Tailoring weak and metallic phases in a strong topological insulator by strain and disorder: Conductance fluctuations signatures

Transport measurements are readily used to probe different phases in disordered topological insulators (TIs), where determining topological invariants explicitly is challenging. On that note, universal conductance fluctuations (UCF) theory asserts the conductance $G$ for an ensemble has a Gaussian distribution, and that standard deviation $\ensuremath{\delta}G$ depends solely on the symmetries and dimensions of the system. Using a real-space tight-binding Hamiltonian on a system with Anderson disorder, we explore conductance fluctuations in a thin ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ film and demonstrate the agreement of their behavior with UCF hypotheses. We further show that magnetic field applied out-of-plane breaks the time-reversal symmetry and transforms the system's Wigner-Dyson class from symplectic to unitary, increasing $\ensuremath{\delta}G$ by $\sqrt{2}$. Finally, we reveal that while ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$ is a strong TI, weak TI and metallic phases can be stabilized in presence of strain and disorder, and detected by monitoring the conductance fluctuations.