Realiazation,Detection And Braiding Of Majorana Zero Modes In Higher-Order Topological Superconductor

Majorana zero modes satisfy non-Abelian braiding statistics and has potential applica-tion in realizing fault-tolerant quantum computation with topology protection.Presently,multiple realizable platforms have been proposed to hold Majorana zero mode including topological insulators with superconductor proximity,semiconductor nanowires,magnetic atomic chains,planar Josephson junctions in the two-dimensional electron gas,and iron-based superconductors.However,due to the complexity of the system implementation and the manufacturing process,there is still no conclusive evidence for the existence of the Majo-rana zero modes.With the further development of topological state research,theorists have proposed higher-order topological states of matter.Different from the first-order topological insulator（superconductor）,the d-dimensional n-order（n≥2）topological insulator（super-conductor）has protected gapless modes at a boundary of the system of codimension n.This has brought new insights in realizing Majorana zero modes.This dissertation focuses on the realization,detection,and braiding of Majorana zero modes in the higher-order topological superconductor.The main conclusions are as follows:（1）We propose a scheme to realize second-order topological superconductors with Ma-jorana corner modes based on the lattice symmetry-assisted two-dimensional topological insulator systems.The lattice symmetry leads to the anisotropic coupling of edge states along with different directions to the in-plane magnetic field and conventional s-wave pair-ings,thus leading to a single Majorana zero mode located at the corners for various lattice patterns.Considering two-dimensional topological insulators with D_3dlattice symmetry in proximity to the s-wave superconductor under in-plane magnetic fields,we find that the edge states along with the armchair and zigzag edges open different types of gaps,and this phe-nomenon does not depend on the direction of the in-plane magnetic field.As a consequence,a single Majorana zero mode exists at the corner between the zigzag and armchair edges and is robust against weakly broken lattice symmetry.Based on the symmetry of the lattice,we propose to realize such corner MZMs in a variety of polygon patterns.We further show their potential in building the Majorana network through constructing the Majorana Y junction under an in-plane magnetic field.（2）We uncover the transverse Majorana spin polarization of the higher-order topolog-ical superconductors which are realized based on a two-dimensional topological insulator,s-wave superconductor,and in-plane magnetic field.Based on this property,we propose a scheme to detect and braid the higher-order Majorana corner modes.Transverse means that the spin polarization of the Majorana zero modes is perpendicular to magnetic field.With this novel Majorana spin property,we predict the spin-selective Andreev reflection occurs at lead polarization perpendicular to the applied magnetic field.The induced topological Josephson?₀-junction shows the qualitative difference from the topologically trivial Joseph-son?₀-junction and provides benefits in constructing all electronically controlled Majorana networks for braiding.We thus provide a comprehensive scheme for probing non-Abelian statistics in this class of higher-order topological superconductors with transverse Majorana spin texture.