Supercell symmetry modified spectral statistics of Kramers-Weyl fermions

Abstract

We calculate the spectral statistics of the Kramers-Weyl Hamiltonian $H=v{\sum }_{\alpha }{\sigma }_{\alpha }\sin p_{\alpha }+t{\sigma }_0{\sum }_{\alpha }\cos p_{\alpha }$ 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 distribution $P(s)\propto s^{\beta }$ 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 $\propto t\cos p$, 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.

arXiv commentContribution to the special issue of J.Phys.A in honour of the life and work of Fritz Haake

References in corpus (10)

• Random-Matrix Theory of Quantum Transport
• Random Matrix Theories in Quantum Physics: Common Concepts
• Kwant: a software package for quantum transport
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Topological quantum properties of chiral crystals
• Finite size scaling in crossover among different random matrix ensembles in microscopic lattice models
• Chirality meets Topology
• Dirac Spectra of 2-dimensional QCD-like theories
• Shift of Symmetries of Naive Fermions in QCD-like Lattice Theories
• Chiral Symmetry and Lattice Fermions