Paper detail

Supercell symmetry modified spectral statistics of Kramers-Weyl fermions

We calculate the spectral statistics of the Kramers-Weyl Hamiltonian $H=v\sum_α σ_α\sin p_α+t σ_0\sum_α\cos p_α$ 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 $P(s)\propto s^β$ 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 $\propto t\cos p$, 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.