Dirac Electrons in AC-Magnetic Fields: $π$-Landau Levels and Chiral Anomaly-Induced Homodyne Effect

TL;DR

The paper explores Dirac electrons in two dimensions subjected to time-periodic AC magnetic fields, uncovering $π$-Landau levels at $ω=±Ω/2$ and, when an AC electric field is added, a zero-energy chiral band with linear dispersion. It develops a Floquet framework and a rotating-frame analysis that maps the $π$-Landau states to a chiral Landau level reminiscent of a 3D Weyl Hamiltonian, and identifies a homodyne Hall current $I_y=-\frac{e}{h}μ$ per valley and spin under concurrent AC fields. The robustness of the flat $π$-bands is shown to stem from dynamical chiral symmetry, while higher-harmonic flat bands appear via generalized rotating frames and Brillouin–Wigner theory. The findings establish a link between Floquet dynamics and chiral-anomaly-like transport, with experimental feasibility anticipated through THz metamaterial field enhancement and related technologies.

Abstract

Floquet engineering, which involves controlling systems through time-periodic driving, is a method for coherently manipulating quantum materials and realizing dynamical states with novel functionalities. Most research in solid-state systems has focused on the use of AC-electric fields as the controlling drive. In this study, we investigate the effects of AC-magnetic fields on two-dimensional (2D) Dirac electrons and report the emergence of new states and new transport phenomena. In a magnetic field that temporarily changes its direction, the 2D Dirac electrons form a new localized state with a flat band dispersion, dubbed as a $π$-Landau level. Its wave function is a superposition of the clockwise and counterclockwise cyclotron orbits with time-periodic amplitudes, resulting in a novel closed trajectory shaped like a figure eight. Then, what would be the counterpart of the Hall effect in AC-magnetic fields? We find that a DC-current in the transverse direction, i.e. a homodyne Hall current, is generated when an additional AC-electric field is applied. In the case of Dirac electrons, several electronic states contribute to this phenomenon including the $π$-Landau level. However, when the chemical potential $μ$ is near the Dirac point, the dominant contribution comes from the low-energy electrons and we numerically find the homodyne Hall current to behave as $I_y=-\frac{e}{h}μ$ per valley and spin. We explain this phenomenon through the high-frequency effective Floquet Hamiltonian which resembles the chiral Landau level Hamiltonian of three-dimensional Weyl Hamiltonian exhibiting chiral anomaly. We discuss the experimental feasibility and conclude that it is possible to realize this new exotic state using techniques such as THz metamaterial enhancement of magnetic fields.

Figures (7)

• Figure 1: (a) Schematic plot of the chiral band and $\pi$-Landau level that emerges at the center of the system. (b) Time average of the density of states. (c,d) The quasienergy spectrum of the 2D Dirac fermions for $B=2\hbar/el_0^{2}$, $E=0$ (c) and $B=2\hbar/el_0^{2}$, $E=0.8\hbar\Omega/el_0$ (d). The intensity is normalized by the peak value for the undriven case. (e) Schematic image of the states in the $\pi$-Landau levels based on semiclassical trajectories.
• Figure 2: Typical trajectories of the semiclassical wave packet under AC magnetic field Eqs. (\ref{['eq:classical1']}) and (\ref{['eq:classical2']}). The initial value of the momentum is taken to be (a) $|\bm{p}|=0.2p_0$, (b) $|\bm{p}|=0.42p_0$, and (c) $|\bm{p}|=0.5p_0$ with $p_0=eBv_F/\Omega$. The direction of the momentum at $t=0$ is taken to be $y$ direction ($p_y(0)=|\bm{p}|$).
• Figure 3: Energy spectrum of the honeycomb lattice model driven by a time-periodic magnetic field, plotted as a function of the canonical momentum $p_y$ and the energy $\hbar\omega$. The spectral function is averaged over a driving period, and the intensity is normalized by the peak value for the undriven case. (a) $B=2\hbar/el_0^{2}$. (b) magnified view of (a). (c) $B=2\hbar/el_0^{2}$ but with an additional AC electric field $E=0.8\hbar\Omega/el_0$.
• Figure 4: The wave function of the flat band state at the boundary of the Floquet Brillouin zone for $B=2\hbar/el_0^{2}, p_y=0$, compared between the numerical result and the ansatz obtained in the rotating frame. We show snapshots at $t=0.1T,0.2T,\dots,1.0T$ here.
• Figure 5: Energy spectrum at $p_y=0$ as a function of magnetic field amplitude $B$.