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REVIEW 3 major objections 4 minor 98 references

Ferroelectricity in a magnon Bose-Einstein condensate: Nonreciprocal superfluidity, exceptional points, and Majorana bosons

T0 review · 3 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

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Pith's one-line read Positive feedback via the Aharonov-Casher phase drives a spontaneous ferroelectric transition in a magnon Bose-Einstein condensate when the spin-orbit coupling η exceeds 1.

desk verdict Clean mean-field theory with a new ferroelectric transition, but the transition rides on a sign of the electromagnetic self-energy that is imported from the authors' own prior paper and not independently derived. read the letter →

arxiv 2512.22073 v2 pith:ZKPG4YZP submitted 2025-12-26 cond-mat.mes-hall cond-mat.quant-gascond-mat.supr-con

Kazuki Yamamoto , Takuto Kawakami , Mikito Koshino This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.quant-gascond-mat.supr-con
keywords magnonBose-EinsteincondensateAharonov-CasherphaseferroelectricityexceptionalpointnonreciprocalsuperfluidMajoranabosonBogoliubov-deGennestheoryspin-orbitcoupling
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper argues that a magnon Bose-Einstein condensate coupled to electric fields through the Aharonov-Casher phase can spontaneously polarize without any external field. The mechanism is a positive feedback loop: an electric field generates magnon orbital currents, those currents produce an electric polarization, and that polarization strengthens the original field. When the dimensionless spin-orbit coupling η exceeds 1, the mean-field energy develops two degenerate minima with opposite persistent supercurrents, so inversion symmetry breaks and the condensate becomes ferroelectric and nonreciprocal. At the critical point η=1, the whole Bogoliubov band collapses into an exceptional point whose coalesced eigenstate is a bosonic analog of a Majorana fermion. If correct, this gives a new route to ferroelectricity and nonreciprocal transport in magnetic insulators.

What carries the argument

The key object is the Aharonov-Casher phase, an effective vector potential A_m = g_AC E × e_z that acts on magnons. The paper's total Hamiltonian includes a self-energy term -(g_AC^2/2ε0 a)Σ j^2 that encodes positive electromagnetic feedback. The dimensionless parameter η = g_AC^2/(m*ε0 a^3 n0) controls the transition. The analysis uses the bosonic Bogoliubov–de Gennes matrix L(q)=σ_z H_B(q), which is pseudo-Hermitian but not Hermitian; its non-diagonalizability at η=1 produces the exceptional point. The self-consistency relation θ_AC = -η sinΔ closes the loop that destabilizes the Δ=0 state.

What would settle it

Compute or measure the sign of the electric-field-induced magnon current contribution to the polarization. If a microscopic calculation of the electromagnetic energy (beyond the minimalist Eq. (4)) yields θ_AC = +η sinΔ, or if an experiment in a magnon ring detects no spontaneous polarization for η>1, the central claim is falsified.

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Extended reading notes

Core claim

The central claim is that the sign of the electromagnetic feedback in magnon systems is positive, unlike the diamagnetic Meissner response in superconductors. With the energy functional H = H0 - (g_AC^2/2ε0 a) Σ j_i^2, the self-consistent Aharonov-Casher phase is θ_AC = -η sinΔ, and the mean-field ground state minimizes f(Δ) = -2 cosΔ - η sin²Δ. For η = g_AC^2/(m*ε0 a^3 n0) ≤ 1 the only minimum is Δ=0, a conventional superfluid with no polarization. For η > 1 the minima are at Δ = ± arccos(1/η), giving a finite magnon supercurrent and a spontaneous electric polarization; the two states are parity partners. At η=1 the bosonic Bogoliubov–de Gennes matrix L(q) becomes proportional to [[1,1],[-1

Load-bearing premise

The whole instability rests on the sign and form of the electromagnetic self-energy in Eq. (4) — specifically that the self-induced Aharonov-Casher phase is θ_AC = -η sinΔ with positive feedback; if the sign were reversed, no ferroelectric transition would occur.

Editorial extensions

If this is right

  • For η > 1 the magnon superfluid is ferroelectric: it carries a persistent supercurrent and a spontaneous electric polarization that can point in either of two directions.
  • The quasiparticle spectrum becomes nonreciprocal, so a magnon moving left and right at the same wave number has different energies, enabling direction-dependent transport.
  • At the transition point η = 1, every momentum mode is an exceptional point and the Bogoliubov band is exactly flat at zero energy.
  • The coalesced zero mode is invariant under particle–hole transformation, giving a bosonic analog of a Majorana fermion — a single self-conjugate quasiparticle.
  • The ferroelectric phase survives only in a stability window set by the interaction strength u: u > 2η for Landau stability and u > 2(η - 1/η) against dynamical collapse.

Reading between the lines

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

  • If the positive-feedback sign is generic, similar self-induced ferroelectricity might appear in other neutral dipole condensates, such as exciton-polaritons or photon BECs with artificial gauge fields.
  • The global exceptional point at η=1 suggests a non-Hermitian topological phase boundary, which could host non-Hermitian edge modes or nonlocal response beyond the simple flat band described here.
  • The Majorana-boson interpretation could be sharpened by computing the noise spectrum or entanglement properties of the coalesced state, since bosonic self-conjugacy differs from fermionic Majorana statistics.
  • A direct experimental test would be to measure a hysteretic electric polarization and a nonreciprocal magnon transmission in a ring or annulus of a magnetic insulator with strong spin-orbit coupling.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The manuscript proposes a ferroelectric instability in a magnon Bose-Einstein condensate, driven by positive electromagnetic feedback through the Aharonov-Casher (AC) phase. Using a one-dimensional Bose-Hubbard model with a feedback term -(g_AC^2/2ε0a)Σj^2, the authors find that for a dimensionless coupling η>1 the mean-field energy is minimized at a nonzero phase twist Δ=±arccos(1/η), producing a persistent supercurrent and spontaneous electric polarization. The bosonic Bogoliubov-de Gennes (BdG) analysis yields a phase diagram with Landau and dynamical instability regions, and at η=1 the BdG matrix becomes globally degenerate and non-diagonalizable, yielding a particle-hole symmetric 'Majorana boson' mode. The paper also includes a classical Bohr-van Leeuwen theorem for electric polarization.

Significance. If the model is correct, the paper presents a conceptually novel ferroelectric mechanism in a magnon BEC, with nonreciprocal superfluidity and an exceptional point that extend the known physics of geometric phases in magnonic systems. The construction is elegant and the algebra from the assumed Hamiltonian is internally consistent. However, the central prediction hinges on the sign and density dependence of the electromagnetic feedback term, which are not firmly established in the manuscript. The exceptional point and Majorana-mode interpretation are notable but rely on the same model.

major comments (3)
  1. [Appendix B, Eq. (B1)] The derivation of the self-coupling term Eq. (4) is not valid as written. The identity E·δD = (-P·δE + D·δD - P·δP)/ε0 in Eq. (B1) is algebraically incorrect: substituting ε0E=D-P and δD=ε0δE+δP gives E·δD = [(D-P)/ε0]·δD, which does not reduce to the stated expression. The standard electrostatic energy density at D=0 in a dielectric is +P²/(2ε0), not -P²/(2ε0). The negative sign of the j² term in Eq. (4) is the origin of the positive feedback and of the ferroelectric instability for η>1. Since the derivation in Appendix B is flawed, the manuscript does not provide a sound basis for this sign. The authors must either give a correct derivation or cite a source that unambiguously establishes the sign.
  2. [Eq. (7) vs Eq. (9)] The density scaling of the control parameter is internally inconsistent. Substituting the condensate ansatz (5) into the current (2) gives j=(2tn0/ℏ)sinΔ. With η=g_AC²/(m*ε0a³n0) as in Eq. (7), the feedback energy from Eq. (4) becomes -tη n0³ sin²Δ, not -tη n0 sin²Δ as in Eq. (9). Correspondingly, the self-consistent AC phase is θ_AC=-η n0² sinΔ, not -η sinΔ. The chemical potential Eq. (13) is also consistent only with η∝n0, because the thermodynamic relation μ=∂⟨H⟩/∂n0 reproduces Eq. (13) when the final term in Eq. (9) scales as n0² (i.e., η∝n0). Thus the phase diagram in Fig. 3 and the instability thresholds in Eq. (18) are based on an incorrect density dependence. Please correct the definition of η or revise the subsequent equations.
  3. [Eq. (4) and central premise] Even apart from the density scaling, the manuscript does not independently justify the positive-feedback Hamiltonian (4). The text states that it follows from a 'standard prescription' without derivation, and Appendix B is flawed. Since the entire conclusion—ferroelectricity, nonreciprocal superfluidity, exceptional point, Majorana boson—relies on the negative sign of the j² term, this is a load-bearing gap. Provide a rigorous derivation, or clearly state the conditions under which Eq. (4) holds, and discuss whether the sign is realized in physical magnon systems.
minor comments (4)
  1. [Abstract and Introduction] Typo: 'quaihole' should be 'quasihole' in the Introduction (also noticed in the abstract as 'quaihole' in the phrase 'quasiparticle and quaihole').
  2. [After Eq. (9)] Typo: 'Hamltonian' should be 'Hamiltonian'.
  3. [Eq. (18)] The low-energy expansion for η≥1 contains a term -√(1/η) q. This is correct for the moving condensate, but the presentation could be clearer: the condition for avoiding negative energies (u>2η) follows from requiring the linear term to be dominated by the positive |q| term. A brief explanation would help.
  4. [Majorana interpretation] The statement that the coalesced eigenvector (1,-1)^T is 'invariant under particle-hole transformation' is up to a sign (σx maps it to its negative). This should be stated precisely, and the physical significance of a bosonic Majorana mode distinguished from a fermionic one.

Circularity Check

1 steps flagged · score 4.0 of 10

Ferroelectric transition depends on the sign of the self-cited −j² term in Eq. (4); the subsequent derivation is algebraically self-contained but not an independent test of that premise.

  1. self citation load bearing [Model Hamiltonian, Eq. (4); Appendix B]
    "In accordance with the standard prescription, we include the term ∫ dV(D²−P²)/2ε0 as an additional contribution to the original Hamiltonian H0. [25] Consequently, for the present system, the total Hamiltonian is expressed as H=H0−(g²AC/(2ε0a))∑i j²i,i+1, (4)"

    The entire ferroelectric mechanism comes from the −j² term: substituting the condensate ansatz gives ⟨H⟩=−2tn0 cosΔ+Un0²/2−tηn0 sin²Δ (Eq. 9), whose only Δ-dependent term that destabilizes Δ=0 for η>1 is −tηn0 sin²Δ. Its sign and coefficient originate in the −P²/2ε0 term of Eq. (4), which the text attributes to Ref. [25] ("standard prescription... [25]") and Appendix B re-derives only by "following the argument in Ref. [25]" and using Eq. (3). Thus the transition, the exceptional point at η=1, and the Majorana-boson state are direct algebraic consequences of the same authors' previous Hamiltonian, not independently established in this paper.

full rationale

The derivation from Eq. (4) onward is algebraically self-contained: f(Δ), the non-diagonalizable L(q)∝[[1,1],[−1,−1]] at η=1, and the Landau/dynamical instability criteria all follow from the stated mean-field ansatz without fitted parameters or data. The new results—nonreciprocal superfluidity and the BZ-wide exceptional point—do not reduce to a previously published result, so this is not a case of every 'prediction' collapsing into its input. However, the load-bearing premise is the positive-feedback Hamiltonian: the −j² term in Eq. (4) is what makes Δ=±arccos(1/η) minima for η>1, and that term is imported from the authors' own Ref. [25]. Appendix B sketchily re-derives it by following that same reference and reusing Eq. (3), so it does not function as independent external support. The central claim still has independent content—the ferroelectric transition and exceptional-point/Majorana-boson interpretation are new—but the mechanism itself rests on a self-cited foundation. Concerns about whether standard electrostatics would give the opposite sign for (D²−P²)/2ε0 are physical-correctness concerns, not additional evidence of circularity, and are not counted in this score.

Assumptions & free parameters 2 free parameters · 6 assumptions · 0 invented entities

No new particles, fields, or conserved quantities are introduced. The 'Majorana boson' label applies a previously discussed concept (Refs. [84,96-98]) to the coalesced BdG eigenvector at η=1 and carries no independent experimental signature beyond the exceptional band. The main ledger items are the dimensionless model parameters η and u, and the self-cited electromagnetic feedback Hamiltonian.

free parameters (2)
  • η (dimensionless Aharonov-Casher coupling) = not fitted; threshold η=1
    Defined in Eq. (7) as proportional to g_AC² n0/(m*ε0 a³); controls the transition. No microscopic value is given for any real magnon insulator, so whether the η>1 regime is accessible is unverified.
  • u = U n0/t (dimensionless interaction) = not fitted; instability lines u=2η and u=2(η-1/η)
    Introduced around Eq. (18) and Fig. 3; the phase diagram depends on u, but no material-specific interaction is specified.
assumptions (6)
  • domain assumption Bogoliubov mean-field approximation: condensation in a single Bloch state with macroscopic occupation, fluctuations retained to quadratic order.
    Invoked in 'Bosonic BdG Hamiltonian' after Eq. (10). Neglects higher-order fluctuations and, in 1D, the absence of true long-range order; standard for BEC but an assumption.
  • ad hoc to paper Electromagnetic energy of the dipole superfluid is H0 + ∫(D²-P²)/(2ε0) with D=0 (Eq. 4).
    Imported from the authors' own Ref. [25]; Appendix B gives a sketch but the functional form is not independently derived in this paper. This is the central modeling premise.
  • domain assumption Magnon electric polarization is P = g_AC j_m × e_z (Eq. 3).
    Taken from magnon magnetoelectric literature [2,3,25]; assumed exact, ignoring material non-idealities.
  • domain assumption The self-induced AC phase is uniform and given by θ_AC = -η sinΔ (Eq. 7), with all induced field contributions captured by the local current.
    Assumes uniform internal field and neglects boundary/depolarization inhomogeneities; used to eliminate θ_AC.
  • domain assumption One-dimensional Bose-Hubbard ring is a sufficient minimal model for magnon BEC with AC coupling.
    The paper states 'as a minimal theoretical description' and imposes periodic boundary conditions; genuine 1D/ring effects (phase slips, Luttinger physics) are not addressed.
  • standard math Stability is determined by positivity of eigenvalues of the pseudo-Hermitian matrix L(q)=σ_z H_B(q); complex eigenvalues signal dynamical instability.
    Standard bosonic BdG stability criterion used in Eqs. (14)-(18).

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Pith. "Pith review of Ferroelectricity in a magnon Bose-Einstein condensate: Nonreciprocal superfluidity, exceptional points, and Majorana bosons." pith.science (2026). https://pith.science/paper/ZKPG4YZP

@misc{pith2026251222073,
  author       = {Pith},
  title        = {Pith review of: Ferroelectricity in a magnon Bose-Einstein condensate: Nonreciprocal superfluidity, exceptional points, and Majorana bosons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/ZKPG4YZP}},
  note         = {Machine review of arXiv:2512.22073}
}
read the original abstract

We investigate a ferroelectric instability of a magnon Bose-Einstein condensate, mediated by its interaction with an electric field through a geometric Aharonov-Casher (AC) phase. A distinct feature of the system is the positive feedback loop in which an electric field induces magnon orbital motion via the AC phase, generating electric polarization that in turn enhances the original field. Based on bosonic Bogoliubov-de Gennes (BdG) mean-field theory, we show that this feedback drives a spontaneous ferroelectric transition in the magnon superfluid, accompanied by a persistent magnon supercurrent. In the resulting ferroelectric phase, the quasiparticle excitation spectrum becomes nonreciprocal, reflecting spontaneous breaking of spatial inversion symmetry. At the critical point of the transition, the bosonic BdG Hamiltonian exhibits a global coalescence of both eigenvalues and eigenvectors, forming exceptional points throughout the entire Brillouin zone. The corresponding eigenvector is an equally weighted superposition of bosonic quasiparticle and quasihole states and is invariant under particle-hole transformation, allowing it to be interpreted as a bosonic analog of a Majorana fermion.

Figures

Figures reproduced from arXiv: 2512.22073 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic figures of (a) the minimal model of the [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. (a),(b): The normalized single-particle mean-field [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Phase diagram for the magnon BEC. Ferroelectric [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

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Works this paper leans on

98 extracted references · 5 canonical work pages

  1. [25]

    Yamamoto, T

    K. Yamamoto, T. Kawakami, and M. Koshino, Electro- magnetic response in dipole superfluids, Communications Physics8, 171 (2025)

    2025

  2. [1]

    Aharonov and A

    Y. Aharonov and A. Casher, Topological quantum effects for neutral particles, Phys. Rev. Lett.53, 319 (1984)

    1984

  3. [2]

    Katsura, N

    H. Katsura, N. Nagaosa, and A. V. Balatsky, Spin current and magnetoelectric effect in noncollinear magnets, Phys. 5 Rev. Lett.95, 057205 (2005)

    2005

  4. [3]

    Liu and G

    T. Liu and G. Vignale, Electric control of spin currents and spin-wave logic, Phys. Rev. Lett.106, 247203 (2011)

    2011

  5. [4]

    Meier and D

    F. Meier and D. Loss, Magnetization transport and quan- tized spin conductance, Phys. Rev. Lett.90, 167204 (2003)

    2003

  6. [5]

    Nakata, P

    K. Nakata, P. Simon, and D. Loss, Wiedemann-franz law for magnon transport, Phys. Rev. B92, 134425 (2015)

    2015

  7. [6]

    Su and X

    Y. Su and X. R. Wang, Chiral anomaly of weyl magnons in stacked honeycomb ferromagnets, Phys. Rev. B96, 104437 (2017)

    2017

  8. [7]

    Nakata, S

    K. Nakata, S. K. Kim, J. Klinovaja, and D. Loss, Magnonic topological insulators in antiferromagnets, Phys. Rev. B96, 224414 (2017)

    2017

Show all 98 references
  1. [8]

    Nakata, J

    K. Nakata, J. Klinovaja, and D. Loss, Magnonic quantum hall effect and wiedemann-franz law, Phys. Rev. B95, 125429 (2017)

    2017

  2. [9]

    Owerre, Magnonic floquet hofstadter butterfly, Annals of Physics399, 93 (2018)

    S. Owerre, Magnonic floquet hofstadter butterfly, Annals of Physics399, 93 (2018)

    2018

  3. [10]

    S. A. Owerre, Photoinduced topological phase transitions in topological magnon insulators, Scientific Reports8, 4431 (2018)

    2018

  4. [11]

    Proskurin, R

    I. Proskurin, R. Macˆ edo, and R. L. Stamps, Microscopic origin of level attraction for a coupled magnon-photon system in a microwave cavity, New Journal of Physics 21, 095003 (2019)

    2019

  5. [12]

    Avishai, K

    Y. Avishai, K. Totsuka, and N. Nagaosa, Non-abelian aharonov–casher phase factor in mesoscopic systems, Journal of the Physical Society of Japan88, 084705 (2019), https://doi.org/10.7566/JPSJ.88.084705

    2019 doi

  6. [13]

    Li and A

    B. Li and A. A. Kovalev, Magnon landau levels and spin responses in antiferromagnets, Phys. Rev. Lett.125, 257201 (2020)

    2020

  7. [14]

    R. O. Serha, V. I. Vasyuchka, A. A. Serga, and B. Hille- brands, Towards an experimental proof of the magnonic aharonov-casher effect, Phys. Rev. B108, L220404 (2023)

    2023

  8. [15]

    V. N. Krivoruchko and A. S. Savchenko, Controlled re- fraction and focusing of spin waves determined by the aharonov-casher effect, Phys. Rev. B109, 184437 (2024)

    2024

  9. [16]

    Wang, Z.-G

    Y. Wang, Z.-G. Zhu, and G. Su, Magnon spin photo- galvanic effect induced by aharonov-casher phase, Phys. Rev. B110, 054434 (2024)

    2024

  10. [17]

    Z. Jin, Z. Zeng, Y. Cao, and P. Yan, Skyrmion hall effect in altermagnets, Phys. Rev. Lett.133, 196701 (2024)

    2024

  11. [18]

    Kuzmenko, Y

    I. Kuzmenko, Y. B. Band, and Y. Avishai, The aharonov- casher phase is geometrical and not topological, Phys. Rev. B112, L020501 (2025)

    2025

  12. [19]

    O. O. Boliasova and V. N. Krivoruchko, Magnonic aharonov-casher effect and electric field control of chirality-dependent spin-wave dynamics in antiferromag- nets, Phys. Rev. B111, 174440 (2025)

    2025

  13. [20]

    Wang, Z.-G

    Y. Wang, Z.-G. Zhu, and G. Su, Magnon landau-zener tunneling and spin-current generation by electric field, Phys. Rev. B111, 165150 (2025)

    2025

  14. [21]

    Birnkammer, M

    S. Birnkammer, M. Knap, J. Knolle, A. Mook, and A. Bastianello, Scattering theory of chiral edge modes in topological magnon insulators, Phys. Rev. B112, 094417 (2025)

    2025

  15. [22]

    Chen, F.-J

    Q.-H. Chen, F.-J. Huang, Y.-P. Fu, and H. Su, Floquet no-go theorem and engineering topological magnons, Phys. Rev. B111, 064426 (2025)

    2025

  16. [23]

    Yokoyama and Y

    T. Yokoyama and Y. Tada, Anomalous enhancement of n´ eel order in the𝑠= 1 2 square lattice heisenberg model under fictitious magnetic field, Phys. Rev. B111, 064415 (2025)

    2025

  17. [24]

    Li and A

    J.-C. Li and A. Du, Quantum controlling and the topological properties of the magnon photo- transport in two-dimensional collinear ferromagnet (2025), arXiv:2504.06852 [cond-mat.mes-hall]

    2025 arXiv

  18. [26]

    S. O. Demokritov, V. E. Demidov, O. Dzyapko, G. A. Melkov, A. A. Serga, B. Hillebrands, and A. N. Slavin, Bose–einstein condensation of quasi-equilibrium magnons at room temperature under pumping, Nature 443, 430 (2006)

    2006

  19. [27]

    Nikuni, M

    T. Nikuni, M. Oshikawa, A. Oosawa, and H. Tanaka, Bose-einstein condensation of dilute magnons in tlcucl 3, Phys. Rev. Lett.84, 5868 (2000)

    2000

  20. [28]

    R¨ uegg, N

    C. R¨ uegg, N. Cavadini, A. Furrer, H.-U. G¨ udel, K. Kr¨ amer, H. Mutka, A. Wildes, K. Habicht, and P. Vorderwisch, Bose–einstein condensation of the triplet states in the magnetic insulator tlcucl3, Nature423, 62 (2003)

    2003

  21. [29]

    Giamarchi, C

    T. Giamarchi, C. R¨ uegg, and O. Tchernyshyov, Bose– einstein condensation in magnetic insulators, Nature Physics4, 198 (2008)

    2008

  22. [30]

    A. A. Aczel, Y. Kohama, C. Marcenat, F. Weickert, M. Jaime, O. E. Ayala-Valenzuela, R. D. McDonald, S. D. Selesnic, H. A. Dabkowska, and G. M. Luke, Field- induced bose-einstein condensation of triplons up to 8 k in sr3cr2o8, Phys. Rev. Lett.103, 207203 (2009)

    2009

  23. [31]

    Sonin, Spin currents and spin superflu- idity, Advances in Physics59, 181 (2010), https://doi.org/10.1080/00018731003739943

    E. Sonin, Spin currents and spin superflu- idity, Advances in Physics59, 181 (2010), https://doi.org/10.1080/00018731003739943

    2010 doi

  24. [32]

    V. Zapf, M. Jaime, and C. D. Batista, Bose-einstein con- densation in quantum magnets, Rev. Mod. Phys.86, 563 (2014)

    2014

  25. [33]

    Nakata, K

    K. Nakata, K. A. van Hoogdalem, P. Simon, and D. Loss, Josephson and persistent spin currents in bose-einstein condensates of magnons, Phys. Rev. B90, 144419 (2014)

    2014

  26. [34]

    D. A. Bozhko, A. A. Serga, P. Clausen, V. I. Vasyuchka, F. Heussner, G. A. Melkov, A. Pomyalov, V. S. L’vov, and B. Hillebrands, Supercurrent in a room-temperature bose–einstein magnon condensate, Nature Physics12, 1057 (2016)

    2016

  27. [35]

    C. Sun, T. Nattermann, and V. L. Pokrovsky, Unconven- tional superfluidity in yttrium iron garnet films, Phys. Rev. Lett.116, 257205 (2016)

    2016

  28. [36]

    Kimura, K

    S. Kimura, K. Kakihata, Y. Sawada, K. Watanabe, M. Matsumoto, M. Hagiwara, and H. Tanaka, Ferroelec- tricity by bose–einstein condensation in a quantum mag- net, Nature Communications7, 12822 (2016)

    2016

  29. [37]

    Kimura, K

    S. Kimura, K. Kakihata, Y. Sawada, K. Watanabe, M. Matsumoto, M. Hagiwara, and H. Tanaka, Magne- toelectric effect in the quantum spin gap system tlcucl 3, Phys. Rev. B95, 184420 (2017)

    2017

  30. [38]

    E. L. Fjærbu, N. Rohling, and A. Brataas, Electrically driven bose-einstein condensation of magnons in antifer- romagnets, Phys. Rev. B95, 144408 (2017)

    2017

  31. [39]

    W. Yuan, Q. Zhu, T. Su, Y. Yao, W. Xing, Y. Chen, Y. Ma, X. Lin, J. Shi, R. Shindou, X. C. Xie, and W. Han, Experimental signatures of spin superfluid ground state in canted antiferromagnet cr2o3 via nonlo- cal spin transport, Science Advances4, eaat1098 (2018), https://www.sc...

    2018 doi

  32. [40]

    D. A. Bozhko, A. J. E. Kreil, H. Y. Musiienko-Shmarova, A. A. Serga, A. Pomyalov, V. S. L’vov, and B. Hille- brands, Bogoliubov waves and distant transport of magnon condensate at room temperature, Nature Com- munications10, 2460 (2019)

    2019

  33. [41]

    Okuma, Nonreciprocal superposition state in anti- ferromagnetic optospintronics, Phys

    N. Okuma, Nonreciprocal superposition state in anti- ferromagnetic optospintronics, Phys. Rev. B99, 094401 (2019)

    2019

  34. [42]

    Takei, Spin transport in an electrically driven magnon gas near bose-einstein condensation: Hartree- fock-keldysh theory, Phys

    S. Takei, Spin transport in an electrically driven magnon gas near bose-einstein condensation: Hartree- fock-keldysh theory, Phys. Rev. B100, 134440 (2019)

    2019

  35. [43]

    Kimura, M

    S. Kimura, M. Matsumoto, and H. Tanaka, Electrical switching of the nonreciprocal directional microwave re- sponse in a triplon bose-einstein condensate, Phys. Rev. Lett.124, 217401 (2020)

    2020

  36. [44]

    Sakurai, S

    K. Sakurai, S. Kimura, S. Awaji, M. Matsumoto, and H. Tanaka, Spin-driven ferroelectricity in the quantum magnet tlcucl 3 under high pressure, Phys. Rev. B102, 064104 (2020)

    2020

  37. [45]

    K. S. Olsson, K. An, G. A. Fiete, J. Zhou, L. Shi, and X. Li, Pure spin current and magnon chemical potential in a nonequilibrium magnetic insulator, Phys. Rev. X10, 021029 (2020)

    2020

  38. [46]

    Schneider, T

    M. Schneider, T. Br¨ acher, D. Breitbach, V. Lauer, P. Pirro, D. A. Bozhko, H. Y. Musiienko-Shmarova, B. Heinz, Q. Wang, T. Meyer, F. Heussner, S. Keller, E. T. Papaioannou, B. L¨ agel, T. L¨ ober, C. Dubs, A. N. Slavin, V. S. Tiberkevich, A. A. Serga, B. Hillebrands, and A. V...

    2020

  39. [47]

    I. V. Borisenko, B. Divinskiy, V. E. Demidov, G. Li, T. Nattermann, V. L. Pokrovsky, and S. O. Demokritov, Direct evidence of spatial stability of bose-einstein con- densate of magnons, Nature Communications11, 1691 (2020)

    2020

  40. [48]

    Divinskiy, H

    B. Divinskiy, H. Merbouche, V. E. Demidov, K. O. Niko- laev, L. Soumah, D. Gou´ er´ e, R. Lebrun, V. Cros, J. B. Youssef, P. Bortolotti, A. Anane, and S. O. Demokri- tov, Evidence for spin current driven bose-einstein con- densation of magnons, Nature Communications12, 6541 (2021)

    2021

  41. [49]

    A. J. E. Kreil, H. Y. Musiienko-Shmarova, P. Frey, A. Pomyalov, V. S. L’vov, G. A. Melkov, A. A. Serga, and B. Hillebrands, Experimental observation of josephson oscillations in a room-temperature bose-einstein magnon condensate, Phys. Rev. B104, 144414 (2021)

    2021

  42. [50]

    P. O. Sukhachov, S. Banerjee, and A. V. Balatsky, Bose- einstein condensate of dirac magnons: Pumping and col- lective modes, Phys. Rev. Res.3, 013002 (2021)

    2021

  43. [51]

    Nakata, Optomagnonic josephson effect in antiferro- magnets, Phys

    K. Nakata, Optomagnonic josephson effect in antiferro- magnets, Phys. Rev. B104, 104402 (2021)

    2021

  44. [52]

    Hayashida, L

    S. Hayashida, L. Huberich, D. Flavi´ an, Z. Yan, K. Y. Po- varov, S. Gvasaliya, and A. Zheludev, Critical dielectric susceptibility at a magnetic bec quantum critical point, Phys. Rev. Res.3, 033053 (2021)

    2021

  45. [53]

    Yun and S

    J. Yun and S. K. Kim, Superfluidlike spin transport in the dynamic states of easy-axis magnets, Phys. Rev. B 107, 104417 (2023)

    2023

  46. [54]

    Aftergood and S

    J. Aftergood and S. Takei, Conductivity enhancement in a diffusive fermi liquid due to bose-einstein condensation of magnons, Phys. Rev. Lett.130, 086702 (2023)

    2023

  47. [55]

    Flavi´ an, P

    D. Flavi´ an, P. A. Volkov, S. Hayashida, K. Y. Povarov, S. Gvasaliya, P. Chandra, and A. Zheludev, Dielectric relaxation by quantum critical magnons, Phys. Rev. Lett. 130, 216501 (2023)

    2023

  48. [56]

    V. S. L’vov, A. Pomyalov, S. V. Nazarenko, D. A. Bozhko, A. J. E. Kreil, B. Hillebrands, and A. A. Serga, Bose-einstein condensation in systems with flux equilib- rium, Phys. Rev. B109, 014301 (2024)

    2024

  49. [57]

    Matsumoto, S

    Y. Matsumoto, S. Schnierer, J. A. N. Bruin, J. Nuss, P. Reiss, G. Jackeli, K. Kitagawa, and H. Takagi, A quantum critical bose gas of magnons in the quasi-two- dimensional antiferromagnet ybcl3 under magnetic fields, Nature Physics20, 1131 (2024)

    2024

  50. [58]

    Esaki, Y

    N. Esaki, Y. Akagi, and H. Katsura, Electric field induced thermal hall effect of triplons in the quantum dimer mag- netsXcucl 3 (X=Tl,K), Phys. Rev. Res.6, L032050 (2024)

    2024

  51. [59]

    Frostad, P

    T. Frostad, P. Pirro, A. A. Serga, B. Hillebrands, A. Brataas, and A. Qaiumzadeh, Anisotropy-assisted magnon condensation in ferromagnetic thin films, Phys. Rev. Res.6, L012011 (2024)

    2024

  52. [60]

    Nakata, J

    K. Nakata, J. Zou, J. Klinovaja, and D. Loss, Magnonic 𝜑josephson junctions and synchronized precession, Phys. Rev. Res.6, 033207 (2024)

    2024

  53. [61]

    Y. Zhu, E. Kleinherbers, L. Levitov, and Y. Tserkovnyak, Proposal for spin superfluid quantum interference device, Phys. Rev. B112, L100405 (2025)

    2025

  54. [62]

    Khatua, S

    J. Khatua, S. M. Kumawat, G. S. Murugan, C.-L. Huang, H.-S. Kim, K. Sritharan, R. Sankar, and K.-Y. Choi, Pos- sible bose-einstein condensation of magnons in an𝑠= 5 2 honeycomb lattice, Phys. Rev. B112, 134422 (2025)

    2025

  55. [63]

    Frostad, A

    T. Frostad, A. L. Kristoffersen, V. Brehm, R. E. Tron- coso, A. Brataas, and A. Qaiumzadeh, Stability of chiral magnon condensates in collinear antiferromagnetic insu- lators, Phys. Rev. B111, 184402 (2025)

    2025

  56. [64]

    Sheng, J.-W

    J. Sheng, J.-W. Mei, L. Wang, X. Xu, W. Jiang, L. Xu, H. Ge, N. Zhao, T. Li, A. Candini, B. Xi, J. Zhao, Y. Fu, J. Yang, Y. Zhang, G. Biasiol, S. Wang, J. Zhu, P. Miao, X. Tong, D. Yu, R. Mole, Y. Cui, L. Ma, Z. Zhang, Z. Ouyang, W. Tong, A. Podlesnyak, L. Wang, F. Ye, D. Yu, ...

    2025

  57. [65]

    Flynn and B

    V. Flynn and B. Flebus, Nonlinear magnetization dy- namics as a route to nonreciprocal phases, spin super- fluidity, and analogue gravity (2025), arXiv:2510.21963 [cond-mat.mes-hall]

    2025

  58. [66]

    Shi and A

    H. Shi and A. Griffin, Finite-temperature excitations in a dilute bose-condensed gas, Physics Reports304, 1 (1998)

    1998

  59. [67]

    Wu and Q

    B. Wu and Q. Niu, Landau and dynamical instabilities of the superflow of bose-einstein condensates in optical lattices, Phys. Rev. A64, 061603 (2001)

    2001

  60. [68]

    Wu and Q

    B. Wu and Q. Niu, Superfluidity of bose–einstein con- densate in an optical lattice: Landau–zener tunnelling and dynamical instability, New Journal of Physics5, 104 (2003)

    2003

  61. [69]

    Y.-Z. You, Z. Chen, X.-Q. Sun, and H. Zhai, Superfluidity of bosons in kagome lattices with frustration, Phys. Rev. Lett.109, 265302 (2012)

    2012

  62. [70]

    Zhang and C

    Y. Zhang and C. Zhang, Bose-einstein condensates in spin-orbit-coupled optical lattices: Flat bands and su- perfluidity, Phys. Rev. A87, 023611 (2013)

    2013

  63. [71]

    Shindou, R

    R. Shindou, R. Matsumoto, S. Murakami, and J.-i. Ohe, Topological chiral magnonic edge mode in a magnonic crystal, Phys. Rev. B87, 174427 (2013). 7

    2013

  64. [72]

    Lieu, Topological symmetry classes for non-hermitian models and connections to the bosonic bogoliubov–de gennes equation, Phys

    S. Lieu, Topological symmetry classes for non-hermitian models and connections to the bosonic bogoliubov–de gennes equation, Phys. Rev. B98, 115135 (2018)

    2018

  65. [73]

    Lein and K

    M. Lein and K. Sato, Krein-schr¨ odinger formalism of bosonic bogoliubov–de gennes and certain classical sys- tems and their topological classification, Phys. Rev. B 100, 075414 (2019)

    2019

  66. [74]

    Kawabata, K

    K. Kawabata, K. Shiozaki, M. Ueda, and M. Sato, Sym- metry and topology in non-hermitian physics, Phys. Rev. X9, 041015 (2019)

    2019

  67. [75]

    Ohashi, S

    T. Ohashi, S. Kobayashi, and Y. Kawaguchi, General- ized berry phase for a bosonic bogoliubov system with exceptional points, Phys. Rev. A101, 013625 (2020)

    2020

  68. [76]

    C. Lyu, C. Lv, and Q. Zhou, Geometrizing quantum dy- namics of a bose-einstein condensate, Phys. Rev. Lett. 125, 253401 (2020)

    2020

  69. [77]

    Julku, G

    A. Julku, G. M. Bruun, and P. T¨ orm¨ a, Quantum geome- try and flat band bose-einstein condensation, Phys. Rev. Lett.127, 170404 (2021)

    2021

  70. [78]

    Julku, G

    A. Julku, G. M. Bruun, and P. T¨ orm¨ a, Excitations of a bose-einstein condensate and the quantum geometry of a flat band, Phys. Rev. B104, 144507 (2021)

    2021

  71. [79]

    Yokomizo and S

    K. Yokomizo and S. Murakami, Non-bloch band theory in bosonic bogoliubov–de gennes systems, Phys. Rev. B 103, 165123 (2021)

    2021

  72. [80]

    L.-L. Wan, Z. Zhou, and Z.-F. Xu, Squeezing-induced topological gap opening on bosonic bogoliubov excita- tions, Phys. Rev. A103, 013308 (2021)

    2021

  73. [81]

    Okuma, Boundary-dependent dynamical instability of bosonic green’s function: Dissipative bogoliubov–de gennes hamiltonian and its application to non-hermitian skin effect, Phys

    N. Okuma, Boundary-dependent dynamical instability of bosonic green’s function: Dissipative bogoliubov–de gennes hamiltonian and its application to non-hermitian skin effect, Phys. Rev. B105, 224301 (2022)

    2022

  74. [82]

    Jalali-mola, T

    Z. Jalali-mola, T. Grass, V. Kasper, M. Lewenstein, and U. Bhattacharya, Topological bogoliubov quasiparticles from bose-einstein condensate in a flat band system, Phys. Rev. Lett.131, 226601 (2023)

    2023

  75. [83]

    Iskin, Quantum-geometric contribution to the bo- goliubov modes in a two-band bose-einstein condensate, Phys

    M. Iskin, Quantum-geometric contribution to the bo- goliubov modes in a two-band bose-einstein condensate, Phys. Rev. A107, 023313 (2023)

    2023

  76. [84]

    Okuma, Bosonic andreev bound state, Phys

    N. Okuma, Bosonic andreev bound state, Phys. Rev. B 110, 014516 (2024)

    2024

  77. [85]

    Guo, L.-L

    L.-X. Guo, L.-L. Wan, L.-G. Si, X.-Y. L¨ u, and Y. Wu, Topological bosonic bogoliubov excitations with sublat- tice symmetry, Phys. Rev. A109, 023307 (2024)

    2024

  78. [86]

    Tesfaye and A

    I. Tesfaye and A. Eckardt, Quantum geometry of bosonic bogoliubov quasiparticles, Phys. Rev. Res.7, L042052 (2025)

    2025

  79. [87]

    Sylju ˚ asen, A

    E. Sylju ˚ asen, A. Qaiumzadeh, and A. Sudbø, Quantum geometry and magnon hall transport in an altermagnet, Phys. Rev. B112, 064429 (2025)

    2025

  80. [88]

    C. Yu, M. Tian, N. Kong, M. Fadel, X. Huang, and Q. He, Exceptional-point-induced nonequilibrium entanglement dynamics in bosonic networks, npj Quantum Information 10.1038/s41534-025-01158-y (2025)

    2025 doi

  81. [89]

    Proskurin, A

    I. Proskurin, A. S. Ovchinnikov, J.-i. Kishine, and R. L. Stamps, Excitation of magnon spin photocurrents in antiferromagnetic insulators, Phys. Rev. B98, 134422 (2018)

    2018

  82. [90]

    Fujiwara, S

    K. Fujiwara, S. Kitamura, and T. Morimoto, Nonlinear spin current of photoexcited magnons in collinear anti- ferromagnets, Phys. Rev. B107, 064403 (2023)

    2023

  83. [91]

    G. Go, D. An, H.-W. Lee, and S. K. Kim, Magnon or- bital nernst effect in honeycomb antiferromagnets with- out spin–orbit coupling, Nano Letters24, 5968 (2024)

    2024

  84. [92]

    D. Q. To, F. Garcia-Gaitan, Y. Ren, J. M. O. Zide, M. B. Jungfleisch, J. Q. Xiao, B. K. Nikoli´ c, G. W. Bryant, and M. F. Doty, Magnon-induced electric polar- ization and magnon nernst effects, Proceedings of the National Academy of Sciences122, e2507255122 (2025), https://ww...

    2025 doi

  85. [93]

    Tang and R

    J. Tang and R. Cheng, Proper theory of magnon or- bital angular momentum (2025), arXiv:2510.03322 [cond- mat.mes-hall]

    2025 arXiv

  86. [94]

    Ashida, Z

    Y. Ashida, Z. Gong, and M. Ueda, Non-hermitian physics, Advances in Physics69, 249 (2020), https://doi.org/10.1080/00018732.2021.1876991

    2020

  87. [95]

    Deng and R

    K. Deng and R. Cheng, Emerging(2+1)D electrodynam- ics and topological instanton in pseudo-hermitian two- level systems, Phys. Rev. Lett.135, 126609 (2025)

    2025

  88. [96]

    Q.-R. Xu, V. P. Flynn, A. Alase, E. Cobanera, L. Viola, and G. Ortiz, Squaring the fermion: The threefold way and the fate of zero modes, Phys. Rev. B102, 125127 (2020)

    2020

  89. [97]

    V. P. Flynn, E. Cobanera, and L. Viola, Topology by dissipation: Majorana bosons in metastable quadratic markovian dynamics, Phys. Rev. Lett.127, 245701 (2021)

    2021

  90. [98]

    V. P. Flynn, E. Cobanera, and L. Viola, Topological zero modes and edge symmetries of metastable marko- vian bosonic systems, Phys. Rev. B108, 214312 (2023). 8 Appendix A: Magnonic Bohr-van Leeuwen theorem The original Bohr-van Leeuwen theorem states that a classical electroni...

    2023

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