We study the tunneling effect in an AIII-class insulator proximity coupled with a spin-singlet $s$-wave superconductor, in which three phases are characterized by the integer topological invariant $\mathcal{ N}$. By solving the Bogoliubov-de Gennes equation explicitly, we analytically obtain a normal reflection coefficient $R_{ \sigma\sigma'}$ and an Andreev reflection coefficient $A_{ \sigma\sigma'}$, and derive a charge conductance formula,where $\sigma(\sigma')$ is the spin index of a reflected (injected) wave. The resulting conductance indicates a wide variety of line shapes: (i)gap structure without coherence peaks for $\mathcal{ N}=0$, (ii)quantized zero-bias conductance peak (ZBCP) with height $2e^{ 2}/h$ for $\mathcal{ N}=1$, and (iii)ZBCP spitting for $\mathcal{ N}=2$. At zero bias voltage $eV=0$, $\sum_{ \sigma\sigma'} R_{ \sigma\sigma'} = \sum_{ \sigma\sigma'} A_{ \sigma\sigma'}$ is satisfied and the spin direction of an injected electron is rotated at approximately $90^\circ$ for the $\mathcal{ N}=1$ state. Meanwhile, $A_{ \sigma\sigma'}=0$ is satisfied for the $\mathcal{ N}=2$ state, and the spin rotation angle can become $180^\circ$.
Categories: cond-mat.supr-con