Theoretical Study Of Transport Properties Under The Coexistence Of Superconducting And Unconventional Bands

Topological excited states have stimulated people’s interest in topological materials in condensed matter physics.In particular,full-gap materials such as topological insulators and topological superconductors have attracted wide attention due to their exotic topological edge states at their edges.Majorana fermions,as exotic excited states in topological super-conductors,are considered as possible for topological quantum computing.However,the quest for topological superconductors is fraught with difficulties,and so far there is no accu-rate signal of the existence of Majorana fermions or Majorana zero modes.Experimentally,topological superconductivity can be achieved by combining conventional superconductors with topological insulators or semiconductors with strong spin-orbit coupling.In addition,superconducting materials with unconventional topological properties such as doped Bi₂Se₃,UPt₃and iron-based superconductors have been of interest.The study of transport in the system can give us a deeper understanding of the physical properties of topological excited states and thus plays a key role in the search of Majorana fermions.My thesis focuses on the theoretical study of the transport problems in doped Bi₂Se₃and Nb Se₂-bilayer graphene van der Waals heterojunction,and the main content is summarized as follows:（1）We introduce the unconventional superconductivity that spontaneous breaking of rotational symmetry,i.e.,nematic superconductivity,that occurs in doped Bi₂Se₃.By mean-s of the quasi-degenerate perturbation theory,we demonstrate that the odd-parity pairing potential in doped Bi₂Se₃can be projected as an effective p-wave pairing,and the super-conducting gap anisotropy in the doped Bi₂Se₃comes from spin nematic superconductivity.Moreover,two of the particular pairings have both nematicity and direct superconducting gaps,which proves that doped Bi₂Se₃is an ideal alternative material for nematic topological superconductors.We find that for a time-reversal-invariant and centrosymmetric supercon-ductor,there exists an intrinsicπ-phase in the spin-triplet channel of the Andreev reflection occurring at its surface.The doped Bi₂Se₃with special odd-parity pairing potential has this phenomenon.Importantly,in U-type Josephson junctions where the conductors are connect-ed on the same side of two superconductors,competition between the intrinsicπ-phase and the orbital phase carried by the odd-parity pairing may lead to the unconventional Josephson effect.Using scattering theory as well as model numerical calculations,we demonstrate that different superconducting order parameters lead to different Josephson effects in the same U-type Josephson junction.This phenomenon can be used to determine the specific pair-ing in doped Bi₂Se₃,which is important for the application of doped Bi₂Se₃in the field of topological quantum computing.（2）We present the study of the transport in two-dimensional Nb Se₂-bilayer graphene junctions.At low temperatures,the conductance of the junction is as high as 1.8 times that of the normal state.Moreover,a significant segmentation of the conductivity profile appears within the superconducting energy gap.We attribute the apparent conductance enhancement with the special conductance profile to the superconducting proximity effect due to the highly transparent interface.Due to the superconducting proximity effect of Nb Se₂on bilayer graphene,two Andreev reflection interfaces are formed in the Nb Se₂-bilayer graphene heterojunction.We construct a double Andreev reflection model for understanding the transport phenomena in two-dimensional van der Waals superconducting heterojunctions.Quantum transport simulations accurately reproduce the special conductivity behavior resulting from the double Andreev reflection interfaces,demonstrating the existence of a proximity induced superconducting gap in the bilayer graphene and enabling a deeper physical understanding of our two-dimensional van der Waals superconducting heterojunction.We predict that this is a prevalent phenomenon in high quality van der Waals superconducting heterojunctions and is crucial for the realization of exotic interfacial quantum phenomena such as topological superconductivity.