Quantum Spin Hall Effect in an Altermagnet

Altermagnetism was recently proposed as a framework to describe a class of spin-orbit-coupling free magnetic systems with broken time-reversal symmetry and perfect compensation of spin-up/down species due to a crystal symmetry different from translation or inversion. It has been shown that if spin-orbit coupling is restored as a perturbation, the system may exhibit weak ferromagnetism and anomalous Hall effect. In our work, we employ a minimal tight-binding model for a square-lattice altermagnet and show that the system can also realize the quantum spin Hall effect. We further explore what types of altermagnetism can be stabilized by correlation-driven orbital order, and employ group theory to predict which orders are stable with respect to inclusion of spin-orbit coupling and which ones exhibit weak ferromagnetism.