Supercell symmetry modified spectral statistics of Kramersâ€"Weyl fermions.

We calculate the spectral statistics of the Kramersâ€"Weyl Hamiltonian H = v âˆ' α σ α  sin  p α + tσ 0âˆ' 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. [ABSTRACT FROM AUTHOR]