Hydrodynamics and unconventional superconductivity in new topological semimetals

点击翻译按钮获取中文摘要

This project is dedicated to the theoretical description of hydrodynamic transport and unconventional superconductivity in new topological semimetals. The materials under consideration are systems with two or more energy bands that touch each other in one Fermi point and which are topological different from the well known Weyl-semimetals and graphene. Examples of these materials are the Luttinger semimetals such as GaAs, HgTe, and alpha-Sn which have due to a strong spin-orbit coupling a parabolic energy dispersion and a total angular momentum of J=3/2. Another class of materials are the antiperovskite materials which have a linear energy dispersion and again a total angular momentum of J=3/2. The transport properties of these new materials are investigated in the proposed project.A special focus is put on the transport properties of Luttinger semimetals in the hydrodynamic regime. The hydrodynamic regime is an unique setting where only the Coulomb interaction between the electrons and holes dominates the physics, and effects due to coupling to vibrational degrees of freedom of the lattice and the influence of defects can be neglected. The transport quantities being studied are the electrical conductivity and the shear viscosity of the quasiparticle fluid. In particular we plan to answer the question whether the Luttinger semimetals are a strongly interacting system which is reflected in the question whether the ratio of viscosity over entropy is small and if it approaches or even violates the lower bound proposed for this quantity by Kovtun, Son, and Starinets.Another goal of this project is to derive and study the Ginzburg-Landau theory for systems having a total angular momentum of J=3/2 and J=1 in combination with a linear energy dispersion at low energies as realized by the anitperovskite materials or the CoSi crystal. The occurrence of unconventional and topological superconductivity, such as d-wave superconductivity, is expected in these materials due to the large angular momentum of the particles. The tensorial structure of the d-wave order parameter will lead to the competition between new and exotic states. We plan to investigate this competition between the different states and describe the unconventional superconductivity in these new topological semimetals.