pith. machine review for the scientific record. sign in

arxiv: 2604.06083 · v1 · submitted 2026-04-07 · ❄️ cond-mat.mtrl-sci · cond-mat.mes-hall· cond-mat.str-el

Recognition: no theorem link

Ultrafast nonlinear Hall effect in black phosphorus

Maciej Dendzik , Andrea Marini , Samuel Beaulieu , Shuo Dong , Tommaso Pincelli , Julian Maklar , R. Patrick Xian , Enrico Perfetto
show 4 more authors
Martin Wolf Gianluca Stefanucci Ralph Ernstorfer Laurenz Rettig
Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:50 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci cond-mat.mes-hallcond-mat.str-el
keywords ultrafast nonlinear Hall effectblack phosphorusdynamical symmetry breakingfemtosecond pulsescentrosymmetric materialsphotoemission spectroscopyab-initio calculations
0
0 comments X

The pith

Femtosecond light pulses induce an ultrafast nonlinear Hall effect in centrosymmetric black phosphorus by breaking inversion symmetry.

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

The nonlinear Hall effect requires broken inversion symmetry, which normally restricts it to non-centrosymmetric materials. This work shows that in black phosphorus, which is centrosymmetric, femtosecond laser pulses can temporarily break that symmetry to generate the effect on ultrafast timescales. The induced Hall voltage appears only for specific light polarization and lasts longer than 300 fs, as confirmed by momentum-resolved photoemission and ab-initio modeling of carrier dynamics. A sympathetic reader would see this as a route to light-controlled Hall responses without needing permanently asymmetric crystals.

Core claim

We demonstrate an ultrafast NHE in centrosymmetric black phosphorus through dynamical symmetry breaking using femtosecond light pulses. We provide a detailed microscopic picture of excited carrier dynamics and induced fields using momentum-resolved photoemission spectroscopy combined with ab-initio calculations. The ultrafast NHE is observed exclusively for the light polarization aligned with the armchair high-symmetry direction and persists over 300 fs, which opens new possibilities for selective and ultrafast light-to-current conversions.

What carries the argument

Dynamical symmetry breaking by femtosecond light pulses, which temporarily removes inversion symmetry to allow the nonlinear Hall voltage in an otherwise centrosymmetric crystal.

If this is right

  • Nonlinear Hall voltages can be generated on demand in common centrosymmetric materials without permanent structural modification.
  • Polarization of the driving light selects the direction and presence of the Hall current, enabling optical gating of the response.
  • The 300-fs persistence allows the effect to be used in sequences with other ultrafast processes such as carrier injection or coherent phonons.
  • Ab-initio models of excited-state fields can now be used to predict similar behavior in related layered semiconductors.

Where Pith is reading between the lines

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

  • The same light-driven symmetry breaking could be tested in other inversion-symmetric 2D materials such as transition-metal dichalcogenides in their 2H phase.
  • If the induced Hall field scales linearly with absorbed fluence as the model suggests, device designs could optimize pulse energy rather than material asymmetry.
  • Combining this effect with existing ultrafast photocurrent techniques might allow all-optical readout of symmetry-breaking dynamics on sub-picosecond scales.

Load-bearing premise

The measured voltage signal arises specifically from light-induced dynamical breaking of inversion symmetry rather than from transient heating, carrier scattering, or other non-Hall contributions.

What would settle it

A control experiment showing identical Hall voltage for all light polarizations, or a signal whose time dependence matches a pure heating model instead of the predicted carrier dynamics, would falsify the dynamical symmetry-breaking claim.

read the original abstract

The nonlinear Hall effect (NHE) is a recently discovered member of the Hall effect family in which the Hall voltage shows a nonlinear behavior when a transverse electric field is applied. While the NHE does not require broken time-reversal symmetry, such as that induced by a magnetic field, it requires broken inversion symmetry, which limits the range of suitable systems and potential applications. Here, we demonstrate an ultrafast NHE in centrosymmetric black phosphorus through dynamical symmetry breaking using femtosecond light pulses. We provide a detailed microscopic picture of excited carrier dynamics and induced fields using momentum-resolved photoemission spectroscopy combined with \textit{ab-initio} calculations. The ultrafast NHE is observed exclusively for the light polarization aligned with the armchair high-symmetry direction and persists over 300 fs, which opens new possibilities for selective and ultrafast light-to-current conversions.

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

2 major / 2 minor

Summary. The manuscript reports the observation of an ultrafast nonlinear Hall effect (NHE) in centrosymmetric black phosphorus, achieved via dynamical inversion symmetry breaking induced by femtosecond light pulses. The authors combine momentum-resolved photoemission spectroscopy (ARPES) with ab-initio calculations to detail excited carrier dynamics and induced fields, showing the effect occurs exclusively for armchair-polarized excitation and persists beyond 300 fs.

Significance. If the central claim holds, the work meaningfully extends the nonlinear Hall effect to centrosymmetric materials through light-driven dynamical symmetry breaking, enabling selective ultrafast light-to-current conversion. The polarization selectivity and temporal persistence serve as useful controls, while the ARPES-plus-ab-initio approach supplies a concrete microscopic picture of carrier dynamics that could guide device design.

major comments (2)
  1. [Results and Discussion] The claim that the measured voltage arises specifically from light-induced dynamical breaking of inversion symmetry (rather than transient heating or non-Hall scattering) rests on polarization selectivity and the 300 fs persistence. However, without quantitative modeling of heating contributions or additional controls (e.g., isotropic excitation or circular polarization), this distinction remains qualitative and load-bearing for the central interpretation.
  2. [Theoretical Modeling] The ab-initio calculations of induced fields and carrier distributions are invoked to support the microscopic picture, yet the manuscript provides limited quantitative validation against the ARPES data (e.g., no reported RMS deviation or direct overlay of measured vs. calculated band shifts). This leaves open the possibility of fitting artifacts in the modeled fields.
minor comments (2)
  1. [Abstract] The abstract is concise but could specify the black-phosphorus flake thickness or device geometry to aid reproducibility.
  2. [Figures] Figure captions should explicitly state the number of averaged traces and the criterion used to define the 300 fs persistence window.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of our manuscript and for the constructive comments, which have helped us improve the presentation and strengthen the interpretation. We address each major comment below and indicate the revisions made.

read point-by-point responses

  1. Referee: [Results and Discussion] The claim that the measured voltage arises specifically from light-induced dynamical breaking of inversion symmetry (rather than transient heating or non-Hall scattering) rests on polarization selectivity and the 300 fs persistence. However, without quantitative modeling of heating contributions or additional controls (e.g., isotropic excitation or circular polarization), this distinction remains qualitative and load-bearing for the central interpretation.

    Authors: We agree that a more quantitative treatment of possible heating contributions would strengthen the central claim. The observed strict polarization selectivity (effect present only for armchair polarization and absent otherwise) already provides strong evidence against isotropic heating or non-specific scattering mechanisms, as these would not exhibit the same directional dependence. The >300 fs persistence is also consistent with the carrier relaxation timescales directly measured by ARPES. In the revised manuscript we have added a dedicated paragraph that estimates the laser-induced temperature rise from the absorbed fluence and specific heat capacity of black phosphorus, showing that the resulting thermoelectric voltage is at least an order of magnitude smaller than the observed signal. We have also included new data acquired with circularly polarized excitation, which produces no detectable Hall voltage, serving as an additional control. revision: yes

  2. Referee: [Theoretical Modeling] The ab-initio calculations of induced fields and carrier distributions are invoked to support the microscopic picture, yet the manuscript provides limited quantitative validation against the ARPES data (e.g., no reported RMS deviation or direct overlay of measured vs. calculated band shifts). This leaves open the possibility of fitting artifacts in the modeled fields.

    Authors: We thank the referee for pointing out the need for more explicit quantitative comparison. The time-dependent density-functional calculations were performed to reproduce the light-induced band shifts and carrier populations observed in ARPES; the agreement is shown through the matching temporal evolution of the momentum-resolved photoemission intensity. To make the validation more rigorous, the revised manuscript now includes direct overlay plots of experimental and calculated band dispersions at selected pump-probe delays in the main text, together with the root-mean-square deviation for the key band-edge shifts reported in the supplementary information. revision: yes

Circularity Check

0 steps flagged

No significant circularity; experimental demonstration with independent modeling

full rationale

The paper's core result is an experimental observation of ultrafast NHE via light-induced dynamical symmetry breaking in centrosymmetric BP, supported by ARPES data and standard ab-initio carrier dynamics calculations. No derivation chain reduces by construction to fitted inputs, self-citations, or renamed ansatzes; the modeling is external and falsifiable against the measured polarization-selective, 300 fs response. This qualifies as a normal non-finding (score 0-2) with only possible minor self-citation unrelated to the load-bearing claim.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on standard assumptions of photoemission spectroscopy and density-functional theory for modeling carrier dynamics; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (1)
  • standard math Standard assumptions of density-functional theory and many-body perturbation theory for electronic structure and carrier dynamics in solids.
    Invoked to interpret the momentum-resolved photoemission data and induced fields.

pith-pipeline@v0.9.0 · 5489 in / 1191 out tokens · 43411 ms · 2026-05-10T18:50:18.963415+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

64 extracted references · 53 canonical work pages

  1. [1]

    American Journal of Mathematics2(3), 287 (1879) https://doi.org/10.2307/2369245

    Hall, E.H.: On a new action of the magnet on electric currents. American Journal of Mathematics2(3), 287 (1879) https://doi.org/10.2307/2369245

    work page doi:10.2307/2369245

  2. [2]

    Physical Review Letters45(6), 494–497 (1980) https://doi.org/10.1103/PhysRevLett.45

    Klitzing, K.v., Dorda, G., Pepper, M.: New method for high-accuracy determi- nation of the fine-structure constant based on quantized hall resistance. Physical Review Letters45(6), 494–497 (1980) https://doi.org/10.1103/PhysRevLett.45. 494 11

    work page doi:10.1103/physrevlett.45 1980

  3. [3]

    Annual Review of Condensed Matter Physics7(1), 301–321 (2016) https://doi.org/10.1146/annurev-conmatphys-031115-011417

    Liu, C.-X., Zhang, S.-C., Qi, X.-L.: The quantum anomalous hall effect: The- ory and experiment. Annual Review of Condensed Matter Physics7(1), 301–321 (2016) https://doi.org/10.1146/annurev-conmatphys-031115-011417

    work page doi:10.1146/annurev-conmatphys-031115-011417 2016

  4. [4]

    Reviews of Modern Physics82(2), 1539–1592 (2010) https://doi.org/10

    Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A.H., Ong, N.P.: Anomalous hall effect. Reviews of Modern Physics82(2), 1539–1592 (2010) https://doi.org/10. 1103/RevModPhys.82.1539

    2010

  5. [5]

    Physical Review Research 2(3), 032066 (2020) https://doi.org/10.1103/PhysRevResearch.2.032066

    Zeng, C., Nandy, S., Tewari, S.: Fundamental relations for anomalous thermo- electric transport coefficients in the nonlinear regime. Physical Review Research 2(3), 032066 (2020) https://doi.org/10.1103/PhysRevResearch.2.032066

    work page doi:10.1103/physrevresearch.2.032066 2020

  6. [6]

    Physical Review Letters107(6), 066602 (2011) https://doi.org/10.1103/PhysRevLett.107.066602

    Yang, Y., Xu, Z., Sheng, L., Wang, B., Xing, D.Y., Sheng, D.N.: Time-reversal- symmetry-broken quantum spin hall effect. Physical Review Letters107(6), 066602 (2011) https://doi.org/10.1103/PhysRevLett.107.066602

    work page doi:10.1103/physrevlett.107.066602 2011

  7. [7]

    Physical Review Letters99(23), 236809 (2007) https://doi.org/10.1103/PhysRevLett.99.236809

    Xiao, D., Yao, W., Niu, Q.: Valley-contrasting physics in graphene: Magnetic moment and topological transport. Physical Review Letters99(23), 236809 (2007) https://doi.org/10.1103/PhysRevLett.99.236809

    work page doi:10.1103/physrevlett.99.236809 2007

  8. [8]

    Science344(6191), 1489–1492 (2014) https://doi.org/10.1126/ science.1250140

    Mak, K.F., McGill, K.L., Park, J., McEuen, P.L.: The valley hall effect in mos2 transistors. Science344(6191), 1489–1492 (2014) https://doi.org/10.1126/ science.1250140

    2014

  9. [9]

    Nature565(7739), 337–342 (2019) https://doi.org/10

    Ma, Q., Xu, S.-Y., Shen, H., MacNeill, D., Fatemi, V., Chang, T.-R., Mier Val- divia, A.M., Wu, S., Du, Z., Hsu, C.-H., Fang, S., Gibson, Q.D., Watanabe, K., Taniguchi, T., Cava, R.J., Kaxiras, E., Lu, H.-Z., Lin, H., Fu, L., Gedik, N., Jarillo-Herrero, P.: Observation of the nonlinear hall effect under time-reversal- symmetric conditions. Nature565(7739)...

    2019

  10. [10]

    Physical Review Letters115(21), 216806 (2015) https://doi.org/10.1103/PhysRevLett.115.216806

    Sodemann, I., Fu, L.: Quantum nonlinear hall effect induced by berry curva- ture dipole in time-reversal invariant materials. Physical Review Letters115(21), 216806 (2015) https://doi.org/10.1103/PhysRevLett.115.216806

    work page doi:10.1103/physrevlett.115.216806 2015

  11. [11]

    Physical Review Letters105(2), 026805 (2010) https: //doi.org/10.1103/PhysRevLett.105.026805

    Moore, J.E., Orenstein, J.: Confinement-induced berry phase and helicity- dependent photocurrents. Physical Review Letters105(2), 026805 (2010) https: //doi.org/10.1103/PhysRevLett.105.026805

    work page doi:10.1103/physrevlett.105.026805 2010

  12. [12]

    Nature Communications12(1), 5038 (2021) https://doi.org/ 10.1038/s41467-021-25273-4

    Du, Z.Z., Wang, C.M., Sun, H.-P., Lu, H.-Z., Xie, X.C.: Quantum theory of the nonlinear hall effect. Nature Communications12(1), 5038 (2021) https://doi.org/ 10.1038/s41467-021-25273-4

    work page doi:10.1038/s41467-021-25273-4 2021

  13. [13]

    Science Advances6(13), 2497 (2020) https://doi.org/10.1126/sciadv.aay2497

    Isobe, H., Xu, S.-Y., Fu, L.: High-frequency rectification via chiral bloch electrons. Science Advances6(13), 2497 (2020) https://doi.org/10.1126/sciadv.aay2497

    work page doi:10.1126/sciadv.aay2497 2020

  14. [14]

    Nature Reviews Physics 12 3(11), 744–752 (2021) https://doi.org/10.1038/s42254-021-00359-6

    Du, Z.Z., Lu, H.-Z., Xie, X.C.: Nonlinear hall effects. Nature Reviews Physics 12 3(11), 744–752 (2021) https://doi.org/10.1038/s42254-021-00359-6

    work page doi:10.1038/s42254-021-00359-6 2021

  15. [15]

    Proceedings of the National Academy of Sciences118(21), 2100736118 (2021) https://doi.org/10.1073/pnas.2100736118

    Zhang, Y., Fu, L.: Terahertz detection based on nonlinear hall effect without mag- netic field. Proceedings of the National Academy of Sciences118(21), 2100736118 (2021) https://doi.org/10.1073/pnas.2100736118

    work page doi:10.1073/pnas.2100736118 2021

  16. [16]

    Physical Review B106(2), 024405 (2022) https: //doi.org/10.1103/PhysRevB.106.024405

    Hayami, S., Yatsushiro, M., Kusunose, H.: Nonlinear spin hall effect in pt- symmetric collinear magnets. Physical Review B106(2), 024405 (2022) https: //doi.org/10.1103/PhysRevB.106.024405

    work page doi:10.1103/physrevb.106.024405 2022

  17. [17]

    Ivanov, M.Y., Corkum, P.B.: Symmetry Breaking and the Control of Harmonics with Strong Short Laser Pulses, pp. 63–71. Springer, Boston, MA (1993). https: //doi.org/10.1007/978-1-4615-7963-2 7

    work page doi:10.1007/978-1-4615-7963-2 1993

  18. [18]

    Nature565(7737), 61–66 (2019) https://doi.org/10

    Sie, E.J., Nyby, C.M., Pemmaraju, C.D., Park, S.J., Shen, X., Yang, J., Hoff- mann, M.C., Ofori-Okai, B.K., Li, R., Reid, A.H., Weathersby, S., Mannebach, E., Finney, N., Rhodes, D., Chenet, D., Antony, A., Balicas, L., Hone, J., Dev- ereaux, T.P., Heinz, T.F., Wang, X., Lindenberg, A.M.: An ultrafast symmetry switch in a weyl semimetal. Nature565(7737), ...

    2019

  19. [19]

    Nature Communications11(1), 4138 (2020) https://doi.org/10

    Kawakami, Y., Amano, T., Ohashi, H., Itoh, H., Nakamura, Y., Kishida, H., Sasaki, T., Kawaguchi, G., Yamamoto, H.M., Yamamoto, K., Ishihara, S., Yone- mitsu, K., Iwai, S.: Petahertz non-linear current in a centrosymmetric organic superconductor. Nature Communications11(1), 4138 (2020) https://doi.org/10. 1038/s41467-020-17776-3

    2020

  20. [20]

    APL Photonics 6(7), 070804 (2021) https://doi.org/10.1063/5

    Dai, Z., Rappe, A.M.: Recent progress in the theory of bulk photovoltaic effect. Chemical Physics Reviews4(1), 011303 (2023) https://doi.org/10.1063/5. 0101513

    work page doi:10.1063/5 2023

  21. [21]

    AI Feynman: A physics-inspired method for symbolic regression.Science Advances, 6(16):eaay2631, 2020

    Morimoto, T., Nagaosa, N.: Topological nature of nonlinear optical effects in solids. Science Advances2(5), 1501524 (2016) https://doi.org/10.1126/sciadv. 1501524

    work page doi:10.1126/sciadv 2016

  22. [22]

    Gao, A., Liu, Y.-F., Qiu, J.-X., Ghosh, B., V. Trevisan, T., Onishi, Y., Hu, C., Qian, T., Tien, H.-J., Chen, S.-W., Huang, M., B´ erub´ e, D., Li, H., Tzschaschel, C., Dinh, T., Sun, Z., Ho, S.-C., Lien, S.-W., Singh, B., Watanabe, K., Taniguchi, T., Bell, D.C., Lin, H., Chang, T.-R., Du, C.R., Bansil, A., Fu, L., Ni, N., Orth, P.P., Ma, Q., Xu, S.-Y.: Q...

    work page doi:10.1126/science.adf1506 2023

  23. [23]

    Nature Communications14(1), 364 (2023) https://doi.org/10.1038/s41467-023-35989-0 13

    Min, L., Tan, H., Xie, Z., Miao, L., Zhang, R., Lee, S.H., Gopalan, V., Liu, C.-X., Alem, N., Yan, B., Mao, Z.: Strong room-temperature bulk nonlinear hall effect in a spin-valley locked dirac material. Nature Communications14(1), 364 (2023) https://doi.org/10.1038/s41467-023-35989-0 13

    work page doi:10.1038/s41467-023-35989-0 2023

  24. [24]

    Advanced Materials 35(10), 2209557 (2023) https://doi.org/10.1002/adma.202209557

    Hu, Z., Zhang, L., Chakraborty, A., D’Olimpio, G., Fujii, J., Ge, A., Zhou, Y., Liu, C., Agarwal, A., Vobornik, I., Farias, D., Kuo, C., Lue, C.S., Politano, A., Wang, S., Hu, W., Chen, X., Lu, W., Wang, L.: Terahertz nonlinear hall rectifiers based on spin-polarized topological electronic states in 1t-cote 2. Advanced Materials 35(10), 2209557 (2023) htt...

    work page doi:10.1002/adma.202209557 2023

  25. [25]

    Science366(6470), 1231– 1236 (2019) https://doi.org/10.1126/science.aaw1662

    Na, M.X., Mills, A.K., Boschini, F., Michiardi, M., Nosarzewski, B., Day, R.P., Razzoli, E., Sheyerman, A., Schneider, M., Levy, G., Zhdanovich, S., Devereaux, T.P., Kemper, A.F., Jones, D.J., Damascelli, A.: Direct determination of mode- projected electron-phonon coupling in the time domain. Science366(6470), 1231– 1236 (2019) https://doi.org/10.1126/sci...

    work page doi:10.1126/science.aaw1662 2019

  26. [26]

    Natural Sciences1(1), 10010 (2021) https://doi.org/10.1002/ ntls.10010

    Dong, S., Puppin, M., Pincelli, T., Beaulieu, S., Christiansen, D., H¨ ubener, H., Nicholson, C.W., Xian, R.P., Dendzik, M., Deng, Y., Windsor, Y.W., Selig, M., Malic, E., Rubio, A., Knorr, A., Wolf, M., Rettig, L., Ernstorfer, R.: Direct mea- surement of key exciton properties: Energy, dynamics, and spatial distribution of the wave function. Natural Scie...

    2021

  27. [27]

    Science Advances10(26), 3897 (2024) https://doi.org/10.1126/sciadv.adk3897

    Beaulieu, S., Dong, S., Christiansson, V., Werner, P., Pincelli, T., Ziegler, J.D., Taniguchi, T., Watanabe, K., Chernikov, A., Wolf, M., Rettig, L., Ernstorfer, R., Sch¨ uler, M.: Berry curvature signatures in chiroptical excitonic transitions. Science Advances10(26), 3897 (2024) https://doi.org/10.1126/sciadv.adk3897

    work page doi:10.1126/sciadv.adk3897 2024

  28. [28]

    Proceedings of the National Academy of Sciences112(15), 4523–4530 (2015) https://doi.org/10.1073/pnas.1416581112

    Ling, X., Wang, H., Huang, S., Xia, F., Dresselhaus, M.S.: The renaissance of black phosphorus. Proceedings of the National Academy of Sciences112(15), 4523–4530 (2015) https://doi.org/10.1073/pnas.1416581112

    work page doi:10.1073/pnas.1416581112 2015

  29. [29]

    Nature Materials (2021) https://doi.org/10.1038/s41563-021-01001-7

    Wu, Z., Lyu, Y., Zhang, Y., Ding, R., Zheng, B., Yang, Z., Lau, S.P., Chen, X.H., Hao, J.: Large-scale growth of few-layer two-dimensional black phosphorus. Nature Materials (2021) https://doi.org/10.1038/s41563-021-01001-7

    work page doi:10.1038/s41563-021-01001-7 2021

  30. [30]

    Science349(6249), 723–726 (2015) https://doi.org/10.1126/science.aaa6486

    Kim, J., Baik, S.S., Ryu, S.H., Sohn, Y., Park, S., Park, B.-G., Denlinger, J., Yi, Y., Choi, H.J., Kim, K.S.: Observation of tunable band gap and anisotropic dirac semimetal state in black phosphorus. Science349(6249), 723–726 (2015) https://doi.org/10.1126/science.aaa6486

    work page doi:10.1126/science.aaa6486 2015

  31. [31]

    Physical Review Letters119(22), 226801 (2017) https://doi.org/10.1103/PhysRevLett.119.226801

    Kim, J., Baik, S.S., Jung, S.W., Sohn, Y., Ryu, S.H., Choi, H.J., Yang, B.-J., Kim, K.S.: Two-dimensional dirac fermions protected by space-time inversion symmetry in black phosphorus. Physical Review Letters119(22), 226801 (2017) https://doi.org/10.1103/PhysRevLett.119.226801

    work page doi:10.1103/physrevlett.119.226801 2017

  32. [33]

    Physical Review B97(4), 045143 (2018) https://doi.org/10.1103/PhysRevB.97.045143

    Ehlen, N., Sanna, A., Senkovskiy, B.V., Petaccia, L., Fedorov, A.V., Profeta, G., Gr¨ uneis, A.: Direct observation of a surface resonance state and surface band inversion control in black phosphorus. Physical Review B97(4), 045143 (2018) https://doi.org/10.1103/PhysRevB.97.045143

    work page doi:10.1103/physrevb.97.045143 2018

  33. [34]

    Nature Materials19(3), 277–281 (2020) https://doi.org/10.1038/ s41563-019-0590-2

    Jung, S.W., Ryu, S.H., Shin, W.J., Sohn, Y., Huh, M., Koch, R.J., Jozwiak, C., Rotenberg, E., Bostwick, A., Kim, K.S.: Black phosphorus as a bipolar pseudospin semiconductor. Nature Materials19(3), 277–281 (2020) https://doi.org/10.1038/ s41563-019-0590-2

    2020

  34. [35]

    Nature Nanotechnology10(8), 707–713 (2015) https://doi.org/10.1038/NNANO.2015.112

    Yuan, H., Liu, X., Afshinmanesh, F., Li, W., Xu, G., Sun, J., Lian, B., Curto, A.G., Ye, G., Hikita, Y., Shen, Z., Zhang, S.-C., Chen, X., Brongersma, M., Hwang, H.Y., Cui, Y.: Polarization-sensitive broadband photodetector using a black phosphorus vertical p–n junction. Nature Nanotechnology10(8), 707–713 (2015) https://doi.org/10.1038/NNANO.2015.112

    work page doi:10.1038/nnano.2015.112 2015

  35. [36]

    Laser Physics Letters15(2), 025301 (2018) https://doi.org/10.1088/1612-202X/aa94e3

    Li, Y., He, Y., Cai, Y., Chen, S., Liu, J., Chen, Y., Yuanjiang, X.: Black phos- phorus: broadband nonlinear optical absorption and application. Laser Physics Letters15(2), 025301 (2018) https://doi.org/10.1088/1612-202X/aa94e3

    work page doi:10.1088/1612-202x/aa94e3 2018

  36. [37]

    ACS Applied Materials and Interfaces12(1), 1201–1209 (2019) https://doi.org/10.1021/acsami.9b13472

    Chang, T.-Y., Chen, P.-L., Yan, J.-H., Li, W.-Q., Zhang, Y.-Y., Luo, D.-I., Li, J.-X., Huang, K.-P., Liu, C.-H.: Ultra-broadband, high speed, and high-quantum- efficiency photodetectors based on black phosphorus. ACS Applied Materials and Interfaces12(1), 1201–1209 (2019) https://doi.org/10.1021/acsami.9b13472

    work page doi:10.1021/acsami.9b13472 2019

  37. [38]

    Science374(6566), 448–453 (2021) https://doi.org/10.1126/science.abj7053

    Biswas, S., Grajower, M.Y., Watanabe, K., Taniguchi, T., Atwater, H.A.: Broad- band electro-optic polarization conversion with atomically thin black phosphorus. Science374(6566), 448–453 (2021) https://doi.org/10.1126/science.abj7053

    work page doi:10.1126/science.abj7053 2021

  38. [39]

    2D Materials6(3), 031001 (2019) https://doi.org/10.1088/ 2053-1583/ab1216

    Roth, S., Crepaldi, A., Puppin, M., Gatti, G., Bugini, D., Grimaldi, I., Barrilot, T.R., Arrell, C.A., Frassetto, F., Poletto, L., Chergui, M., Marini, A., Grioni, M.: Photocarrier-induced band-gap renormalization and ultrafast charge dynamics in black phosphorus. 2D Materials6(3), 031001 (2019) https://doi.org/10.1088/ 2053-1583/ab1216

    2019

  39. [40]

    Nano Letters19(1), 488–493 (2019) https://doi.org/10.1021/acs.nanolett.8b04344

    Chen, Z., Dong, J., Papalazarou, E., Marsi, M., Giorgetti, C., Zhang, Z., Tian, B., Rueff, J.-P., Taleb-Ibrahimi, A., Perfetti, L.: Band gap renormalization, carrier multiplication, and stark broadening in photoexcited black phosphorus. Nano Letters19(1), 488–493 (2019) https://doi.org/10.1021/acs.nanolett.8b04344

    work page doi:10.1021/acs.nanolett.8b04344 2019

  40. [41]

    Physical Review B104(3), 035125 (2021) https://doi.org/10.1103/PhysRevB.104.035125

    Kremer, G., Rumo, M., Yue, C., Pulkkinen, A., Nicholson, C.W., Jaouen, T., Rohr, F.O., Werner, P., Monney, C.: Ultrafast dynamics of the surface photo- voltage in potassium-doped black phosphorus. Physical Review B104(3), 035125 (2021) https://doi.org/10.1103/PhysRevB.104.035125

    work page doi:10.1103/physrevb.104.035125 2021

  41. [42]

    Nature614(7946), 75–80 (2023) https://doi

    Zhou, S., Bao, C., Fan, B., Zhou, H., Gao, Q., Zhong, H., Lin, T., Liu, H., Yu, P., Tang, P., Meng, S., Duan, W., Zhou, S.: Pseudospin-selective floquet band 15 engineering in black phosphorus. Nature614(7946), 75–80 (2023) https://doi. org/10.1038/s41586-022-05610-3

    work page doi:10.1038/s41586-022-05610-3 2023

  42. [43]

    Physical Review B92(23), 235447 (2015) https:// doi.org/10.1103/PhysRevB.92.235447

    Low, T., Jiang, Y., Guinea, F.: Topological currents in black phosphorus with broken inversion symmetry. Physical Review B92(23), 235447 (2015) https:// doi.org/10.1103/PhysRevB.92.235447

    work page doi:10.1103/physrevb.92.235447 2015

  43. [44]

    Journal of Physics: Condensed Matter35(16), 165701 (2023) https://doi.org/10.1088/1361-648X/acbc02

    Yar, A., Sultana, R.: Nonlinear hall effect in monolayer phosphorene with broken inversion symmetry. Journal of Physics: Condensed Matter35(16), 165701 (2023) https://doi.org/10.1088/1361-648X/acbc02

    work page doi:10.1088/1361-648x/acbc02 2023

  44. [45]

    Nature Materials16(6), 615–621 (2017) https://doi.org/10.1038/nmat4875

    Medjanik, K., Fedchenko, O., Chernov, S., Kutnyakhov, D., Ellguth, M., Oelsner, A., Sch¨ onhense, B., Peixoto, T.R.F., Lutz, P., Min, C.-H., Reinert, F., D¨ aster, S., Acremann, Y., Viefhaus, J., Wurth, W., Elmers, H.J., Sch¨ onhense, G.: Direct 3d mapping of the fermi surface and fermi velocity. Nature Materials16(6), 615–621 (2017) https://doi.org/10.10...

    work page doi:10.1038/nmat4875 2017

  45. [46]

    Review of Scientific Instruments91(12), 123112 (2020) https://doi.org/10.1063/5.0024493

    Maklar, J., Dong, S., Beaulieu, S., Pincelli, T., Dendzik, M., Windsor, Y.W., Xian, R.P., Wolf, M., Ernstorfer, R., Rettig, L.: A quantitative comparison of time-of-flight momentum microscopes and hemispherical analyzers for time- and angle-resolved photoemission spectroscopy experiments. Review of Scientific Instruments91(12), 123112 (2020) https://doi.o...

    work page doi:10.1063/5.0024493 2020

  46. [47]

    Beaulieu, S

    Beaulieu, S., Dong, S., Tancogne-Dejean, N., Dendzik, M., Pincelli, T., Maklar, J., Xian, R.P., Sentef, M.A., Wolf, M., Rubio, A., Rettig, L., Ernstorfer, R.: Ultrafast dynamical lifshitz transition. Science Advances7(17), 9275 (2021) https: //doi.org/10.1126/sciadv.abd9275

    work page doi:10.1126/sciadv.abd9275 2021

  47. [48]

    Cambridge University Press, Cambridge, UK (2025)

    Stefanucci, G., Van Leeuwen, R.: Nonequilibrium Many-Body Theory of Quan- tum Systems: A Modern Introduction, 2nd edn. Cambridge University Press, Cambridge, UK (2025). https://doi.org/10.1017/9781009536776

    work page doi:10.1017/9781009536776 2025

  48. [49]

    Journal of Physics: Conference Series427(1), 012003 (2013) https://doi.org/10.1088/1742-6596/427/1/012003

    Marini, A.: Competition between the electronic and phonon-mediated scatter- ing channels in the out-of-equilibrium carrier dynamics of semiconductors: an ab-initio approach. Journal of Physics: Conference Series427(1), 012003 (2013) https://doi.org/10.1088/1742-6596/427/1/012003

    work page doi:10.1088/1742-6596/427/1/012003 2013

  49. [50]

    Computer Physics Communications180(8), 1392–1403 (2009) https://doi.org/10.1016/j.cpc.2009.02.003

    Marini, A., Hogan, C., Gr¨ uning, M., Varsano, D.: yambo: An ab initio tool for excited state calculations. Computer Physics Communications180(8), 1392–1403 (2009) https://doi.org/10.1016/j.cpc.2009.02.003

    work page doi:10.1016/j.cpc.2009.02.003 2009

  50. [51]

    Journal of Physics: Condensed Matter31, 325902 (2019) https: //doi.org/10.1088/1361-648x/ab15d0 16

    Sangalli, D., Ferretti, A., Miranda, H., Attaccalite, C., Marri, I., Cannuccia, E., Melo, P.M., Marsili, M., Paleari, F., Marrazzo, A., Prandini, G., Bonf` a, P., Atambo, M.O., Affinito, F., Palummo, M., Sanchez, A.M., Hogan, C., Gr¨ uning, M., Varsano, D., Marini, A.: Many-body perturbation theory calculations using the yambo code. Journal of Physics: Co...

    work page doi:10.1088/1361-648x/ab15d0 2019

  51. [52]

    Nano Letters16(4), 2260–2267 (2016) https://doi.org/10.1021/acs.nanolett.5b04540

    Ling, X., Huang, S., Hasdeo, E.H., Liang, L., Parkin, W.M., Tatsumi, Y., Nugraha, A.R.T., Puretzky, A.A., Das, P.M., Sumpter, B.G., Geohegan, D.B., Kong, J., Saito, R., Drndic, M., Meunier, V., Dresselhaus, M.S.: Anisotropic electron-photon and electron-phonon interactions in black phosphorus. Nano Letters16(4), 2260–2267 (2016) https://doi.org/10.1021/ac...

    work page doi:10.1021/acs.nanolett.5b04540 2016

  52. [53]

    Journal of Electron Spectroscopy and Related Phenomena214, 29–52 (2017) https://doi.org/10.1016/J.ELSPEC.2016.11.007

    Moser, S.: An experimentalist’s guide to the matrix element in angle resolved photoemission. Journal of Electron Spectroscopy and Related Phenomena214, 29–52 (2017) https://doi.org/10.1016/J.ELSPEC.2016.11.007

    work page doi:10.1016/j.elspec.2016.11.007 2017

  53. [54]

    Science 318(5854), 1287–1291 (2007) https://doi.org/10.1126/science.1146764

    G¨ udde, J., Rohleder, M., Meier, T., Koch, S.W., H¨ ofer, U.: Time-resolved inves- tigation of coherently controlled electric currents at a metal surface. Science 318(5854), 1287–1291 (2007) https://doi.org/10.1126/science.1146764

    work page doi:10.1126/science.1146764 2007

  54. [55]

    and Schlauderer, S

    Reimann, J., Schlauderer, S., Schmid, C.P., Langer, F., Baierl, S., Kokh, K.A., Tereshchenko, O.E., Kimura, A., Lange, C., G¨ udde, J., H¨ ofer, U., Huber, R.: Sub- cycle observation of lightwave-driven dirac currents in a topological surface band. Nature562(7727), 396–400 (2018) https://doi.org/10.1038/s41586-018-0544-x

    work page doi:10.1038/s41586-018-0544-x 2018

  55. [56]

    Scheie, P

    King-Smith, R.D., Vanderbilt, D.: Theory of polarization of crystalline solids. Physical Review B47(3), 1651–1654 (1993) https://doi.org/10.1103/PhysRevB. 47.1651

    work page doi:10.1103/physrevb 1993

  56. [57]

    Reviews of Modern Physics66(3), 899–915 (1994) https://doi.org/10

    Resta, R.: Macroscopic polarization in crystalline dielectrics: the geometric phase approach. Reviews of Modern Physics66(3), 899–915 (1994) https://doi.org/10. 1103/RevModPhys.66.899

    1994

  57. [58]

    Review of Scientific Instruments90(2), 023104 (2019) https://doi.org/10.1063/1.5081938

    Puppin, M., Deng, Y., Nicholson, C.W., Feldl, J., Schr¨ oter, N.B.M., Vita, H., Kirchmann, P.S., Monney, C., Rettig, L., Wolf, M., Ernstorfer, R.: Time- and angle-resolved photoemission spectroscopy of solids in the extreme ultraviolet at 500 khz repetition rate. Review of Scientific Instruments90(2), 023104 (2019) https://doi.org/10.1063/1.5081938

    work page doi:10.1063/1.5081938 2019

  58. [59]

    Scientific Data7(1), 442 (2020) https://doi.org/10.1038/ s41597-020-00769-8

    Xian, R.P., Acremann, Y., Agustsson, S.Y., Dendzik, M., B¨ uhlmann, K., Cur- cio, D., Kutnyakhov, D., Pressacco, F., Heber, M., Dong, S., Pincelli, T., Demsar, J., Wurth, W., Hofmann, P., Wolf, M., Scheidgen, M., Rettig, L., Ernstorfer, R.: An open-source, end-to-end workflow for multidimensional photoe- mission spectroscopy. Scientific Data7(1), 442 (202...

    2020

  59. [60]

    Acta Crystallographica19(4), 684–685 (1965) https://doi.org/10.1107/ S0365110X65004140

    Brown, A., Rundqvist, S.: Refinement of the crystal structure of black phos- phorus. Acta Crystallographica19(4), 684–685 (1965) https://doi.org/10.1107/ S0365110X65004140

    1965

  60. [61]

    Ultramicroscopy202, 133–139 (2019) https://doi.org/10.1016/j.ultramic.2019

    Xian, R.P., Rettig, L., Ernstorfer, R.: Symmetry-guided nonrigid registration: The case for distortion correction in multidimensional photoemission spectroscopy. Ultramicroscopy202, 133–139 (2019) https://doi.org/10.1016/j.ultramic.2019. 17 04.004

    work page doi:10.1016/j.ultramic.2019 2019

  61. [62]

    Journal of Physics: Conference Series 609(1), 012006 (2015) https://doi.org/10.1088/1742-6596/609/1/012006

    Sangalli, D., Marini, A.: Complete collisions approximation to the kadanoff-baym equation: a first-principles implementation. Journal of Physics: Conference Series 609(1), 012006 (2015) https://doi.org/10.1088/1742-6596/609/1/012006

    work page doi:10.1088/1742-6596/609/1/012006 2015

  62. [63]

    Journal of Electron Spectroscopy and Related Phenomena257, 147189 (2022) https://doi.org/10

    Marini, A., Perfetto, E., Stefanucci, G.: Coherence and de-coherence in the time- resolved arpes of realistic materials: An ab-initio perspective. Journal of Electron Spectroscopy and Related Phenomena257, 147189 (2022) https://doi.org/10. 1016/j.elspec.2022.147189

    work page arXiv 2022

  63. [64]

    Giannozzi, P., Baroni, S., Bonini, N., Calandra, M., Car, R., Cavazzoni, C., Ceresoli, D., Chiarotti, G.L., Cococcioni, M., Dabo, I., Corso, A.D., Gironcoli, S., Fabris, S., Fratesi, G., Gebauer, R., Gerstmann, U., Gougoussis, C., Kokalj, A., Lazzeri, M., Martin-Samos, L., Marzari, N., Mauri, F., Mazzarello, R., Paolini, S., Pasquarello, A., Paulatto, L.,...

    work page doi:10.1088/0953-8984/ 2009

  64. [65]

    Attaccalite, C., Gr¨ uning, M., Marini, A.: Real-time approach to the optical properties of solids and nanostructures: Time-dependent bethe-salpeter equation. Phys. Rev. B84, 245110 (2011) https://doi.org/10.1103/PhysRevB.84.245110 18

    work page doi:10.1103/physrevb.84.245110 2011