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Ferroelectricity in magnon Bose-Einstein condensate: non-reciprocal superfluidity, exceptional points and Majorana bosons

Kazuki Yamamoto, Takuto Kawakami, Mikito Koshino

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 coalescence of both eigenvalues and eigenvectors, forming an exceptional point. 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.

Ferroelectricity in magnon Bose-Einstein condensate: non-reciprocal superfluidity, exceptional points and Majorana bosons

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 coalescence of both eigenvalues and eigenvectors, forming an exceptional point. 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.
Paper Structure (2 sections, 21 equations, 3 figures)

This paper contains 2 sections, 21 equations, 3 figures.

Table of Contents

  1. Magnonic Bohr-van Leeuwen theorem
  2. Derivation of the total Hamiltonian

Figures (3)

  • Figure 1: Schematic figures of (a) the minimal model of the magnon Bose-Einstein condensate (BEC) with Aharonov-Casher (AC) phase and (b) ferroelectric polarizations induced by persistent magnon supercurrent with $\Delta=\pm\Delta_0$.
  • Figure 2: (a),(b): The normalized single-particle mean-field energy $f(\Delta)$ is shown as a function of $\Delta$, with color representing different values of $\eta$. (c),(d): The Bogoliubov spectrum of the bosonic quasiparticle $E_+(q)=E(q)$ and quasihole $E_-(q)=-E(-q)$ are presented, where we set $u=5$.
  • Figure 3: Phase diagram for the magnon BEC. Ferroelectric phase transition occurs at $\eta=1$, corresponding to exceptional points. The Landau instability occurs at $u=2\eta$ and the dynamical instability occurs at $u=2(\eta-1/\eta)$.