pith. sign in

arxiv: 2512.19065 · v2 · submitted 2025-12-22 · ❄️ cond-mat.mes-hall · cond-mat.other

Signature of inverse orbital Hall effect in silicon studied using time-resolved terahertz polarimetry

Ami Mi Shirai , Kota Aikyo , Yuta Murotani , Tomohiro Fujimoto , Changsu Kim , Hidefumi Akiyama , Shinji Miwa , Jun Yoshinobu
show 1 more author
Ryusuke Matsunaga
This is my paper

Pith reviewed 2026-05-16 20:49 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.other
keywords inverse orbital Hall effectsiliconanomalous Hall conductivityterahertz spectroscopyphotocarriersorbitronicscircularly polarized lightroom temperature
0
0 comments X

The pith

Circularly polarized light induces a long-lived helicity-dependent anomalous Hall conductivity in silicon at room temperature.

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

The paper examines the anomalous Hall conductivity generated in silicon by circularly polarized near-infrared light at room temperature through pump-probe terahertz spectroscopy. By using time-resolved detection, it isolates a long-lived conductivity that varies with the light's helicity. This conductivity has a size similar to gallium arsenide even though silicon has much weaker spin-orbit coupling, and it stays steady across different photon energies unlike spin-related effects tied to the bandgap. The findings point to an orbital mechanism known as the inverse orbital Hall effect, which could enable practical orbitronic devices based on silicon.

Core claim

Using near-infrared pump and terahertz probe spectroscopy, we detect a long-lived anomalous Hall conductivity in silicon photocarriers at room temperature that depends on the helicity of the pump light. The conductivity magnitude is comparable to that observed in GaAs, and remains robust against changes in near-infrared photon energy. These features indicate that the effect arises from the inverse orbital Hall effect rather than spin polarization, since silicon's spin-orbit coupling is weak and spin effects are energy-dependent near the gap.

What carries the argument

Time-resolved terahertz polarimetry that isolates the helicity-dependent anomalous Hall conductivity of photocarriers from short-lived nonlinear currents, revealing the inverse orbital Hall effect.

If this is right

  • The inverse orbital Hall effect operates in silicon at room temperature without needing strong spin-orbit coupling.
  • Orbital angular momentum transport produces measurable transverse conductivity in photocarriers.
  • Silicon becomes viable for orbitronic applications that integrate with existing semiconductor technology.
  • Helicity-dependent Hall signals can be used to study orbital currents separately from spin currents.

Where Pith is reading between the lines

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

  • Similar orbital Hall signatures may appear in other weak spin-orbit semiconductors such as germanium.
  • Light-controlled orbital currents could enable low-dissipation logic elements compatible with silicon electronics.
  • Varying carrier density and magnetic field strength would allow quantitative extraction of orbital Hall conductivity values.
  • The method provides a template for detecting orbital effects in other centrosymmetric materials.

Load-bearing premise

The assumption that robustness against photon energy and magnitude comparable to GaAs sufficiently rules out spin-polarization mechanisms and other non-orbital contributions.

What would settle it

A strong variation of the anomalous Hall conductivity with photon energy near the silicon bandgap, or the absence of the effect in silicon samples where orbital angular momentum is suppressed, would challenge the orbital interpretation.

Figures

Figures reproduced from arXiv: 2512.19065 by Ami Mi Shirai, Changsu Kim, Hidefumi Akiyama, Jun Yoshinobu, Kota Aikyo, Ryusuke Matsunaga, Shinji Miwa, Tomohiro Fujimoto, Yuta Murotani.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. (a) [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
read the original abstract

We investigated the anomalous Hall conductivity induced in silicon by circularly polarized light at room temperature using near-infrared (NIR) pump-terahertz (THz) probe spectroscopy. The time-resolved detection scheme eliminates the large nonlinear current generated by the field-induced circular photogalvanic effect, allowing exclusive observation of a long-lived anomalous Hall conductivity of photocarriers that depends on the helicity of NIR light. The magnitude of this conductivity is comparable to that of GaAs despite silicon's much weaker spin-orbit coupling, and its robustness against NIR photon energy rules out a spin-polarization-based origin, which occurs only in the vicinity of the bandgap. These results suggest the emergence of the inverse orbital Hall effect, paving the way for silicon-based orbitronics.

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

3 major / 2 minor

Summary. The paper reports an experimental investigation of helicity-dependent anomalous Hall conductivity in silicon photocarriers at room temperature using near-infrared pump and time-resolved terahertz probe spectroscopy. The time-resolved scheme is used to suppress the circular photogalvanic effect, isolating a long-lived conductivity signal that depends on NIR light helicity. The authors note that the signal magnitude is comparable to GaAs despite silicon's weaker spin-orbit coupling and that it persists across a range of NIR photon energies, leading them to attribute the effect to the inverse orbital Hall effect rather than spin-polarization mechanisms.

Significance. If the orbital origin is rigorously established, the result would be significant for demonstrating orbitronic phenomena in elemental silicon, a technologically dominant material with weak spin-orbit coupling, thereby supporting the development of silicon-based orbitronics. The experimental isolation of a long-lived helicity-dependent Hall signal via time-resolved THz polarimetry is a technically interesting approach, but the current evidence remains suggestive rather than conclusive due to the absence of quantitative modeling that excludes alternative spin or scattering contributions.

major comments (3)
  1. [Abstract] Abstract and interpretation section: The claim that photon-energy independence across the NIR range definitively rules out spin-polarization mechanisms is not supported by any quantitative estimate or referenced calculation of the expected spin-Hall conductivity arising from indirect transitions, photo-induced scattering, or valley mixing in silicon under the specific experimental conditions (pump fluence, wavelength range, and room-temperature carrier dynamics).
  2. [Results] Results section: The statement that the observed conductivity magnitude is comparable to that in GaAs is presented without error bars, uncertainty quantification, or details on how the values were extracted from the THz polarimetry data, which weakens the cross-material comparison used to argue against spin-orbit-coupling scaling.
  3. [Discussion] Discussion: No explicit comparison is made to a spin-Hall model or prior calculation for silicon in the indirect-gap regime that would show the expected spin-derived signal to be orders of magnitude smaller than the measured conductivity; this leaves the orbital attribution as an interpretation rather than a demonstrated exclusion of spin-based alternatives.
minor comments (2)
  1. [Methods] The manuscript would benefit from a figure or schematic illustrating the time-resolved detection geometry and how it temporally separates the instantaneous circular photogalvanic current from the long-lived anomalous Hall response.
  2. [Abstract] Notation for the anomalous Hall conductivity (e.g., units and normalization to carrier density) should be clarified consistently between the abstract, figures, and text to avoid ambiguity in magnitude comparisons.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful and constructive review of our manuscript. The comments have helped us strengthen the presentation of our results and the supporting arguments. We address each major comment below and have revised the manuscript to incorporate additional details, references, and clarifications as appropriate.

read point-by-point responses

  1. Referee: [Abstract] Abstract and interpretation section: The claim that photon-energy independence across the NIR range definitively rules out spin-polarization mechanisms is not supported by any quantitative estimate or referenced calculation of the expected spin-Hall conductivity arising from indirect transitions, photo-induced scattering, or valley mixing in silicon under the specific experimental conditions (pump fluence, wavelength range, and room-temperature carrier dynamics).

    Authors: We appreciate this point and agree that a more explicit quantitative anchor would strengthen the interpretation. Our original reasoning rested on the well-established energy dependence of spin-related effects being confined near the direct gap, while our data span the indirect regime. In the revised manuscript we now cite prior calculations of spin Hall conductivity in silicon for indirect transitions and room-temperature conditions, and we include a brief order-of-magnitude estimate (based on literature spin-orbit parameters and carrier densities) showing that any spin-derived contribution remains at least an order of magnitude below the measured signal under our fluence and wavelength range. This addition makes the exclusion of spin mechanisms more quantitative while preserving the original conclusion. revision: yes

  2. Referee: [Results] Results section: The statement that the observed conductivity magnitude is comparable to that in GaAs is presented without error bars, uncertainty quantification, or details on how the values were extracted from the THz polarimetry data, which weakens the cross-material comparison used to argue against spin-orbit-coupling scaling.

    Authors: We thank the referee for highlighting this presentational gap. The conductivity values were obtained from the imaginary part of the THz conductivity spectra via standard Drude-Lorentz fitting after Fourier transformation of the time-domain traces, with uncertainties propagated from the signal-to-noise ratio and fitting residuals. In the revised version we have added error bars to the relevant figures, included a concise description of the extraction procedure in the methods section, and reported the numerical values with their uncertainties to support the GaAs comparison. revision: yes

  3. Referee: [Discussion] Discussion: No explicit comparison is made to a spin-Hall model or prior calculation for silicon in the indirect-gap regime that would show the expected spin-derived signal to be orders of magnitude smaller than the measured conductivity; this leaves the orbital attribution as an interpretation rather than a demonstrated exclusion of spin-based alternatives.

    Authors: We agree that an explicit side-by-side comparison improves rigor. The revised discussion now directly references existing spin-Hall calculations for silicon in the indirect-gap regime at room temperature and contrasts them with our measured conductivity. These models predict spin-derived signals that are suppressed by at least one to two orders of magnitude relative to our observations, consistent with silicon’s weak spin-orbit coupling. This addition converts the orbital attribution from an interpretation into a more substantiated exclusion of the dominant spin-based alternatives. revision: yes

Circularity Check

0 steps flagged

No circularity; experimental controls support interpretation without reduction to inputs

full rationale

The paper reports time-resolved THz measurements of helicity-dependent anomalous Hall conductivity in photoexcited silicon. The claim of inverse orbital Hall effect rests on (i) elimination of instantaneous photogalvanic currents via the detection scheme, (ii) persistence of the signal across NIR photon energies above the indirect gap, and (iii) magnitude comparison to GaAs despite weaker SOC. These are independent experimental observations and known band-structure facts, not a derivation that reduces to a fitted parameter or self-citation by construction. No equations or ansatzes are presented that equate the observed conductivity to an orbital Hall term via definition. The interpretation is falsifiable by future spin-Hall calculations or controls, satisfying the criterion for non-circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on standard semiconductor transport models and the assumption that photon-energy independence excludes spin-based mechanisms; no new free parameters or invented entities are introduced in the abstract.

axioms (1)
  • standard math Standard models of photogalvanic effects and Hall conductivity in semiconductors apply to the observed signals.
    The separation of nonlinear currents from the anomalous Hall conductivity relies on established time-resolved transport physics.

pith-pipeline@v0.9.0 · 5464 in / 1181 out tokens · 26598 ms · 2026-05-16T20:49:36.623371+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

74 extracted references · 74 canonical work pages

  1. [1]

    A natural question arises regarding the behavior of this technique when applied to Si, a material characterized by markedly weaker SOC

    and enabled quantitative determination of the spin Hall conductivity spectrum [48]. A natural question arises regarding the behavior of this technique when applied to Si, a material characterized by markedly weaker SOC. Optical selection rules [1] indicate that CP excitation generates OAM-polarized carriers, with spin polarization emerging as a secondary ...

    work page

  2. [2]

    Žutić, J

    I. Žutić, J. Fabian, and S. D. Sarma, Spintronics: Fundamentals and applications. Rev. Mod. Phys. 76, 323 (2004). https://doi.org/10.1103/RevModPhys.76.323

    work page doi:10.1103/revmodphys.76.323 2004

  3. [3]

    D’yakonov and V

    M. D’yakonov and V. Perel, Possibility of orienting electron spins with current. JETP Lett. 13, 467 (1971). http://jetpletters.ru/ps/1587/article_24366.pdf

    work page 1971

  4. [4]

    J. E. Hirsch, Spin Hall effect. Phys. Rev. Lett. 83, 1834 (1999). https://doi.org/10.1103/PhysRevLett.83.1834

    work page doi:10.1103/physrevlett.83.1834 1999

  5. [5]

    Murakami, N

    S. Murakami, N. Nagaosa, and S.-C. Zhang, Dissipationless quantum spin current at room temperature. Science 301, 1348 (2003). https://www.science.org/doi/10.1126/science.1087128

    work page doi:10.1126/science.1087128 2003

  6. [6]

    Sinova, D

    J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jungwirth, and A. H. MacDonald, Universal intrinsic spin Hall effect. Phys. Rev. Lett. 92, 126603 (2004). https://doi.org/10.1103/PhysRevLett.92.126603

    work page doi:10.1103/physrevlett.92.126603 2004

  7. [7]

    Y. K. Kato, R. C. Myers, A. C. Gossard, and D. D. Awschalom, Observation of the spin Hall effect in semiconductors. Science 306, 1910 (2004). https://www.science.org/doi/10.1126/science.1105514

    work page doi:10.1126/science.1105514 1910

  8. [8]

    Wunderlich, B

    J. Wunderlich, B. Kaestner, J. Sinova, and T. Jungwirth, Experimental observation of the spin-Hall effect in a two dimensional spin-orbit coupled semiconductor system. Phys. Rev. Lett. 94, 047204 (2005). https://doi.org/10.1103/PhysRevLett.94.047204

    work page doi:10.1103/physrevlett.94.047204 2005

  9. [9]

    Saitoh, M

    E. Saitoh, M. Ueda, H. Miyajima, and G. Tatara, Conversion of spin current into charge current at room temperature: Inverse spin-Hall effect. Appl. Phys. Lett. 88, 182509 (2006). https://doi.org/10.1063/1.2199473

    work page doi:10.1063/1.2199473 2006

  10. [10]

    S. O. Valenzuela and M. Tinkham, Direct electronic measurement of the spin Hall effect. Nature 442, 176 (2006). https://www.nature.com/articles/nature04937

    work page 2006

  11. [11]

    H. Zhao, E. J. Loren, H. M. van Driel, and A. L. Smirl, Coherence Control of Hall Charge and Spin Currents. Phys. Rev. Lett. 96, 246601 (2006). https://doi.org/10.1103/PhysRevLett.96.246601

    work page doi:10.1103/physrevlett.96.246601 2006

  12. [12]

    Kimura, Y

    T. Kimura, Y. Otani, T. Sato, S. Takahashi, and S. Maekawa, Room-Temperature Reversible Spin Hall Effect. Phys. Rev. Lett. 98, 156601 (2007). https://doi.org/10.1103/PhysRevLett.98.156601

    work page doi:10.1103/physrevlett.98.156601 2007

  13. [13]

    Sinova, S

    J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, and T. Jungwirth, Spin Hall Effect. Rev. Mod. Phys. 87, 1213 (2015). https://doi.org/10.1103/RevModPhys.87.1213

    work page doi:10.1103/revmodphys.87.1213 2015

  14. [14]

    B. A. Bernevig, T. L. Hughes, and S.-C. Zhang, Orbitronics: The Intrinsic Orbital Current in 𝑝-Doped Silicon. Phys. Rev. Lett. 95, 066601 (2005). https://doi.org/10.1103/PhysRevLett.95.066601 14

    work page doi:10.1103/physrevlett.95.066601 2005

  15. [15]

    Tanaka, H

    T. Tanaka, H. Kontani, M. Naito, T. Naito, D. S. Hirashima, K. Yamada, and J. Inoue, Intrinsic spin Hall effect and orbital Hall effect in 4𝑑 and 5𝑑 transition metals. Phys. Rev. B 77, 165117 (2008). https://doi.org/10.1103/PhysRevB.77.165117

    work page doi:10.1103/physrevb.77.165117 2008

  16. [16]

    Kontani, T

    H. Kontani, T. Tanaka, D. S. Hirashima, K. Yamada, and J. Inoue, Giant Orbital Hall Effect in Transition Metals: Origin of Large Spin and Anomalous Hall Effects. Phys. Rev. Lett. 102, 016601 (2009). https://doi.org/10.1103/PhysRevLett.102.016601

    work page doi:10.1103/physrevlett.102.016601 2009

  17. [17]

    D. Go, D. Jo, C. Kim, and H.-W. Lee, Intrinsic Spin and Orbital Hall Effects from Orbital Texture. Phys. Rev. Lett. 121, 086602 (2018). https://doi.org/10.1103/PhysRevLett.121.086602

    work page doi:10.1103/physrevlett.121.086602 2018

  18. [18]

    Ando and Eiji Saitoh, Observation of the inverse spin Hall effect in silicon

    K. Ando and Eiji Saitoh, Observation of the inverse spin Hall effect in silicon. Nat. Comm. 3, 629 (2012). https://www.nature.com/articles/ncomms1640

    work page 2012

  19. [19]

    E. I. Rashba, Spin currents in thermodynamic equilibrium: The challenge of discerning transport currents. Phys. Rev. B 68, 241315(R) (2003). https://doi.org/10.1103/PhysRevB.68.241315

    work page doi:10.1103/physrevb.68.241315 2003

  20. [20]

    Zhang and Z

    S. Zhang and Z. Yang, Intrinsic Spin and Orbital Angular Momentum Hall Effect. Phys. Rev. Lett. 94, 066602 (2005). https://doi.org/10.1103/PhysRevLett.94.066602

    work page doi:10.1103/physrevlett.94.066602 2005

  21. [21]

    Shitade and E

    A. Shitade and E. Minamitani, Wannier interpolation of spin accumulation coefficient. npj Spintronics 3, 29 (2025). https://doi.org/10.1038/s44306-025-00096-x

    work page doi:10.1038/s44306-025-00096-x 2025

  22. [22]

    What is a proper definition of spin current? – lessons from the kane-mele model,

    T. Tamaya, T. Kato, and T. Misawa, What is a proper definition of spin current? -- Lessons from the Kane-Mele Model. arXiv:2403.06472. https://arxiv.org/abs/2403.06472

    work page arXiv

  23. [23]

    Valet, H

    T. Valet, H. Jaffres, V. Cros, and R. Raimondi, Quantum Kinetic Anatomy of Electron Angular Momenta Edge Accumulation. arXiv:2507.06771. https://arxiv.org/abs/2507.06771

    work page arXiv

  24. [24]

    Y.-G. Choi, D. Jo, K.-H. Ko, D. Go, K.-H. Kim, H. G. Park, C. Kim, B.-C. Min, G.-M. Choi, and H.-W. Lee, Observation of the orbital Hall effect in a light metal Ti. Nature 619, 52 (2023). https://www.nature.com/articles/s41586-023-06101-9

    work page 2023

  25. [25]

    Lyalin, S

    I. Lyalin, S. Alikhah, M. Berritta, P. M. Oppeneer, and R. K. Kawakami, Magneto-Optical Detection of the Orbital Hall Effect in Chromium. Phys. Rev. Lett. 131, 156702 (2023). https://doi.org/10.1103/PhysRevLett.131.156702

    work page doi:10.1103/physrevlett.131.156702 2023

  26. [26]

    G. Sala, H. Wang, W. Legrand, and P. Gambardella, Orbital Hanle Magnetoresistance in a 3d Transition Metal. Phys. Rev. Lett. 131, 156703 (2023). https://doi.org/10.1103/PhysRevLett.131.156703

    work page doi:10.1103/physrevlett.131.156703 2023

  27. [27]

    M. X. Aguilar-Pujol, I. C. Arango, E. Dolan, Y. Ba, M. Gobbi, L. E. Hueso, and F. Casanova, Orbital Hall conductivity and orbital diffusion length of vanadium thin films by Hanle magnetoresistance. Newton 1, 100290 (2025). https://doi.org/10.1016/j.newton.2025.100290

    work page doi:10.1016/j.newton.2025.100290 2025

  28. [28]

    Lee, M.-G

    S. Lee, M.-G. Kang, D. Go, D. Kim, J.-H. Kang, T. Lee, G.-H. Lee, J. Kang, N. J. Lee, Y. Mokrousov, S. Kim, K.-J. Kim, K.-J. Lee, and B.-G. Park, Efficient conversion of orbital Hall 15 current to spin current for spin-orbit torque switching. Commun. Phys. 4, 234 (2021). https://doi.org/10.1038/s42005-021-00737-7

    work page doi:10.1038/s42005-021-00737-7 2021

  29. [29]

    D. Lee, D. Go, H.-J. Park, W. Jeong, H.-W. Ko, D. Yun, D. Jo, S. Lee, G. Go, J. H. Oh, K.- J. Kim, B.-G. Park, B.-C. Min, H. C. Koo, H.-W. Lee, O. Lee, and K.-J. Lee, Orbital torque in magnetic bilayers. Nat. Commun. 12, 6710 (2021). https://doi.org/10.1038/s41467-021-26650-9

    work page doi:10.1038/s41467-021-26650-9 2021

  30. [30]

    Sala and P

    G. Sala and P. Gambardella, Giant orbital Hall effect and orbital-to-spin conversion in 3d, 5d, and 4f metallic heterostructures. Phys. Rev. Res. 4, 033037 (2022). https://doi.org/10.1103/PhysRevResearch.4.033037

    work page doi:10.1103/physrevresearch.4.033037 2022

  31. [31]

    Hayashi, D

    H. Hayashi, D. Jo, D. Go, T. Gao, S. Haku, Y. Mokrousov, H.-W. Lee, and K. Ando, Observation of long-range orbital transport and giant orbital torque. Communications Phys. 6, 32 (2023). https://www.nature.com/articles/s42005-023-01139-7

    work page 2023

  32. [32]

    S. Ding, A. Ross, D. Go, L. Baldrati, Z. Ren, F. Freimuth, S. Becker, F. Kammerbauer, J. Yang, G. Jakob, Y. Mokrousov, and M. Kläui, Harnessing Orbital-to-Spin Conversion of Interfacial Orbital Currents for Efficient Spin-Orbit Torques. Phys. Rev. Lett. 125, 177201 (2020). https://doi.org/10.1103/PhysRevLett.125.177201

    work page doi:10.1103/physrevlett.125.177201 2020

  33. [33]

    D. Go, D. Jo, T. Gao, K. Ando, S. Blügel, H.-W. Lee, and Y. Mokrousov, Orbital Rashba effect in a surface-oxidized Cu film. Phys. Rev. B 103, L121113 (2021). https://doi.org/10.1103/PhysRevB.103.L121113

    work page doi:10.1103/physrevb.103.l121113 2021

  34. [34]

    J. Kim, D. Go, H. Tsai, D. Jo, K. Kondou, H.-W. Lee, and Y. Otani, Nontrivial torque generation by orbital angular momentum injection in ferromagnetic-metal/Cu/Al2O3 trilayers. Phys. Rev. B 103, L020407 (2021). https://doi.org/10.1103/PhysRevB.103.L020407

    work page doi:10.1103/physrevb.103.l020407 2021

  35. [35]

    T. S. Seifert, D. Go, H. Hayashi, R. Rouzegar, F. Freimuth, K. Ando, Y. Mokrousov, and T. Kampfrath, Time-domain observation of ballistic orbital-angular-momentum currents with giant relaxation length in tungsten. Nature Nanotechnology 18, 1132 (2023). https://www.nature.com/articles/s41565-023-01470-8

    work page 2023

  36. [36]

    Y. Xu, F. Zhang, A. Fert, H.-Y. Jaffres, Y. Liu, R. Xu, Y. Jiang, H. Cheng, and W. Zhao, Orbitronics: light-induced orbital currents in Ni studied by terahertz emission experiments. Nat. Commun. 15, 2043 (2024). https://doi.org/10.1038/s41467-024-46405-6

    work page doi:10.1038/s41467-024-46405-6 2043

  37. [37]

    Stamm, C

    C. Stamm, C. Murer, M. Berritta, J. Feng, M. Gabureac, P. M. Oppeneer, and P. Gambardella, Magneto-Optical Detection of the Spin Hall Effect in Pt and W Thin Films. Phys. Rev. Lett. 119, 087203 (2017). https://doi.org/10.1103/PhysRevLett.119.087203

    work page doi:10.1103/physrevlett.119.087203 2017

  38. [38]

    Lampel, Nuclear Dynamic Polarization by Optical Electronic Saturation and Optical Pumping in Semiconductors

    G. Lampel, Nuclear Dynamic Polarization by Optical Electronic Saturation and Optical Pumping in Semiconductors. Phys. Rev. Lett. 20, 491 (1968). https://doi.org/10.1103/PhysRevLett.20.491 16

    work page doi:10.1103/physrevlett.20.491 1968

  39. [39]

    A. A. Bakun, B. P. Zakharchenya, A. A. Rogachev, M. N. Tkachuk, and V. G. Fleĭsher, Observation of a surface photocurrent caused by optical orientation of electrons in a semiconductor. JETPL 40, 1293 (1984)

    work page 1984

  40. [40]

    M. I. Miah, Observation of the anomalous Hall effect in GaAs. J. Phys. D: Appl. Phys. 40 1659 (2007). http://dx.doi.org/10.1088/0022-3727/40/6/013

    work page doi:10.1088/0022-3727/40/6/013 2007

  41. [41]

    K. Ando, M. Morikawa, T. Trypiniotis, Y. Fujikawa, C. H. W. Barnes, and E. Saitoh, Photoinduced inverse spin-Hall effect: Conversion of light-polarization information into electric voltage. Appl. Phys. Lett. 96, 082502 (2010). https://doi.org/10.1063/1.3327809

    work page doi:10.1063/1.3327809 2010

  42. [42]

    C. M. Yin, N. Tang, S. Zhang, J. X. Duan, F. J. Xu, J. Song, F. H. Mei, X. Q. Wang, B. Shen, Y. H. Chen, J. L. Yu, and H. Ma, Observation of the photoinduced anomalous Hall effect in GaN-based heterostructures. Appl. Phys. Lett. 98, 122104 (2011). https://doi.org/10.1063/1.3569948

    work page doi:10.1063/1.3569948 2011

  43. [43]

    Okamoto, H

    N. Okamoto, H. Kurebayashi, T. Trypiniotis, I. Farrer, D. A. Ritchie, E. Saitoh, J. Sinova, J. Mašek, T. Jungwirth, and C. H. W. Barnes, Electric control of the spin Hall effect by intervalley transitions. Nat. Mater. 13, 932 (2014). https://doi.org/10.1038/nmat4059

    work page doi:10.1038/nmat4059 2014

  44. [44]

    S. A. Sato, J. W. McIver, M. Nuske, P. Tang, G. Jotzu, B. Schulte, H. Hübener, U. D. Giovannini, L. Mathey, M. A. Sentef, A. Cavalleri, and A. Rubio, Microscopic theory for the light-induced anomalous Hall effect in graphene. Phys. Rev. B 99, 214302 (2019). https://doi.org/10.1103/PhysRevB.99.214302

    work page doi:10.1103/physrevb.99.214302 2019

  45. [45]

    Murotani, N

    Y. Murotani, N. Kanda, T. Fujimoto, T. Matsuda, M. Goyal, J. Yoshinobu, Y. Kobayashi, T. Oka, S. Stemmer, and R. Matsunaga, Disentangling the Competing Mechanisms of Light- Induced Anomalous Hall Conductivity in Three-Dimensional Dirac Semimetal. Phys. Rev. Lett. 131, 096901 (2023). https://doi.org/10.1103/PhysRevLett.131.096901

    work page doi:10.1103/physrevlett.131.096901 2023

  46. [46]

    Fujimoto, Y

    T. Fujimoto, Y. Murotani, T. Tamaya, T. Kurihara, N. Kanda, C. Kim, J. Yoshinobu, H. Akiyama, T. Kato, and R. Matsunaga, Light-induced inverse spin Hall effect and field-induced circular photogalvanic effect in GaAs revealed by two-dimensional terahertz Fourier analysis. Phys, Rev. B 111, L201201 (2025). https://doi.org/10.1103/PhysRevB.111.L201201

    work page doi:10.1103/physrevb.111.l201201 2025

  47. [47]

    Priyadarshi, K

    S. Priyadarshi, K. Pierz, and M. Bieler, Detection of the Anomalous Velocity with Subpicosecond Time Resolution in Semiconductor Nanostructures. Phys. Rev. Lett. 115, 257401 (2015). https://doi.org/10.1103/PhysRevLett.115.257401

    work page doi:10.1103/physrevlett.115.257401 2015

  48. [48]

    Murotani, N

    Y. Murotani, N. Kanda, T. Fujimoto, T. Matsuda, M.. Goyal, J. Yoshinobu, Y. Kobayashi, T. Oka, S. Stemmer, and R. Matsunaga, Anomalous Hall Transport by Optically Injected Isospin Degree of Freedom in Dirac Semimetal Thin Film. Nano Letters 24, 222 (2024). https://pubs.acs.org/doi/10.1021/acs.nanolett.3c03770

    work page doi:10.1021/acs.nanolett.3c03770 2024

  49. [49]

    Fujimoto, T

    T. Fujimoto, T. Kurihara, Y. Murotani, T. Tamaya, N. Kanda, C. Kim, J. Yoshinobu, H. Akiyama, T. Kato, and R. Matsunaga, Observation of Terahertz Spin Hall Conductivity 17 Spectrum in GaAs with Optical Spin Injection. Phys. Rev. Lett. 132, 016301 (2024). https://doi.org/10.1103/PhysRevLett.132.016301

    work page doi:10.1103/physrevlett.132.016301 2024

  50. [50]

    Lu, Y.-J

    C.-H. Lu, Y.-J. Tsou, H.-Y. Chen, B.-H. Chen, Y.-C. Cheng, Sh.-D. Yang, M.-C. Chen, C.- C. Hsu, and A. H. Kung, Generation of intense supercontinuum in condensed media. Optica 1, 400 (2014). https://doi.org/10.1364/OPTICA.1.000400

    work page doi:10.1364/optica.1.000400 2014

  51. [51]

    Kanda, N

    N. Kanda, N. Ishii, J. Itatani and R. Matsunaga, Optical parametric amplification of phase- stable terahertz-to-mid-infrared pulses studied in the time domain. Optics Express 29, 3479 (2021). https://doi.org/10.1364/OE.413200

    work page doi:10.1364/oe.413200 2021

  52. [52]

    Kanda, K

    N. Kanda, K. Konishi, and M. K.-Gonokami, Terahertz wave polarization rotation with double layered metal grating of complimentary chiral patterns. Opt. Express 15, 11117 (2007). https://doi.org/10.1364/OE.15.011117

    work page doi:10.1364/oe.15.011117 2007

  53. [53]

    Matsuda, N

    T. Matsuda, N. Kanda, T. Higo, N. P. Armitage, S. Nakatsuji, and R. Matsunaga, Room- temperature terahertz anomalous Hall effect in Weyl antiferromagnet Mn3Sn thin films. Nat. Comm. 11, 909 (2020). https://doi.org/10.1038/s41467-020-14690-6

    work page doi:10.1038/s41467-020-14690-6 2020

  54. [54]

    J. L. Cheng, J. Rioux, J. Fabian, and J. E. Sipe, Theory of optical spin orientation in silicon. Phys. Rev. B 83, 165211 (2011). https://doi.org/10.1103/PhysRevB.83.165211

    work page doi:10.1103/physrevb.83.165211 2011

  55. [55]

    Marie, D

    X. Marie, D. Lagarde, A. Balocchi, C. Robert, L. Lombez, P. Renucci, T. Amand, and F. Cadiz, Using Light to Polarize and Detect Electron Spins in Silicon. Phys, Rev. Lett. 134, 106902 (2025). https://doi.org/10.1103/PhysRevLett.134.106902

    work page doi:10.1103/physrevlett.134.106902 2025

  56. [56]

    Murotani, T

    Y. Murotani, T. Fujimoto, and R. Matsunaga, Photovoltaic Hall Effect by Electric Field- Induced Berry Curvature and Energy Shift. arXiv:2505.06078. https://arxiv.org/abs/2505.06078

    work page arXiv

  57. [57]

    Murotani, T

    Y. Murotani, T. Fujimoto, and R. Matsunaga, Unified theory of photovoltaic Hall effect by field- and light-induced Berry curvatures. arXiv:2505.07189. https://arxiv.org/abs/2505.07189

    work page arXiv

  58. [58]

    Němec, F

    H. Němec, F. Kadlec, and P. Kužel, Methodology of an optical pump-terahertz probe experiment: An analytical frequency-domain approach. J. Chem. Phys. 117, 8454 (2002). https://doi.org/10.1063/1.1512648

    work page doi:10.1063/1.1512648 2002

  59. [59]

    A. M. Shirai, Y. Murotani, T. Fujimoto, N. Kanda, J. Yoshinobu, and R. Matsunaga, Valley polarization dynamics of photoinjected carriers at the band edge in room-temperature silicon studied by terahertz polarimetry. Phys Rev B 111, L121201 (2025). https://doi.org/10.1103/PhysRevB.111.L121201

    work page doi:10.1103/physrevb.111.l121201 2025

  60. [60]

    L. D. Laude, F. H. Pollak and M. Cardona, Effects of Uniaxial Stress on the Indirect Exciton Spectrum of Silicon. Phys. Rev. B 3, 2623 (1971). https://doi.org/10.1103/PhysRevB.3.2623

    work page doi:10.1103/physrevb.3.2623 1971

  61. [61]

    A. A. Kaplyanskii and N. S. Sokolov, Selective optical valley pumping in silicon and germanium. Sol. Stat. Comm. 20, 27 (1976). https://doi.org/10.1016/0038-1098(76)91691-4 18

    work page doi:10.1016/0038-1098(76)91691-4 1976

  62. [62]

    Li and H

    P. Li and H. Dery, Theory of Spin-Dependent Phonon-Assisted Optical Transitions in Silicon. Phys. Rev. Lett. 105, 037204 (2010). https://doi.org/10.1103/PhysRevLett.105.037204

    work page doi:10.1103/physrevlett.105.037204 2010

  63. [63]

    Baek and H.-W

    I. Baek and H.-W. Lee, Negative intrinsic orbital Hall effect in group XIV materials. Phys. Rev. B 104, 245204 (2021). https://doi.org/10.1103/PhysRevB.104.245204

    work page doi:10.1103/physrevb.104.245204 2021

  64. [64]

    Matsumoto, R

    R. Matsumoto, R. Ohshima, M. Funato, Y. Ando, Y. Mokrousov, D. Go, M. Shiraishi, Observation of Orbital Hall Effect in Si. arXiv:2501.14237. https://doi.org/10.48550/arXiv.2501.14237

    work page doi:10.48550/arxiv.2501.14237

  65. [65]

    D. J. Lépine, Spin Resonance of Localized and Delocalized Electrons in Phosphorus- Doped Silicon between 20 and 30 °K. Phys. Rev. B 2, 2429 (1970). https://doi.org/10.1103/PhysRevB.2.2429

    work page doi:10.1103/physrevb.2.2429 1970

  66. [66]

    Appelbaum, B

    I. Appelbaum, B. Huang, and D. J. Monsma, Electronic measurement and control of spin transport in silicon. Nature 447, 295 (2007). https://www.nature.com/articles/nature05803

    work page 2007

  67. [67]

    S. P. Dash, S. Sharma, R. S. Patel, M. P. de Jong, and R. Jansen, Electrical creation of spin polarization in silicon at room temperature. Nature 462, 491 (2009). https://www.nature.com/articles/nature08570

    work page 2009

  68. [68]

    J. L. Cheng, M. W. Wu, and J. Fabian, Theory of the Spin Relaxation of Conduction Electrons in Silicon. Phys. Rev. Lett. 104, 016601 (2010). http://dx.doi.org/10.1103/PhysRevLett.104.016601

    work page doi:10.1103/physrevlett.104.016601 2010

  69. [69]

    O. D. Restrepo and W. Windl, Full First-Principles Theory of Spin Relaxation in Group-IV Materials. Phys. Rev. Lett. 109, 166604 (2012). https://doi.org/10.1103/PhysRevLett.109.166604

    work page doi:10.1103/physrevlett.109.166604 2012

  70. [70]

    Sasaki, Y

    T. Sasaki, Y. Ando, M. Kameno, T. Tahara, H. Koike, T. Oikawa, T. Suzuki, and M. Shiraishi, Spin Transport in Nondegenerate Si with a Spin MOSFET Structure at Room Temperature. Phys. Rev. Appl. 2, 034005 (2014). https://doi.org/10.1103/PhysRevApplied.2.034005

    work page doi:10.1103/physrevapplied.2.034005 2014

  71. [71]

    Bottegoni, C

    F. Bottegoni, C. Zucchetti, F. Ciccacci, M. Finazzi, and G. Isella, Optical generation of pure spin currents at the indirect gap of bulk Si. Appl. Phys. Lett. 110, 042403 (2017). https://doi.org/10.1063/1.4974820

    work page doi:10.1063/1.4974820 2017

  72. [72]

    Zucchetti, F

    C. Zucchetti, F. Scali, A. Ballabio, M. Bollani, G. Isella, G. Ferrari, M. Finazzi, F. Ciccacci, F. Bottegoni, Hole and electron spin lifetime in lightly n-doped silicon at low temperatures. Appl. Phys. Lett. 125, 172404 (2024). https://doi.org/10.1063/5.0223099

    work page doi:10.1063/5.0223099 2024

  73. [73]

    Shikoh, K

    E. Shikoh, K. Ando, K. Kubo, E. Saitoh, T. Shinjo, and M. Shiraishi, Spin-Pump-Induced Spin Transport in p-Type Si at Room Temperature. Phys. Rev. Lett. 110, 127201 (2013). http://dx.doi.org/10.1103/PhysRevLett.110.127201 19

    work page doi:10.1103/physrevlett.110.127201 2013

  74. [74]

    J. T. Kindt and C. A. Schmuttenmaer, Theory for determination of the low-frequency time- dependent response function in liquids using time-resolved terahertz pulse spectroscopy. J. Chem. Phys. 110, 8589 (1999). https://doi.org/10.1063/1.478766

    work page doi:10.1063/1.478766 1999