Time-reversal and rotation symmetry breaking superconductivity in Dirac materials

Abstract

We consider mixed symmetry superconducting phases in Dirac materials in the odd parity channel, where pseudoscalar and vector order parameters can coexist due to their similar critical temperatures when attractive interactions are of finite range. We show that the coupling of these order parameters to unordered magnetic dopants favors the condensation of novel time-reversal symmetry breaking (TRSB) phases, characterized by a condensate magnetization, rotation symmetry breaking, and simultaneous ordering of the dopant moments. We find a rich phase diagram of mixed TRSB phases characterized by peculiar bulk quasiparticles, with Weyl nodes and nodal lines, and distinctive surface states. These findings are consistent with recent experiments on NbxBi2Se3 that report evidence of point nodes, nematicity, and TRSB superconductivity induced by Nb magnetic moments. [5] and from Josephson tunneling experiments. The two-dimensional p + ip state in particular has attracted great interest as a topological superconductor with protected edge and vortex modes, of potential use in the field of quantum computation [6,7]. In a three dimensions chiral SC is also possible, allowing the realization of a Weyl superconductor with Majorana arcs on the surface [8][9][10], but realistic candidate materials for this superconducting state are lacking.

Nematic and chiral superconductivity induced by odd-parity fluctuations

“…We also note an additional symmetry breaking in the coexistence phase. In (29), H(k) satisfies an inversion symmetry H(k) = H(−k) when |η p | = 0, or an inversion-gauge symmetry τ z H(k)τ z = H(−k) when |η s | = 0. In the coexistence phase, neither the inversion nor inversion-gauge symmetry remains.…”

“…Therefore, the nematic phase with θ = nπ/3 realizes a topological Dirac superconductor with Dirac point nodes in the bulk and Majorana arcs on certain surfaces 25 . In the coexistence phase where s-wave and nematic order parameter has a phase difference ±π/2, the Bogoliubov-de Gennes Hamiltonian is: (29) which is expressed in the basis (c † k↑ , c † k↓ , c −k↓ , −c −k↑ ). ε 0 (k) = 2 k 2 /(2m) − µ, and τ x,y,z are Pauli matrices in the Nambu space.…”

“…So far, experimental evidence of surface Majorana states associated with topological superconductivity has been not conclusive 20,21 . On the theoretical side, different aspects of the nematic states have been explored, including bulk properties [22][23][24] , surface states 25 , vortex states 26,27 , and the interplay between E u superconductivity and magnetism 28,29 .…”

Realization of Weyl semimetal phases in topoelectrical circuits

“…These band degeneracy points are classified as either Dirac [11] or Weyl points (WP) [12,13] depending on their symmetries. Dirac points appear only when both time-reversal [14] and inversion symmetry [15] are conserved in a system. On the contrary, WPs emerge if either or both symmetries are broken.…”

Spin Dynamics and Dirac Nodes in a Kagome Lattice

“…Low‐energy fermionic excitations in electronic band structures have provoked much research into condensed matter physics in recent years to find alternative semiconductors and semi‐metals . Dirac materials provide an interesting symmetry protection; especially for 2D and topological materials, which, in turn, provides the potential for technological applications through the tunability of the electronic interactions by external fields …”