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When phonons couple to fermions in 2D semimetals, the interaction may turn the system into an insulator. There are several insulating phases in which the time reversal and the sublattice symmetries are spontaneously broken. Examples are many-body states commensurate to Haldanes staggered flux model or to lattice models with periodically modulated strain. We find that the effective field theories of these phases exhibit characteristic Chern-Simons terms, whose coefficients are related to the topological invariants of the microscopic model. This implies that the corresponding quantized Hall conductivities characterize these insulating states.
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Antiferromagnetism (AF) such as Neel ordering is often closely related to Coulomb interactions such as Hubbard repulsion in two-dimensional (2D) systems. Whether Neel AF ordering in 2D can be dominantly induced by electron-phonon couplings (EPC) has not been completely understood. Here, by employing numerically-exact sign-problem-free quantum Monte Carlo (QMC) simulations, we show that optical Su-Schrieffer-Heeger (SSH) phonons with frequency $omega$ and EPC constant $lambda$ can induce AF ordering for a wide range of phonon frequency $omega>omega_c$. For $omega<omega_c$, a valence-bond-solid (VBS) order appears and there is a direct quantum phase transition between VBS and AF phases at $omega_c$. The phonon mechanism of the AF ordering is related to the fact that SSH phonons directly couple to electron hopping whose second-order process can induce an effective AF spin exchange. Our results shall shed new lights to understanding AF ordering in correlated quantum materials.
We propose a new mechanism for the thermal Hall effect in exchange spin-wave systems, which is induced by the magnon-phonon interaction. Using symmetry arguments, we first show that this effect is quite general, and exists whenever the mirror symmetry in the direction of the magnetization is broken. We then demonstrate our result in a collinear ferromagnet on a square lattice, with perpendicular easy-axis anisotropy and Dzyaloshinskii-Moriya interaction from mirror symmetry breaking. We show that the thermal Hall conductivity is controlled by the resonant contribution from the anti-crossing points between the magnon and phonon branches, and estimate its size to be comparable to that of the magnon mediated thermal Hall effect.
Since the first experimental observation of the phonon Hall effect (PHE) in 2005, its physical origin and theoretical explanation have been extensively investigated. While spin-orbit interactions are believed to play important roles under external magnetic fields, nonmagnetic effects are also possible. Here, we propose a mechanism of PHE which is induced by electric current in a nonequilibrium system through electron-phonon interactions. The influence of the drift electrons to the phonon degrees of freedom, as a correction to the Born-Oppenheimer approximation, is represented by an antisymmetric matrix which has the same form as in a typical phonon Hall model. We demonstrate the idea with a graphene-like hexagonal lattice having a finite phonon Hall conductivity under a driven electric current.
Quantized transports of fermions are topological phenomena determined by the sum of the Chern numbers of all the energy bands below the Fermi energy. For bosonic excitations, e.g. phonons and magnons in a crystal, topological transport is dominated by the Chern number of the lowest energy band because the energy distribution of the bosons is limited below the thermal energy. Here, we demonstrate the existence of topological transport by bosonic magnons in a lattice of magnetic skyrmions - topological defects formed by a vortex-like texture of spins. We find a distinct thermal Hall signal when the ferromagnetic spins in an insulating polar magnet GaV4Se8 form magnetic skyrmions. Its origin is identified as the topological thermal Hall effect of magnons in which the trajectories of these magnons are bent by an emergent magnetic field produced by the magnetic skyrmions. Our theoretical simulations confirm that the thermal Hall effect is indeed governed by the Chern number of the lowest energy band of the magnons in a triangular lattice of magnetic skyrmions. Our findings lay a foundation for studying topological phenomena of other bosonic excitations.
We address the problem of Dirac fermions interacting with longitudinal phonons. A gap in the spectrum of fermions leads to the emergence of the Chern--Simons excitations in the spectrum of phonons. We study the effect of those excitations on observable quantities: the phonon dispersion, the phonon spectral density, and the Hall conductivity.
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