Studies Of Topological Superconducting Properties In Rashba Nanowire And Iron-based Superconductor

In recent decades,topological materials such as topological insulators and topological superconductors have been widely studied.The simplest platforms for the realization of topological superconductors consist of 2D spinless superconductor with p_x±ip_ypairing and 1D spinless p wave superconductor.However,the p wave superconductors can rarely emerge intrinsically in nature,which makes it difficult to realize in experiments.Fortunately,Fu and Kane proposed to utilize the surface states of a 3D topological insulator with an s-wave superconductor proximity and the effective p_x±ip_ypairing can be obtained.After that,S.Das Sarma and Felix von Oppen independently proposed to realize 1D topological superconductor in superconductor-semiconductor hybrid nanowires with strong spin-orbit coupling(SOC)and magnetization.Recently,a novel class of TSCs coined“higher-order TSCs”has emerged.They host protected Majorana modes on boundaries of more than one dimension lower.For instance,a second-order 2D(3D)TSCs has gapless corner(hinge)Majorana modes between distinct edges(surfaces)that are gapped.The studies of high-order TSC provide a new platform to realize the Majorana modes.In this paper,we present our two works on Rashba nanowire and Iron-based supercon-ductor respectively.The main results are as follows:(1)For a two dimensional superconducting thin film with an out-of-plane electric field,we find that the Rashba spin orbital coupling will induce unconventional supercurrents.Meanwhile,the current,the electric field and the superconducting spin polarization(ScSP)are mutually perpendicular with each other,so we refer to this phenomenon as spin-orbital coupling driven transverse current(SOCDTS).Next,we study ScSP of bulk states in Ma-jorana nanowire and sub-gap states in the Josephson junctions respectively.We find that the ScSP of both bulk states and sub-gap states are finite only when the nanowire is in he-lical regime,where the Fermi surface crosses odd subbands.According to the SOCDTS effect discussed before,finite ScSP is accompanied with the transverse supercurrent.This indicates that the SOCDTS will only appears in the helical regime which can be used for detecting Majorana zero modes(the helical regime is the prerequisite of realizing topolog-ical superconductivity in a Majorana nanowire).To see it more clearly,we calculate the SOCDTS in the U-shaped junction and find it is finite only in the topologically nontrivial regime and decays rapidly to zero in the trivial regime.We thus propose that the observation of SOCDTS,in addition to the zero-bias conductance peak,would provide strong support for the existence of Majorana zero modes.(2)We study the lattice distortion induced first and second-order topological phase transition in FeSe_xTe_1-x monolayer.When compressing the lattice constant of FeSe_xTe_1-x in one direction,our first-principles calculations show that there is a band inversion at?point in a wide doping range,say x?(0,0.7),which indicates the first-order topological phase transition.Meanwhile,because C4 symmetry is broken,the topological edge states along the(100)and(010) directions have different Dirac energy.This is essential to support Majorana corner states when superconductivity of FeSe_xTe_1-xmonolayer is considered.If the pairing symmetry is s_±,Majorana Krammer pairs will appear at the corners.Especially when the time-reversal symmetry is broken,we can obtain a single Majorana zero mode at each corner without concerning the details of the superconducting pairing symmetries,which can potentially bring advantages in the experimental implementation.