Three-dimensional Chiral Lattice Fermion in Floquet Systems

TL;DR

This paper explores the behavior of Weyl points in 3D Floquet lattice systems, showing that while the no-go theorem applies generally, adiabatic limits allow for purely chiral Weyl points, with implications for realizing such states.

Contribution

It demonstrates that in the adiabatic limit, Floquet bands can host purely left or right-handed Weyl points, and relates their number to the winding number of the Floquet operator, proposing a method to realize these states.

Findings

Nielsen-Ninomiya theorem holds on Floquet lattice.

Adiabatic limit allows for purely chiral Weyl points.

Number of Weyl points relates to the winding number.

Abstract

We show that the Nielsen-Ninomiya no-go theorem still holds on Floquet lattice: there is an equal number of right-handed and left-handed Weyl points in 3D Floquet lattice. However, in the adiabatic limit, where the time evolution of low-energy subspace is decoupled from the high-energy subspace, we show that the bulk dynamics in the low-energy subspace can be described by Floquet bands with purely left/right-handed Weyl points, despite the no-go theorem. For the adiabatic evolution of two bands, we show that the difference of the number of right-handed and left-handed Weyl points equals twice the winding number of the Floquet operator of the low-energy subspace over the Brillouin zone, thus guaranteeing the number of Weyl points to be even. Based on this observation, we propose to realize purely left/right-handed Weyl points in the adiabatic limit using a Hamiltonian obtained through dimensional reduction of four-dimensional quantum Hall system. We address the breakdown of the adiabatic limit on the surface due to the presence of gapless boundary states. This effect induces a circular motion of a wave packet in an applied magnetic field, travelling alternatively in the low-energy and high-energy subspace of the system.