Protected Fermionic Zero Modes in Periodic Gauge Fields
arXiv:2310.05913 · doi:10.1103/PhysRevB.111.125129
Abstract
It is well-known that macroscopically-normalizable zero-energy wavefunctions of spin- particles in a two-dimensional inhomogeneous magnetic field are spin-polarized and exactly calculable with degeneracy equaling the number of flux quanta linking the whole system. Extending this argument to massless Dirac fermions subjected to magnetic fields that have \textit{zero} net flux but are doubly periodic in real space, we show that there exist \textit{only two} Bloch-normalizable zero-energy eigenstates, one for each spin flavor. This result is immediately relevant to graphene multilayer systems subjected to doubly-periodic strain fields, which at low energies, enter the Hamiltonian as periodic pseudo-gauge vector potentials. Furthermore, we explore various related settings including nonlinearly-dispersing band structure models and systems with singly-periodic magnetic fields.
9 pages, 1 figure. Comments are very appreciated!
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