Supercell symmetry modified spectral statistics of Kramers–Weyl fermions* *Contribution to the special issue of J. Phys. A in honour of the life and work of Fritz Haake.

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 distributionP(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.