False Vacuum Decay in Flat-Band Ferromagnets: Role of Quantum Geometry and Chiral Edge States

Abstract

Dynamical control of quantum matter is a challenging, yet promising direction for probing strongly correlated states. Motivated by recent experiments in twisted MoTe$_2$ that demonstrated optical control of magnetization, we propose a protocol for probing magnetization dynamics in flat-band ferromagnets. We investigate the nucleation and dynamical growth of magnetic bubbles prepared on top of a false vaccum in both itinerant ferromagnets and spin-polarized Chern insulators. For ferromagnetic metals, we emphasize the crucial role of a non-trivial quantum geometry in the magnetization dynamics, which in turn also provides a probe for the quantum metric. Furthermore, for quantum Hall ferromagnets, we show how properties of chiral edge modes localized at domain-wall boundaries can be dynamically accessed. Our work demonstrates the potential for nonequilibrium protocols to control and probe strongly correlated phases, with particular relevance for twisted MoTe$_2$ and graphene-based flat-band ferromagnets.

Figures (5)

• Figure 1: Bubbles, domain walls, and false vacuum decay.(a) Itinerant Ising-magnetism in two-dimensional topological bands. Strong correlations drive the $\mathbb{Z}_2$ symmetric metal (left) into a spin-polarized ferromagnetic phase (right), which allows the system to minimize its exchange energy via the Stoner mechanism. Depending on the filling, both quantum Hall ferromagnets and itinerant magnets can be stabilized. (b) In materials such as twisted-MoTe$_2$ bilayers, the magnetization can be optically controlled by impinging the sample with circularly polarized light. (c) An external bias magnetic field $B_z$ prepares the system in a metastable false vacuum. We find that the growth dynamics of a bubble in the true vacuum depend strongly on the underlying electronic state.
• Figure 2: Dynamics of a nucleated bubble. The size of the initial domain $R_0$ relative to the critical bubble radius $R_c$, determines the fate of the metastable system. If $R_0<R_c$ (blue line), the surface tension will dominate and the bubble will shrink, leaving the meta-stable false vacuum intact. By contrast, for $R_0>R_c$ (red line) the bubble will expand asymptotically with a constant velocity $v_B$ driving the system to the lowest energy configuration.
• Figure 3: Consequence of quantum metric on the domain wall formation in itinerant ferromagnets.(a) Magnetization across two domain walls for two different values of the quantum metric; corresponding to $\zeta=3$ and $\zeta=20$ in Model \ref{['eq:TMmodel']}. (b) Normalized magnetization as function of temperature. The critical temperature does not depend on the quantum metric, while the domain wall structure does. (c) Linear dependence of the surface tension on the square root of the Fermi-surface averaged quantum metric $\sqrt{\bar{g}_\mathrm{FS}}$, with a fixed quadratic dispersion. All lengths are given in units of the lattice constant $a$.
• Figure 4: Edge mode contribution to the domain-wall surface tension.(a) Self-consistently determined spectrum of a $\nu=1$ Chern insulator with two domain walls, leading to four chiral edge modes (two per domain wall), with linear dispersion $\pm v k$ around the Fermi surface. (b) Temperature dependence of the surface tension, which for small $T$ is dominated by entropic contributions from the edge modes, Eq. \ref{['eq:edgemodecontribution']}. (c) Magnetization across the system (top) and sketch of domains (bottom). At the domain wall, where the edge modes are present, the magnetization jumps discontinuously.
• Figure A1: Ginzburg temperature and quantum metric in twisted MoTe$_2$. Left: Fermi-surface averaged quantum metric for twisted MoTe$_2$ for different temperatures (from $T=1$ K for the lightest to $T=25$ K for the darkest shade). Right: Reduced Ginzburg temperature $t_G$ for twisted MoTe$_2$ at a twist angle of $\theta=3.7^\circ$ as a function of the filling $\nu$ of the topmost hole band, assuming different interaction strengths $U$.