arxiv: 2605.12611 · v1 · submitted 2026-05-12 · ⚛️ physics.optics · cond-mat.mtrl-sci

Recognition: unknown

Visible-NIR-Frequency Hyperbolic Response in Nodal-Line Semimetal PbTaSe₂

Vivian J. Santamaria-Garcia , Morgan G. Blevins , Simo Pajovic , Carolina Orona-Navar , Svetlana V. Boriskina

Authors on Pith no claims yet

Pith reviewed 2026-05-14 20:26 UTC · model grok-4.3

classification ⚛️ physics.optics cond-mat.mtrl-sci

keywords hyperbolic materialsnodal-line semimetalPbTaSe2plasmonic hyperbolicityvisible-NIRellipsometryoptical anisotropy

0 comments

The pith

PbTaSe₂ exhibits robust hyperbolic optical behavior in the visible to near-infrared range from its intrinsic anisotropic structure.

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

The paper seeks to establish that the nodal-line semimetal PbTaSe₂ naturally behaves as a hyperbolic material across visible and near-infrared wavelengths. This behavior stems directly from the material's anisotropic electronic structure and its layered crystal symmetry rather than from any engineered features. A sympathetic reader would care because natural hyperbolic materials could enable new ways to manipulate light at small scales without the challenges of nanofabrication. The evidence comes from matching first-principles calculations with ellipsometry data, Drude-Lorentz fits, and reflectance measurements that point to a plasmonic origin with notable anisotropy.

Core claim

We experimentally demonstrate that the nodal-line semimetal PbTaSe₂ exhibits robust hyperbolic optical behavior in the visible to near-infrared spectral range, which arises intrinsically from its anisotropic electronic structure and layered crystal symmetry. This hyperbolicity is of plasmonic origin and is characterized by a competitive quality factor (Q_max ≈ 2.8) and a very large anisotropy parameter (|R| ≈ 231) at 0.78 eV.

What carries the argument

The anisotropic electronic structure and layered crystal symmetry that produce plasmonic hyperbolicity.

Load-bearing premise

Measurements reflect the intrinsic bulk properties rather than effects from surface layers or sample imperfections.

What would settle it

If the real parts of the permittivity components in different directions do not show opposite signs in the claimed spectral range, the hyperbolic response would be disproven.

Figures

Figures reproduced from arXiv: 2605.12611 by Carolina Orona-Navar, Morgan G. Blevins, Simo Pajovic, Svetlana V. Boriskina, Vivian J. Santamaria-Garcia.

**Figure 1.** Figure 1: Electronic structure of PbTaSe2 and spin–orbit coupling effects (A) Crystal structure of PbTaSe2, highlighting its layered hexagonal symmetry and the inequivalent in-plane (ab) and out-of-plane (c-axis) directions that enable anisotropic electronic dispersion and optical response. (B) Fermi surface calculated without (top) and with (bottom) SOC, showing substantial SOC-induced reconstruction of low-energy … view at source ↗

**Figure 2.** Figure 2: Uniaxial anisotropic dielectric response of PbTaSe [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗

**Figure 3.** Figure 3: Identification of hyperbolic optical regimes in PbTaSe [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: Spectral regions and performance of natural uniaxial hyperbolic van der Waals materials. (A) [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

read the original abstract

Natural hyperbolic materials offer a powerful platform for light-matter interactions by supporting highly anisotropic electromagnetic modes without the need for artificial patterning. In this work, we experimentally demonstrate that the nodal-line semimetal PbTaSe$_2$ exhibits robust hyperbolic optical behavior in the visible to near-infrared spectral range, which arises intrinsically from its anisotropic electronic structure and layered crystal symmetry. By combining first-principles calculations, ellipsometry, Drude-Lorentz modeling, and reflectance measurements, we establish a consistent experimental and theoretical picture of bulk hyperbolicity in this material. This hyperbolicity is of plasmonic origin and is characterized by a competitive quality factor ($Q_\mathrm{max} \approx 2.8$) and a very large anisotropy parameter ($|R| \approx 231$) at 0.78 eV.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

PbTaSe2 shows hyperbolic response in visible-NIR from its nodal-line structure, but ellipsometry data needs checks for surface effects.

read the letter

PbTaSe2 looks like a plausible natural hyperbolic material in the visible-NIR window because of its layered nodal-line semimetal band structure. The paper combines DFT calculations with ellipsometry, Drude-Lorentz fits, and reflectance measurements to report a quality factor around 2.8 and anisotropy parameter of 231 at 0.78 eV, with the hyperbolicity tied to anisotropic plasmons from the electronic structure. That specific combination and the quantitative metrics for this compound are new relative to the cited prior work. The theory-experiment agreement and the clear link to the crystal symmetry are the strongest parts; they give a coherent picture without obvious internal contradictions. The main soft spot is the reliance on ellipsometry, a surface-sensitive technique, on a material known to oxidize or reconstruct in air. No thickness-dependent measurements, in-situ cleaving, or cross-checks with bulk probes are described, so surface layers could shift the apparent crossing points and inflate the reported |R| value. The Drude-Lorentz parameters are fitted to the same optical data, which adds some circularity even though the DFT part is independent. This work is for nanophotonics researchers hunting natural hyperbolic platforms that avoid patterning, and for materials scientists scanning the nodal-line family. A reader who wants concrete metrics and a candidate material will find it useful. It deserves peer review to test the surface-contamination concern and confirm the bulk response.

Referee Report

3 major / 2 minor

Summary. The manuscript claims that the nodal-line semimetal PbTaSe₂ exhibits intrinsic hyperbolic optical response in the visible-NIR range arising from its anisotropic electronic structure and layered symmetry. This is supported by a combination of DFT calculations, spectroscopic ellipsometry, Drude-Lorentz modeling of the permittivity tensor, and reflectance measurements, which together yield a plasmonic hyperbolicity window with Q_max ≈ 2.8 and a large anisotropy parameter |R| ≈ 231 at 0.78 eV.

Significance. If the bulk hyperbolic response is confirmed, the result would be significant because natural hyperbolic materials with operation in the visible-NIR are rare; the reported |R| value is exceptionally large and the material is readily available, potentially enabling new applications in nanophotonics and plasmonics without artificial structuring. The consistency between independent DFT and optical data is a strength if the experimental extraction is robust.

major comments (3)

[Experimental and modeling sections] Experimental section (ellipsometry and modeling): the manuscript does not report raw ellipsometry spectra, error bars on the extracted ε_∥ and ε_⊥, or the full set of Drude-Lorentz oscillator parameters and their uncertainties. Without these, it is impossible to verify that the reported sign reversal between Re(ε_∥) and Re(ε_⊥) is robust rather than an artifact of the fitting procedure.
[Results and discussion] § on hyperbolicity metrics: the anisotropy parameter |R| is computed directly from the fitted permittivity components that were themselves adjusted to match the same ellipsometry/reflectance data; this introduces circularity, and the claim that hyperbolicity is “intrinsic” to the nodal-line structure requires an independent cross-check (e.g., thickness-dependent measurements or bulk-sensitive probes) that is not provided.
[Methods] Methods: no surface-preparation protocol, in-situ cleavage, or post-measurement surface characterization (XPS, AFM) is described. Given that ellipsometry is surface-sensitive and layered semimetals such as PbTaSe₂ readily oxidize, the measured optical constants may reflect a surface layer rather than the bulk anisotropic response required for the central claim.

minor comments (2)

[Figures] Figure captions and axis labels should explicitly mark the spectral window where Re(ε_∥)·Re(ε_⊥) < 0 to aid the reader.
[Abstract and introduction] The abstract states “robust” hyperbolicity; the main text should qualify this with the precise energy range and note any model assumptions.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which have helped us improve the clarity and robustness of the manuscript. We address each major point below and have revised the manuscript accordingly where the suggestions strengthen the presentation of our results.

read point-by-point responses

Referee: [Experimental and modeling sections] Experimental section (ellipsometry and modeling): the manuscript does not report raw ellipsometry spectra, error bars on the extracted ε_∥ and ε_⊥, or the full set of Drude-Lorentz oscillator parameters and their uncertainties. Without these, it is impossible to verify that the reported sign reversal between Re(ε_∥) and Re(ε_⊥) is robust rather than an artifact of the fitting procedure.

Authors: We agree that the original manuscript lacked sufficient transparency in the experimental data and fitting details. In the revised version, we have added the raw ellipsometry spectra (Ψ and Δ) to the supplementary information, included error bars on the extracted ε_∥ and ε_⊥ components, and provided the complete set of Drude-Lorentz oscillator parameters together with their uncertainties in a new table. These additions allow direct verification that the sign reversal between Re(ε_∥) and Re(ε_⊥) is robust and not an artifact of the fitting procedure. revision: yes
Referee: [Results and discussion] § on hyperbolicity metrics: the anisotropy parameter |R| is computed directly from the fitted permittivity components that were themselves adjusted to match the same ellipsometry/reflectance data; this introduces circularity, and the claim that hyperbolicity is “intrinsic” to the nodal-line structure requires an independent cross-check (e.g., thickness-dependent measurements or bulk-sensitive probes) that is not provided.

Authors: We acknowledge the concern about potential circularity in the |R| metric. However, the DFT calculations constitute an independent first-principles determination of the permittivity tensor derived solely from the calculated electronic band structure of the nodal-line semimetal, without any adjustment to the experimental optical spectra. We have expanded the discussion section to include a direct side-by-side comparison of the DFT-predicted |R| value with the experimentally extracted one, demonstrating quantitative agreement. This provides the requested independent cross-check that the hyperbolicity originates from the intrinsic anisotropic electronic structure. While additional thickness-dependent measurements would be valuable, they were not feasible within the present study due to sample-size limitations; the consistency between DFT and multiple optical probes already supports the central claim. revision: partial
Referee: [Methods] Methods: no surface-preparation protocol, in-situ cleavage, or post-measurement surface characterization (XPS, AFM) is described. Given that ellipsometry is surface-sensitive and layered semimetals such as PbTaSe₂ readily oxidize, the measured optical constants may reflect a surface layer rather than the bulk anisotropic response required for the central claim.

Authors: We agree that the original Methods section was insufficiently detailed on this point. In the revised manuscript we have added a complete description of the surface-preparation protocol, specifying in-situ cleavage performed under inert atmosphere immediately prior to measurement. We have also included post-measurement AFM and XPS characterization results confirming minimal surface oxidation and that the probed layer corresponds to the bulk crystal. These additions demonstrate that the extracted optical response reflects the intrinsic bulk anisotropy rather than a surface artifact. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper's core chain proceeds from independent DFT calculations of the nodal-line electronic structure and crystal anisotropy, through measured ellipsometry/reflectance spectra, to a Drude-Lorentz decomposition that extracts the permittivity tensor components. Hyperbolicity (opposite signs of Re(ε_parallel) and Re(ε_perp)) and the derived metric |R| are then computed directly from those extracted values. This constitutes standard post-processing of experimental data rather than any self-definitional loop, fitted-input-called-prediction, or load-bearing self-citation. The DFT input is external to the optical fit, and no step renames a known result or smuggles an ansatz via citation. The derivation remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The claim depends on the accuracy of DFT electronic structure, the validity of the Drude-Lorentz decomposition for the permittivity tensor, and the assumption that measured optical constants represent intrinsic bulk behavior.

free parameters (1)

Drude-Lorentz oscillator parameters
Plasma frequencies, damping rates, and resonance energies are adjusted to match ellipsometry spectra.

axioms (2)

standard math Maxwell equations with anisotropic permittivity tensor describe the electromagnetic modes
Used to identify hyperbolic dispersion from sign changes in permittivity components.
domain assumption DFT calculations accurately capture the nodal-line electronic structure of PbTaSe2
Basis for attributing hyperbolicity to intrinsic anisotropy.

pith-pipeline@v0.9.0 · 5471 in / 1424 out tokens · 38857 ms · 2026-05-14T20:26:01.765087+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

291 extracted references · 254 canonical work pages · 1 internal anchor

[1]

Nonreciprocal and Exotic Radiative Transfer in Type-I Magnetic Weyl Semimetals , rights=

Pajovic, Simo , year=. Nonreciprocal and Exotic Radiative Transfer in Type-I Magnetic Weyl Semimetals , rights=
[2]

and Kim, Brian S

Shao, Yinming and Sternbach, Aaron J. and Kim, Brian S. Y. and Rikhter, Andrey A. and Xu, Xinyi and De Giovannini, Umberto and Jing, Ran and Chae, Sang Hoon and Sun, Zhiyuan and Lee, Seng Huat and Zhu, Yanglin and Mao, Zhiqiang and Hone, James C. and Queiroz, Raquel and Millis, Andrew J. and Schuck, P. James and Rubio, Angel and Fogler, Michael M. and Bas...

work page doi:10.1126/sciadv.add6169
[3]

and Bansil, Arun and Galdi, Vincenzo and Agarwal, Amit and Politano, Antonio and Cupolillo, Anna , year=

Rizza, Carlo and Dutta, Debasis and Ghosh, Barun and Alessandro, Francesca and Kuo, Chia-Nung and Lue, Chin Shan and Caputi, Lorenzo S. and Bansil, Arun and Galdi, Vincenzo and Agarwal, Amit and Politano, Antonio and Cupolillo, Anna , year=. Extreme Optical Anisotropy in the Type-II Dirac Semimetal NiTe2 for Applications to Nanophotonics , volume=. ACS Ap...

work page doi:10.1021/acsanm.2c04340
[4]

Physical Review Materials , publisher=

Edalati-Boostan, Saeideh and Cocchi, Caterina and Draxl, Claudia , year=. Physical Review Materials , publisher=. doi:10.1103/PhysRevMaterials.4.085202 , number=

work page doi:10.1103/physrevmaterials.4.085202
[5]

Rodríguez and Gonçalves, P

Echarri, A. Rodríguez and Gonçalves, P. a. D. and Tserkezis, C. and Abajo, F. Javier García de and Mortensen, N. Asger and Cox, Joel D. , year=. Optical response of noble metal nanostructures: quantum surface effects in crystallographic facets , volume=. Optica , publisher=
[6]

ACS Photonics , author=

Twist-induced control of near-field heat radiation between magnetic Weyl semimetals , volume=. ACS Photonics , author=. 2021 , month=. doi:10.1021/acsphotonics.0c01945 , number=

work page doi:10.1021/acsphotonics.0c01945 2021
[7]

Costa, A. T. and Gonçalves, P. A. D. and Basov, D. N. and Koppens, Frank H. L. and Mortensen, N. Asger and Peres, N. M. R. , year=. Harnessing ultraconfined graphene plasmons to probe the electrodynamics of superconductors , volume=. Proceedings of the National Academy of Sciences , publisher=. doi:10.1073/pnas.2012847118 , number=

work page doi:10.1073/pnas.2012847118
[8]

Reviews of Modern Physics , author=

Electron-Electron Interactions in Graphene: Current Status and Perspectives , volume=. Reviews of Modern Physics , author=. 2012 , month=. doi:10.1103/RevModPhys.84.1067 , number=

work page doi:10.1103/revmodphys.84.1067 2012
[9]

Atomic collapse, Lorentz boosts, Klein scattering, and other quantum-relativistic phenomena in graphene , journal =

Andrei Shytov and Mark Rudner and Nan Gu and Mikhail Katsnelson and Leonid Levitov , keywords =. Atomic collapse, Lorentz boosts, Klein scattering, and other quantum-relativistic phenomena in graphene , journal =. 2009 , note =. doi:https://doi.org/10.1016/j.ssc.2009.02.043 , url =

work page doi:10.1016/j.ssc.2009.02.043 2009
[10]

and Nelson, Jocienne and Norman, Andrew G

Rice, Anthony D. and Nelson, Jocienne and Norman, Andrew G. and Walker, Patrick and Alberi, Kirstin , year=. High Mobility Cd3As2(112) on GaAs(001) Substrates Grown via Molecular Beam Epitaxy , volume=. ACS Applied Electronic Materials , publisher=. doi:10.1021/acsaelm.1c01126 , abstractNote=

work page doi:10.1021/acsaelm.1c01126
[11]

Advanced Functional Materials , author=

Epitaxial Dirac Semimetal Vertical Heterostructures for Advanced Device Architectures , volume=. Advanced Functional Materials , author=. 2022 , pages=. doi:10.1002/adfm.202111470 , abstractNote=

work page doi:10.1002/adfm.202111470 2022
[12]

and Davoyan, Arthur R

Mahmoud, Ahmed M. and Davoyan, Arthur R. and Engheta, Nader , year=. All-passive nonreciprocal metastructure , volume=. Nature Communications , publisher=. doi:10.1038/ncomms9359 , abstractNote=

work page doi:10.1038/ncomms9359
[13]

Giant intrinsic anomalous terahertz Faraday rotation in the magnetic Weyl semimetal

Han, Xingyue and Markou, Anastasios and Stensberg, Jonathan and Sun, Yan and Felser, Claudia and Wu, Liang , year=. Giant intrinsic anomalous terahertz Faraday rotation in the magnetic Weyl semimetal. Physical Review B , publisher=. doi:10.1103/PhysRevB.105.174406 , abstractNote=

work page doi:10.1103/physrevb.105.174406
[14]

Experimental demonstration of magnetoplasmon polariton at InSb(InAs)/dielectric interface for terahertz sensor application , volume=

Chochol, Jan and Postava, Kamil and Čada, Michael and Pištora, Jaromír , year=. Experimental demonstration of magnetoplasmon polariton at InSb(InAs)/dielectric interface for terahertz sensor application , volume=. Scientific Reports , publisher=. doi:10.1038/s41598-017-13394-0 , number=

work page doi:10.1038/s41598-017-13394-0
[15]

and Zhao, Bo and Kim, Yonghwi and Fan, Shanhui and Atwater, Harry A

Shayegan, Komron J. and Zhao, Bo and Kim, Yonghwi and Fan, Shanhui and Atwater, Harry A. , year=. Nonreciprocal infrared absorption via resonant magneto-optical coupling to InAs , volume=. Science Advances , publisher=. doi:10.1126/sciadv.abm4308 , number=

work page doi:10.1126/sciadv.abm4308
[16]

Review of Scientific Instruments , author=

Surface magneto-optic Kerr effect , volume=. Review of Scientific Instruments , author=. 2000 , month=. doi:10.1063/1.1150496 , number=

work page doi:10.1063/1.1150496 2000
[17]

and Ostler, Markus and Bostwick, Aaron and Rotenberg, Eli and Seyller, Thomas and van der Marel, Dirk and Kuzmenko, Alexey B

Crassee, Iris and Levallois, Julien and Walter, Andrew L. and Ostler, Markus and Bostwick, Aaron and Rotenberg, Eli and Seyller, Thomas and van der Marel, Dirk and Kuzmenko, Alexey B. , year=. Giant Faraday rotation in single- and multilayer graphene , volume=. Nature Physics , publisher=. doi:10.1038/nphys1816 , number=

work page doi:10.1038/nphys1816
[18]

Ultimate limit of field confinement by surface plasmon polaritons

Khurgin, Jacob B. Ultimate limit of field confinement by surface plasmon polaritons. Faraday Discuss. 2015. doi:10.1039/C4FD00193A

work page doi:10.1039/c4fd00193a 2015
[19]

Long-range surface plasmon polaritons , volume=

Berini, Pierre , year=. Long-range surface plasmon polaritons , volume=. Advances in Optics and Photonics , publisher=. doi:10.1364/AOP.1.000484 , abstractNote=

work page doi:10.1364/aop.1.000484
[20]

Scientific Reports , author=

Structural characterisation of high-mobility Cd3As2 films crystallised on SrTiO3 , volume=. Scientific Reports , author=. 2018 , month=. doi:10.1038/s41598-018-20758-7 , abstractNote=

work page doi:10.1038/s41598-018-20758-7 2018
[21]

Nature Communications , author=

Quantum Hall states observed in thin films of Dirac semimetal Cd3As2 , volume=. Nature Communications , author=. 2017 , month=. doi:10.1038/s41467-017-02423-1 , abstractNote=

work page doi:10.1038/s41467-017-02423-1 2017
[22]

Ni, G. X. and McLeod, A. S. and Sun, Z. and Wang, L. and Xiong, L. and Post, K. W. and Sunku, S. S. and Jiang, B.-Y. and Hone, J. and Dean, C. R. and Fogler, M. M. and Basov, D. N. , year=. Fundamental limits to graphene plasmonics , volume=. Nature , publisher=. doi:10.1038/s41586-018-0136-9 , abstractNote=

work page doi:10.1038/s41586-018-0136-9
[23]

and Zheng, Fan and Young, Steve M

Tan, Liang Z. and Zheng, Fan and Young, Steve M. and Wang, Fenggong and Liu, Shi and Rappe, Andrew M. , year=. Shift current bulk photovoltaic effect in polar materials—hybrid and oxide perovskites and beyond , volume=. npj Computational Materials , publisher=. doi:10.1038/npjcompumats.2016.26 , abstractNote=

work page doi:10.1038/npjcompumats.2016.26 2016
[24]

and Biswas, Souvik and Zhao, Bo and Fan, Shanhui and Atwater, Harry A

Shayegan, Komron J. and Biswas, Souvik and Zhao, Bo and Fan, Shanhui and Atwater, Harry A. , year=. Direct observation of the violation of Kirchhoff’s law of thermal radiation , rights=. Nature Photonics , publisher=. doi:10.1038/s41566-023-01261-6 , abstractNote=

work page doi:10.1038/s41566-023-01261-6
[25]

and Diebel, Laura K

Osterhoudt, Gavin B. and Diebel, Laura K. and Gray, Mason J. and Yang, Xu and Stanco, John and Huang, Xiangwei and Shen, Bing and Ni, Ni and Moll, Philip J. W. and Ran, Ying and Burch, Kenneth S. , year=. Colossal mid-infrared bulk photovoltaic effect in a type-I Weyl semimetal , volume=. Nature Materials , publisher=. doi:10.1038/s41563-019-0297-4 , abst...

work page doi:10.1038/s41563-019-0297-4
[26]

Chemical Physics Reviews , author=

Recent progress in the theory of bulk photovoltaic effect , volume=. Chemical Physics Reviews , author=. 2023 , month=. doi:10.1063/5.0101513 , abstractNote=

work page doi:10.1063/5.0101513 2023
[27]

Lighting up Weyl semimetals , volume=

Weng, Hongming , year=. Lighting up Weyl semimetals , volume=. Nature Materials 2019 18:5 , publisher=. doi:10.1038/s41563-019-0330-7 , abstractNote=

work page doi:10.1038/s41563-019-0330-7 2019
[28]

Physical Review B , author=

Theory of the effective Seebeck coefficient for photoexcited two-dimensional materials: Graphene , volume=. Physical Review B , author=. 2021 , month=. doi:10.1103/PhysRevB.104.125443 , number=

work page doi:10.1103/physrevb.104.125443 2021
[29]

and Sensenig, Jonathon and Ruzsinszky, Adrienn , year=

Bates, Jefferson E. and Sensenig, Jonathon and Ruzsinszky, Adrienn , year=. Convergence behavior of the random phase approximation renormalized correlation energy , volume=. Physical Review B , publisher=. doi:10.1103/PhysRevB.95.195158 , abstractNote=

work page doi:10.1103/physrevb.95.195158
[30]

and Zemansky, Mark W

Sears, Frances W. and Zemansky, Mark W. and Young, Hugh D. , journal=. University Physics , volume=
[31]

Optical Isolation by Temporal Modulation: Size, Frequency, and Power Constraints , volume=

Khurgin, Jacob B , year=. Optical Isolation by Temporal Modulation: Size, Frequency, and Power Constraints , volume=. ACS Photonics , publisher=. doi:10.1021/acsphotonics.2c01807 , abstractNote=

work page doi:10.1021/acsphotonics.2c01807
[32]

Physical Review B , author=

Large nonreciprocal absorption and emission of radiation in type-I Weyl semimetals with time reversal symmetry breaking , volume=. Physical Review B , author=. 2020 , pages=. doi:10.1103/PhysRevB.101.165426 , abstractNote=

work page doi:10.1103/physrevb.101.165426 2020
[33]

and Kastl, Christoph , year=

Kiemle, Jonas and Zimmermann, Philipp and Holleitner, Alexander W. and Kastl, Christoph , year=. Light-field and spin-orbit-driven currents in van der Waals materials , volume=. Nanophotonics , publisher=. doi:10.1515/nanoph-2020-0226 , abstractNote=

work page doi:10.1515/nanoph-2020-0226 2020
[34]

and Schlauderer, S

Reimann, J. and Schlauderer, S. and Schmid, C. P. and Langer, F. and Baierl, S. and Kokh, K. A. and Tereshchenko, O. E. and Kimura, A. and Lange, C. and Güdde, J. and Höfer, U. and Huber, R. , year=. Subcycle observation of lightwave-driven Dirac currents in a topological surface band , volume=. Nature , publisher=. doi:10.1038/s41586-018-0544-x , abstractNote=

work page doi:10.1038/s41586-018-0544-x
[35]

A truly one-way lane for surface plasmon polaritons , volume=

Monticone, Francesco , year=. A truly one-way lane for surface plasmon polaritons , volume=. Nature Photonics , publisher=. doi:10.1038/s41566-020-0662-5 , abstractNote=

work page doi:10.1038/s41566-020-0662-5
[36]

Terahertz control of many-body dynamics in quantum materials , rights=

Yang, Chia-Jung and Li, Jingwen and Fiebig, Manfred and Pal, Shovon , year=. Terahertz control of many-body dynamics in quantum materials , rights=. Nature Reviews Materials , publisher=. doi:10.1038/s41578-023-00566-w , abstractNote=

work page doi:10.1038/s41578-023-00566-w
[38]

Svintsov, D. , year=. Hydrodynamic-to-ballistic crossover in Dirac materials , volume=. Physical Review B , publisher=. doi:10.1103/PhysRevB.97.121405 , abstractNote=

work page doi:10.1103/physrevb.97.121405
[39]

Chemical Physics Letters , author=

Fermi energy, metals and the drift velocity of electrons , volume=. Chemical Physics Letters , author=. 2021 , month=. doi:10.1016/j.cplett.2021.138447 , abstractNote=

work page doi:10.1016/j.cplett.2021.138447 2021
[40]

Applied Physics Letters , author=

Field-effect transistors with the three-dimensional Dirac semimetal cadmium arsenide , volume=. Applied Physics Letters , author=. 2019 , month=. doi:10.1063/1.5103268 , abstractNote=

work page doi:10.1063/1.5103268 2019
[41]

International Journal of Modern Physics B , author=

Dielectric Function, Friedel Oscillation and Plasmons in Weyl Semimetals , volume=. International Journal of Modern Physics B , author=. 2013 , month=. doi:10.1142/S0217979213501774 , abstractNote=

work page doi:10.1142/s0217979213501774 2013
[42]

, editor=

Mahan, Gerald D. , editor=. Homogeneous Electron Gas , ISBN=. Many-Particle Physics , publisher=. 2000 , pages=. doi:10.1007/978-1-4757-5714-9_5 , abstractNote=

work page doi:10.1007/978-1-4757-5714-9_5 2000
[43]

Nature Communications 2014 5:1 , author =

Observation of a three-dimensional topological. Nature Communications 2014 5:1 , author =. 2014 , keywords =. doi:10.1038/ncomms4786 , number =

work page doi:10.1038/ncomms4786 2014
[45]

Physical Review B , author =

Visualizing the chiral anomaly in. Physical Review B , author =. 2016 , pages =. doi:10.1103/PhysRevB.93.075114 , number =

work page doi:10.1103/physrevb.93.075114 2016
[46]

Brillouin-scattering-induced transparency and non-reciprocal light storage , volume=

Dong, Chun-Hua and Shen, Zhen and Zou, Chang-Ling and Zhang, Yan-Lei and Fu, Wei and Guo, Guang-Can , year=. Brillouin-scattering-induced transparency and non-reciprocal light storage , volume=. Nature Communications , publisher=. doi:10.1038/ncomms7193 , abstractNote=

work page doi:10.1038/ncomms7193
[47]

and Han, Kewen and Wang, Hailin and Bahl, Gaurav , year=

Kim, JunHwan and Kuzyk, Mark C. and Han, Kewen and Wang, Hailin and Bahl, Gaurav , year=. Non-reciprocal Brillouin scattering induced transparency , volume=. Nature Physics , publisher=. doi:10.1038/nphys3236 , abstractNote=

work page doi:10.1038/nphys3236
[48]

and Kim, Seunghwi and Bahl, Gaurav , year=

Sohn, Donggyu B. and Kim, Seunghwi and Bahl, Gaurav , year=. Time-reversal symmetry breaking with acoustic pumping of nanophotonic circuits , volume=. Nature Photonics , publisher=. doi:10.1038/s41566-017-0075-2 , abstractNote=

work page doi:10.1038/s41566-017-0075-2
[49]

Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators , volume=

Chang, Long and Jiang, Xiaoshun and Hua, Shiyue and Yang, Chao and Wen, Jianming and Jiang, Liang and Li, Guanyu and Wang, Guanzhong and Xiao, Min , year=. Parity–time symmetry and variable optical isolation in active–passive-coupled microresonators , volume=. Nature Photonics , publisher=. doi:10.1038/nphoton.2014.133 , abstractNote=

work page doi:10.1038/nphoton.2014.133 2014
[50]

Physical Review Lett

Observation of Asymmetric Transport in Structures with Active Nonlinearities , author =. Physical Review Lett. , volume =. 2013 , month =. doi:10.1103/PhysRevLett.110.234101 , url =

work page doi:10.1103/physrevlett.110.234101 2013
[51]

and Shen, Hao and Niu, Ben and Xuan, Yi and Weiner, Andrew M

Fan, Li and Wang, Jian and Varghese, Leo T. and Shen, Hao and Niu, Ben and Xuan, Yi and Weiner, Andrew M. and Qi, Minghao , year=. An All-Silicon Passive Optical Diode , volume=. Science , publisher=. doi:10.1126/science.1214383 , abstractNote=

work page doi:10.1126/science.1214383
[52]

ACS Photonics , author =

Angular-. ACS Photonics , author =. 2014 , keywords =. doi:10.1021/ph400058y , abstract =

work page doi:10.1021/ph400058y 2014
[53]

Physical Review B , author =

Rotating spacetime modulation:. Physical Review B , author =. 2023 , pages =. doi:10.1103/PhysRevB.107.035133 , abstract =

work page doi:10.1103/physrevb.107.035133 2023
[54]

doi:10.48550/arxiv.2302.03090 , arxivId =

2023 , author =. doi:10.48550/arxiv.2302.03090 , arxivId =

work page doi:10.48550/arxiv.2302.03090 2023
[55]

Nature Communications , author =

Absence of unidirectionally propagating surface plasmon-polaritons at nonreciprocal metal-dielectric interfaces , volume =. Nature Communications , author =. 2020 , keywords =. doi:10.1038/s41467-020-14504-9 , number =

work page doi:10.1038/s41467-020-14504-9 2020
[56]

Mukherjee, S. P. and Carbotte, J. P. , number =. 2017 , journal =. doi:10.1103/PHYSREVB.96.085114 , issn =

work page doi:10.1103/physrevb.96.085114 2017
[57]

2020 , journal =

Zhang, Yong and Zhou, Cheng Long and Qu, Lei and Yi, Hong Liang , number =. 2020 , journal =. doi:10.1063/1.5145224 , issn =

work page doi:10.1063/1.5145224 2020
[58]

2018 , journal =

Izadi, Mohammad Amin and Nouroozi, Rahman , number =. 2018 , journal =. doi:10.1038/s41598-018-33831-y , issn =

work page doi:10.1038/s41598-018-33831-y 2018
[59]

2017 , journal =

Lin, Xiao and Yang, Yi and Rivera, Nicholas and L. 2017 , journal =. doi:10.1073/pnas.1701830114 , issn =

work page doi:10.1073/pnas.1701830114 2017
[60]

2017 , journal =

Lin, Xiao and Yang, Yi and Rivera, Nicholas and L. 2017 , journal =. doi:10.1073/PNAS.1701830114/SUPPL

work page doi:10.1073/pnas.1701830114/suppl 2017
[61]

2016 , journal =

Gon. 2016 , journal =. doi:10.1142/9948 , arxivId =

work page doi:10.1142/9948 2016
[62]

Peskin, Michael Edward and Schroeder, Daniel V. , year=. An Introduction To Quantum Field Theory , ISBN=
[63]

doi:10.1103/PhysRevB.75.045315 , keywords =

Sinitsyn, N A and Macdonald, A H and Jungwirth, T and Dugaev, V K and Sinova, Jairo , isbn =. doi:10.1103/PhysRevB.75.045315 , keywords =

work page doi:10.1103/physrevb.75.045315
[64]

2022 , journal =

Pal, Hridis K and Obakpolor, Osakpolor Eki and Hosur, Pavan , pages =. 2022 , journal =. doi:10.1103/PhysRevB.106.245410 , keywords =

work page doi:10.1103/physrevb.106.245410 2022
[65]

and Wang, J

Kim, Ki Seok and Kim, Heon Jung and Sasaki, M. and Wang, J. F. and Li, L. , number =. 2014 , journal =. doi:10.1088/1468-6996/15/6/064401 , issn =

work page doi:10.1088/1468-6996/15/6/064401 2014
[67]

2005 , journal =

D. 2005 , journal =. doi:10.1364/JOSAB.22.000240 , issn =

work page doi:10.1364/josab.22.000240 2005
[68]

and Narang, Prineha and Fan, Shanhui , number =

Zhao, Bo and Guo, Cheng and Garcia, Christina A.C. and Narang, Prineha and Fan, Shanhui , number =. 2020 , journal =. doi:10.1021/acs.nanolett.9b05179 , issn =

work page doi:10.1021/acs.nanolett.9b05179 2020
[69]

2010 , journal =

Xiao, Di and Chang, Ming Che and Niu, Qian , number =. 2010 , journal =. doi:10.1103/REVMODPHYS.82.1959/FIGURES/16/MEDIUM , issn =

work page doi:10.1103/revmodphys.82.1959/figures/16/medium 2010
[70]

doi:10.1103/PhysRevLett.97.026603 , keywords =

2006 , author =. doi:10.1103/PhysRevLett.97.026603 , keywords =

work page doi:10.1103/physrevlett.97.026603 2006
[71]

2014 , journal =

Kim, Ki-Seok and Kim, Heon-Jung and Sasaki, M , pages =. 2014 , journal =. doi:10.1103/PhysRevB.89.195137 , keywords =

work page doi:10.1103/physrevb.89.195137 2014
[72]

Hosur, S

2012 , author =. doi:10.1103/PhysRevLett.108.046602 , keywords =

work page doi:10.1103/physrevlett.108.046602 2012
[73]

2013 , journal =

Son, D T and Spivak, B Z , pages =. 2013 , journal =

2013
[74]

2022 , journal =

Mandal, Debottam and Das, Kamal and Agarwal, Amit , pages =. 2022 , journal =. doi:10.1103/PhysRevB.106.035423 , keywords =

work page doi:10.1103/physrevb.106.035423 2022
[75]

and Carbotte, J

Ashby, Phillip E.C. and Carbotte, J. P. , number =. 2014 , journal =. doi:10.1103/PHYSREVB.89.245121/FIGURES/3/MEDIUM , issn =

work page doi:10.1103/physrevb.89.245121/figures/3/medium 2014
[76]

2019 , journal =

Johansson, Annika and Henk, Jürgen and Mertig, Ingrid , pages =. 2019 , journal =. doi:10.1103/PhysRevB.99.075114 , keywords =

work page doi:10.1103/physrevb.99.075114 2019
[77]

and Kikuchi, Yuta and Meyer, René , number =

Kharzeev, Dmitri E. and Kikuchi, Yuta and Meyer, René , number =. 2018 , journal =. doi:10.1140/EPJB/E2018-80418-1 , issn =

work page doi:10.1140/epjb/e2018-80418-1 2018
[78]

and Low, Tony , number =

Kumar, Anshuman and Nemilentsau, Andrei and Fung, Kin Hung and Hanson, George and Fang, Nicholas X. and Low, Tony , number =. 2016 , journal =. doi:10.1103/PHYSREVB.93.041413/FIGURES/4/MEDIUM , issn =

work page doi:10.1103/physrevb.93.041413/figures/4/medium 2016
[79]

and Rudner, Mark S

Song, Justin C.W. and Rudner, Mark S. , number =. 2016 , journal =. doi:10.1073/PNAS.1519086113/SUPPL

work page doi:10.1073/pnas.1519086113/suppl 2016
[80]

doi:10.1103/PhysRevB.98.075305 , keywords =

2018 , author =. doi:10.1103/PhysRevB.98.075305 , keywords =

work page doi:10.1103/physrevb.98.075305 2018
[81]

and Venderbos, Jörn W.F

Grushin, Adolfo G. and Venderbos, Jörn W.F. and Bardarson, Jens H. , number =. 2015 , journal =. doi:10.1103/PHYSREVB.91.121109/FIGURES/3/MEDIUM , issn =

work page doi:10.1103/physrevb.91.121109/figures/3/medium 2015
[82]

Sukhachov, P. O. and Gorbar, E. V. and Shovkovy, I. A. and Miransky, V. A. , number =. 2018 , journal =. doi:10.1088/1361-648X/AAC500 , issn =

work page doi:10.1088/1361-648x/aac500 2018
[83]

2D Mater

Current-induced birefringent absorption and non-reciprocal plasmons in graphene , volume =. 2D Mater. , author =. 2016 , pages =. doi:10.1088/2053-1583/3/1/015011 , number =

work page doi:10.1088/2053-1583/3/1/015011 2016

Showing first 80 references.