Robustness of Half-Integer Quantized Hall Conductivity Against Disorder in an Anisotropic Dirac Semimetal with Parity Anomaly

Two-dimensional Dirac semimetals with a single massless Dirac cone exhibit a parity anomaly. Usually, such a kind of anomalous topological semimetallic phase in real materials is unstable where any amount of disorder can drive it into a diffusive metal and destroy the half-integer quantized Hall conductivity as an indicator of parity anomaly. Here, based on a low-energy effective model, we propose an anisotropic Dirac semimetal which explicitly breaks time-reversal symmetry and carries half-integer quantized Hall conductivity. This topological semimetallic phase can be realized on a deformed honeycomb lattice subjected to a magnetic flux. Moreover, we perceptively investigate the disorder correction to the Hall conductivity. The results show that the effects of disorder can be strongly suppressed and thereby the nearly half-integer quantization of Hall conductivity can exist in a wide region of disorder, indicating that our proposed anisotropic Dirac semimetal is an exciting platform to investigate the parity anomaly phenomena.