Field-free transverse response in altermagnet and topological insulator heterojunctions

Abstract We theoretically investigate the transport properties of a topological insulator (TI) connected to two-dimensional altermagnetic (AM) leads in the absence of an external magnetic field. Exploiting the intrinsic time-reversal symmetry breaking of altermagnets, we report the emergence of a field-free transverse differential conductivity in the resulting AM-TI-AM heterostructure. Our analysis reveals that this transverse response is highly sensitive to the orientation of the N\'eel vector: a finite transverse conductivity manifests when the N\'eel vector possesses an out-of-plane component, whereas it strictly vanishes for in-plane orientations ($\theta = \pi/2$) under symmetric chemical potentials ($\mu_t = \mu_b$) due to the restoration of symmetry between the $k_y$ and $-k_y$ momentum channels. Conversely, when asymmetric chemical potentials are applied ($\mu_t \neq \mu_b$), this symmetry is broken, yielding a finite transverse response even for an in-plane N\'eel vector. Furthermore, we demonstrate that while the longitudinal differential conductivity exhibits Fabry-P\'erot-type oscillations as a function of the TI's chemical potential, the transverse conductivity displays a distinct antisymmetric dependence. Notably, the oscillatory behavior of the longitudinal conductivity persists even at finite temperatures. Spatially, the transverse current contribution decays exponentially with position inside the TI region. We also find that both the longitudinal and transverse differential conductivity exhibit periodic oscillations with the junction parameter $\chi_t=\chi_b$. These findings provide a fundamental understanding of field-free transverse responses in spin-momentum locked boundary states, highlighting the potential of AM-TI heterojunctions for next-generation spintronic applications.