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REVIEW 3 major objections 6 minor 54 references

Orbital Hall Effect and Angular Momentum Dynamics in Confined Geometries

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The paper derives a closed-form steady-state profile for orbital angular momentum accumulation at the edges of a Hall strip, tying it to the band gap and the m=0 scattering rate through a Dyakonov-Perel-like decay time.

desk verdict Solid Boltzmann treatment of OAM in a strip, but Eq. (47) misses a 1/lbar and Eq. (43) inverts the lbar dependence; both need correction. read the letter →

arxiv 2507.00982 v1 pith:BVDYSYBA submitted 2025-07-01 cond-mat.mes-hall

Egor I. Kiselev , Benoît Douçot , Roderich Moessner This is my paper · ORCID
classification cond-mat.mes-hall
keywords orbitalHalleffectangularmomentumaccumulationquantumBoltzmannequationDyakonov-Perelrelaxationstripgeometrytimeapproximationnon-Ohmictransportorbitronics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper aims to turn the orbital Hall effect's central observable — the buildup of orbital angular momentum (OAM) at the edges of a sample — into a closed formula in terms of the band gap and scattering rates, so that experiments can read off microscopic physics from an easy-to-measure profile. Using a quantum Boltzmann treatment of a two-band model with harmonic-resolved relaxation times, it derives a lossy continuity equation for OAM and, for an Ohmic Hall strip, the explicit edge profile $\rho_{L_z}(y)=\tau_{L_z}\sigma_1 E_x\sinh(y/\bar{l})/\cosh(w/2\bar{l})$. The key content is that the effective OAM decay time $\tau_{L_z}=2\hbar^2\tau_0^{-1}/\Delta\varepsilon^2$ follows Dyakonov-Perel scaling — inversely proportional to the m=0 scattering rate — even in the weak-scattering limit, and that a single band at the Fermi energy makes scalar impurity scattering irrelevant for OAM decay. The same analysis uncovers new nonlocal mechanisms by which shear flows and spatially varying charge currents contribute to the orbital Hall effect, distinct from the intrinsic and extrinsic ones.

What carries the argument

The central object is the quantum Boltzmann equation for the two-band tight-binding Hamiltonian of Eq. (1), written in the band basis with the nonequilibrium density matrix expanded in angular harmonics $\cos(m\varphi_k)$ and $\sin(m\varphi_k)$ and with distinct relaxation times $\tau_{(m)}$ per harmonic. The small parameter $\xi=\tau^{-1}\hbar/\Delta\varepsilon_k$ justifies keeping only the $m=0,1,2$ components, which close on the four coupled Eqs. (24)–(27). The workhorse identity is the lossy continuity relation $\rho_{L_z}=-\tau_{L_z}\,\partial_y J_{L_z,y}+\tau_{L_z,e}\,\partial_y(\hbar/e\,J_{e,x})$ with the Dyakonov-Perel time $\tau_{L_z}=2\hbar^2\tau_0^{-1}/\Delta\varepsilon_k^2$; combined with the current-diffusion equation $J''_{L_z}-J_{L_z}/\bar{l}^2=-\sigma_1 E_x/\bar{l}^2+\sigma_2 E_x''$ it produces the edge profile $\rho_{L_z}(y)=\tau_{L_z}\sigma_1 E_x\sinh(y/\bar{l})/\cosh(w/2\bar{l})$.

What would settle it

Solve the same quantum Boltzmann equations for a two-band model whose interband gap varies steeply with $|k|$ beyond the Fermi wavevector, without the approximation $\Delta\varepsilon(k)=\Delta\varepsilon(k_F)$; if the resulting OAM profile no longer follows $\tau_{L_z}\sigma_1 E_x\sinh(y/\bar{l})/\cosh(w/2\bar{l})$ or the coefficient no longer scales as $1/\tau_0$, the closed-form claim is falsified.

Watch

Extended reading notes

Core claim

The central claim is that the steady-state orbital angular momentum buildup at the edges of a Hall strip is not an independent transport coefficient but is fixed by the same microscopic data that set the orbital Hall current: the interband gap at the Fermi surface and the relaxation rates of the low angular harmonics, with the m=0 interband coherence channel playing a special role. Concretely, the authors derive the closed relation $\rho_{L_z}=-\tau_{L_z}\,\partial_y J_{L_z,y}+\tau_{L_z,e}\,\partial_y(\hbar/e\,J_{e,x})$, and from it the explicit Ohmic profile $\rho_{L_z}(y)=\tau_{L_z}\sigma_1 E_x\sinh(y/\bar{l})/\cosh(w/2\bar{l})$. The coefficient $\tau_{L_z}=2\hbar^2\tau_0^{-1}/\Delta\varepsilon^2$ is an effective OAM decay time of Dyakonov-Perel form: it grows as the m=0 scattering rate decreases, even though the underlying scattering is weak. The paper further claims that when the Fermi energy cuts only one band, scalar impurity scattering does not relax the OAM density at all ($\tau_0^{-1}=0$), so the accumulation is governed by other scattering mechanisms, and that inhomogeneous or non-Ohmic charge flows generate OAM through new nonlocal terms absent in uniform Ohmic transport.

Load-bearing premise

The edge-accumulation formula assumes the interband gap is roughly the same for all electron states beyond the Fermi surface that contribute to the intrinsic response, i.e., $\Delta\varepsilon(k)\approx\Delta\varepsilon(k_F)$; if the gap varies strongly with momentum there, the simple closed-form profile breaks down.

Editorial extensions

If this is right

  • In an Ohmic Hall strip the steady-state OAM density at the edges is fixed by the Fermi-surface band gap and the m=0 scattering rate, so a measurement of the edge signal together with band-structure data determines the m=0 relaxation time.
  • The effective OAM decay time follows Dyakonov-Perel scaling $\tau_{L_z}=2\hbar^2\tau_0^{-1}/\Delta\varepsilon^2$ even for weak scattering, so cleaner samples in that channel accumulate more OAM, not less.
  • If the Fermi energy cuts only one band, scalar-impurity scattering gives $\tau_0^{-1}=0$, so the OAM lifetime is set by other mechanisms such as electron-phonon or electron-electron scattering, whose distinct temperature dependences should appear in the edge signal.
  • Spatially varying or non-Ohmic charge currents create an extra OAM accumulation term $\tau_{L_z,e}\,\partial_y(\hbar/e\,J_{e,x})$ and a nonlocal contribution to the orbital Hall conductivity, both absent for uniform Ohmic flow.
  • In strips narrower than the scattering length $\bar{l}$, uniform-field OHE currents are suppressed, which in ultra-clean samples favors wider strips or non-uniform field geometries to observe the effect.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • One direct test would be to tune impurity density in a single-band-crossing sample and measure the edge OAM signal; if the m=0 channel is impurity-limited the signal should grow with the m=0 lifetime, a scaling signature the formula makes explicit.
  • If impurity scattering is inactive in the m=0 channel, temperature-dependent measurements of the edge accumulation should reveal the dominant relaxing mechanism (phonon or electron-electron), giving a spectroscopic handle the authors do not work out.
  • The $\partial_y J_{e,x}$ term suggests a probe geometry: a constriction or curved flow that makes the charge current spatially varying could localize OAM accumulation even without a net orbital Hall current, isolating the off-diagonal-velocity mechanism from intrinsic and extrinsic ones.
  • The sinh/cosh profile is structurally rigid; any observed deviation — for example in samples where the gap changes rapidly with momentum — would point either to the constant-gap approximation failing or to unmodeled relaxation channels.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. This paper develops a quantum Boltzmann approach to the orbital Hall effect (OHE) in a finite-width strip, retaining spatial inhomogeneity and distinguishing scattering rates in different angular-harmonic channels of the momentum distribution. The principal result is Eq. (47), a formula for the steady-state orbital angular momentum (OAM) accumulation at the strip edges, expressed in terms of the band gap Δε(k_F), scattering times, and the longitudinal electric field. The authors also identify a Dyakonov-Perel-like scaling of the effective OAM decay time, discuss non-local contributions to the orbital Hall conductivity for non-uniform fields, and note that scalar-impurity scattering does not relax OAM in the m=0 channel when only one band crosses the Fermi energy.

Significance. If the main formula and its supporting approximations are corrected, the paper offers a useful microscopic link between OAM accumulation experiments and band-structure/scattering parameters. The explicit power-counting control in Appendix D, the separation of m=0,1,2 angular harmonics, and the observation that the steady-state OAM decay follows Dyakonov-Perel scaling even in the weak-scattering regime are valuable contributions to the current orbitronics literature. The paper does not ship machine-checked proofs, but the derivations are explicit and reproducible in structure.

major comments (3)
  1. [Section VIII, Eq. (47)] The steady-state OAM density formula printed in Eq. (47) is missing a factor 1/lbar. Substituting the derivative of Eq. (42) into Eq. (46) gives rho_Lz(y) = tau_Lz sigma_1 E_x sinh(y/lbar)/(lbar cosh(w/2lbar)), whereas Eq. (47) omits the divisor lbar. Dimensional analysis confirms the problem: tau_Lz sigma_1 E_x has units of OAM per unit length, while rho_Lz is an areal density and requires the extra 1/length from the spatial derivative. Because Eq. (47) is advertised as the main quantitative link to experiments, this must be corrected.
  2. [Section VII, Eq. (43)] The same length-scale error appears in the small-width limit: expanding Eq. (42) for w/lbar << 1 yields J_Lz(y) = sigma_1 E_x (w^2/8 - y^2/2)/lbar^2, not sigma_1 E_x lbar^2 (w^2/8 - y^2/2) as printed. The printed version has the factor lbar^2 in the numerator instead of the denominator, which is dimensionally inconsistent with J_Lz being a current density.
  3. [Section VIII, paragraph preceding Eq. (46)] The closed-form relation (46) assumes Delta_epsilon(k) ≈ Delta_epsilon(k_F) for all k > k_F, but this approximation is not controlled by the small parameter xi defined in Eq. (16). As acknowledged in Section VI, the intrinsic contribution to J_Lz,y involves an extended k-integral over the occupied states of the lower band. If the gap varies appreciably over this range, the simple proportionality rho_Lz ∝ -tau_Lz ∂_y J_Lz,y with a single tau_Lz(k_F) fails. Please quantify the error introduced by this approximation or identify a class of models in which Delta_epsilon(k) is exactly constant for k > k_F.
minor comments (6)
  1. [Abstract and throughout] The name "Dyakonov-Perel" is misspelled as "Dykonov-Perel" in the abstract, the introduction, Section V, and Figure 2.
  2. [Section I] There are several typos: "obserations" should be "observations", "couterpart" should be "counterpart", "Staring from" should be "Starting from", and "much larger then the inverse" should use "than".
  3. [Appendix A] The text contains "Hamlitonian", "convariant", and "stemms", which should read "Hamiltonian", "covariant", and "stems" respectively.
  4. [References] References [5] and [36] are the same paper (Kontani et al.), and references [56] and [57] are the same paper (Culcer, Sekine, and MacDonald); these duplicates should be removed or consolidated.
  5. [Eq. (13)] The four-index notation for scattering rates in Eq. (13) is dense; a brief sentence defining the meaning of each index (initial band, final band, harmonic, etc.) immediately after the equation would improve readability.
  6. [Section IV C] The sentence "Note that the ratio of the second and third terms in Eq. (24) is of order xi. We shall keep the second term, nevertheless." is confusing because the third term is subsequently argued to vanish for Ohmic flows; please reword to clarify the ordering argument.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the OAM accumulation profile is derived from the quantum Boltzmann hierarchy, with scattering times and band parameters as independent inputs.

full rationale

The derivation chain is self-contained. Eq. (24) is the projected m=0 off-diagonal quantum Boltzmann equation; inverting it gives Eq. (44), and integrating over k with the stated Delta_epsilon(k) ≈ Delta_epsilon(k_F) approximation yields Eq. (46). tau_Lz is not inserted as a fit: it is the Dyakonov-Perel relaxation time obtained from the homogeneous eigenvalue problem Eq. (29) and defined in Eq. (30), so its appearance in the steady-state continuity-type relation is derived, not posited. Eq. (47) is obtained by combining Eq. (46) with the boundary-value solution Eq. (42); the skeptic's dimensional objection (missing factor 1/lbar) is an algebraic error, not circularity — indeed it shows Eq. (47) is a genuine derived formula rather than a restatement of inputs. Scattering rates tau_(m) and band parameters Delta_epsilon, nu are independent inputs; none is fitted to the predicted OAM accumulation. The only explicit uncontrolled approximation is Sec. VIII's Delta_epsilon(k) ≈ Delta_epsilon(k_F) for k > k_F, which limits quantitative accuracy of the closed form but does not reduce Eq. (46) to an identity. Self-citations [47,48,51,52] are for boundary conditions and hydrodynamic context and are not load-bearing; the Dyakonov-Perel scaling is independently referenced [18] and rederived from Eq. (28). No circular step identified.

Assumptions & free parameters 1 free parameters · 7 assumptions · 0 invented entities

The central result depends on many inputs from the model (band parameters, scattering times), but no numerical fitting is done. The listed axioms are the physical assumptions that make the quantum Boltzmann reduction valid. The m=0 relaxation time tau_(0) is treated as an external input; its value is not computed, so the final formula is a relation between observables and parameters rather than a parameter-free prediction.

free parameters (1)
  • Scattering times tau_(m),a|b and tau_(1),a|b in m=0,1,2 channels
    The derived formulas (38), (46), and (47) are functions of these rates. Their values are not computed or fitted in this paper; they are inputs from impurity, phonon, and electron-electron scattering mechanisms.
assumptions (7)
  • domain assumption Weak scattering limit: xi = hbar tau^{-1}/Delta_epsilon_k << 1 holds throughout.
    Used to truncate the quantum Boltzmann equation and discard subleading density matrix components; see Section IVA and Appendix D.
  • domain assumption Collision operator is rotationally invariant and does not mix angular harmonics m.
    Section III and Appendix C, Eq. (A12); this justifies the harmonic-by-harmonic scattering-time structure.
  • domain assumption Mirror symmetry across the x-y plane enforces vanishing of certain scattering rates (Eq. 15).
    Used to simplify the collision operator and to prohibit transverse charge currents and longitudinal spin currents; see Appendix C.
  • domain assumption Orbital texture has constant winding: d_phi_k Theta_k = nu, an even integer.
    Section II, Eq. (4); valid for the d-vector model d_x ~ k_x k_y, d_z ~ k_x^2 - k_y^2 with nu=2, but not for general band structures.
  • domain assumption Single band crosses the Fermi energy and the lower band is fully occupied.
    Sections VII and VIII; used to drop the sum over bands and to evaluate extrinsic and non-local contributions at a single Fermi surface.
  • ad hoc to paper Band gap Delta_epsilon(k) is approximately constant for k > k_F.
    Section VIII, just before Eq. (46); needed to integrate the intrinsic contribution and obtain the closed form. This approximation is not controlled by the small parameter xi.
  • domain assumption Angular harmonic expansion is truncated at m=2.
    Justified by the smallness of xi and tau_q^{-1} hbar / Delta_epsilon_k; higher harmonics are neglected in the gradient expansion.

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Cite this review

Pith. "Pith review of Orbital Hall Effect and Angular Momentum Dynamics in Confined Geometries." pith.science (2026). https://pith.science/paper/BVDYSYBA

@misc{pith2026250700982,
  author       = {Pith},
  title        = {Pith review of: Orbital Hall Effect and Angular Momentum Dynamics in Confined Geometries},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BVDYSYBA}},
  note         = {Machine review of arXiv:2507.00982}
}
read the original abstract

We present an analysis of the orbital Hall effect (OHE) in a strip geometry and derive a formula for the orbital angular momentum (OAM) accumulation at the edges. The result is expressed in terms of band structure parameters and scattering rates, providing a link between experimental observations of the OHE and the underlying microscopics. A key result is that the effective OAM decay rate follows a Dykonov-Perel-like scaling and is inversely proportional to the electron scattering rate, even if the latter is small. Furthermore, investigating OAM transport in an inhomogeneous setting, we show that non-Ohmic flows and spatially varying electric fields result in contributions to the OHE which are distinct from the well known intrinsic and extrinsic mechanisms.

Figures

Figures reproduced from arXiv: 2507.00982 by the authors.

Figure 1
Figure 1. The Hall strip geometry studied in this paper. An [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Relaxation of an initial orbital angular momentum [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Profiles of accumulated orbital angular momentum [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

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Works this paper leans on

54 extracted references · 53 canonical work pages

  1. [1]

    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, Nature619, 52 (2023). 18

    work page 2023

  2. [2]

    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, Physical Review Letters131, 156702 (2023)

    work page 2023

  3. [3]

    G. Sala, H. Wang, W. Legrand, and P. Gambardella,Orbital hanle magnetoresistance in a 3 d transition metal, Physical Review Letters131, 156703 (2023)

    work page 2023

  4. [4]

    B. A. Bernevig, T. L. Hughes, and S.-C. Zhang,Orbitronics: The intrinsic orbital current in p-doped silicon, Physical review letters95, 066601 (2005)

    work page 2005

  5. [6]

    D. Go, D. Jo, C. Kim, and H.-W. Lee,Intrinsic spin and orbital hall effects from orbital texture, Physical review letters 121, 086602 (2018)

    work page 2018

  6. [7]

    Burgos Atencia, A

    R. Burgos Atencia, A. Agarwal, and D. Culcer,Orbital angular momentum of bloch electrons: equilibrium formulation, magneto-electric phenomena, and the orbital hall effect, Advances in Physics: X9, 2371972 (2024)

    work page 2024

  7. [8]

    Y. Yang, P. Wang, J. Chen, D. Zhang, C. Pan, S. Hu, T. Wang, W. Yue, C. Chen, W. Jianget al., Orbital torque switching in perpendicularly magnetized materials, Nature Communications15, 8645 (2024)

    work page 2024

  8. [9]

    Busch, I

    O. Busch, I. Mertig, and B. Göbel,Orbital hall effect and orbital edge states caused by s electrons, Physical Review Research 5, 043052 (2023)

    work page 2023

Show all 54 references
  1. [10]

    Tang and G

    P. Tang and G. E. Bauer,Role of disorder in the intrinsic orbital hall effect, Physical Review Letters133, 186302 (2024)

    2024

  2. [11]

    J. Voss, I. Ado, and M. Titov,Orbital magnetization from interface reflections in a conductor with charge current, Physical Review B111, L121402 (2025)

    2025

  3. [12]

    Go, H.-W

    D. Go, H.-W. Lee, P. M. Oppeneer, S. Blügel, and Y. Mokrousov,First-principles calculation of orbital hall effect by wannier interpolation: Role of orbital dependence of the anomalous position, Physical Review B109, 174435 (2024)

    2024

  4. [13]

    Liu and D

    H. Liu and D. Culcer,Dominance of extrinsic scattering mechanisms in the orbital hall effect: Graphene, transition metal dichalcogenides, and topological antiferromagnets, Physical Review Letters132, 186302 (2024)

    2024

  5. [15]

    D. B. Fonseca, L. L. Pereira, and A. L. Barbosa,Orbital hall effect in mesoscopic devices, Physical Review B108, 245105 (2023)

    2023

  6. [16]

    D. Jo, D. Go, and H.-W. Lee,Gigantic intrinsic orbital hall effects in weakly spin-orbit coupled metals, Physical Review B 98, 214405 (2018)

    2018

  7. [17]

    Han, H.-W

    S. Han, H.-W. Lee, and K.-W. Kim,Orbital dynamics in centrosymmetric systems, Physical review letters128, 176601 (2022)

    2022

  8. [18]

    J. Sohn, J. M. Lee, and H.-W. Lee,Dyakonov-perel-like orbital and spin relaxations in centrosymmetric systems, Physical Review Letters132, 246301 (2024)

    2024

  9. [19]

    Matsumoto, R

    R. Matsumoto, R. Ohshima, Y. Ando, D. Go, Y. Mokrousov, and M. Shiraishi,Observation of giant orbital hall effect in si, arXiv preprint arXiv:2501.14237 (2025)

    2025

  10. [20]

    Gupta, C

    R. Gupta, C. Bouard, F. Kammerbauer, J. O. Ledesma-Martin, A. Bose, I. Kononenko, S. Martin, P. Usé, G. Jakob, M. Drouard, and M. Klaeui,Harnessing orbital hall effect in spin-orbit torque mram, Nature Communications16, 130 (2025)

    2025

  11. [21]

    Bhowal and G

    S. Bhowal and G. Vignale,Orbital hall effect as an alternative to valley hall effect in gapped graphene, Physical Review B 103, 195309 (2021)

    2021

  12. [22]

    Fukunaga, S

    R. Fukunaga, S. Haku, H. Hayashi, and K. Ando,Orbital torque originating from orbital hall effect in zr, Physical Review Research 5, 023054 (2023)

    2023

  13. [23]

    Z. Chen, R. Li, Y. Bai, N. Mao, M. Zeer, D. Go, Y. Dai, B. Huang, Y. Mokrousov, and C. Niu,Topology-engineered orbital hall effect in two-dimensional ferromagnets, Nano letters24, 4826 (2024)

    2024

  14. [24]

    Veneri, T

    A. Veneri, T. G. Rappoport, and A. Ferreira,Extrinsic orbital hall effect: Orbital skew scattering and crossover between diffusive and intrinsic orbital transport, Physical Review Letters134, 136201 (2025)

    2025

  15. [25]

    Gurzhi,Minimum of resistance in impurity-free conductors, Sov

    R. Gurzhi,Minimum of resistance in impurity-free conductors, Sov. Phys. JETP44, 045443 (1963)

    1963

  16. [26]

    Gurzhi,Hydrodynamic effects in solids at low temperature, Soviet Physics Uspekhi11, 255 (1968)

    R. Gurzhi,Hydrodynamic effects in solids at low temperature, Soviet Physics Uspekhi11, 255 (1968)

    1968

  17. [27]

    De Jong and L

    M. De Jong and L. Molenkamp,Hydrodynamic electron flow in high-mobility wires, Physical Review B51, 13389 (1995)

    1995

  18. [28]

    P. J. Moll, P. Kushwaha, N. Nandi, B. Schmidt, and A. P. Mackenzie,Evidence for hydrodynamic electron flow in pdcoo2, Science 351, 1061 (2016)

    2016

  19. [29]

    Levitov and G

    L. Levitov and G. Falkovich,Electron viscosity, current vortices and negative nonlocal resistance in graphene, Nature Physics 12, 672 (2016)

    2016

  20. [30]

    J. A. Sulpizio, L. Ella, A. Rozen, J. Birkbeck, D. J. Perello, D. Dutta, M. Ben-Shalom, T. Taniguchi, K. Watanabe, T. Holderet al., Visualizing poiseuille flow of hydrodynamic electrons, Nature576, 75 (2019)

    2019

  21. [31]

    Aharon-Steinberg, T

    A. Aharon-Steinberg, T. Völkl, A. Kaplan, A. K. Pariari, I. Roy, T. Holder, Y. Wolf, A. Y. Meltzer, Y. Myasoedov, M. E. Huber et al., Direct observation of vortices in an electron fluid, Nature607, 74 (2022)

    2022

  22. [32]

    Baker, T

    G. Baker, T. W. Branch, J. Bobowski, J. Day, D. Valentinis, M. Oudah, P. McGuinness, S. Khim, P. Surówka, Y. Maeno et al., Nonlocal electrodynamics in ultrapure pdcoo 2, Physical Review X14, 011018 (2024)

    2024

  23. [33]

    Baker, M

    G. Baker, M. Moravec, and A. P. Mackenzie,A perspective on non-local electronic transport in metals: Viscous, ballistic, and beyond, Annalen der Physik536, 2400087 (2024)

    2024

  24. [34]

    Y. Wolf, A. Aharon-Steinberg, B. Yan, and T. Holder,Para-hydrodynamics from weak surface scattering in ultraclean thin flakes, Nature Communications14, 2334 (2023)

    2023

  25. [35]

    Han, H.-W

    S. Han, H.-W. Lee, and K.-W. Kim,Microscopic study of orbital textures, Current Applied Physics50, 13 (2023). 19

    2023

  26. [36]

    Kontani, T

    H. Kontani, T. Tanaka, D. Hirashima, K. Yamada, and J. Inoue,Giant orbital hall effect in transition metals: Origin of large spin and anomalous hall effects, Physical review letters102, 016601 (2009)

    2009

  27. [37]

    Sekine, D

    A. Sekine, D. Culcer, and A. H. MacDonald,Quantum kinetic theory of the chiral anomaly, Physical Review B96, 235134 (2017)

    2017

  28. [38]

    H. Liu, J. H. Cullen, D. P. Arovas, and D. Culcer,Quantum correction to the orbital hall effect, Physical Review Letters 134, 036304 (2025)

    2025

  29. [39]

    Huang,Statistical mechanics, John Wiley & Sons (2008)

    K. Huang,Statistical mechanics, John Wiley & Sons (2008)

    2008

  30. [40]

    For scattering on scalar impurities, in the Born approximation, all scattering times are real. As shown in AppendixC, time-reversal symmetry and rotational invariance imply that most (except for exampleτ(m),a¯a|a¯a and ¯τ(m),a¯a|¯aa) scattering rates that appear in the above c...

  31. [41]

    Žutić, J

    I. Žutić, J. Fabian, and S. D. Sarma,Spintronics: Fundamentals and applications, Reviews of modern physics76, 323 (2004)

    2004

  32. [42]

    Fabian, A

    J. Fabian, A. Matos-Abiague, C. Ertler, P. Stano, and I. Zutic,Semiconductor spintronics, arXiv preprint arXiv:0711.1461 (2007)

    2007 arXiv

  33. [43]

    R. J. Elliott,Theory of the effect of spin-orbit coupling on magnetic resonance in some semiconductors, Physical Review 96, 266 (1954)

    1954

  34. [44]

    Yafet,g factors and spin-lattice relaxation of conduction electrons, inSolid state physics, vol

    Y. Yafet,g factors and spin-lattice relaxation of conduction electrons, inSolid state physics, vol. 14, Elsevier, (1–98) (1963)

    1963

  35. [45]

    Dyakonov and V

    M. Dyakonov and V. Perel,Spin relaxation of conduction electrons in noncentrosymmetric semiconductors, Soviet Physics Solid State, Ussr13, 3023 (1972)

    1972

  36. [46]

    M. I. Dyakonov and V. I. Perel,Theory of optical spin orientation of electrons and nuclei in semiconductors, Optical orientation 8, 11 (1984)

    1984

  37. [47]

    E. I. Kiselev and J. Schmalian,Nonlocal hydrodynamic transport and collective excitations in dirac fluids, Physical Review B 102, 245434 (2020)

    2020

  38. [48]

    Ledwith, H

    P. Ledwith, H. Guo, A. Shytov, and L. Levitov,Tomographic dynamics and scale-dependent viscosity in 2d electron systems, Physical Review Letters123, 116601 (2019)

    2019

  39. [49]

    These effects do not lead to qualitative changes in the orbital Hall conductivity, but can be absorbed in a redefinition of the Fermi velocities and scattering times (see AppendixE)

  40. [50]

    Zhang,Spin hall effect in the presence of spin diffusion, Physical review letters85, 393 (2000)

    S. Zhang,Spin hall effect in the presence of spin diffusion, Physical review letters85, 393 (2000)

    2000

  41. [51]

    E. I. Kiselev and J. Schmalian,Boundary conditions of viscous electron flow, Physical Review B99, 035430 (2019)

    2019

  42. [52]

    Moessner, N

    R. Moessner, N. Morales-Durán, P. Surówka, and P. Witkowski,Boundary-condition and geometry engineering in electronic hydrodynamics, Physical Review B100, 155115 (2019)

    2019

  43. [53]

    K. G. Nazaryan and L. Levitov,Nonlocal conductivity, continued fractions, and current vortices in electron fluids, Physical Review B110, 045147 (2024)

    2024

  44. [54]

    R. J. Doornenbal, M. Polini, and R. A. Duine, Spin–vorticity coupling in viscous electron fluids, Journal of Physics: Materials 2, 015006 (2019)

    2019

  45. [55]

    Khaetskii,Nonexistence of intrinsic spin currents, Physical review letters96, 056602 (2006)

    A. Khaetskii,Nonexistence of intrinsic spin currents, Physical review letters96, 056602 (2006)

    2006

  46. [57]

    Culcer, A

    D. Culcer, A. Sekine, and A. H. MacDonald, Interband coherence response to electric fields in crystals: Berry-phase contributions and disorder effects, Physical Review B96, 035106 (2017)

    2017

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.