Supercell symmetry modified spectral statistics of Kramers–Weyl fermions*

Source abstract

Abstract We calculate the spectral statistics of the Kramers–Weyl Hamiltonian H = v ∑ α σ α sin p α + tσ 0 ∑ α cos p α in a chaotic quantum dot. The Hamiltonian has symplectic time-reversal symmetry ( H is invariant when spin σ α and momentum p α both change sign), and yet for small t the level spacing distribution P ( s ) ∝ s β follows the β = 1 orthogonal ensemble instead of the β = 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 ∝ t cos p , which induces a transition from β = 1 to β = 4 statistics that shows up in the conductance as a transition from weak localization to weak antilocalization.