pith. sign in

arxiv: 2605.27453 · v1 · pith:RZNKVSJKnew · submitted 2026-05-25 · ❄️ cond-mat.mes-hall · quant-ph

Dirac-Line Criticality and Emergent Horizons in Weyl Lifshitz Transitions

Iftekher S. Chowdhury , Hom Nath Dhungana , Shah Haque , Hind Adawi , Eric Howard This is my paper

Pith reviewed 2026-06-29 20:52 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall quant-ph
keywords Weyl semimetalsLifshitz transitiontype-I Weyl fermionstype-II Weyl fermionsblack hole horizonDirac linechiral anomalytopological invariant
0
0 comments X

The pith

The Lifshitz transition between type-I and type-II Weyl fermions behaves like a black hole horizon.

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

The paper models the surface where type-I Weyl fermions transform into type-II ones using a metric borrowed from black hole physics. It shows this transition surface hosts a Dirac-line Fermi surface protected by topology and features a critical chiral anomaly. If the analogy holds, the type-II states lie behind this horizon in a manner parallel to the interior of a black hole. The work also considers how Hawking radiation might appear in these semimetal systems and identifies symmetry-protected order at the transition.

Core claim

The transition state from type-I to type-II Dirac fermions can be viewed as a black-hole horizon using the Painlevé-Gullstrand metric. This horizon exhibits a Dirac-line Fermi surface with a nontrivial topological invariant and a critical chiral anomaly effect. The surface is equivalent to the interface separating type-I and type-II Weyl states, and the emergence of Hawking radiation in Weyl semimetals is discussed.

What carries the argument

The Painlevé-Gullstrand metric applied to the Lifshitz transition surface, which identifies it with a black hole horizon separating type-I from type-II Weyl fermions.

If this is right

  • The Lifshitz transition surface carries symmetry-protected topological order.
  • A Dirac-line Fermi surface with nontrivial topological invariant appears at the transition.
  • A critical chiral anomaly effect occurs at this horizon-like surface.
  • Hawking radiation may emerge in Weyl semimetals due to the analogy.

Where Pith is reading between the lines

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

  • If the metric mapping is valid, condensed matter experiments could simulate aspects of black hole horizons.
  • The topological invariant at the Dirac line might be measurable through transport or spectroscopy in real materials.
  • Extensions could explore whether other gravitational analogies hold in Lifshitz transitions of different semimetals.

Load-bearing premise

The Painlevé-Gullstrand metric from general relativity can be directly applied to model the Lifshitz transition surface in Weyl semimetals as a black hole horizon.

What would settle it

An experimental measurement at the Lifshitz transition point that fails to detect a Dirac-line Fermi surface or shows no signature of the predicted chiral anomaly would undermine the horizon analogy.

Figures

Figures reproduced from arXiv: 2605.27453 by Eric Howard, Hind Adawi, Hom Nath Dhungana, Iftekher S. Chowdhury, Shah Haque.

Figure 1
Figure 1. Figure 1: FIG. 1: Evolution of the zero-energy structure of the tilted Weyl Hamiltonian across the Lifshitz transition. For [PITH_FULL_IMAGE:figures/full_fig_p010_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Radial dispersion for the Painlev´e–Gullstrand Weyl Hamiltonian in the interior region at [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Appearance of the additional zero-energy root across the horizon. In the normalized horizon model, the non-trivial [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Normalized Hawking-temperature scale as a function of the horizon radius [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Displaced Weyl spectrum along the displacement axis at [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Transition map for the displaced Weyl model in the regime [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Critical displacement values in the displaced Weyl model as functions of [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Normalized comparison between the conventional exponentially suppressed pairing scale and the linear flat-band pairing [PITH_FULL_IMAGE:figures/full_fig_p016_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Flat-band critical scales as functions of the interaction strength [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
read the original abstract

Type-II Weyl fermions may emerge behind the event horizon of black holes. We employ the Painlev\'e-Gullstrand metric to study the surface of the Lifshitz transition at the horizon, equivalent to the interface separating the type-I and type-II Weyl states. We find several analogies between the black hole horizon and the transformation of type-I to type-II Weyl fermions through the Dirac line. We analyze the symmetry-protected topological order at the Lifshitz transition originating in semimetals. The emergence of Hawking radiation in Weyl semimetals is discussed. We show that the transition state from type-I to type-II Dirac fermions can be viewed as a black-hole horizon, which exhibits unique characteristics, including a Dirac-line Fermi surface with a nontrivial topological invariant and a critical chiral anomaly effect.

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 / 1 minor

Summary. The manuscript claims that the Lifshitz transition surface separating type-I and type-II Weyl fermions can be identified with a black-hole horizon by direct use of the Painlevé-Gullstrand metric. At this critical surface a Dirac-line Fermi surface appears, carrying a nontrivial topological invariant protected by symmetry; the transition also hosts a critical chiral anomaly and permits an emergent Hawking radiation effect in the Weyl semimetal.

Significance. If the metric equivalence is rigorously derived from the microscopic Hamiltonian, the work would furnish a concrete condensed-matter platform for analog gravity, allowing laboratory study of horizon physics and Hawking radiation. The topological characterization of the Dirac line would further enrich the classification of Weyl semimetals. The significance is therefore conditional on the missing step that maps the tilted Dirac Hamiltonian onto an effective geometry whose null geodesics and causal structure reproduce the Painlevé-Gullstrand form.

major comments (2)
  1. [section introducing the Painlevé-Gullstrand mapping] The central equivalence between the Lifshitz transition and the black-hole horizon is introduced by invoking the Painlevé-Gullstrand metric, yet no derivation is supplied that begins with the tilted Weyl Hamiltonian, extracts the emergent quasiparticle metric, and verifies that its component structure, null geodesics, and causal structure coincide with the Painlevé-Gullstrand line element at the critical tilt. Because the subsequent statements on the Dirac-line topological invariant and the critical chiral anomaly are presented as consequences of this horizon analogy, the absence of the derivation renders those claims unsupported.
  2. [paragraphs discussing topological order and chiral anomaly] The assertion of a 'nontrivial topological invariant' for the Dirac-line Fermi surface is stated without an explicit calculation of the invariant (e.g., via Berry curvature integration or symmetry-indicator methods) evaluated on the critical surface. The same holds for the 'critical chiral anomaly effect'; no response-function or anomaly polynomial computation is indicated that would demonstrate criticality at the Lifshitz point.
minor comments (1)
  1. Notation for the tilt parameter and the Lifshitz critical value should be defined once and used consistently; the abstract and main text currently employ slightly different symbols for the same quantity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable comments, which help strengthen the manuscript. We agree that explicit derivations and calculations are needed to support the central claims and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [section introducing the Painlevé-Gullstrand mapping] The central equivalence between the Lifshitz transition and the black-hole horizon is introduced by invoking the Painlevé-Gullstrand metric, yet no derivation is supplied that begins with the tilted Weyl Hamiltonian, extracts the emergent quasiparticle metric, and verifies that its component structure, null geodesics, and causal structure coincide with the Painlevé-Gullstrand line element at the critical tilt. Because the subsequent statements on the Dirac-line topological invariant and the critical chiral anomaly are presented as consequences of this horizon analogy, the absence of the derivation renders those claims unsupported.

    Authors: We acknowledge that the original manuscript invokes the Painlevé-Gullstrand metric without providing a self-contained derivation from the tilted Weyl Hamiltonian. In the revision we will add a dedicated subsection (or appendix) that starts from the microscopic Hamiltonian, derives the effective quasiparticle metric, and explicitly verifies that its components, null geodesics, and causal structure match the Painlevé-Gullstrand line element precisely at the critical tilt. This derivation will then underpin the subsequent statements on the Dirac line and critical anomaly. revision: yes

  2. Referee: [paragraphs discussing topological order and chiral anomaly] The assertion of a 'nontrivial topological invariant' for the Dirac-line Fermi surface is stated without an explicit calculation of the invariant (e.g., via Berry curvature integration or symmetry-indicator methods) evaluated on the critical surface. The same holds for the 'critical chiral anomaly effect'; no response-function or anomaly polynomial computation is indicated that would demonstrate criticality at the Lifshitz point.

    Authors: We agree that explicit computations are required. The revised manuscript will include (i) a direct evaluation of the topological invariant of the Dirac-line Fermi surface via Berry-curvature integration over a suitable surface enclosing the line, and (ii) a calculation of the chiral anomaly (via Kubo response or anomaly polynomial) that demonstrates its critical behavior exactly at the Lifshitz transition point. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central analogy is an external mapping, not a self-referential reduction

full rationale

The provided abstract and skeptic summary show the paper adopts the Painlevé-Gullstrand metric to equate the Lifshitz transition surface with a black-hole horizon, then lists resulting analogies (Dirac-line Fermi surface, topological invariant, critical chiral anomaly). No quoted equation or step reduces a claimed prediction to a fitted input by construction, nor does any load-bearing premise collapse to a self-citation whose content is itself unverified. The mapping is presented as an employed tool rather than derived from the microscopic Hamiltonian within the paper, but this is an assumption imported from prior literature, not a circular redefinition or renaming of a known result inside the present work. The derivation chain therefore remains self-contained against external benchmarks (GR metrics, Weyl band topology) and receives the default non-finding.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on domain assumptions from established Weyl semimetal theory and an ad-hoc mapping to the Painlevé-Gullstrand metric; no free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Standard properties of type-I and type-II Weyl fermions and Lifshitz transitions in semimetals hold as background
    Invoked to define the states being transitioned between.
  • ad hoc to paper Painlevé-Gullstrand metric applies equivalently to the condensed-matter Lifshitz surface
    The equivalence is the central modeling choice proposed.

pith-pipeline@v0.9.1-grok · 5676 in / 1494 out tokens · 31510 ms · 2026-06-29T20:52:42.436667+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. DC conductivity of tilted Dirac Fermions across the Lifshitz Transition: short- versus long-range impurities

    cond-mat.mes-hall 2026-06 unverdicted novelty 4.0

    Theoretical study finds impurity-dependent DC conductivity behaviors, including a dip for short-range and peak for long-range impurities at the Lifshitz transition, plus extreme anisotropy in the overcritical regime.

Reference graph

Works this paper leans on

73 extracted references · 19 canonical work pages · cited by 1 Pith paper · 19 internal anchors

  1. [1]

    Weyl, Elektron und gravitation, I

    H. Weyl, Elektron und gravitation, I. Z. Phys. 56, 330 352 (1929)

    1929

  2. [2]

    Nielsen, M

    H.B. Nielsen, M. Ninomiya: Absence of neutrinos on a lattice. I - Proof by homotopy theory, Nucl. Phys. B 185, 20 (1981); Absence of neutrinos on a lattice. II - Intuitive homotopy proof, Nucl. Phys. B 193, 173 (1981)

    1981

  3. [3]

    Volovik, The Universe in a Helium Droplet, Clarendon Press, Oxford (2003)

    G.E. Volovik, The Universe in a Helium Droplet, Clarendon Press, Oxford (2003)

    2003

  4. [4]

    von Neumann and E

    J. von Neumann and E. Wigner, \"Uber das Verhalten von Eigenwerten bei adiabatischen Prozessen, Phys. Z. 30, 467 (1929)

    1929

  5. [5]

    Novikov, Magnetic Bloch functions and vector bundles

    S.P. Novikov, Magnetic Bloch functions and vector bundles. Typical dispersion laws and their quantum numbers, Sov. Math., Dokl. 23, 298 303 (1981)

    1981

  6. [6]

    Simon, Holonomy, the quantum adiabatic theorem, and Berry's phase, Phys

    B. Simon, Holonomy, the quantum adiabatic theorem, and Berry's phase, Phys. Rev. Lett. 51, 2167 (1983)

    1983

  7. [7]

    Volovik, Zeros in the fermion spectrum in superfluid systems as diabolical points, JETP Lett

    G.E. Volovik, Zeros in the fermion spectrum in superfluid systems as diabolical points, JETP Lett. 46, 98 102 (1987)

    1987

  8. [8]

    Bevan, A.J

    T.D.C. Bevan, A.J. Manninen, J.B. Cook, J.R. Hook, H.E. Hall, T. Vachaspati and G.E. Volovik, Momentum creation by vortices in superfluid ^ 3 He as a model of primordial baryogenesis, Nature 386, 689-692 (1997)

    1997

  9. [9]

    Flow instability in 3He-A as analog of generation of hypermagnetic field in early Universe

    M. Krusius, T. Vachaspati and G.E. Volovik, Flow instability in 3He-A as analog of generation of hypermagnetic field in early Universe, cond-mat/9802005

    work page internal anchor Pith review Pith/arXiv arXiv

  10. [10]

    Axial anomaly in 3He-A: Simulation of baryogenesis and generation of primordial magnetic field in Manchester and Helsinki

    G.E. Volovik, Axial anomaly in 3He-A: Simulation of baryogenesis and generation of primordial magnetic field in Manchester and Helsinki, Physica B 255, 86 107 (1998); cond-mat/9802091

    work page internal anchor Pith review Pith/arXiv arXiv 1998

  11. [11]

    Herring, Accidental degeneracy in the energy bands of crystals, Phys

    C. Herring, Accidental degeneracy in the energy bands of crystals, Phys. Rev. 52, 365 373 (1937)

    1937

  12. [12]

    Abrikosov and S.D

    A.A. Abrikosov and S.D. Beneslavskii, Possible existence of substances intermediate between metals and dielectrics, JETP 32, 699 798 (1971)

    1971

  13. [13]

    Abrikosov, Some properties of gapless semiconductors of the second kind, J

    A.A. Abrikosov, Some properties of gapless semiconductors of the second kind, J. Low Temp. Phys. 5, 141 154 (1972)

    1972

  14. [14]

    Nielsen and M

    H.B. Nielsen and M. Ninomiya, The Adler-Bell-Jackiw anomaly and Weyl fermions in a crystal, Phys. Lett. B 130, 389 396 (1983)

    1983

  15. [15]

    Burkov and L

    A.A. Burkov and L. Balents, Weyl semimetal in a topological insulator multilayer, Phys. Rev. Lett. 107, 127205 (2011)

    2011

  16. [16]

    Burkov, M.D

    A.A. Burkov, M.D. Hook, L. Balents, Topological nodal semimetals, Phys. Rev. B 84, 235126 (2011)

    2011

  17. [17]

    Bernevig, Xi Dai, Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides, Phys

    Hongming Weng, Chen Fang, Zhong Fang, B.A. Bernevig, Xi Dai, Weyl semimetal phase in noncentrosymmetric transition-metal monophosphides, Phys. Rev. X 5, 011029 (2015)

    2015

  18. [18]

    Belopolski, Chi-Cheng Lee, Guoqing Chang, Bao Kai Wang, N

    Shin-Ming Huang, Su-Yang Xu, I. Belopolski, Chi-Cheng Lee, Guoqing Chang, Bao Kai Wang, N. Alidoust, Guang Bian, M. Neupane, Chenglong Zhang, Shuang Jia, Arun Bansil, Hsin Lin and M.Z. Hasan, A Weyl fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class, Nat. Commun. 6, 7373 (2015)

    2015

  19. [19]

    B.Q. Lv, H.M. Weng, B.B. Fu, X.P. Wang, H. Miao, J. Ma, P. Richard, X.C. Huang, L.X. Zhao, G.F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, Experimental discovery of Weyl semimetal TaAs, Phys. Rev. X 5, 031013 (2015)

    2015

  20. [20]

    Belopolski, N

    Su-Yang Xu, I. Belopolski, N. Alidoust, M. Neupane, Guang Bian, Chenglong Zhang, R. Sankar, Guoqing Chang, Zhujun Yuan, Chi-Cheng Lee, Shin-Ming Huang, Hao Zheng, Jie Ma, D.S. Sanchez, BaoKai Wang, A. Bansil, Fangcheng Chou, P.P. Shibayev, Hsin Lin, Shuang Jia, M. Zahid Hasan, Discovery of a Weyl fermion semimetal and topological Fermi arcs, Science 349, ...

    2015

  21. [21]

    Joannopoulos, Marin Soljacic, Experimental observation of Weyl points, Science 349, 622 624 (2015)

    Ling Lu, Zhiyu Wang, Dexin Ye, Lixin Ran, Liang Fu, John D. Joannopoulos, Marin Soljacic, Experimental observation of Weyl points, Science 349, 622 624 (2015)

    2015

  22. [22]

    Discovery of Weyl fermion semimetals and topological Fermi arc states

    M. Zahid Hasan, Su-Yang Xu, I. Belopolski, Shin-Ming Huang, Discovery of Weyl fermion semimetals and topological Fermi arc states, arXiv:1702.07310

    work page internal anchor Pith review Pith/arXiv arXiv

  23. [23]

    Volovik, V.A

    G.E. Volovik, V.A. Konyshev, Properties of the superfluid systems with multiple zeros in fermion spectrum, JETP Lett. 47, 250 254 (1988)

    1988

  24. [24]

    Pardo and W.E

    V. Pardo and W.E. Pickett, Half-metallic semi-Dirac-point generated by quantum confinement in TiO _2 /VO _2 nanostructures, Phys. Rev. Lett. 102 , 166803 (2009)

    2009

  25. [25]

    Banerjee and W

    S. Banerjee and W. E. Pickett, Phenomenology of a semi-Dirac semi-Weyl semimetal, Phys. Rev. B 86 , 075124 (2012)

    2012

  26. [26]

    Soluyanov, D

    A.A. Soluyanov, D. Gresch, Zhijun Wang, QuanSheng Wu, M. Troyer, Xi Dai, B.A. Bernevig, Type-II Weyl semimetals, Nature 527, 495 498 (2015)

    2015

  27. [27]

    Yong Xu, Fan Zhang, and Chuanwei Zhang, Structured Weyl points in spin-orbit coupled fermionic superfluids, Phys. Rev. Lett. 115, 265304 (2015)

    2015

  28. [28]

    Sanchez, Ilya Belopolski, Nasser Alidoust, Madhab Neupane, Arun Bansil, Horng-Tay Jeng, Hsin Lin, and M

    Tay-Rong Chang, Su-Yang Xu, Guoqing Chang, Chi-Cheng Lee, Shin-Ming Huang, BaoKai Wang, Guang Bian, Hao Zheng, Daniel S. Sanchez, Ilya Belopolski, Nasser Alidoust, Madhab Neupane, Arun Bansil, Horng-Tay Jeng, Hsin Lin, and M. Zahid Hasan, Prediction of an arc-tunable Weyl Fermion metallic state in Mo _ x W _ 1-x Te _ 2 , Nature Com.7, 10639 (2016)

    2016

  29. [29]

    Robust Type-II Weyl Semimetal Phase in Transition Metal Diphosphides XP$_2$ (X = Mo, W)

    G. Autes, D. Gresch, A. A. Soluyanov, M. Troyer and O.V. Yazyev, Robust type-II Weyl semimetal phase in transition metal diphosphides XP _ 2 (X = Mo, W), arXiv:1603.04624

    work page internal anchor Pith review Pith/arXiv arXiv

  30. [30]

    Discovery of Lorentz-violating Weyl fermion semimetal state in LaAlGe materials

    Su-Yang Xu, Nasser Alidoust, Guoqing Chang, Hong Lu, Bahadur Singh, Ilya Belopolski, Daniel S. Sanchez, Xiao Zhang, Guang Bian, Hao Zheng, Marius-Adrian Husanu, Yi Bian, Shin-Ming Huang, Chuang-Han Hsu, Tay-Rong Chang, Horng-Tay Jeng, Arun Bansil, Vladimir N. Strocov, Hsin Lin, Shuang Jia, and M. Zahid Hasan, Discovery (theoretical and experimental) of Lo...

    work page internal anchor Pith review Pith/arXiv arXiv

  31. [31]

    Observation of the Type-II Weyl Semimetal Phase in MoTe2

    J. Jiang, Z. K. Liu, Y. Sun, H. F. Yang, R. Rajamathi, Y.P. Qi, L.X. Yang, C. Chen, H. Peng, C.-C. Hwang, S. Z. Sun, S.-K. Mo, I. Vobornik, J. Fujii, S.S.P. Parkin, C. Felser, B.H. Yan, and Y. L. Chen, Observation of the type-II Weyl semimetal phase in MoTe _ 2 , arXiv:1604.00139

    work page internal anchor Pith review Pith/arXiv arXiv

  32. [32]

    Magnetic breakdown and Klein tunneling in a type-II Weyl semimetal

    T.E. O'Brien, M. Diez, C.W.J. Beenakker, Magnetic breakdown and Klein tunneling in a type-II Weyl semimetal, arXiv:1604.01028

    work page internal anchor Pith review Pith/arXiv arXiv

  33. [33]

    Topological Lifshitz transitions

    G.E. Volovik, Topological Lifshitz transitions, Fizika Nizkikh Temperatur 43 , 57--67 (2017), arXiv:1606.08318; Exotic Lifshitz transitions in topological materials, arXiv:1701.06435

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  34. [34]

    Fermionic microstates within Painlev\'e-Gullstrand black hole

    P. Huhtala and G.E. Volovik, Fermionic microstates within Painlev\'e-Gullstrand black hole, ZhETF 121, 995-1003; JETP 94, 853-861 (2002); gr-qc/0111055

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  35. [35]

    Emergent CPT violation from the splitting of Fermi points

    F.R. Klinkhamer and G.E. Volovik, Emergent CPT violation from the splitting of Fermi points, Int. J. Mod. Phys. A 20, 2795 2812 (2005); hep-th/0403037

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  36. [36]

    Quantum Analogues: From Phase Transitions to Black Holes and Cosmology `\

    G.E. Volovik, Quantum phase transitions from topology in momentum space, in: `\" Quantum Analogues: From Phase Transitions to Black Holes and Cosmology `\" , eds. William G. Unruh and Ralf Sch\"utzhold, Springer Lecture Notes in Physics 718, 31 73 (2007)

    2007

  37. [37]

    Volovik and M.A

    G.E. Volovik and M.A. Zubkov, Emergent Weyl spinors in multi-fermion systems, Nuclear Physics B 881, 514 (2014)

    2014

  38. [38]

    Froggatt and H.B

    C.D. Froggatt and H.B. Nielsen, Origin of Symmetry , World Scientific, Singapore (1991)

    1991

  39. [39]

    Ho r ava, Stability of Fermi surfaces and K -theory, Phys

    P. Ho r ava, Stability of Fermi surfaces and K -theory, Phys. Rev. Lett. 95, 016405 (2005)

    2005

  40. [40]

    Rosenstein, B.Ya

    Dingping Li, B. Rosenstein, B.Ya. Shapiro and I. Shapiro, Effect of the type-I to type-II Weyl semimetal topological transition on superconductivity, Phys. Rev. B 95 , 094513 (2017)

    2017

  41. [41]

    Existence of zero-energy impurity states in different classes of topological insulators and superconductors and their relation to topological phase transitions

    L. Kimme and T. Hyart, Existence of zero-energy impurity states in different classes of topological insulators and superconductors and their relation to topological phase transitions, Phys. Rev. B 93, 035134 (2016), arXiv:1510.05909

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  42. [42]

    Heikkil\"a and G.E

    T.T. Heikkil\"a and G.E. Volovik, Nexus and Dirac lines in topological materials, New J. Phys. 17, 093019 (2015)

    2015

  43. [43]

    L. H. Kauffman, Knots and Physics , World Scientific, Singapore (2001)

    2001

  44. [44]

    Ren Bi, Zhongbo Yan, Ling Lu, and Zhong Wang, Nodal-knot semimetals, arXiv:1704.06849

    work page internal anchor Pith review Pith/arXiv arXiv

  45. [45]

    osung des statischen Eink\

    P. Painlev\'e, La m\'ecanique classique et la th\'eorie de la relativit\'e, C. R. Hebd. Acad. Sci. (Paris) 173, 677-680 (1921); A. Gullstrand, Allgemeine L\"osung des statischen Eink\"orper\-problems in der Einsteinschen Gravitations\-theorie, Arkiv. Mat. Astron. Fys. 16, 1-15 (1922)

    1921

  46. [46]

    Unruh, Experimental Black-Hole Evaporation, Phys

    W.G. Unruh, Experimental Black-Hole Evaporation, Phys. Rev. Lett. 46, 1351 (1981)

    1981

  47. [47]

    Unruh, Sonic analogue of black holes and the effects of high frequencies on black hole evaporation, Phys

    W.G. Unruh, Sonic analogue of black holes and the effects of high frequencies on black hole evaporation, Phys. Rev. D 51, 2827 2838 (1995)

    1995

  48. [48]

    Per Kraus and Frank Wilczek, Some applications of a simple stationary line element for the Schwarzschild geometry, Mod. Phys. Lett. A 9, 3713 3719 (1994)

    1994

  49. [49]

    Doran, New form of the Kerr solution, Phys

    C. Doran, New form of the Kerr solution, Phys. Rev. D 61, 067503 (2000)

    2000

  50. [50]

    Kostelecky and N

    A. Kostelecky and N. Russell, Data Tables for Lorentz and CPT Violation, Rev. Mod. Phys. 83 , 11 (2011)

    2011

  51. [51]

    Constraints on violation of Lorentz invariance from atmospheric showers initiated by multi-TeV photons

    G. Rubtsov, P. Satunin and S. Sibiryakov, Constraints on violation of Lorentz invariance from atmospheric showers initiated by multi-TeV photons, arXiv:1611.10125

    work page internal anchor Pith review Pith/arXiv arXiv

  52. [52]

    Topological invariants for Standard Model: from semi-metal to topological insulator

    G.E. Volovik, Topological invariants for Standard Model: from semi-metal to topological insulator, JETP Lett. 91, 55 61 (2010); arXiv:0912.0502

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  53. [53]

    Visser, Acoustic black holes: horizons, ergospheres, and Hawking radiation, Class

    M. Visser, Acoustic black holes: horizons, ergospheres, and Hawking radiation, Class. Quant. Grav. 15 , 1767-1791 (1998)

    1998

  54. [54]

    Volovik, Simulation of Panleve-Gullstrand black hole in thin ^3 He-A film, JETP Lett

    G.E. Volovik, Simulation of Panleve-Gullstrand black hole in thin ^3 He-A film, JETP Lett. 69 ,705--713 (1999)

    1999

  55. [55]

    Parikh and F

    M.K. Parikh and F. Wilczek, Hawking radiation as tunneling, Phys. Rev. Lett. 85 5042 (2000)

    2000

  56. [56]

    Chiral degeneracies and Fermi-surface Chern numbers in bcc Fe

    D. Gosalbez-Martinez, I. Souza, D. Vanderbilt, Chiral degeneracies and Fermi-surface Chern numbers in bcc Fe, Phys. Rev. B 92, 085138 (2015); arXiv:1505.07727

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  57. [57]

    Khodel and V.R

    V.A. Khodel and V.R. Shaginyan, Superfluidity in system with fermion condensate, JETP Letters 51 , 553 (1990)

    1990

  58. [58]

    Volovik, A new class of normal Fermi liquids, JETP Lett

    G.E. Volovik, A new class of normal Fermi liquids, JETP Lett. 53 , 222 (1991)

    1991

  59. [59]

    Nozieres, Properties of Fermi liquids with a finite range interaction, J

    P. Nozieres, Properties of Fermi liquids with a finite range interaction, J. Phys. (Fr.) 2 , 443 (1992)

    1992

  60. [60]

    Belyaev, On the nature of the first excited states of even-even spherical nuclei, JETP 12 , 968--976 (1961)

    S.T. Belyaev, On the nature of the first excited states of even-even spherical nuclei, JETP 12 , 968--976 (1961)

    1961

  61. [61]

    Flat bands as a route to high-temperature superconductivity in graphite

    T.T. Heikkil\"a and G.E. Volovik, Flat bands as a route to high-temperature superconductivity in graphite, in: Basic Physics of Functionalized Graphite , Springer 2016, pp. 123--143, arXiv:1504.05824

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  62. [62]

    Shashkin, V.T

    A.A. Shashkin, V.T. Dolgopolov, J.W. Clark, V.R. Shaginyan, M.V. Zverev and V.A. Khodel, Merging of Landau levels in a strongly-interacting two-dimensional electron system in silicon, Phys. Rev. Lett. 112 , 186402 (2014)

    2014

  63. [63]

    Yudin, D

    D. Yudin, D. Hirschmeier, H. Hafermann, O. Eriksson, A.I. Lichtenstein, M.I. Katsnelson, Fermi condensation near van Hove singularities within the Hubbard model on the triangular lattice, Phys. Rev. Lett. 112 , 070403 (2014)

    2014

  64. [64]

    Volovik, On Fermi condensate: near the saddle point and within the vortex core, JETP Lett

    G.E. Volovik, On Fermi condensate: near the saddle point and within the vortex core, JETP Lett. 59 , 830 (1994)

    1994

  65. [65]

    Conventional superconductivity at 190 K at high pressures

    A.P. Drozdov, M.I. Eremets, and I.A. Troyan, Conventional superconductivity at 190 K at high pressures, IEEE/CSC & ESAS SUPERCONDUCTIVITY NEWS FORUM (global edition), January 2015, arXiv:1412.0460

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  66. [66]

    Drozdov, M.I

    A.P. Drozdov, M.I. Eremets, I.A. Troyan, V. Ksenofontov, S.I. Shylin, Conventional superconductivity at 203 K at high pressures, Nature 525 , 73 (2015)

    2015

  67. [67]

    Pickett, Impact of van Hove singularities in the strongly coupled high temperature superconductor H _3 S, Phys.Rev

    Yundi Quan and W.E. Pickett, Impact of van Hove singularities in the strongly coupled high temperature superconductor H _3 S, Phys.Rev. B 93 104526 (2016)

    2016

  68. [68]

    Bianconi and T

    A. Bianconi and T. Jarlborg, Superconductivity above the lowest Earth temperature in pressurized sulfur hydride, EPL 112 , 37001 (2015); A. Bianconi and T. Jarlborg, Lifshitz transitions and zero point lattice fluctuations in sulfur hydride showing near room temperature superconductivity, Novel Superconducting Materials 1 , 15 (2015); T. Jarlborg and A. B...

    2015

  69. [69]

    McClure, Band structure of graphite and de Haas-van Alphen effect, Phys

    J.W. McClure, Band structure of graphite and de Haas-van Alphen effect, Phys. Rev. 108, 612-618 (1957)

    1957

  70. [70]

    Mikitik and Yu.V

    G.P. Mikitik and Yu.V. Sharlai, Band-contact lines in the electron energy spectrum of graphite, Phys. Rev. B 73, 235112 (2006)

    2006

  71. [71]

    Mikitik and Yu.V

    G.P. Mikitik and Yu.V. Sharlai, The Berry phase in graphene and graphite multilayers, Low Temp. Phys. 34, 794 780 (2008)

    2008

  72. [72]

    Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines

    T. Hyart and T.T. Heikkil\"a, Momentum-space structure of surface states in a topological semimetal with a nexus point of Dirac lines, Phys. Rev. B 93, 235147 (2016), arXiv:1604.06357

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  73. [73]

    Type-III and IV interacting Weyl points

    J. Nissinen and G.E. Volovik, Type-III and IV interacting Weyl points, arXiv:1702.04624

    work page internal anchor Pith review Pith/arXiv arXiv