Supercell symmetry modified spectral statistics of Kramers-Weyl fermions

Abstract

We calculate the spectral statistics of the Kramers-Weyl Hamiltonian H = v n-ary sumation ( alpha ) sigma ( alpha ) sin p ( alpha ) + t sigma (0) n-ary sumation ( alpha )cos p ( alpha ) in a chaotic quantum dot. The Hamiltonian has symplectic time-reversal symmetry (H is invariant when spin sigma ( alpha ) and momentum p ( alpha ) both change sign), and yet for small t the level spacing distributionP(s) proportional to s ( beta ) follows the beta = 1 orthogonal ensemble instead of the beta = 4 symplectic ensemble. We identify a supercell symmetry of H that explains this finding. The supercell symmetry is broken by the spin-independent hopping energy proportional to t cos p, which induces a transition from beta = 1 to beta = 4 statistics that shows up in the conductance as a transition from weak localization to weak antilocalization.