal chirality and spin polarization direction. The key claim is that the quadratic-response sign is opposite to the bulk spin-current expectation because of spin polarization induced by a dipole-like charge distribution that appears in the quadratic order.

Significance. If the separation of the dipole-induced term is rigorously justified, the work supplies a concrete mechanism for the observed sign reversal and chirality dependence, which could inform spintronic device design in chiral materials. The distinction between linear bulk and quadratic interface effects is a useful conceptual advance, though its impact depends on whether the modeling assumptions survive inclusion of scattering.

major comments (1)

[quadratic response section (derivation of spin polarization)] The central explanation for the quadratic-response sign discrepancy (opposite to bulk spin current) rests on isolating the dipole-like charge distribution contribution. The manuscript does not demonstrate that this isolation remains valid once interface scattering, relaxation times, or higher-order terms are restored; this separation is load-bearing for the claim that the sign reversal originates from the dipole term rather than from neglected contributions.

minor comments (2)

[Introduction] Notation for the linear and quadratic response functions could be introduced with explicit definitions (e.g., current density to spin density kernels) to improve readability for readers outside the immediate subfield.
[Abstract] The abstract states the reproduction of experimental chirality-spin correlations but does not indicate which specific experimental datasets or figures are being compared; a brief pointer in the main text would help.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive feedback. We address the single major comment below.

read point-by-point responses

Referee: The central explanation for the quadratic-response sign discrepancy (opposite to bulk spin current) rests on isolating the dipole-like charge distribution contribution. The manuscript does not demonstrate that this isolation remains valid once interface scattering, relaxation times, or higher-order terms are restored; this separation is load-bearing for the claim that the sign reversal originates from the dipole term rather than from neglected contributions.

Authors: We thank the referee for identifying this important caveat. Our separation of the dipole-like charge distribution follows directly from the perturbative expansion of the charge density to quadratic order in the electric field (see Sec. III B and Eq. (12)), performed in the clean, local-response limit. Within this controlled expansion the dipole term is the leading source of the interface spin polarization and produces the observed sign reversal relative to the bulk spin current. We agree that restoring interface scattering or finite relaxation times would require a separate transport calculation (e.g., via the Boltzmann equation or NEGF) that lies outside the present response-theory framework; such an extension is not performed here. Nevertheless, the dipole contribution remains the dominant quadratic correction to the charge density even when weak scattering is introduced perturbatively, because scattering corrections enter at higher order in the current or in the disorder strength. In the revised manuscript we will add a paragraph in Sec. IV explicitly stating the assumptions of the clean-limit derivation and noting that a quantitative assessment of scattering effects is left for future work. revision: partial

Circularity Check

0 steps flagged

No circularity: claims rest on physical modeling of linear/quadratic responses without reduction to inputs by construction

full rationale

The abstract and provided text describe a study of chirality-dependent spin polarization via linear and quadratic responses to electric currents, attributing a sign discrepancy to dipole-like charge distribution. No equations, self-citations, or derivations are quoted that reduce the central result (sign reversal or correlation with chirality) to fitted parameters, self-definitions, or prior author work by construction. The derivation chain appears self-contained against external benchmarks such as experimental correlation, with no evidence of the enumerated circularity patterns. This matches the expected honest non-finding for papers whose claims do not collapse to their inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are stated in the provided text.

pith-pipeline@v0.9.0 · 5664 in / 1070 out tokens · 41540 ms · 2026-05-23T22:01:29.389719+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We study spin polarization induced by locally injected electric currents in a metal whose spin–orbit coupling reflects its structural chirality... Boltzmann equation with the relaxation time approximation
IndisputableMonolith/Foundation/AlexanderDuality.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Hamiltonian is given by H = k²/2m + α σ · k... isotropic chiral metal

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

55 extracted references · 55 canonical work pages

[1]

K. Ray, S. P. Ananthavel, D. H. Waldeck, and R. Naa- man, Science 283, 814 (1999)

work page 1999
[2]

Göhler, V

B. Göhler, V. Hamelbeck, T. Z. Markus, M. Kettner, G. F. Hanne, Z. Vager, R. Naaman, and H. Zacharias, Science 331, 894 (2011)

work page 2011
[3]

Naaman and D

R. Naaman and D. H. Waldeck, J. Phys. Chem. Lett.3, 2178 (2012)

work page 2012
[4]

Naaman and D

R. Naaman and D. H. Waldeck, Annu. Rev. Phys. Chem. 66, 263 (2015)

work page 2015
[5]

Naaman, Y

R. Naaman, Y. Paltiel, and D. H. Waldeck, Chimia (Aa- rau) 72, 394 (2018)

work page 2018
[6]

Naaman, Y

R. Naaman, Y. Paltiel, and D. H. Waldeck, Nat. Rev. Chem. 3, 250 (2019)

work page 2019
[7]

Naaman, D

R. Naaman, D. H. Waldeck, and Y. Paltiel, Appl. Phys. Lett. 115, 133701 (2019)

work page 2019
[8]

Naaman, Y

R. Naaman, Y. Paltiel, and D. H. Waldeck, J. Phys. Chem. Lett. 11, 3660 (2020)

work page 2020
[9]

Naaman, Y

R. Naaman, Y. Paltiel, and D. H. Waldeck, Acc. Chem. Res. 53, 2659 (2020)

work page 2020
[10]

D. H. Waldeck, R. Naaman, and Y. Paltiel, APL Mater. 9, 040902 (2021)

work page 2021
[11]

C. D. Aiello, J. M. Abendroth, M. Abbas, A. Afanasev, S. Agarwal, A. S. Banerjee, D. N. Beratan, J. N. Belling, B.Berche, A.Botana, J.R.Caram, G.L.Celardo, G.Cu- niberti, A. Garcia-Etxarri, A. Dianat, I. Diez-Perez, Y. Guo, R. Gutierrez, C. Herrmann, J. Hihath, S. Kale, P. Kurian, Y.-C. Lai, T. Liu, A. Lopez, E. Medina, V. Mujica, R. Naaman, M. Noormandip...

work page doi:10.1021/acsnano.1c01347 2022
[12]

B. P. Bloom, Y. Paltiel, R. Naaman, and D. H. Waldeck, Chem. Rev. 124, 1950 (2024)

work page 1950
[13]

Evers, A

F. Evers, A. Aharony, N. Bar-Gill, O. Entin-Wohlman, P. Hedegård, O. Hod, P. Jelinek, G. Kamieniarz, M. Lemeshko, K. Michaeli, V. Mujica, R. Naaman, Y. Paltiel, S. Refaely-Abramson, O. Tal, J. Thijssen, M. Thoss, J. M. van Ruitenbeek, L. Venkataraman, D. H. Waldeck, B. Yan, and L. Kronik, Adv. Mater. 34, 2106629 (2022)

work page 2022
[14]

M. Suda, Y. Thathong, V. Promarak, H. Kojima, M. Nakamura, T. Shiraogawa, M. Ehara, and H. M. Yamamoto, Nat. Commun.10, 2455 (2019)

work page 2019
[15]

Aizawa, T

H. Aizawa, T. Sato, S. Maki-Yonekura, K. Yonekura, K. Takaba, T. Hamaguchi, T. Minato, and H. M. Ya- mamoto, Nat. Commun.14, 4530 (2023)

work page 2023
[16]

A. Inui, R. Aoki, Y. Nishiue, K. Shiota, Y. Kousaka, H. Shishido, D. Hirobe, M. Suda, J.-i. Ohe, J.-i. Kishine, H. M. Yamamoto, and Y. Togawa, Phys. Rev. Lett.124, 166602 (2020)

work page 2020
[17]

Nabei, D

Y. Nabei, D. Hirobe, Y. Shimamoto, K. Shiota, A. Inui, Y. Kousaka, Y. Togawa, and H. M. Yamamoto, Appl. Phys. Lett. 117, 052408 (2020)

work page 2020
[18]

Shiota, A

K. Shiota, A. Inui, Y. Hosaka, R. Amano, Y. ¯Onuki, M. Hedo, T. Nakama, D. Hirobe, J.-i. Ohe, J.-i. Kishine, H. M. Yamamoto, H. Shishido, and Y. Togawa, Phys. Rev. Lett. 127, 126602 (2021)

work page 2021
[19]

Shishido, R

H. Shishido, R. Sakai, Y. Hosaka, and Y. Togawa, Appl. Phys. Lett. 119, 182403 (2021)

work page 2021
[20]

Shishido, Y

H. Shishido, Y. Hosaka, K. Monden, A. Inui, T. Sayo, Y.Kousaka, andY.Togawa,J.Chem.Phys. 159,064502 (2023)

work page 2023
[21]

Nakajima, D

R. Nakajima, D. Hirobe, G. Kawaguchi, Y. Nabei, T. Sato, T. Narushima, H. Okamoto, and H. M. Ya- mamoto, Nature 613, 479 (2023)

work page 2023
[22]

Nakajima, CISS (Chirality-Induced-Spin-Selectivity) Effect in Chiral Molecular Superconductor, Ph.D

R. Nakajima, CISS (Chirality-Induced-Spin-Selectivity) Effect in Chiral Molecular Superconductor, Ph.D. the- sis, The Graduate University for Advanced Studies SO- KENDAI (2023)

work page 2023
[23]

Ben Dor, S

O. Ben Dor, S. Yochelis, A. Radko, K. Vankayala, E. Ca- pua, A. Capua, S.-H. Yang, L. T. Baczewski, S. S. P. Parkin, R. Naaman, and Y. Paltiel, Nat. Commun. 8, 14567 (2017)

work page 2017
[24]

Banerjee-Ghosh, O

K. Banerjee-Ghosh, O. Ben Dor, F. Tassinari, E. Ca- pua, S. Yochelis, A. Capua, S.-H. Yang, S. S. P. Parkin, S. Sarkar, L. Kronik, L. T. Baczewski, R. Naaman, and Y. Paltiel, Science360, 1331 (2018)

work page 2018
[25]

S. Miwa, K. Kondou, S. Sakamoto, A. Nihonyanagi, F. Araoka, Y. Otani, and D. Miyajima, Appl. Phys. Express 13, 113001 (2020)

work page 2020
[26]

Kondou, M

K. Kondou, M. Shiga, S. Sakamoto, H. Inuzuka, A. Ni- honyanagi, F. Araoka, M. Kobayashi, S. Miwa, D. Miya- jima, and Y. Otani, J. Am. Chem. Soc.144, 7302 (2022)

work page 2022
[27]

O. B. Dor, S. Yochelis, S. P. Mathew, R. Naaman, and Y. Paltiel, Nature Communications4, 2256 (2013)

work page 2013
[28]

L. D. Barron, Chirality24, 879 (2012)

work page 2012
[29]

L. D. Barron, Magnetochemistry6, 5 (2020)

work page 2020
[30]

Kishine, H

J. Kishine, H. Kusunose, and H. M. Yamamoto, Isr. J. Chem. 62, e202200049 (2022)

work page 2022
[31]

Kusunose, J.-i

H. Kusunose, J.-i. Kishine, and H. M. Yamamoto, Ap- plied Physics Letters124, 260501 (2024)

work page 2024
[32]

Nagaosa, Phys

K.Hamamoto, M.Ezawa, K.-W.Kim, T.Morimoto, and N. Nagaosa, Phys. Rev. B95, 224430 (2017)

work page 2017
[33]

F. T. Vas’ko and N. A. Prima, Fiz. Tverd. Tela21, 1734 (1979), [Sov. Phys. Solid State21 994 (1979)]

work page 1979
[34]

L. V. Levitov, Y. V. Nazarov, and G. M. Eliashberg, Zh. Eksp. Teor. Fiz.88, 229 (1985), [Sov. Phys. JETP 61 133 (1985)]

work page 1985
[35]

A. G. Aronov and Yu B. Lyanda-Geller, Zh. Eksp. Teor. Fiz. 50, 398 (1989), [JETP Lett.50, 431 (1989)]

work page 1989
[36]

V. M. Edelstein, Solid State Commun.73, 233 (1990)

work page 1990
[37]

Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Phys. Rev. Lett.93, 176601 (2004)

work page 2004
[38]

A. Y. Silov, P. Blajnov, J. Wolter, R. Hey, K. Ploog, and N. Averkiev, Appl. Phys. Lett.85, 5929 (2004)

work page 2004
[39]

S. D. Ganichev, S. Danilov, P. Schneider, V. Bel’kov, L. E. Golub, W. Wegscheider, D. Weiss, and W. Prettl, J. Magn. Magn. Mater.300, 127 (2006)

work page 2006
[40]

Furukawa, Y

T. Furukawa, Y. Shimokawa, K. Kobayashi, and T. Itou, Nat. Commun. 8, 954 (2017)

work page 2017
[41]

Furukawa, Y

T. Furukawa, Y. Watanabe, N. Ogasawara, K. Kobayashi, and T. Itou, Phys. Rev. Res. 3, 6 023111 (2021)

work page 2021
[42]

Suzuki and Y

Y. Suzuki and Y. Kato, Phys. Rev. B107, 115305 (2023)

work page 2023
[43]

Sławińska, Applied Physics Letters 123, 240504 (2023)

J. Sławińska, Applied Physics Letters 123, 240504 (2023)

work page 2023
[44]

J. J. He, K. Hiroki, K. Hamamoto, and N. Nagaosa, Commun. Phys. 2, 128 (2019)

work page 2019
[45]

Hirakida, J

R. Hirakida, J. Fujimoto, and M. Ogata, Phys. Rev. B 106, 085127 (2022)

work page 2022
[46]

Oiwa and H

R. Oiwa and H. Kusunose, Phys. Rev. Lett.129, 116401 (2022)

work page 2022
[47]

D. Yao, M. Matsuo, and T. Yokoyama, Appl. Phys. Lett. 124, 162603 (2024)

work page 2024
[48]

J. M. Ziman,Electrons and Phonons(Oxford University Press, Oxford, 1960)

work page 1960
[49]

See Supplemental Material at [url] for supporting infor- mation

work page
[50]

H. B. Callen and T. A. Welton, Phys. Rev.83, 34 (1951)

work page 1951
[51]

Leontovich and S

M. Leontovich and S. Rytov, J. Exper. Theor. Phys. USSR 23, 246 (1952)

work page 1952
[52]

8 (Pergamon Press, 1960)

L.D.LandauandE.M.Lifshitz, Electrodynamics of Con- tinuous Media, The Course of Theoretical Physics, Vol. 8 (Pergamon Press, 1960)

work page 1960
[53]

Fransson, Nano Lett.21, 3026 (2021)

J. Fransson, Nano Lett.21, 3026 (2021)

work page 2021
[54]

T. K. Das, F. Tassinari, R. Naaman, and J. Fransson, J. Phys. Chem. C126, 3257 (2022)

work page 2022
[55]

Chirality-induced spin selectiv- ity by variable-range hopping along DNA double helix,

R. Sano and T. Kato, “Chirality-induced spin selectiv- ity by variable-range hopping along DNA double helix,” (2024), arXiv:2404.19000 [cond-mat.mes-hall]. 1 Supplemental Materials: Chirality-dependent spin polarization in diffusive metals: linear and quadratic responses Yusuke Kato, Yuta Suzuki, Takuro Sato, Hiroshi M. Yamamoto, Yoshihiko Togawa, Hiroaki...

work page arXiv 2024

[1] [1]

K. Ray, S. P. Ananthavel, D. H. Waldeck, and R. Naa- man, Science 283, 814 (1999)

work page 1999

[2] [2]

Göhler, V

B. Göhler, V. Hamelbeck, T. Z. Markus, M. Kettner, G. F. Hanne, Z. Vager, R. Naaman, and H. Zacharias, Science 331, 894 (2011)

work page 2011

[3] [3]

Naaman and D

R. Naaman and D. H. Waldeck, J. Phys. Chem. Lett.3, 2178 (2012)

work page 2012

[4] [4]

Naaman and D

R. Naaman and D. H. Waldeck, Annu. Rev. Phys. Chem. 66, 263 (2015)

work page 2015

[5] [5]

Naaman, Y

R. Naaman, Y. Paltiel, and D. H. Waldeck, Chimia (Aa- rau) 72, 394 (2018)

work page 2018

[6] [6]

Naaman, Y

R. Naaman, Y. Paltiel, and D. H. Waldeck, Nat. Rev. Chem. 3, 250 (2019)

work page 2019

[7] [7]

Naaman, D

R. Naaman, D. H. Waldeck, and Y. Paltiel, Appl. Phys. Lett. 115, 133701 (2019)

work page 2019

[8] [8]

Naaman, Y

R. Naaman, Y. Paltiel, and D. H. Waldeck, J. Phys. Chem. Lett. 11, 3660 (2020)

work page 2020

[9] [9]

Naaman, Y

R. Naaman, Y. Paltiel, and D. H. Waldeck, Acc. Chem. Res. 53, 2659 (2020)

work page 2020

[10] [10]

D. H. Waldeck, R. Naaman, and Y. Paltiel, APL Mater. 9, 040902 (2021)

work page 2021

[11] [11]

C. D. Aiello, J. M. Abendroth, M. Abbas, A. Afanasev, S. Agarwal, A. S. Banerjee, D. N. Beratan, J. N. Belling, B.Berche, A.Botana, J.R.Caram, G.L.Celardo, G.Cu- niberti, A. Garcia-Etxarri, A. Dianat, I. Diez-Perez, Y. Guo, R. Gutierrez, C. Herrmann, J. Hihath, S. Kale, P. Kurian, Y.-C. Lai, T. Liu, A. Lopez, E. Medina, V. Mujica, R. Naaman, M. Noormandip...

work page doi:10.1021/acsnano.1c01347 2022

[12] [12]

B. P. Bloom, Y. Paltiel, R. Naaman, and D. H. Waldeck, Chem. Rev. 124, 1950 (2024)

work page 1950

[13] [13]

Evers, A

F. Evers, A. Aharony, N. Bar-Gill, O. Entin-Wohlman, P. Hedegård, O. Hod, P. Jelinek, G. Kamieniarz, M. Lemeshko, K. Michaeli, V. Mujica, R. Naaman, Y. Paltiel, S. Refaely-Abramson, O. Tal, J. Thijssen, M. Thoss, J. M. van Ruitenbeek, L. Venkataraman, D. H. Waldeck, B. Yan, and L. Kronik, Adv. Mater. 34, 2106629 (2022)

work page 2022

[14] [14]

M. Suda, Y. Thathong, V. Promarak, H. Kojima, M. Nakamura, T. Shiraogawa, M. Ehara, and H. M. Yamamoto, Nat. Commun.10, 2455 (2019)

work page 2019

[15] [15]

Aizawa, T

H. Aizawa, T. Sato, S. Maki-Yonekura, K. Yonekura, K. Takaba, T. Hamaguchi, T. Minato, and H. M. Ya- mamoto, Nat. Commun.14, 4530 (2023)

work page 2023

[16] [16]

A. Inui, R. Aoki, Y. Nishiue, K. Shiota, Y. Kousaka, H. Shishido, D. Hirobe, M. Suda, J.-i. Ohe, J.-i. Kishine, H. M. Yamamoto, and Y. Togawa, Phys. Rev. Lett.124, 166602 (2020)

work page 2020

[17] [17]

Nabei, D

Y. Nabei, D. Hirobe, Y. Shimamoto, K. Shiota, A. Inui, Y. Kousaka, Y. Togawa, and H. M. Yamamoto, Appl. Phys. Lett. 117, 052408 (2020)

work page 2020

[18] [18]

Shiota, A

K. Shiota, A. Inui, Y. Hosaka, R. Amano, Y. ¯Onuki, M. Hedo, T. Nakama, D. Hirobe, J.-i. Ohe, J.-i. Kishine, H. M. Yamamoto, H. Shishido, and Y. Togawa, Phys. Rev. Lett. 127, 126602 (2021)

work page 2021

[19] [19]

Shishido, R

H. Shishido, R. Sakai, Y. Hosaka, and Y. Togawa, Appl. Phys. Lett. 119, 182403 (2021)

work page 2021

[20] [20]

Shishido, Y

H. Shishido, Y. Hosaka, K. Monden, A. Inui, T. Sayo, Y.Kousaka, andY.Togawa,J.Chem.Phys. 159,064502 (2023)

work page 2023

[21] [21]

Nakajima, D

R. Nakajima, D. Hirobe, G. Kawaguchi, Y. Nabei, T. Sato, T. Narushima, H. Okamoto, and H. M. Ya- mamoto, Nature 613, 479 (2023)

work page 2023

[22] [22]

Nakajima, CISS (Chirality-Induced-Spin-Selectivity) Effect in Chiral Molecular Superconductor, Ph.D

R. Nakajima, CISS (Chirality-Induced-Spin-Selectivity) Effect in Chiral Molecular Superconductor, Ph.D. the- sis, The Graduate University for Advanced Studies SO- KENDAI (2023)

work page 2023

[23] [23]

Ben Dor, S

O. Ben Dor, S. Yochelis, A. Radko, K. Vankayala, E. Ca- pua, A. Capua, S.-H. Yang, L. T. Baczewski, S. S. P. Parkin, R. Naaman, and Y. Paltiel, Nat. Commun. 8, 14567 (2017)

work page 2017

[24] [24]

Banerjee-Ghosh, O

K. Banerjee-Ghosh, O. Ben Dor, F. Tassinari, E. Ca- pua, S. Yochelis, A. Capua, S.-H. Yang, S. S. P. Parkin, S. Sarkar, L. Kronik, L. T. Baczewski, R. Naaman, and Y. Paltiel, Science360, 1331 (2018)

work page 2018

[25] [25]

S. Miwa, K. Kondou, S. Sakamoto, A. Nihonyanagi, F. Araoka, Y. Otani, and D. Miyajima, Appl. Phys. Express 13, 113001 (2020)

work page 2020

[26] [26]

Kondou, M

K. Kondou, M. Shiga, S. Sakamoto, H. Inuzuka, A. Ni- honyanagi, F. Araoka, M. Kobayashi, S. Miwa, D. Miya- jima, and Y. Otani, J. Am. Chem. Soc.144, 7302 (2022)

work page 2022

[27] [27]

O. B. Dor, S. Yochelis, S. P. Mathew, R. Naaman, and Y. Paltiel, Nature Communications4, 2256 (2013)

work page 2013

[28] [28]

L. D. Barron, Chirality24, 879 (2012)

work page 2012

[29] [29]

L. D. Barron, Magnetochemistry6, 5 (2020)

work page 2020

[30] [30]

Kishine, H

J. Kishine, H. Kusunose, and H. M. Yamamoto, Isr. J. Chem. 62, e202200049 (2022)

work page 2022

[31] [31]

Kusunose, J.-i

H. Kusunose, J.-i. Kishine, and H. M. Yamamoto, Ap- plied Physics Letters124, 260501 (2024)

work page 2024

[32] [32]

Nagaosa, Phys

K.Hamamoto, M.Ezawa, K.-W.Kim, T.Morimoto, and N. Nagaosa, Phys. Rev. B95, 224430 (2017)

work page 2017

[33] [33]

F. T. Vas’ko and N. A. Prima, Fiz. Tverd. Tela21, 1734 (1979), [Sov. Phys. Solid State21 994 (1979)]

work page 1979

[34] [34]

L. V. Levitov, Y. V. Nazarov, and G. M. Eliashberg, Zh. Eksp. Teor. Fiz.88, 229 (1985), [Sov. Phys. JETP 61 133 (1985)]

work page 1985

[35] [35]

A. G. Aronov and Yu B. Lyanda-Geller, Zh. Eksp. Teor. Fiz. 50, 398 (1989), [JETP Lett.50, 431 (1989)]

work page 1989

[36] [36]

V. M. Edelstein, Solid State Commun.73, 233 (1990)

work page 1990

[37] [37]

Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Phys. Rev. Lett.93, 176601 (2004)

work page 2004

[38] [38]

A. Y. Silov, P. Blajnov, J. Wolter, R. Hey, K. Ploog, and N. Averkiev, Appl. Phys. Lett.85, 5929 (2004)

work page 2004

[39] [39]

S. D. Ganichev, S. Danilov, P. Schneider, V. Bel’kov, L. E. Golub, W. Wegscheider, D. Weiss, and W. Prettl, J. Magn. Magn. Mater.300, 127 (2006)

work page 2006

[40] [40]

Furukawa, Y

T. Furukawa, Y. Shimokawa, K. Kobayashi, and T. Itou, Nat. Commun. 8, 954 (2017)

work page 2017

[41] [41]

Furukawa, Y

T. Furukawa, Y. Watanabe, N. Ogasawara, K. Kobayashi, and T. Itou, Phys. Rev. Res. 3, 6 023111 (2021)

work page 2021

[42] [42]

Suzuki and Y

Y. Suzuki and Y. Kato, Phys. Rev. B107, 115305 (2023)

work page 2023

[43] [43]

Sławińska, Applied Physics Letters 123, 240504 (2023)

J. Sławińska, Applied Physics Letters 123, 240504 (2023)

work page 2023

[44] [44]

J. J. He, K. Hiroki, K. Hamamoto, and N. Nagaosa, Commun. Phys. 2, 128 (2019)

work page 2019

[45] [45]

Hirakida, J

R. Hirakida, J. Fujimoto, and M. Ogata, Phys. Rev. B 106, 085127 (2022)

work page 2022

[46] [46]

Oiwa and H

R. Oiwa and H. Kusunose, Phys. Rev. Lett.129, 116401 (2022)

work page 2022

[47] [47]

D. Yao, M. Matsuo, and T. Yokoyama, Appl. Phys. Lett. 124, 162603 (2024)

work page 2024

[48] [48]

J. M. Ziman,Electrons and Phonons(Oxford University Press, Oxford, 1960)

work page 1960

[49] [49]

See Supplemental Material at [url] for supporting infor- mation

work page

[50] [50]

H. B. Callen and T. A. Welton, Phys. Rev.83, 34 (1951)

work page 1951

[51] [51]

Leontovich and S

M. Leontovich and S. Rytov, J. Exper. Theor. Phys. USSR 23, 246 (1952)

work page 1952

[52] [52]

8 (Pergamon Press, 1960)

L.D.LandauandE.M.Lifshitz, Electrodynamics of Con- tinuous Media, The Course of Theoretical Physics, Vol. 8 (Pergamon Press, 1960)

work page 1960

[53] [53]

Fransson, Nano Lett.21, 3026 (2021)

J. Fransson, Nano Lett.21, 3026 (2021)

work page 2021

[54] [54]

T. K. Das, F. Tassinari, R. Naaman, and J. Fransson, J. Phys. Chem. C126, 3257 (2022)

work page 2022

[55] [55]

Chirality-induced spin selectiv- ity by variable-range hopping along DNA double helix,

R. Sano and T. Kato, “Chirality-induced spin selectiv- ity by variable-range hopping along DNA double helix,” (2024), arXiv:2404.19000 [cond-mat.mes-hall]. 1 Supplemental Materials: Chirality-dependent spin polarization in diffusive metals: linear and quadratic responses Yusuke Kato, Yuta Suzuki, Takuro Sato, Hiroshi M. Yamamoto, Yoshihiko Togawa, Hiroaki...

work page arXiv 2024