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In this paper, we present the standard form of the scattering matrix of mesocopic system with spin-orbital coupling which preserves time reversal symmetry. We found some analytical structure of the scattering matrix related to the sub-matrices between arbitrary two channels. In particular, we proved that in the two-terminal mono-channel scattering problem, the transmission matrix is proportional to a SU(2) matrix. We obtained these properties through direct and elementary way and found it in agreement with polar decomposition known before.
The electrical Hall effect is the production of a transverse voltage under an out-of-plane magnetic field. Historically, studies of the Hall effect have led to major breakthroughs including the discoveries of Berry curvature and the topological Chern
We investigate hybrid structures based on a bilayer quantum spin Hall system in proximity to an s-wave superconductor as a platform to mimic time-reversal symmetric topological superconductors. In this bilayer setup, the induced pairing can be of int
We demonstrate that the one-dimensional helical Majorana edges of two-dimensional time-reversal symmetric topological superconductors (class DIII) can become gapless and insulating by a combination of random edge velocity and interaction. Such a gapl
Here we describe how certain classes of two dimensional topological insulators, including the CdTe$/$HgTe quantum wells, display a new type of optical activity in two dimensions similar to the magneto-optical Kerr effect in the quantum Hall effect. T
We propose a minimal lattice model for two-dimensional class DIII superconductors with $C_2$-protected higher-order topology. While this class of superconductors cannot be topologically characterized by symmetry eigenvalues at high symmetry momenta,