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Title: Three-Dimensional Chiral Lattice Fermion in Floquet Systems

Here, 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.
Authors:
 [1] ;  [1] ;  [1] ;  [1] ;  [1]
  1. Stanford Univ., Stanford, CA (United States)
Publication Date:
Grant/Contract Number:
AC02-76SF00515; CBET-1641069; N00014-17-1-3030; GBMF4302
Type:
Accepted Manuscript
Journal Name:
Physical Review Letters
Additional Journal Information:
Journal Volume: 121; Journal Issue: 19; Journal ID: ISSN 0031-9007
Publisher:
American Physical Society (APS)
Research Org:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 74 ATOMIC AND MOLECULAR PHYSICS
OSTI Identifier:
1490073
Alternate Identifier(s):
OSTI ID: 1481233

Sun, Xiao -Qi, Xiao, Meng, Bzdušek, Tomáš, Zhang, Shou -Cheng, and Fan, Shanhui. Three-Dimensional Chiral Lattice Fermion in Floquet Systems. United States: N. p., Web. doi:10.1103/physrevlett.121.196401.
Sun, Xiao -Qi, Xiao, Meng, Bzdušek, Tomáš, Zhang, Shou -Cheng, & Fan, Shanhui. Three-Dimensional Chiral Lattice Fermion in Floquet Systems. United States. doi:10.1103/physrevlett.121.196401.
Sun, Xiao -Qi, Xiao, Meng, Bzdušek, Tomáš, Zhang, Shou -Cheng, and Fan, Shanhui. 2018. "Three-Dimensional Chiral Lattice Fermion in Floquet Systems". United States. doi:10.1103/physrevlett.121.196401.
@article{osti_1490073,
title = {Three-Dimensional Chiral Lattice Fermion in Floquet Systems},
author = {Sun, Xiao -Qi and Xiao, Meng and Bzdušek, Tomáš and Zhang, Shou -Cheng and Fan, Shanhui},
abstractNote = {Here, 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.},
doi = {10.1103/physrevlett.121.196401},
journal = {Physical Review Letters},
number = 19,
volume = 121,
place = {United States},
year = {2018},
month = {11}
}

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