Real and momentum space analysis of topological phases in 2D d-wave altermagnets

Manuel Calixto

arxiv: 2602.04854 · v2 · pith:KB63PLZUnew · submitted 2026-02-04 · ❄️ cond-mat.mes-hall · math-ph· math.MP· quant-ph

Real and momentum space analysis of topological phases in 2D d-wave altermagnets

Manuel Calixto This is my paper

Pith reviewed 2026-05-21 13:44 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall math-phmath.MPquant-ph

keywords altermagnetstopological phasesedge statesnanoribbonsfield-effect transistorspintronicsBerry curvatureconductivity anisotropy

0 comments

The pith

Hybridization of edge states in narrow altermagnetic nanoribbons opens a tunable gap for gated spin-polarized transport.

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

The paper shows that two-dimensional d-wave altermagnets undergo a topological phase transition when intra-sublattice hopping reaches a critical value, producing Dirac nodal points and associated spin splitting. In ribbon geometries the edge states hybridize when the ribbon is made ultra-narrow, opening an energy gap whose size can be controlled by an electrostatic gate. This gap enables ballistic, spatially spin-polarized currents to be switched on or off without requiring net magnetization, forming the basis for a proposed topological altermagnetic field-effect transistor. The analysis relies on both momentum-space Berry curvature and real-space information-theoretic markers such as fidelity susceptibility to characterize the topology even when translational symmetry is broken.

Core claim

In a tight-binding model of two-dimensional d-wave altermagnets, a topological phase transition occurs at critical intra-sublattice hopping strength t_a^C, marked by the appearance of Dirac nodal points, Berry curvature singularities, and pseudospin texture winding. Real-space examination of ribbon geometries demonstrates that hybridization of edge states in ultra-narrow nanoribbons produces a controllable energy gap. This gap is used to design a topological altermagnetic field-effect transistor in which ballistic and spatially spin-polarized transport is switched by electrostatic gating.

What carries the argument

Hybridization of topological edge states in ultra-narrow nanoribbons, which generates a gate-tunable energy gap while preserving spin polarization.

If this is right

Giant conductivity anisotropy appears because group velocities on the Fermi surface become strongly spin-dependent.
Spin-dependent steering of currents follows directly from the momentum-space distribution of velocities.
Ballistic transport through the gated gap supports high-speed spin-splitter logic without external magnetic fields.
The zero net magnetization of altermagnets combined with the tunable gap removes stray-field problems that limit conventional spintronic devices.

Where Pith is reading between the lines

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

The same edge-state hybridization mechanism could be tested in other altermagnetic symmetries or in three-dimensional geometries to broaden the range of possible devices.
Fidelity-susceptibility and inverse-participation-ratio markers might detect topological transitions in disordered or finite altermagnetic samples where conventional Chern-number calculations are unavailable.
Integration of these nanoribbons with conventional semiconductor gates could produce hybrid altermagnetic logic elements compatible with existing fabrication flows.

Load-bearing premise

The chosen tight-binding Hamiltonian with intra-sublattice hopping fully captures the low-energy electronic structure and edge-state behavior of actual d-wave altermagnets.

What would settle it

Transport measurements on fabricated ultra-narrow altermagnetic nanoribbons that either show or fail to show an electrostatically tunable gap in conductance, together with spatially resolved spin polarization of the current, would confirm or refute the hybridization mechanism.

Figures

Figures reproduced from arXiv: 2602.04854 by Manuel Calixto.

**Figure 2.** Figure 2: FIG. 2. Berry curvature (top row) and pseudo-spin (pseudo-Zeeman field) texture (bottom row) as a function of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: FIG. 3. Left: Energy dispersion as a function of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗

**Figure 5.** Figure 5: FIG. 5. Group velocity distribution accros the FS ( [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: FIG. 6. Polar plot showing the conductivity’s angular dependence for the [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

**Figure 7.** Figure 7: FIG. 7. Fidelity (left) and fidelity-susceptibility (right) of spin-down edge states as a function of [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗

**Figure 8.** Figure 8: FIG. 8. Four-spinor probability density [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗

**Figure 9.** Figure 9: FIG. 9. DOS for spin up (similar results for spin down) in the BI ( [PITH_FULL_IMAGE:figures/full_fig_p011_9.png] view at source ↗

**Figure 10.** Figure 10: FIG. 10. LDOS as a function of the energy [PITH_FULL_IMAGE:figures/full_fig_p012_10.png] view at source ↗

**Figure 11.** Figure 11: FIG. 11. Left panel: hibridization gap for spin-down electrons in a strip geometry of length [PITH_FULL_IMAGE:figures/full_fig_p013_11.png] view at source ↗

**Figure 12.** Figure 12: FIG. 12. Energy spectrum [PITH_FULL_IMAGE:figures/full_fig_p014_12.png] view at source ↗

**Figure 13.** Figure 13: FIG. 13. Four spinor probability density [PITH_FULL_IMAGE:figures/full_fig_p015_13.png] view at source ↗

**Figure 14.** Figure 14: FIG. 14. IPR of spin-up (red) and spin-down (blue) edge conduction states for [PITH_FULL_IMAGE:figures/full_fig_p015_14.png] view at source ↗

read the original abstract

Altermagnetism has recently emerged as a third fundamental branch of magnetism, combining the vanishing net magnetization of antiferromagnets with the high-momentum-dependent spin splitting of ferromagnets. This study provides a comprehensive real- and momentum-space analysis of topological phases in two-dimensional d-wave altermagnets. By employing a tight-binding Hamiltonian, we characterize the topological phase transition occurring at a critical intra-sublattice hopping strength ($t_a^C$). We examine the emergence of Dirac nodal points and the resulting Berry curvature singularities, supported by a visual analysis of pseudospin texture winding. Crucially, we analize spin splitting, effective altermagnetic strength, and investigate the transport implications of these phases, uncovering giant conductivity anisotropy and spin-dependent ``steering'' effects driven by group velocity distribution across the Fermi surface. Beyond bulk properties, we analyze the edge state topology in ribbon geometries through the lens of information-theoretic markers like fidelity-susceptibility and inverse participation ratio, offering a robust alternative to traditional Chern number calculations, without relying on translational symmetry. Our results demonstrate that the hybridization of edge states in ultra-narrow nanoribbons opens a controllable energy gap, a feature we exploit to propose a novel topological altermagnetic field-effect transistor design where ballistic and spatially spin-polarized transport can be electrostatically gated. This work establishes a theoretical and information-theoretic framework for ``edgetronics'' in altermagnetic materials, paving the way for next-generation, high-speed spintronic and ``spin-splitter'' logic devices and architectures.

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

This applies standard tight-binding tools to d-wave altermagnets, maps a topological transition and edge hybridization, then sketches a gated nanoribbon transistor, but the device step assumes the minimal model holds without further checks.

read the letter

The main thing to know is that the authors take a simple tight-binding Hamiltonian for 2D d-wave altermagnets, identify a topological transition at a critical intra-sublattice hopping t_a^C, and then examine edge states in ribbons to suggest an electrostatically gated transistor that exploits a hybridization gap for spin-polarized ballistic transport. The bulk analysis covers Dirac points, Berry curvature singularities, pseudospin winding, spin splitting, and resulting conductivity anisotropy plus velocity-based steering effects. For the ribbons they switch to information-theoretic markers such as fidelity susceptibility and inverse participation ratio, which let them track edge topology without assuming translational symmetry. That choice is practical for narrow finite-width structures and gives a concrete alternative to Chern numbers. The calculations appear to follow directly from the model parameters, with no obvious post-hoc fitting visible in the description. The soft spot sits in the device proposal. The controllable gap and gate tunability are shown inside the minimal model that includes only the intra-sublattice term, yet real d-wave altermagnets may require next-nearest-neighbor hoppings, ab-initio corrections, or self-consistent electrostatics. Without those comparisons the claimed giant anisotropy, steering, and transistor functionality remain tied to the lattice approximation; any mismatch at the edge spectrum would weaken the practical claim. The abstract states the transition and transport results but does not include robustness tests or error estimates, so the strength of the anisotropy and steering statements is hard to judge from the given material alone. This paper is aimed at researchers already working on altermagnets or 2D topological spintronics who want a phase diagram plus an edge-state toolkit. A reader interested in device ideas could extract the transistor sketch as a starting hypothesis, though they would need to test the model assumptions themselves. It deserves peer review because the core numerics are standard and the edge-marker approach adds a usable detail, even if the broader device implications need more material grounding to stand up.

Referee Report

2 major / 2 minor

Summary. The manuscript analyzes topological phases in 2D d-wave altermagnets via a tight-binding Hamiltonian. It locates a phase transition at critical intra-sublattice hopping t_a^C, studies Dirac points, Berry curvature singularities, pseudospin winding, spin splitting, and transport features such as giant conductivity anisotropy and spin-dependent steering. Edge states in ribbon geometries are characterized with fidelity-susceptibility and inverse participation ratio as alternatives to Chern numbers; the hybridization gap in ultra-narrow nanoribbons is then used to propose an electrostatically gated topological altermagnetic field-effect transistor with ballistic, spin-polarized transport.

Significance. If the minimal-model results hold, the work offers a useful theoretical and information-theoretic framework for edge-state physics in altermagnets and a concrete device concept for gate-tunable spintronics. The combination of momentum-space topology diagnostics with real-space ribbon analysis and the explicit proposal for an altermagnetic FET constitute the main potential contributions.

major comments (2)

[§2 and §4] §2: The tight-binding Hamiltonian is restricted to intra-sublattice hopping t_a, with the topological transition placed at t_a^C. The subsequent claim in §4 that edge-state hybridization produces a controllable gap exploitable for an electrostatically gated FET inherits any limitations of this minimal model. No comparison to DFT-derived parameters, next-nearest-neighbor terms, or self-consistent gate potential is provided; without such checks the gap tunability and device functionality remain unverified for realistic d-wave altermagnets.
[transport analysis] Abstract and transport section: The reported giant conductivity anisotropy and spin-dependent steering are stated to arise from group-velocity distribution on the Fermi surface. Explicit formulas, numerical values, or Fermi-surface plots quantifying the anisotropy ratio and steering angle are needed to confirm that these effects follow directly from the model rather than from post-hoc interpretation.

minor comments (2)

[Abstract] Abstract: 'analise' is a typographical error and should read 'analyze'.
[§2] Notation for the critical hopping t_a^C and the effective altermagnetic strength should be defined consistently between the model section and the figures.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive suggestions. We address the two major comments in turn, clarifying the scope of our minimal model while indicating revisions that will strengthen the presentation of both the topological analysis and the transport results.

read point-by-point responses

Referee: [§2 and §4] §2: The tight-binding Hamiltonian is restricted to intra-sublattice hopping t_a, with the topological transition placed at t_a^C. The subsequent claim in §4 that edge-state hybridization produces a controllable gap exploitable for an electrostatically gated FET inherits any limitations of this minimal model. No comparison to DFT-derived parameters, next-nearest-neighbor terms, or self-consistent gate potential is provided; without such checks the gap tunability and device functionality remain unverified for realistic d-wave altermagnets.

Authors: Our tight-binding model is deliberately minimal, retaining only the intra-sublattice hopping t_a that encodes the d-wave altermagnetic symmetry breaking while allowing an analytic location of the topological transition at t_a^C. This framework isolates the emergence of Dirac points, Berry curvature singularities, and the subsequent edge-state hybridization without extraneous parameters. We agree that the FET proposal in §4 therefore rests on the same idealization and that explicit checks against DFT parameters, next-nearest-neighbor hoppings, or a self-consistent gate potential would be desirable for quantitative realism. In the revised manuscript we will add a dedicated paragraph in §2 and a short subsection in §4 that (i) states the model assumptions explicitly, (ii) discusses how additional hoppings would renormalize t_a^C but are not expected to destroy the topological character, and (iii) notes that a fully self-consistent treatment of the gate potential lies beyond the present scope and is left for future device-oriented studies. revision: yes
Referee: [transport analysis] Abstract and transport section: The reported giant conductivity anisotropy and spin-dependent steering are stated to arise from group-velocity distribution on the Fermi surface. Explicit formulas, numerical values, or Fermi-surface plots quantifying the anisotropy ratio and steering angle are needed to confirm that these effects follow directly from the model rather than from post-hoc interpretation.

Authors: The conductivity anisotropy and spin-dependent steering are obtained directly from the semiclassical expression for the current carried by states on the Fermi surface, where the group-velocity vectors are computed from the tight-binding dispersion. While the manuscript presents supporting Fermi-surface contours and velocity distributions, we accept that explicit formulas and numerical ratios were not tabulated. In the revision we will insert (i) the explicit integral expression for the conductivity tensor components in terms of the velocity distribution, (ii) numerical values of the anisotropy ratio for representative fillings and t_a, and (iii) an enhanced Fermi-surface plot that overlays velocity arrows and indicates the resulting steering angle. These additions will make the quantitative link between the band-structure features and the transport observables unambiguous. revision: yes

Circularity Check

0 steps flagged

No circularity: model-derived gap and transistor proposal follow directly from Hamiltonian solution

full rationale

The paper introduces a tight-binding Hamiltonian, locates the topological transition at a critical intra-sublattice hopping t_a^C by solving the bulk band structure, and then computes edge-state hybridization and gap opening in nanoribbon geometries as direct numerical consequences of that same Hamiltonian. These steps constitute standard model-based calculations rather than any redefinition, parameter fit renamed as prediction, or load-bearing self-citation. Information-theoretic markers (fidelity-susceptibility, inverse participation ratio) are applied to the model's eigenstates as an alternative diagnostic, without circular dependence on the final claim. The altermagnetic FET proposal is an interpretation of the computed gate-tunable gap within the model; no external data or prior result is required to close the derivation loop. The chain is therefore self-contained.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Based on abstract only; the model implicitly assumes a standard tight-binding lattice with d-wave altermagnetic order and that information-theoretic quantities (fidelity-susceptibility, IPR) serve as faithful topological markers without translational symmetry.

free parameters (1)

t_a^C
Critical intra-sublattice hopping strength at which the topological transition occurs; its numerical value is not given but is treated as a well-defined threshold in the model.

axioms (2)

domain assumption Tight-binding approximation suffices to capture Dirac nodal points and Berry curvature singularities in d-wave altermagnets.
Invoked by the choice of Hamiltonian to characterize the phase transition.
domain assumption Fidelity-susceptibility and inverse participation ratio reliably detect edge-state topology in ribbon geometries without requiring translational symmetry.
Presented as a robust alternative to Chern-number calculations.

pith-pipeline@v0.9.0 · 5816 in / 1464 out tokens · 30183 ms · 2026-05-21T13:44:10.376325+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The Hamiltonian for spins electrons in momentum space adopts the form Hs(k)=ds(k)·τ ... ds^z(k)=sJ+ta∑sgn(δ′)e^{ik·δ′}
IndisputableMonolith/Foundation/DimensionForcing.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

topological phase transition occurring at a critical intra-sublattice hopping strength (t_a^C = J/4)

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

32 extracted references · 32 canonical work pages · 1 internal anchor

[1]

I. I. Mazin, Editorial: Altermagnetism—a new punch line of fundamental magnetism, Phys. Rev. X12, 040002 (2022)

work page 2022
[2]

Šmejkal, J

L. Šmejkal, J. Sinova, and T. Jungwirth, Beyond conventional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Phys. Rev. X12, 031042 (2022)

work page 2022
[3]

Šmejkal, J

L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X12, 040501 (2022)

work page 2022
[4]

Krempaský, L

J. Krempaský, L. Šmejkal, S. W. D’Souza, M. Hajlaoui, G. Springholz,et al. , Altermagnetic lifting of Kramers spin degeneracy, Nature626, 517 (2024)

work page 2024
[5]

Schiff, A

H. Schiff, A. Corticelli, A. Guerreiro, J. Romhányi, and P. McClarty, The crystallographic spin point groups and their representations, SciPost Phys.18, 109 (2025)

work page 2025
[6]

I. I. Mazin, Altermagnetism in MnTe: Origin, predicted manifestations, and routes to detwinning, Phys. Rev. B107, L100418 (2023)

work page 2023
[7]

W. Feng, X. Zhou, L. Šmejkal, L. Wu, Z. Zhu, H. Guo, and Y. Yao, An anomalous hall effect in altermagnetic ruthenium dioxide, Nat. Electron.5, 735 (2022)

work page 2022
[8]

Fedchenko, J

O. Fedchenko, J. Minár, A. Akashdeep, S. W. D’Souza,et al., Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO2, Sci. Adv.10, eadj4883 (2024)

work page 2024
[9]

Manchon and S

A. Manchon and S. Zhang, Theory of nonequilibrium intrinsic spin torque in a single nanomagnet, Phys. Rev. B78, 212405 (2008)

work page 2008
[10]

I. M. Miron, K. Garello, G. Gaudin, P.-J. Zermatten, M. V. Costache, S. Auffret, S. Bandiera, B. Rodmacq, A. Schuhl, and P. Gambardella, Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection, Nature 476, 189 (2011)

work page 2011
[11]

Liu, C.-F

L. Liu, C.-F. Pai, Y. Li, H. W. Tseng, D. C. Ralph, and R. A. Buhrman, Spin-torque switching with the giant spin Hall effect of tantalum, Science336, 555–558 (2012)

work page 2012
[12]

González-Hernández, L

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

work page 2021
[13]

H. Bai, L. Han, X. Feng, Y. J. Zhou, R. Su, Q. Wang, L. Liao, W. Zhu, X. Chen, F. Pan, X. Fan, and C. Song, Observation of spin splitting torque in a collinear antiferromagnet RuO2., Phys. Rev. Lett.128 19, 197202 (2021)

work page 2021
[14]

V. D. Nguyen, S. Rao, K. Wostyn, and S. Couet, Recent progress in spin-orbit torque magnetic random-access memory, npj Spintronics2, 48 (2024)

work page 2024
[15]

M.CalixtoandE.Romera,Identifyingtopological-bandinsulatortransitionsinsiliceneandother2Dgappeddiracmaterials by means of Rényi-Wehrl entropy, EPL (Europhysics Letters)109, 40003 (2015)

work page 2015
[16]

Romera and M

E. Romera and M. Calixto, Uncertainty relations and topological-band insulator transitions in 2D gapped dirac materials, Journal of Physics: Condensed Matter27, 175003 (2015)

work page 2015
[17]

Calixto and E

M. Calixto and E. Romera, Inverse participation ratio and localization in topological insulator phase transitions, Journal of Statistical Mechanics: Theory and Experiment2015, P06029 (2015)

work page 2015
[18]

Calixto, E

M. Calixto, E. Romera, and O. Castaños, Analogies between the topological insulator phase of 2D Dirac materials and the superradiant phase of atom-field systems, International Journal of Quantum Chemistry121, e26464 (2021)

work page 2021
[19]

Castaños, E

O. Castaños, E. Romera, and M. Calixto, Information theoretic analysis of landau levels in monolayer phosphorene under magnetic and electric fields, Materials Research Express6, 106316 (2019)

work page 2019
[20]

Calixto, N

M. Calixto, N. A. Cordero, E. Romera, and O. Castaños, Signatures of topological phase transitions in higher Landau levels of HgTe/CdTe quantum wells from an information theory perspective, Physica A: Statistical Mechanics and its Applications 605, 128057 (2022)

work page 2022
[21]

Calixto, A

M. Calixto, A. Mayorgas, N. A. Cordero, E. Romera, and O. Castaños, Faraday rotation and transmittance as markers of topological phase transitions in 2d materials, SciPost Phys.16, 077 (2024)

work page 2024
[22]

Calixto and O

M. Calixto and O. Castaños, Localization and entanglement characterization of edge states in HgTe quantum wells in a finite strip geometry, International Journal of Modern Physics B39, 2550263 (2025)

work page 2025
[23]

Calixto, A

M. Calixto, A. Mayorgas, and O. Castaños, Capturing magic angles in twisted bilayer graphene from information theory markers, Physica E: Low-dimensional Systems and Nanostructures169, 116199 (2025)

work page 2025
[24]

Gu, Fidelity approach to quantum phase transitions, International Journal of Modern Physics B24, 4371–4458 (2010)

S.-J. Gu, Fidelity approach to quantum phase transitions, International Journal of Modern Physics B24, 4371–4458 (2010)

work page 2010
[25]

Zanardi and N

P. Zanardi and N. Paunković, Ground state overlap and quantum phase transitions, Phys. Rev. E74, 031123 (2006)

work page 2006
[26]

Bistritzer and A

R. Bistritzer and A. H. MacDonald, Moiré bands in twisted double-layer graphene, Proceedings of the National Academy of Sciences108, 12233–12237 (2011)

work page 2011
[27]

Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature556, 80–84 (2018)

work page 2018
[28]

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional superconduc- tivity in magic-angle graphene superlattices, Nature556, 43–50 (2018). 18

work page 2018
[29]

Zhou, H.-Z

B. Zhou, H.-Z. Lu, R.-L. Chu, S.-Q. Shen, and Q. Niu, Finite size effects on helical edge states in a quantum spin-hall system, Phys. Rev. Lett.101, 246807 (2008)

work page 2008
[30]

S. Fang, Z. Yang, J. Wang, X. Yang, J. Lu, C. H. Lee, X. Wang, and Y. S. Ang, Edgetronics in two-dimensional altermagnets (2025), arXiv:2508.10451 [cond-mat.mes-hall]

work page internal anchor Pith review arXiv 2025
[31]

Jungwirth, R

T. Jungwirth, R. M. Fernandes, E. Fradkin, A. H. MacDonald, J. Sinova, and L. Šmejkal, Altermagnetism: An unconven- tional spin-ordered phase of matter, Newton1, 100162 (2025)

work page 2025
[32]

Y.Fukaya, B.Lu, K.Yada, Y.Tanaka,andJ.Cayao,Superconductingphenomenainsystemswithunconventionalmagnets, Journal of Physics: Condensed Matter37, 313003 (2025)

work page 2025

[1] [1]

I. I. Mazin, Editorial: Altermagnetism—a new punch line of fundamental magnetism, Phys. Rev. X12, 040002 (2022)

work page 2022

[2] [2]

Šmejkal, J

L. Šmejkal, J. Sinova, and T. Jungwirth, Beyond conventional ferromagnetism and antiferromagnetism: A phase with nonrelativistic spin and crystal rotation symmetry, Phys. Rev. X12, 031042 (2022)

work page 2022

[3] [3]

Šmejkal, J

L. Šmejkal, J. Sinova, and T. Jungwirth, Emerging research landscape of altermagnetism, Phys. Rev. X12, 040501 (2022)

work page 2022

[4] [4]

Krempaský, L

J. Krempaský, L. Šmejkal, S. W. D’Souza, M. Hajlaoui, G. Springholz,et al. , Altermagnetic lifting of Kramers spin degeneracy, Nature626, 517 (2024)

work page 2024

[5] [5]

Schiff, A

H. Schiff, A. Corticelli, A. Guerreiro, J. Romhányi, and P. McClarty, The crystallographic spin point groups and their representations, SciPost Phys.18, 109 (2025)

work page 2025

[6] [6]

I. I. Mazin, Altermagnetism in MnTe: Origin, predicted manifestations, and routes to detwinning, Phys. Rev. B107, L100418 (2023)

work page 2023

[7] [7]

W. Feng, X. Zhou, L. Šmejkal, L. Wu, Z. Zhu, H. Guo, and Y. Yao, An anomalous hall effect in altermagnetic ruthenium dioxide, Nat. Electron.5, 735 (2022)

work page 2022

[8] [8]

Fedchenko, J

O. Fedchenko, J. Minár, A. Akashdeep, S. W. D’Souza,et al., Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO2, Sci. Adv.10, eadj4883 (2024)

work page 2024

[9] [9]

Manchon and S

A. Manchon and S. Zhang, Theory of nonequilibrium intrinsic spin torque in a single nanomagnet, Phys. Rev. B78, 212405 (2008)

work page 2008

[10] [10]

I. M. Miron, K. Garello, G. Gaudin, P.-J. Zermatten, M. V. Costache, S. Auffret, S. Bandiera, B. Rodmacq, A. Schuhl, and P. Gambardella, Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection, Nature 476, 189 (2011)

work page 2011

[11] [11]

Liu, C.-F

L. Liu, C.-F. Pai, Y. Li, H. W. Tseng, D. C. Ralph, and R. A. Buhrman, Spin-torque switching with the giant spin Hall effect of tantalum, Science336, 555–558 (2012)

work page 2012

[12] [12]

González-Hernández, L

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

work page 2021

[13] [13]

H. Bai, L. Han, X. Feng, Y. J. Zhou, R. Su, Q. Wang, L. Liao, W. Zhu, X. Chen, F. Pan, X. Fan, and C. Song, Observation of spin splitting torque in a collinear antiferromagnet RuO2., Phys. Rev. Lett.128 19, 197202 (2021)

work page 2021

[14] [14]

V. D. Nguyen, S. Rao, K. Wostyn, and S. Couet, Recent progress in spin-orbit torque magnetic random-access memory, npj Spintronics2, 48 (2024)

work page 2024

[15] [15]

M.CalixtoandE.Romera,Identifyingtopological-bandinsulatortransitionsinsiliceneandother2Dgappeddiracmaterials by means of Rényi-Wehrl entropy, EPL (Europhysics Letters)109, 40003 (2015)

work page 2015

[16] [16]

Romera and M

E. Romera and M. Calixto, Uncertainty relations and topological-band insulator transitions in 2D gapped dirac materials, Journal of Physics: Condensed Matter27, 175003 (2015)

work page 2015

[17] [17]

Calixto and E

M. Calixto and E. Romera, Inverse participation ratio and localization in topological insulator phase transitions, Journal of Statistical Mechanics: Theory and Experiment2015, P06029 (2015)

work page 2015

[18] [18]

Calixto, E

M. Calixto, E. Romera, and O. Castaños, Analogies between the topological insulator phase of 2D Dirac materials and the superradiant phase of atom-field systems, International Journal of Quantum Chemistry121, e26464 (2021)

work page 2021

[19] [19]

Castaños, E

O. Castaños, E. Romera, and M. Calixto, Information theoretic analysis of landau levels in monolayer phosphorene under magnetic and electric fields, Materials Research Express6, 106316 (2019)

work page 2019

[20] [20]

Calixto, N

M. Calixto, N. A. Cordero, E. Romera, and O. Castaños, Signatures of topological phase transitions in higher Landau levels of HgTe/CdTe quantum wells from an information theory perspective, Physica A: Statistical Mechanics and its Applications 605, 128057 (2022)

work page 2022

[21] [21]

Calixto, A

M. Calixto, A. Mayorgas, N. A. Cordero, E. Romera, and O. Castaños, Faraday rotation and transmittance as markers of topological phase transitions in 2d materials, SciPost Phys.16, 077 (2024)

work page 2024

[22] [22]

Calixto and O

M. Calixto and O. Castaños, Localization and entanglement characterization of edge states in HgTe quantum wells in a finite strip geometry, International Journal of Modern Physics B39, 2550263 (2025)

work page 2025

[23] [23]

Calixto, A

M. Calixto, A. Mayorgas, and O. Castaños, Capturing magic angles in twisted bilayer graphene from information theory markers, Physica E: Low-dimensional Systems and Nanostructures169, 116199 (2025)

work page 2025

[24] [24]

Gu, Fidelity approach to quantum phase transitions, International Journal of Modern Physics B24, 4371–4458 (2010)

S.-J. Gu, Fidelity approach to quantum phase transitions, International Journal of Modern Physics B24, 4371–4458 (2010)

work page 2010

[25] [25]

Zanardi and N

P. Zanardi and N. Paunković, Ground state overlap and quantum phase transitions, Phys. Rev. E74, 031123 (2006)

work page 2006

[26] [26]

Bistritzer and A

R. Bistritzer and A. H. MacDonald, Moiré bands in twisted double-layer graphene, Proceedings of the National Academy of Sciences108, 12233–12237 (2011)

work page 2011

[27] [27]

Y. Cao, V. Fatemi, A. Demir, S. Fang, S. L. Tomarken, J. Y. Luo, J. D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R. C. Ashoori, and P. Jarillo-Herrero, Correlated insulator behaviour at half-filling in magic-angle graphene superlattices, Nature556, 80–84 (2018)

work page 2018

[28] [28]

Y. Cao, V. Fatemi, S. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, and P. Jarillo-Herrero, Unconventional superconduc- tivity in magic-angle graphene superlattices, Nature556, 43–50 (2018). 18

work page 2018

[29] [29]

Zhou, H.-Z

B. Zhou, H.-Z. Lu, R.-L. Chu, S.-Q. Shen, and Q. Niu, Finite size effects on helical edge states in a quantum spin-hall system, Phys. Rev. Lett.101, 246807 (2008)

work page 2008

[30] [30]

S. Fang, Z. Yang, J. Wang, X. Yang, J. Lu, C. H. Lee, X. Wang, and Y. S. Ang, Edgetronics in two-dimensional altermagnets (2025), arXiv:2508.10451 [cond-mat.mes-hall]

work page internal anchor Pith review arXiv 2025

[31] [31]

Jungwirth, R

T. Jungwirth, R. M. Fernandes, E. Fradkin, A. H. MacDonald, J. Sinova, and L. Šmejkal, Altermagnetism: An unconven- tional spin-ordered phase of matter, Newton1, 100162 (2025)

work page 2025

[32] [32]

Y.Fukaya, B.Lu, K.Yada, Y.Tanaka,andJ.Cayao,Superconductingphenomenainsystemswithunconventionalmagnets, Journal of Physics: Condensed Matter37, 313003 (2025)

work page 2025