Hydrodynamics and unconventional superconductivity in new topological semimetals

该项目致力于新拓扑半金属中流体动力学输运和非常规超导性的理论描述。所考虑的材料是具有两个或更多个能带的系统，这些能带在一个费米点彼此接触，并且与众所周知的Weyl半金属和石墨烯在拓扑上不同。这些材料的例子是诸如GaAs、HgTe和α-Sn的Luttinger半金属，其由于强自旋-轨道耦合而具有抛物线能量色散和J=3/2的总角动量。另一类材料是反钙钛矿材料，其具有线性能量色散和J=3/2的总角动量。本项目主要研究这些新材料的输运性质，重点研究了Luttinger半金属在流体力学体系中的输运性质。流体动力学制度是一个独特的设置，其中只有电子和空穴之间的库仑相互作用占主导地位的物理，和由于耦合到晶格的振动自由度的影响和缺陷的影响可以忽略不计。所研究的输运量是准粒子流体的电导率和剪切粘度。 特别地，我们计划回答Luttinger半金属是否是强相互作用系统的问题，这反映在粘度与熵的比值是否很小，以及它是否接近甚至违反Kovtun，Son，这个项目的另一个目标是推导和研究总角动量为J=3/2和J= 1的系统的金兹伯格-朗道理论。1与如由反钙钛矿材料或CoSi晶体实现的低能量下的线性能量色散组合。由于这些粒子的角动量很大，预计在这些材料中会出现非常规和拓扑超导性，如d波超导性。d波序参量的张量结构将导致新态与奇异态之间的竞争。我们计划研究不同状态之间的竞争，并描述这些新的拓扑半金属中的非常规超导性。

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.