Generalized bulk-interface correspondence for non-quantized spin transport

Abstract

This paper establishes a rigorous mathematical framework for a generalized bulk-interface correspondence (BIC) in electronic systems with possibly nonconserved spin charge, where the Hamiltonian and spin operator do not commute. We first introduce the bulk spin conductance as a character of the bulk medium, which is defined as a potential-current correlation function and is not quantized if the spin charge is nonconserved. Then we establish the principle of BIC, which states that the difference of bulk spin conductances across an interface equals the sum of two quantities associated with the spin transport along the interface: the spin-drift conductance, which captures spin transport carried by interface modes, and the spin-torque conductance, which accounts for spin generation near the interface due to the non-conservation of spin. Furthermore, when the spin charge is conserved, our result recovers the existing BIC based on the spin Chern number or Fu-Kane-Mele $\mathbb{Z}_2$ index. Our findings demonstrate that the principle of BIC is not restricted to systems with quantized characters and provides new insights into spin transport phenomena.