Quantum percolation in honeycomb lattices under random spin-orbit coupling

TL;DR

This study explores quantum percolation in honeycomb lattices with site dilution and random spin-orbit coupling, revealing how spin-orbit effects influence the metal-insulator transition and spectral properties.

Contribution

It provides the first detailed analysis of quantum percolation thresholds and critical exponents in honeycomb lattices with random spin-orbit coupling using exact diagonalization.

Findings

Quantum percolation threshold $p_q$ is higher than classical $p_c$ without spin-orbit coupling.

Spin-orbit coupling shifts $p_q$ to lower values, promoting delocalization.

Spectral statistics transition from GOE to GSE, indicating symmetry class change.

Abstract

We investigate quantum percolation in a honeycomb lattice with site dilution and random spin-orbit coupling. Using exact diagonalization combined with finite-size scaling analysis, we study the metal-insulator transition, extracting the quantum percolation threshold $p_q$, and the correlation-length exponent, $\nu$. In the absence of spin-orbit coupling, we find that $p_q$ remains finite and demonstrate that the quantum threshold is significantly higher than the classical site-percolation threshold $p_c$ of the honeycomb lattice. When spin-orbit coupling is present, the spectral statistics exhibit a crossover from the Gaussian orthogonal ensemble to the Gaussian symplectic ensemble, reflecting the change in symmetry class. Simultaneously, the quantum percolation threshold shifts systematically to lower occupation probabilities, indicating that the spin-orbit coupling favors delocalization. For sufficiently strong spin-orbit coupling, $p_q$ tends to saturate, while the critical exponent approaches the expected one of the two-dimensional symplectic universality class.