Hydrodynamics and unconventional superconductivity in new topological semimetals
Final Report Abstract
This project was dedicated to the theoretical description of hydrodynamic transport and unconventional superconductivity in new topological semimetals. The materials under consideration were 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 Rarita-Schwinger-Weyl (RSW) semimetals such as 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 were investigated in the project in both the hydrodynamic and the superconducting regime. A special focus was set on the shear viscosity of the electron fluid in 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. We could demonstrate that Luttinger semimetals are a nearly perfect fluid and they are strongly interacting, since the ratio of shear viscosity over entropy for the quasiparticles of the Luttinger semimetals approaches the famous lower bound for this quantity proposed by Kovtun, Son, and Starinets. Furthermore, we investigated unconventional superconductivity in Luttinger semimetals, Rarita- Schwinger-Weyl semimetals, and triple-point fermions with a total angular momentum of J=1 by deriving the Ginzburg-Landau free energy for these systems. Due to the large angular momentum of the quasiparticles, unconventional and topological superconductivity such as d-wave (p-wave) can occur, which leads to a competition between new and exotic states. We demonstrated that in the d-wave channel the superconducting groundstate of RSW-semimetals with a finite chemical potential is the “cyclic state”, which breaks time-reversal symmetry maximally and has a vanishing average value of magnetization. However, for triple-point fermions we find a competition between the two states that break time-reversal symmetry maximally, namely the ferromagnetic state with maximal magnetization and the “cyclic state”. Depending on the curvature of the energy bands either one of the time-reversal maximally breaking states is stabilized. Hence, the triple-point fermions are the first system (to the best of our knowledge) where such a possibility arises. Furthermore, we determined the elaborate phase-diagram for the Luttinger semimetals in the p-wave channel, which differs for particle- and hole-doped systems. During our studies of d-wave superconductivity in RSW systems we predicted the existence of Bogoliubov-Fermi surfaces (BFS) in noncentrosymmetric superconductors, which was suprising since the believed necessary condition for the existence of BFS was the inversion symmetry of the system. We explained the emergence of BFSs in non-centrosymmetric multiband superconductors in terms of shifts of energy bands due to a pseudomagnetic field. Furthermore, we studied the stability of BFSs in centrosymmetric systems under inversion-symmetry breaking and found an instability in the way that the BFSs is only partially gapped out, deformed, and reduced in size.
Publications
- Bogoliubov-Fermi surfaces in non-centrosymmetric multi-component superconductors, Phys. Rev. Lett. 125, 237004 (2020)
J. M. Link and I. F. Herbut
(See online at https://doi.org/10.1103/PhysRevLett.125.237004) - d-wave superconductivity and Bogoliubov-Fermi surfaces in Rarita-Schwinger-Weyl semimetals, Phys. Rev. B 101, 184503 (2020)
J. M. Link, I. Boettcher, and I. F. Herbut
(See online at https://doi.org/10.1103/PhysRevB.101.184503) - Hydrodynamic transport in the Luttinger-Abrikosov-Beneslavskii non-Fermi liquid, Phys. Rev. B 101, 125128 (2020)
J. M. Link and I. F. Herbut
(See online at https://doi.org/10.1103/PhysRevB.101.125128) - Bogoliubov-Fermi surface with inversion symmetry and electron-electron interactions: relativistic analogies and lattice theory, Phys. Rev. B 103, 144517 (2021)
I. F. Herbut and J. M. Link
(See online at https://doi.org/10.1103/PhysRevB.103.144517) - Time-reversal symmetry breaking and d-wave superconductivity of triple-point fermions, Phys. Rev. B 104, 134512 (2021)
S. Mandal, J. M. Link, and I. F. Herbut
(See online at https://doi.org/10.1103/PhysRevB.104.134512) - p-wave superconductivity in Luttinger semimetals, Phys. Rev. B 105, 134522 (2022)
J. M. Link and I. F. Herbut
(See online at https://doi.org/10.1103/PhysRevB.105.134522)
