Conductance fluctuations in disordered 2D topological insulator wires: From quantum spin-Hall to ordinary quantum phases

Impurities and defects are ubiquitous in topological insulators (TIs) and thus understanding the effects of disorder on electronic transport is important. We calculate the distribution of the random conductance fluctuations $P(G)$ of disordered 2D TI wires modeled by the Bernevig-Hughes-Zhang (BHZ) Hamiltonian with realistic parameters. As we show, the disorder drives the TIs into different regimes: metal (M), quantum spin-Hall insulator (QSHI), and ordinary insulator (OI). By varying the disorder strength and Fermi energy, we calculate analytically and numerically $P(G)$ across the entire phase diagram. The conductance fluctuations follow the statistics of the unitary universality class $\beta=2$. At strong disorder and high energy, however, the size of the fluctutations $\delta G$ reaches the universal value of the orthogonal symmetry class ($\beta=1$). At the QSHI-M and QSHI-OI crossovers, the interplay between edge and bulk states plays a key role in the statistical properties of the conductance.