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REVIEW 3 major objections 4 minor 92 references

The electrical transport of intrinsic two-dimensional ferroelectric metal PtBi2

T0 review · 3 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Monolayer PtBi2 is an intrinsic two-dimensional ferroelectric metal with an 800 K transition and platinum-like spin conversion.

desk verdict Solid first-principles transport study of a 2D ferroelectric metal whose headline magnitudes depend on an assumed tau and L_eff. read the letter →

arxiv 2608.12152 v1 pith:2KTSIR5H submitted 2026-08-12 cond-mat.mtrl-sci cond-mat.mes-hall

Dan Li , Liu Yang , Lei Li This is my paper · ORCID
classification cond-mat.mtrl-scicond-mat.mes-hall
keywords two-dimensionalferroelectricmetalPtBi2monolayerspinHalleffectEdelsteinnonlinearBerrycurvaturedipolecharge-to-spinconversionfield-effecttransistor
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 sets out to establish that a single layer of PtBi2 breaks the usual rule that ferroelectrics must be insulating: it is simultaneously switchably polarized and metallic, and its electrical transport carries measurable fingerprints of that combination. If the calculations are correct, the monolayer stays ferroelectric up to about 800 K, so the polarization survives at room temperature. The same first-principles transport calculations predict that a simple in-plane conductivity measurement identifies which paraelectric structure forms above the transition, that the Edelstein effect reverses with polarization, and that charge current converts to spin current with an efficiency comparable to platinum. These features point toward atomically thin nonvolatile memory and spintronic devices controlled by electric fields.

What carries the argument

The argument is carried by the semiclassical Boltzmann equation in the relaxation-time approximation, evaluated on first-principles band structures through a first-principles tight-binding Hamiltonian. The load-bearing objects are the spin Berry curvature $\Omega^{s}_{n,ab}$, whose occupied-state integral gives the intrinsic spin Hall conductivity; the Berry curvature dipole $D_{bd}$, which controls the second-order nonlinear Hall conductivity; and a symmetry analysis that fixes which tensor components survive in the $C_{3z}$-symmetric ferroelectric and 1T phases versus the lower-symmetry NP phase. A normal-mode decomposition of atomic displacements identifies the $B_{1u}$ soft mode that drives the ferroelectric transition, and a power-law fit to the AIMD polarization yields $T_C \approx 800$ K. All Boltzmann coefficients are evaluated with a relaxation time $\tau = 20$ fs and converted to three-dimensional units with an effective thickness $L_{\mathrm{eff}} = 10$ Å.

What would settle it

A four-probe measurement of exfoliated monolayer PtBi2 that finds isotropic in-plane conductivity above roughly 800 K would contradict the predicted anisotropic NP paraelectric phase, and a spin Hall or spin-torque measurement whose angle lies far from the predicted $\theta^z_{xy}=0.032$ would falsify the quantitative spin-conversion claim.

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Extended reading notes

Core claim

On the paper's own terms, monolayer PtBi2 is an intrinsic two-dimensional ferroelectric metal: it retains metallic in-plane conduction while hosting switchable out-of-plane polarization, with a Curie temperature $T_C \approx 800$ K extracted from ab initio molecular dynamics. The first-principles Boltzmann transport calculation finds that the ferroelectric phase has lower in-plane conductivity than either candidate paraelectric phase, and that the anisotropy pattern ($\sigma_{yy}/\sigma_{xx}=0.79$ for the NP state, isotropic conductivity 3.93 times larger for the 1T state) tells the two high-temperature structures apart. The Edelstein coefficient is sizable and reverses sign when the polarization is switched. The intrinsic spin Hall conductivity is computed as $\sigma^{x;xy}_{\mathrm{int}}=-135$ and $\sigma^{z;xy}_{\mathrm{int}}=509$ in units of $(\hbar/2e)\,\mathrm{S\,cm^{-1}}$ at $E_F=0$, giving spin Hall angles $\theta^x_{xy}=0.008$ and $\theta^z_{xy}=0.032$, the latter comparable to platinum. In the pristine monolayer the nonlinear Hall effect is forbidden by the threefold rotation symmetry, but uniaxial strain activates a Berry curvature dipole and a nonlinear Hall response. The authors close with a conceptual ferroelectric-metal field-effect transistor in which gate-controlled domain-wall scattering switches nonvolatilely between high- and low-resistance states.

Load-bearing premise

The predicted conductivities, spin Hall angles, and Edelstein coefficients all scale linearly with the assumed electron scattering time of 20 femtoseconds and the assumed effective layer thickness of 10 angstroms, so if the real material scatters electrons faster or slower, or has a different effective thickness, the absolute magnitudes change proportionally.

Editorial extensions

If this is right

  • Above the transition temperature, measuring the in-plane conductivity distinguishes the two competing paraelectric structures: the NP state is anisotropic with $\sigma_{yy}/\sigma_{xx}=0.79$, while the 1T state is isotropic with conductivity 3.93 times that of the ferroelectric phase.
  • Switching the ferroelectric polarization with a vertical electric field reverses the Edelstein coefficient, so the direction of current-induced spin polarization is electrically controllable.
  • The predicted intrinsic spin Hall conductivity of $\sigma^{z;xy}_{\mathrm{int}}=509\,(\hbar/2e)\,\mathrm{S\,cm^{-1}}$ and spin Hall angle $0.032$ make the monolayer competitive with platinum for charge-to-spin conversion.
  • Uniaxial strain of a fraction of a percent activates a Berry curvature dipole and a nonlinear Hall response, providing a strain-tunable second-harmonic signal.
  • A ferroelectric-metal field-effect transistor can use a gate voltage to change domain-wall density and nonvolatilely toggle between high- and low-resistance states, without depleting the conducting channel.

Reading between the lines

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

  • Because every absolute transport coefficient scales linearly with the assumed $\tau=20$ fs and $L_{\mathrm{eff}}=10$ Å, a future experiment that fixes $\tau$ by measuring the longitudinal conductivity would convert all predicted spin Hall angles and Edelstein magnitudes into parameter-free comparisons.
  • The conductivity-based phase identification suggests a general strategy: for other 2D ferroelectric metals, a four-probe transport measurement above $T_C$ may be a cheaper way to discriminate competing high-symmetry structures than structural probes.
  • The FEM-FET switching mechanism implies that poling history and domain-wall density, not carrier depletion, set the resistance state; devices with deliberately patterned domains would be a direct test.
  • If the same gate-controllable domain-wall scattering affects the superconductivity that the paper notes in PtBi2 at low temperature, the FEM-FET concept could extend to electrically switchable superconducting circuits.
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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 / 4 minor

Summary. The manuscript investigates monolayer PtBi2 as an intrinsic two-dimensional ferroelectric metal. Using DFT, AIMD, and a Wannier tight-binding model, the authors estimate a Curie temperature TC≈800 K from a power-law fit to AIMD polarization data, and evaluate linear and nonlinear transport within the semiclassical Boltzmann relaxation-time approximation. They predict an anisotropic in-plane conductivity for the high-temperature NP phase, compute the Edelstein coefficient and intrinsic spin Hall conductivity as functions of Fermi energy, analyze the Berry-curvature-dipole nonlinear Hall effect under uniaxial strain, and propose a ferroelectric-metal field-effect transistor (FEM-FET) based on ferroelectric domain-wall scattering. The central quantitative claims are a sizable intrinsic spin Hall effect with σ_x;xy_int = -135 and σ_z;xy_int = 509 in units of (ℏ/2e) S/cm at EF=0, spin Hall angles θ_xy^x=0.008 and θ_xy^z=0.032 quoted as comparable to platinum, and polarization-switchable Edelstein and nonlinear Hall responses.

Significance. If the quantitative predictions are correct, the paper provides a concrete example of a room-temperature two-dimensional ferroelectric metal with a switchable Edelstein effect and a sizable intrinsic spin Hall response, and it proposes a falsifiable way to identify the high-temperature paraelectric phase via conductivity anisotropy. The symmetry-based conclusions are robust and valuable: the C3z-protected in-plane isotropy of the FE and 1T phases versus the broken-C3z anisotropy of the NP phase, the polarization-switchable sign of the Edelstein coefficient, and the strain-induced nonlinear Hall selection rules are all clearly derived from symmetry and are independent of the transport parameters. The authors also check k-mesh convergence with a 1000×1000×1 versus 1500×1500×1 comparison and present the Boltzmann derivations in a self-contained manner. However, the absolute magnitudes highlighted in the abstract—the S/cm values of the spin Hall conductivity and the spin Hall angles—are not parameter-free: they depend on the assumed relaxation time τ=20 fs and the chosen effective thickness L_eff=10 Å, and no sensitivity analysis is provided.

major comments (3)
  1. [Sec. VI, Eq. (25); Sec. II] The charge-to-spin conversion efficiency quoted as comparable to platinum is not a parameter-free result. In Eq. (20) the intrinsic spin Hall conductivity is independent of τ, whereas the longitudinal conductivity σ_bb in Eq. (11) is proportional to τ; therefore the spin Hall angle θ_i^ab in Eq. (25) scales as 1/τ. With the chosen τ=20 fs, θ_xy^z=0.032 lies below the quoted Pt range 0.056–0.16; for τ=10 fs it would be about 0.064, while for τ=50 fs it would be about 0.013. The text should either present θ as a function of τ, justify τ from a microscopic scattering calculation, or clearly label the Pt comparison as an order-of-magnitude illustration. The Gaussian broadening width of 20 meV is a further free parameter whose influence on the reported Fermi-surface integrals is not tested.
  2. [Sec. II, Eq. (1); Sec. VI] The absolute values of the spin Hall conductivity and of all other coefficients converted to 3D units are convention-dependent through the effective thickness L_eff=10 Å. Equation (1) rescales slab results by L_slab/L_eff, so a different but equally plausible choice of L_eff changes every value quoted in S/cm, including σ_x;xy_int=-135 and σ_z;xy_int=509 in Sec. VI. The spin Hall angle is a ratio of two coefficients that scale by the same factor and is therefore unaffected by L_eff, but the paper should still state explicitly that the S/cm magnitudes are defined with respect to a chosen L_eff, and ideally also report the 2D sheet values.
  3. [Sec. VIII] The FEM-FET proposal is presented as one of the main conclusions, but it rests entirely on the assumption that ferroelectric domain walls in a metallic monolayer scatter conduction electrons analogously to magnetic domain walls. No microscopic estimate is given for the domain-wall resistance, for the dependence of domain-wall density on gate voltage, or for why metallic screening does not suppress the proposed effect. As written, Sec. VIII is a plausible qualitative idea rather than a supported design; at minimum, a rough estimate of the resistance contrast between the high-resistance and low-resistance states should be added, or the section should be explicitly framed as speculative.
minor comments (4)
  1. [Sec. VII, Eqs. (35)-(36)] The second argument of σ(2ω;ω,−ω) appears to be a typo; the second-harmonic conductivity should be σ(2ω;ω,ω) in both Eq. (35) and Eq. (36).
  2. [Sec. III, Eq. (2)] The TC≈800 K headline value is obtained from a three-parameter fit of Eq. (2) to AIMD data from a single 4×4×1 supercell; reporting the number of independent temperatures, error bars, and a supercell-size dependence check would make the claimed Curie temperature more robust.
  3. [Sec. V, Eq. (15)] The units of the Edelstein coefficient χ_i;a are not stated, and the text says Eq. (1) is not applied to χ; a sentence clarifying whether χ is defined per unit cell, per area, or per effective thickness would help the reader compare with literature values.
  4. [Sec. VI, Eqs. (22)-(24)] The matrix notation in Eqs. (22)-(24) is not self-explanatory; the row and column labels (a,b indices of the spin-current direction and electric-field direction) should be defined explicitly.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: transport coefficients are evaluated from DFT bands via standard semiclassical/Kubo formulas, the self-cited FE structure is background, and the Curie temperature is a transparent fit to AIMD data.

full rationale

The central transport results are self-contained first-principles evaluations. Eqs. (11), (15), (19)-(20), and (36)-(37) are standard Boltzmann/Kubo expressions evaluated with a Wannier tight-binding Hamiltonian fitted to DFT bands; the numerical values (sigma_int, chi, BCD, conductivity anisotropy) follow from those band-structure inputs, not from the claims they are used to support. The Curie temperature is explicitly presented as a fit to AIMD polarization data with Eq. (2); reporting the fitted TC ~ 800 K is a fit result, not a prediction forced by the fit formula. The relaxation time tau = 20 fs and L_eff = 10 A are stated input conventions; the spin Hall angle in Eq. (25) depends on tau and absolute S/cm values depend on L_eff, but this is parameter sensitivity, not circularity, because no parameter was tuned to reproduce the spin Hall angle or any target coefficient. The only overlap with prior work is Ref. [21] (same first-author lineage) supplying the FE structural ground state and the P-relation of the two FE states; the present paper independently re-derives stability through phonon dispersion, AIMD, and energy landscapes, so the self-citation is background rather than load-bearing. No equation reduces by construction to its input, and no fitted parameter is renamed as a prediction.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central quantitative claims rest on a modest set of modeling choices: DFT band structure, a fixed relaxation time, an arbitrary thickness for unit conversion, and a power-law fit to AIMD data. No new physical entities are introduced. The FEM-FET mechanism is an additional domain-wall-scattering assumption.

free parameters (4)
  • Relaxation time tau = 20 fs
    Assumed constant scattering time for all states and temperatures; controls the magnitude of conductivity, Edelstein coefficient, nonlinear Hall conductivity, and spin Hall angle.
  • Effective thickness L_eff = 10 Angstrom
    Ad hoc conversion from 2D monolayer to 3D-equivalent units; scales absolute conductivities and spin Hall conductivity values.
  • Gaussian broadening width = 20 meV
    Numerical smearing for the Dirac delta in Fermi-surface integrals; convergence checked with denser mesh but width not varied.
  • Critical exponent delta = 0.57
    Free parameter in the fit of P(T) to Eq. (2); used together with T_C to extract the Curie temperature from AIMD data.
assumptions (5)
  • standard math Semiclassical Boltzmann equation in relaxation time approximation
    Eqs. (9)-(10) in Sec. IV; the standard framework for transport used throughout the paper.
  • domain assumption PBE-GGA DFT with spin-orbit coupling accurately describes the band structure of monolayer PtBi2
    All transport coefficients are computed from the resulting Wannier Hamiltonian; no hybrid functionals or GW corrections are applied.
  • domain assumption AIMD with a 4x4x1 supercell and Nosé-Hoover thermostat captures the phase transition
    Finite-size and timescale effects could bias the fitted T_C ~ 800 K; no systematic size dependence study is reported.
  • domain assumption Static DFT energy barrier comparison determines the favored paraelectric phase
    The FE1 to NP to FE2 path is favored over FE1 to 1T to FE2 based on zero-temperature energy landscapes.
  • ad hoc to paper Ferroelectric domain walls scatter electrons analogously to magnetic domain walls
    Underlies the FEM-FET concept; no microscopic calculation of domain wall resistance or gate response is provided.

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Cite this review

Pith. "Pith review of The electrical transport of intrinsic two-dimensional ferroelectric metal PtBi2." pith.science (2026). https://pith.science/paper/2KTSIR5H

@misc{pith2026260812152,
  author       = {Pith},
  title        = {Pith review of: The electrical transport of intrinsic two-dimensional ferroelectric metal PtBi2},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/2KTSIR5H}},
  note         = {Machine review of arXiv:2608.12152}
}
abstract

Breaking the conventional stereotype that ferroelectrics are necessarily insulating, two-dimensional (2D) ferroelectric metals combine seemingly incompatible switchable electric polarization and metallic conductivity, providing a fertile ground for the discovery of novel electrical transport phenomena and the development of innovative electronic devices. Using the semiclassical Boltzmann equation and first-principles calculations, we systematically investigate the linear and nonlinear transport responses of the intrinsic 2D ferroelectric metal \ch{PtBi2} to an applied electric field. Our \textit{ab initio} molecular dynamics simulations reveal that it possesses a high Curie temperature reaching $800~\text{K}$. We propose that the crystal structure of its high-temperature paraelectric phase can be explicitly distinguished through simple measurements of the in-plane electrical conductivity. Quantitative calculations of the Edelstein effect and the intrinsic spin Hall effect demonstrate a sizable charge-to-spin conversion efficiency, highlighting its potential in spintronics. We also find that a Berry curvature dipole-induced nonlinear Hall effect emerges in uniaxially strained \ch{PtBi2}. Furthermore, we highlight the unique advantages of 2D ferroelectric metals in gate-controlled transport applications. Based on the domain wall scattering mechanism, we conceptually design a novel ferroelectric metal field-effect transistor (FEM-FET) capable of nonvolatile switching between high-resistance and low-resistance states under a gate voltage. Our work not only unveils the rich transport physics in 2D ferroelectric metals but also provides valuable insights into the design of next-generation nonvolatile memory and spintronic devices.

Figures

Figures reproduced from arXiv: 2608.12152 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Temperature-dependent normalized ferroelec [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a) Top and side views of the atomic structures for [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. (a) The calculated Edelstein coefficient [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. (a) The independent non-zero components of the intrinsic spin Hall conductivity, [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. (a),(c) The nonlinear Hall conductivity [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The (a) high-resistance state (HR) and (b) low [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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Reference graph

Works this paper leans on

92 extracted references · 42 canonical work pages

  1. [56]

    A.Johansson,Theoryofspinandorbitaledelsteineffects, JournalofPhysics: CondensedMatter36,423002(2024)

    2024

  2. [1]

    A. K. Geim and K. S. Novoselov, The rise of graphene, Nature materials6, 183 (2007)

    2007

  3. [2]

    0” and “1

    =χ i;aEa (14) where ˆs=ℏ/2 ˆσis the spin operator and ˆσare Pauli matrices.s 0 is the spin polarization in the absence of an electric field, which is zero in PtBi2.V 0 is the volume of the unit cell,µB is the Bohr magneton andgs≈2is the electron sping-factor. Using Eq. (7), we obtain the Edelstein coefficient [55] χi;a =− eτµ BgsV0 ℏ X n Z [dk]si nkva nk ...

    2000

  4. [3]

    A. K. Geim, Graphene: status and prospects, science 324, 1530 (2009)

    2009

  5. [4]

    A. H. Castro Neto, F. Guinea, N. M. Peres, K. S. Novoselov, and A. K. Geim, The electronic properties of graphene, Reviews of modern physics81, 109 (2009)

    2009

  6. [5]

    K. S. Novoselov, A. K. Geim, S. V. Morozov, D.-e. Jiang, Y. Zhang, S. V. Dubonos, I. V. Grigorieva, and A. A. Firsov, Electric field effect in atomically thin carbon films, science306, 666 (2004)

    2004

  7. [6]

    K. S. Novoselov, A. K. Geim, S. V. Morozov, D. Jiang, M. I. Katsnelson, I. V. Grigorieva, S. V. Dubonos, and A. A. Firsov, Two-dimensional gas of massless dirac fermions in graphene, nature438, 197 (2005)

    2005

  8. [7]

    C. Lee, X. Wei, J. W. Kysar, and J. Hone, Measurement of the elastic properties and intrinsic strength of mono- layer graphene, science321, 385 (2008)

    2008

Show all 92 references
  1. [8]

    A. A. Balandin, S. Ghosh, W. Bao, I. Calizo, D. Tewelde- brhan, F. Miao, and C. N. Lau, Superior thermal conduc- tivity of single-layer graphene, Nano letters8, 902 (2008)

    2008

  2. [9]

    J. R. Schaibley, H. Yu, G. Clark, P. Rivera, J. S. Ross, K. L. Seyler, W. Yao, and X. Xu, Valleytronics in 2d materials, Nature Reviews Materials1, 16055 (2016)

    2016

  3. [10]

    K. F. Mak, C. Lee, J. Hone, J. Shan, and T. F. Heinz, Atomically thin MoS2: A new direct-gap semiconductor, Phys. Rev. Lett.105, 136805 (2010)

    2010

  4. [11]

    X. Xu, W. Yao, D. Xiao, and T. F. Heinz, Spin and pseudospins in layered transition metal dichalcogenides, Nature Physics10, 343 (2014)

    2014

  5. [12]

    H. Zeng, J. Dai, W. Yao, D. Xiao, and X. Cui, Valley polarization in mos2 monolayers by optical pumping, Na- ture nanotechnology7, 490 (2012)

    2012

  6. [13]

    P. Miró, M. Audiffred, and T. Heine, An atlas of two- dimensional materials, Chemical Society Reviews43, 6537 (2014)

    2014

  7. [14]

    Mounet, M

    N. Mounet, M. Gibertini, P. Schwaller, D. Campi, A. Merkys, A. Marrazzo, T. Sohier, I. E. Castelli, A. Ce- pellotti, G. Pizzi,et al., Two-dimensional materials from high-throughput computational exfoliation of experimen- tally known compounds, Nature nanotechnology13, 246 (2018)

    2018

  8. [15]

    W. Gao, X. Zhu, F. Zheng, M. Wu, J. Zhang, C. Xi, P. Zhang, Y. Zhang, N. Hao, W. Ning,et al., A possible candidate for triply degenerate point fermions in trigonal layered ptbi2, Nature communications9, 3249 (2018)

    2018

  9. [16]

    J. Qu, A. Veyrat, B. Büchner, and J. Dufouleur, Super- conductivity and topology of trigonal ptbi2: Status and prospects, Applied Physics Reviews13, 021332 (2026)

    2026

  10. [17]

    Changdar, O

    S. Changdar, O. Suvorov, A. Kuibarov, S. Thirupatha- iah, G. Shipunov, S. Aswartham, S. Wurmehl, I. Ko- valchuk, K. Koepernik, C. Timm,et al., Topological nodal i-wave superconductivity in ptbi2, Nature647, 613 (2025)

    2025

  11. [18]

    Veyrat, V

    A. Veyrat, V. Labracherie, D. L. Bashlakov, F. Caglieris, J. I. Facio, G. Shipunov, T. Charvin, R. Acharya, Y. Naidyuk, R. Giraud,et al., Berezinskii–kosterlitz– thouless transition in the type-i weyl semimetal ptbi2, Nano Letters23, 1229 (2023)

    2023

  12. [19]

    Schimmel, Y

    S. Schimmel, Y. Fasano, S. Hoffmann, J. Besproswanny, L. T. Corredor Bohorquez, J. Puig, B.-C. Elshalem, B. Kalisky, G. Shipunov, D. Baumann,et al., Surface superconductivity in the topological weyl semimetal t- ptbi2, Nature Communications15, 9895 (2024)

    2024

  13. [20]

    J. A. Moreno, P. G. Talavera, E. Herrera, S. L. Valle, Z. Li, L.-L. Wang, S. Bud’ko, A. I. Buzdin, I. Guillamón, P. C. Canfield,et al., Robust two-dimensional surface su- perconductivity and vortex lattice in the weyl semimetal γ-PtBi2, arXiv preprint arXiv:2508.04867 (2025)

    2025

  14. [21]

    L. Yang, L. Li, Z.-M. Yu, M. Wu, and Y. Yao, Two- dimensional topological ferroelectric metal with giant shift current, Phys. Rev. Lett.133, 186801 (2024)

    2024

  15. [22]

    D. L. Bashlakov, O. E. Kvitnitskaya, G. Shipunov, S. Aswartham, O. D. Feya, D. V. Efremov, B. Büch- ner, and Y. G. Naidyuk, Electron-phonon interaction and point contact enhanced superconductivity in trigonal ptbi2, Low Temperature Physics48, 747 (2022)

    2022

  16. [23]

    C. Jia, W. Huang, H. Yang, C. Luo, L. Jiang, S. Wu, M. Li, M. Fan, Y. Yang, and H. Zhang, Coexistence of ferroelectricity and metallicity in weakly coupled (SnSe)1.16(nbse2)crystal, Phys. Rev. Lett.135, 236802 (2025)

    2025

  17. [24]

    Z. Fei, W. Zhao, T. A. Palomaki, B. Sun, M. K. Miller, Z. Zhao, J. Yan, X. Xu, and D. H. Cobden, Ferroelectric switching of a two-dimensional metal, Nature560, 336 (2018)

    2018

  18. [25]

    M. E. Lines and A. M. Glass,Principles and applications of ferroelectrics and related materials(Oxford university press, 2001)

    2001

  19. [26]

    Z. Liu, S. Song, X. Yin, C. Xu, F. Liu, G. Wang, P. Chen, S. Jiang, C. Xu, X. Xu,et al., Ferroelectricity in atomi- callythinmetallicTaNiTe 5withultrahighcarrierdensity, arXiv preprint arXiv:2602.05398 (2026)

    2026

  20. [27]

    Kresse and J

    G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B54, 11169 (1996)

    1996

  21. [28]

    Kresse and J

    G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci.6, 15 (1996)

    1996

  22. [29]

    P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B50, 17953 (1994)

    1994

  23. [30]

    J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996)

    1996

  24. [31]

    Makov and M

    G. Makov and M. C. Payne, Periodic boundary condi- tions in ab initio calculations, Phys. Rev. B51, 4014 (1995)

    1995

  25. [32]

    MethfesselandA

    M. MethfesselandA. T.Paxton,High-precisionsampling for brillouin-zone integration in metals, Phys. Rev. B40, 3616 (1989)

    1989

  26. [33]

    A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Imple- mentation strategies in phonopy and phono3py, J. Phys. Condens. Matter35, 353001 (2023). 10

    2023

  27. [34]

    Neugebauer and M

    J. Neugebauer and M. Scheffler, Adsorbate-substrate and adsorbate-adsorbate interactions of Na and K adlayers on al(111), Phys. Rev. B46, 16067 (1992)

    1992

  28. [35]

    Nosé, A unified formulation of the constant tempera- ture molecular dynamics methods, The Journal of Chem- ical Physics81, 511 (1984)

    S. Nosé, A unified formulation of the constant tempera- ture molecular dynamics methods, The Journal of Chem- ical Physics81, 511 (1984)

    1984

  29. [36]

    Togo, First-principles phonon calculations with phonopy and phono3py, J

    A. Togo, First-principles phonon calculations with phonopy and phono3py, J. Phys. Soc. Jpn.92, 012001 (2023)

    2023

  30. [37]

    W. G. Hoover, Canonical dynamics: Equilibrium phase- space distributions, Phys. Rev. A31, 1695 (1985)

    1985

  31. [38]

    Shuichi, Constant temperature molecular dynamics methods, Progress of Theoretical Physics Supplement 103, 1 (1991)

    N. Shuichi, Constant temperature molecular dynamics methods, Progress of Theoretical Physics Supplement 103, 1 (1991)

    1991

  32. [39]

    Gall, Electron mean free path in elemental metals, Journal of Applied Physics119, 085101 (2016)

    D. Gall, Electron mean free path in elemental metals, Journal of Applied Physics119, 085101 (2016)

    2016

  33. [40]

    Pizzi, V

    G. Pizzi, V. Vitale, R. Arita, S. Blügel, F. Freimuth, G. Géranton, M. Gibertini, D. Gresch, C. Johnson, T. Koretsune, J. Ibañez-Azpiroz, H. Lee, J.-M. Lihm, D. Marchand, A. Marrazzo, Y. Mokrousov, J. I. Mustafa, Y. Nohara, Y. Nomura, L. Paulatto, S. Poncé, T. Pon- weiser, J. ...

    2020

  34. [41]

    Krishnaswamy, B

    K. Krishnaswamy, B. Himmetoglu, Y. Kang, A. Janotti, and C. G. Van de Walle, First-principles analysis of elec- trontransportinbasno 3,Phys.Rev.B95,205202(2017)

    2017

  35. [42]

    S. K. Vasheghani Farahani, T. D. Veal, P. D. C. King, J. Zúñiga-Pérez, V. Muñoz-Sanjosé, and C. F. Mc- Conville, Electron mobility in cdo films, Journal of Ap- plied Physics109, 073712 (2011)

    2011

  36. [43]

    As shown in previous work [21], the FE phase tran- sition of the PtBi2 monolayer is mainly contributed by two zone-center soft modes [B1u andB 2u in Fig

    and 3D FE PbTiO3 [42]. As shown in previous work [21], the FE phase tran- sition of the PtBi2 monolayer is mainly contributed by two zone-center soft modes [B1u andB 2u in Fig. 1(b)] of the centrosymmetric nonpolar (NP) state. To further elucidate their role in the phase trans...

  37. [44]

    J. C. Wojdeł and J. Íñiguez, Testing simple predictors for the temperature of a structural phase transition, Phys. Rev. B90, 014105 (2014)

    2014

  38. [45]

    R. Fei, W. Kang, and L. Yang, Ferroelectricity and phase transitions in monolayer group-iv monochalcogenides, Phys. Rev. Lett.117, 097601 (2016)

    2016

  39. [46]

    Newman and G

    M. Newman and G. Barkema, Monte carlo methods in statistical physics, New York, USA (1999)

    1999

  40. [47]

    Dove, Introduction to the theory of lattice dynamics, École thématique de la Société Française de la Neutron- ique12, 123 (2011)

    M. Dove, Introduction to the theory of lattice dynamics, École thématique de la Société Française de la Neutron- ique12, 123 (2011)

    2011

  41. [48]

    A. Togo, L. Chaput, T. Tadano, and I. Tanaka, Imple- mentation strategies in phonopy and phono3py, Journal of Physics: Condensed Matter35, 353001 (2023)

    2023

  42. [49]

    Xiao, M.-C

    D. Xiao, M.-C. Chang, and Q. Niu, Berry phase effects on electronic properties, Rev. Mod. Phys.82, 1959 (2010)

    2010

  43. [50]

    Nagaosa, J

    N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Anomalous hall effect, Rev. Mod. Phys.82, 1539 (2010)

    2010

  44. [51]

    Y. Yao, L. Kleinman, A. H. MacDonald, J. Sinova, T. Jungwirth, D.-s. Wang, E. Wang, and Q. Niu, First principles calculation of anomalous hall conductivity in ferromagnetic bcc fe, Phys. Rev. Lett.92, 037204 (2004)

    2004

  45. [52]

    L. Li, J. Cao, C. Cui, Z.-M. Yu, and Y. Yao, Planar hall effect in topological weyl and nodal-line semimetals, Phys. Rev. B108, 085120 (2023)

    2023

  46. [53]

    L. Li, C. Cui, R.-W. Zhang, Z.-M. Yu, and Y. Yao, Pla- nar hall plateau in magnetic weyl semimetals, Science Bulletin70, 187 (2025)

    2025

  47. [54]

    N. W. Ashcroft and N. D. Mermin,Solid state physics (Holt, Rinehart and Winston, 1976)

    1976

  48. [55]

    V. M. Edelstein, Spin polarization of conduction elec- trons induced by electric current in two-dimensional asymmetric electron systems, Solid State Communica- tions73, 233 (1990)

    1990

  49. [57]

    X.-J. Luo, D. Li, R.-C. Xiao, D.-F. Shao, L. Li, M. Tian, and Y. Yao, Unconventional magnetism: Symmetry clas- sification, hybrid-parity and unconstrained-parity classes (2026), arXiv:2605.21336 [cond-mat.mtrl-sci]

    2026 arXiv

  50. [58]

    Pan and J

    W. Pan and J. Fabian, Tunable edelstein effect in the intrinsic two-dimensional ferroelectric metal PtBi2, Phys. Rev. B113, 165140 (2026)

    2026

  51. [59]

    Sinova, S

    J. Sinova, S. O. Valenzuela, J. Wunderlich, C. H. Back, and T. Jungwirth, Spin hall effects, Rev. Mod. Phys.87, 1213 (2015)

    2015

  52. [60]

    Sinova, D

    J. Sinova, D. Culcer, Q. Niu, N. A. Sinitsyn, T. Jung- wirth, and A. H. MacDonald, Universal intrinsic spin hall effect, Phys. Rev. Lett.92, 126603 (2004)

    2004

  53. [61]

    G. Y. Guo, Y. Yao, and Q. Niu, Ab initio calculation of the intrinsic spin hall effect in semiconductors, Phys. Rev. Lett.94, 226601 (2005)

    2005

  54. [62]

    Yao and Z

    Y. Yao and Z. Fang, Sign changes of intrinsic spin hall effect in semiconductors and simple metals: First- principles calculations, Phys. Rev. Lett.95, 156601 (2005)

    2005

  55. [63]

    G. Y. Guo, S. Murakami, T.-W. Chen, and N. Nagaosa, Intrinsic spin hall effect in platinum: First-principles cal- culations, Phys. Rev. Lett.100, 096401 (2008)

    2008

  56. [64]

    W. Feng, Y. Yao, W. Zhu, J. Zhou, W. Yao, and D. Xiao, Intrinsic spin hall effect in monolayers of group- vi dichalcogenides: A first-principles study, Phys. Rev. B 86, 165108 (2012)

    2012

  57. [65]

    S. M. Farzaneh and S. Rakheja, Intrinsic spin hall effect in topological insulators: A first-principles study, Phys. Rev. Mater.4, 114202 (2020)

    2020

  58. [66]

    Pei, R.-W

    F. Pei, R.-W. Zhang, L. Li, D. Li, and Y. Yao, Switchable giant spin injection current in janus altermagnet fe2sseo (2025), arXiv:2512.17315 [cond-mat.mtrl-sci]

    2025

  59. [67]

    Salemi and P

    L. Salemi and P. M. Oppeneer, Theory of magnetic spin and orbital hall and nernst effects in bulk ferromagnets, Phys. Rev. B106, 024410 (2022)

    2022

  60. [68]

    Kimata, H

    M. Kimata, H. Chen, K. Kondou, S. Sugimoto, P. K. Muduli, M. Ikhlas, Y. Omori, T. Tomita, A. H. Mac- Donald, S. Nakatsuji,et al., Magnetic and magnetic in- verse spin hall effects in a non-collinear antiferromagnet, Nature565, 627 (2019)

    2019

  61. [69]

    Freimuth, S

    F. Freimuth, S. Blügel, and Y. Mokrousov, Spin-orbit torques in co/pt(111) and mn/w(001) magnetic bilayers from first principles, Phys. Rev. B90, 174423 (2014)

    2014

  62. [70]

    Gradhand, D

    M. Gradhand, D. V. Fedorov, P. Zahn, and I. Mertig, Extrinsic spin hall effect from first principles, Phys. Rev. Lett.104, 186403 (2010)

    2010

  63. [71]

    H.-Y. Ma, M. Hu, N. Li, J. Liu, W. Yao, J.-F. Jia, and J. Liu, Multifunctional antiferromagnetic materials with giant piezomagnetism and noncollinear spin current, Na- ture communications12, 2846 (2021)

    2021

  64. [72]

    González-Hernández, L

    R. González-Hernández, L. Šmejkal, K. Výborný, Y. Ya- hagi, J. Sinova, T. c. v. Jungwirth, and J. Železný, Efficient electrical spin splitter based on nonrelativis- tic collinear antiferromagnetism, Phys. Rev. Lett.126, 127701 (2021)

    2021

  65. [73]

    Železný, Y

    J. Železný, Y. Zhang, C. Felser, and B. Yan, Spin- polarized current in noncollinear antiferromagnets, Phys. Rev. Lett.119, 187204 (2017)

    2017

  66. [74]

    A. Roy, M. H. D. Guimarães, and J. Sławińska, Uncon- ventional spin hall effects in nonmagnetic solids, Phys. 11 Rev. Mater.6, 045004 (2022)

    2022

  67. [75]

    F. Li, X. Liu, V. Chaudhary, R. Xie, C. Shen, H. Wang, and H. Zhang, High-throughput screening of spin hall conductivity in two-dimensional materials, Nano Letters 26, 2289 (2026)

    2026

  68. [76]

    J. Zhou, S. Poncé, and J.-C. Charlier, High-throughput calculations of spin hall conductivity in non-magnetic 2d materials, npj 2D Materials and Applications9, 39 (2025)

    2025

  69. [77]

    L. Liu, T. Moriyama, D. C. Ralph, and R. A. Buhrman, Spin-torque ferromagnetic resonance induced by the spin hall effect, Phys. Rev. Lett.106, 036601 (2011)

    2011

  70. [78]

    Sodemann and L

    I. Sodemann and L. Fu, Quantum nonlinear hall effect induced by berry curvature dipole in time-reversal in- variant materials, Phys. Rev. Lett.115, 216806 (2015)

    2015

  71. [79]

    Zhang and L

    Y. Zhang and L. Fu, Terahertz detection based on nonlin- ear hall effect without magnetic field, Proceedings of the National Academy of Sciences118, e2100736118 (2021)

    2021

  72. [80]

    Du, H.-Z

    Z. Du, H.-Z. Lu, and X. Xie, Nonlinear hall effects, Na- ture Reviews Physics3, 744 (2021)

    2021

  73. [81]

    R. W. Boyd,Nonlinear Optics, 4th ed. (Academic Press, 2020)

    2020

  74. [82]

    Ratnesh, A

    R. Ratnesh, A. Goel, G. Kaushik, H. Garg, Chandan, M. Singh, and B. Prasad, Advancement and challenges in mosfet scaling, Materials Science in Semiconductor Pro- cessing134, 106002 (2021)

    2021

  75. [83]

    Ziese, Extrinsic magnetotransport phenomena in fer- romagnetic oxides, Reports on Progress in Physics65, 143 (2002)

    M. Ziese, Extrinsic magnetotransport phenomena in fer- romagnetic oxides, Reports on Progress in Physics65, 143 (2002)

    2002

  76. [84]

    Klein, Y

    L. Klein, Y. Kats, A. F. Marshall, J. W. Reiner, T. H. Geballe, M. R. Beasley, and A. Kapitulnik, Domain wall resistivity insrruo 3, Phys. Rev. Lett.84, 6090 (2000)

    2000

  77. [85]

    P. M. Levy and S. Zhang, Resistivity due to domain wall scattering, Phys. Rev. Lett.79, 5110 (1997)

    1997

  78. [86]

    Vásquez-Mansilla, M

    B.Pianciola, S.Flewett, E.DeBiasi, C.Hepburn, L.Lou- nis, M. Vásquez-Mansilla, M. Granada, M. Barturen, M. Eddrief, M. Sacchi, M. Marangolo, and J. Milano, Magnetoresistance infe 0.8ga0.2 thin films with magnetic stripes: Theroleofthethree-dimensionalmagneticstruc- ture, Phys....

    2020

  79. [87]

    Orfila, D

    G. Orfila, D. Sanchez-Manzano, A. Arora, F. Cuellar, S. Ruiz-Gómez, S. Rodriguez-Corvillo, S. López, A. Per- alta, S. J. Carreira, F. Gallego,et al., Large magne- toresistance of isolated domain walls in la2/3sr1/3mno3 nanowires, Advanced Materials35, 2211176 (2023)

    2023

  80. [88]

    C. Liu, P. Lu, Z. Gu, J. Yang, and Y. Chen, Bidirectional tuning of thermal conductivity in ferroelectric materials using e-controlled hysteresis characteristic property, The Journal of Physical Chemistry C124, 26144 (2020)

    2020

  81. [89]

    Langenberg, D

    E. Langenberg, D. Saha, M. E. Holtz, J.-J. Wang, D. Bugallo, E. Ferreiro-Vila, H. Paik, I. Hanke, S. Gan- schow, D. A. Muller,et al., Ferroelectric domain walls in PbTiO3 are effective regulators of heat flow at room temperature, Nano Lett.19, 7901 (2019)

    2019

  82. [90]

    J.-J. Wang, Y. Wang, J. F. Ihlefeld, P. E. Hopkins, and L.-Q. Chen, Tunable thermal conductivity via domain structure engineering in ferroelectric thin films: A phase- field simulation, Acta Mater.111, 220 (2016)

    2016

  83. [91]

    J. F. Ihlefeld, B. M. Foley, D. A. Scrymgeour, J. R. Michael, B. B. McKenzie, D. L. Medlin, M. Wal- lace, S. Trolier-McKinstry, and P. E. Hopkins, Room- temperature voltage tunable phonon thermal conductiv- ity via reconfigurable interfaces in ferroelectric thin films, Nano Le...

    2015

  84. [92]

    Jindal, A

    A. Jindal, A. Saha, Z. Li, T. Taniguchi, K. Watanabe, J. C. Hone, T. Birol, R. M. Fernandes, C. R. Dean, A. N. Pasupathy,et al., Coupled ferroelectricity and supercon- ductivity in bilayer td-mote2, Nature613, 48 (2023)

    2023

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