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Three-Dimensional Chiral Lattice Fermion in Floquet Systems.

Xiao-Qi Sun1,2, Meng Xiao3, Tomáš Bzdušek1,2

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The Nielsen-Ninomiya no-go theorem holds for Floquet lattices, but adiabatic approximations reveal extra Weyl points. Researchers propose realizing purely left- or right-handed Weyl particles in 3D lattices.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Mechanics
  • Topological Matter

Background:

  • The Nielsen-Ninomiya no-go theorem is a fundamental principle in condensed matter physics.
  • Floquet lattices are periodically driven quantum systems with unique topological properties.
  • Weyl points are topological defects in the electronic band structure of materials.

Purpose of the Study:

  • To investigate the validity of the Nielsen-Ninomiya no-go theorem in three-dimensional Floquet lattices.
  • To explore the emergence of Weyl points in the low-energy subspace under adiabatic conditions.
  • To propose a method for realizing purely left- or right-handed Weyl particles.

Main Methods:

  • Analysis of the Nielsen-Ninomiya no-go theorem in the context of Floquet lattices.
  • Application of adiabatic approximation to decouple low- and high-energy subspaces.
  • Calculation of winding numbers for adiabatic Floquet operators.
  • Dimensional reduction of a four-dimensional quantum Hall system to a 3D lattice Hamiltonian.

Main Results:

  • The Nielsen-Ninomiya no-go theorem holds, predicting an equal number of left- and right-handed Weyl points.
  • Adiabatic evolution reveals Floquet bands with additional Weyl points in the low-energy subspace.
  • The difference in Weyl point numbers is twice the winding number of the adiabatic Floquet operator.
  • A 3D lattice Hamiltonian is proposed for realizing purely chiral Weyl particles.

Conclusions:

  • Despite the no-go theorem, the adiabatic limit allows for the emergence of unbalanced Weyl points.
  • The proposed method offers a pathway to engineer topological states with purely left- or right-handed Weyl particles.
  • Surface state dynamics under magnetic fields exhibit unusual behavior due to the breakdown of adiabatic approximation.