Interplay between topology and disorder in a two-dimensional semi-Dirac material

We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one direction and a parabolic dispersion in the orthogonal direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semimetal, as it generates a momentum-independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three distinct regimes-single-node trivial, two-node trivial, and two-node Chern. We find that disorder can drive topological transitions from both the single-and two-node trivial to the two-node Chern regime. We further analyze these transitions in an appropriate tight-binding Hamiltonian of an anisotropic hexagonal lattice by calculating the real-space Chern number. Additionally, we compute the disorder-averaged entanglement entropy which signals both the topological Lifshitz and Chern transition as a function of the anisotropy of the hexagonal lattice. Finally, we discuss experimental aspects of our results.