Three-Dimensional Chiral Lattice Fermion in Floquet Systems

We show that the Nielsen-Ninomiya no-go theorem still holds on a Floquet lattice: there is an equal number of right-handed and left-handed Weyl points in a three-dimensional Floquet lattice. However, in the adiabatic limit, where the time evolution of the low-energy subspace is decoupled from the hi...

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Bibliographic Details
Published in:Physical review letters 2018-11, Vol.121 (19), p.196401-196401, Article 196401
Main Authors: Sun, Xiao-Qi, Xiao, Meng, Bzdušek, Tomáš, Zhang, Shou-Cheng, Fan, Shanhui
Format: Article
Language:English
Subjects:
Adiabatic flow
ATOMIC AND MOLECULAR PHYSICS
Band theory
Brillouin zones
CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
Energy industry
Evolution
Fermions
Quantum Hall effect
Subspaces
Theorems
Wave packets
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Summary:We show that the Nielsen-Ninomiya no-go theorem still holds on a Floquet lattice: there is an equal number of right-handed and left-handed Weyl points in a three-dimensional Floquet lattice. However, in the adiabatic limit, where the time evolution of the 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 extra left- or right-handed Weyl points, despite the no-go theorem. Assuming 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 adiabatic Floquet operator over the Brillouin zone. Based on these findings, we propose a realization of purely left- or right-handed Weyl particles on a 3D lattice using a Hamiltonian obtained through dimensional reduction of a four-dimensional quantum Hall system. We argue that the breakdown of the adiabatic approximation on the surface facilitates unusual closed orbits of wave packets in an applied magnetic field, which traverse alternatively through the low-energy and high-energy sector of the spectrum.
ISSN:0031-9007
1079-7114
DOI:10.1103/PhysRevLett.121.196401