Experimental consequences of Bogoliubov Fermi surfaces

Abstract

Superconductors involving electrons with internal degrees of freedom beyond spin can have internally anisotropic pairing states that are impossible in single-band superconductors. As a case in point, in even-parity multiband superconductors that break time-reversal symmetry, nodes of the superconducting gap are generically inflated into two-dimensional Bogoliubov Fermi surfaces. The detection and characterization of these quasiparticle Fermi surfaces requires the understanding of their experimental consequences. In this paper, we derive the low-energy density of states for a broad range of possible nodal structures. Based on this, we calculate the low-temperature form of observables that are commonly employed for the characterization of nodal superconductors, i.e., the single-particle tunneling rate, the electronic specific heat and Sommerfeld coefficient, the thermal conductivity, the magnetic penetration depth, and the NMR spin-lattice relaxation rate, in the clean limit. We also address the question whether the topological invariant of the Bogoliubov Fermi surfaces is associated with topologically protected surface states, with negative results. This work is meant to serve as a guide for experimental searches for Bogoliubov Fermi surfaces in time-reversal-symmetry-breaking superconductors. arXiv:1909.10370v1 [cond-mat.supr-con]

Bogoliubov Fermi surfaces stabilized by spin-orbit coupling

“…The flat DOS at zero energy results from the lifting of the pseudospin degeneracy by the pseudomagnetic field h. This shifts the DOS for each pseudospin species, leading to the scaling ρ(E) ∝ (|E + |h|| + |E − |h||)/2 instead of ρ(E) ∝ |E|, as would be the case for line nodes. This gives a constant DOS for −|h| < E < |h|, as previously reported in [34]. The effect of the pseudomagnetic field is also seen in the splitting of the coherence peaks: in the absence of the pseudomagnetic field, we expect a single coherence peak at |E| = ∆ 0 .…”

“…Moreover, although the TRSB state becomes more stable with increasing SOC, the size of the BFS decreases, as shown below. It is thus unclear if BFSs can be realized in a limit where they have a detectable effect on the electronic structure [34]. Another interesting question raised by the analysis in [2,3] is what happens at SOC strengths insufficient for a stable TRSB state.…”

Stabilizing even-parity chiral superconductivity in Sr2RuO4

“…This value is proportional to the gap amplitude, here set to 0.15 meV. While the total residual density of states from the BFSs is not large and may be difficult to observe [67], such a nodal structure implies that some experimental results require reinterpretation. In particular, given that the BFSs extend along the k z axis, the argument that thermal conductivity measurements rule out the E g state because it has horizontal line nodes [24] no longer applies.…”

Supercurrent-Induced Weyl Superconductivity

“…It has been known that the superconducting gap structure can be predicted by the temperature dependence of various physical quantities, e.g., penetration depth, specific heat, thermal conductivity, and NMR relaxation rate [14,52]. For experimental measurements of the observables, in many cases we need to apply an external field such as a magnetic field.…”