Effect of interorbital scattering on superconductivity in doped Dirac semimetals

Abstract

Unconventional superconductivity has been discovered in a variety of doped quantum materials, including topological insulators and semimetals. A unifying property of these systems is strong orbital hybridization, which leads to pairing of states with nontrivial Bloch wave functions. In contrast to naive expectation, however, many of these superconductors are relatively resilient to disorder. Here we study the interplay of superconductivity and disorder in doped three-dimensional Dirac systems, which serve as a paradigmatic dispersion in quantum materials, using Abrikosov-Gor'kov theory. In this way, the role of disorder is captured by a single parameter , the pair scattering rate. In contrast to previous studies, we argue that interorbital scattering cannot be neglected due to the strong orbital hybridization in Dirac systems. We find that the robustness of different pairing states highly depends on the relative strength of the different interorbital scattering channels. In particular, we find that the "nematic" superconducting state, which is argued to be the ground state in many Bi 2 Se 3-related compounds, is not protected from disorder in any way. The pair scattering rate in this case is at best smaller by a factor of 3 compared to systems without spin-orbit coupling. We also find that the odd-parity pairing state with total angular momentum zero (the B phase of superfluid 3 He) is protected against certain types of disorder, which include a family of time-reversal odd (magnetic) impurities. Namely, this odd-parity state is a singlet of partners under CT symmetry (rather than T symmetry in the standard Anderson's theory), where C and T are chiral and time-reversal symmetries, respectively. As a result, it is protected against any disorder potential that respects CT symmetry. Our procedure is very general and can be readily applied to different band structures and disorder configurations.

Sensitivity of superconducting states to the impurity location in layered materials

“…As we can infer from Table VI, all gap functions have a finite fitness measure, whose size depends on the details of the microscopic Hamiltonian. This aspect was already emphasized in previous works [24][25][26]. However, we also observe that the evolution of the share of symmetric configurations, S i (n), affects the scattering rate, which is a feature that does not depend on the structure of the Hamiltonian, but on the distribution of impurities.…”

“…Specific results for Cudoped Bi 2 Se 3 report that the robustness of the superconducting state depends not only on the superconducting order parameter, but on details of the electronic structure in the normal state [24]. Recently, this understanding was corroborated by a more complete analysis of the sensitivity of pairing states to various scattering potentials in two-orbital systems [25,26].…”

Time-reversal symmetry breaking and multigap superconductivity in the noncentrosymmetric superconductor La7Ni3

“…One would, thus, naively expect that any superconducting state with a significantly momentum-dependent order parameter, such as the k-dependent phases of (k) above, should be strongly suppressed [74,75]. However, more recent theoretical works [20][21][22][23][24] have shown that the pair-breaking effect of impurities can be significantly reduced in the presence of spin-orbit coupling; this is also confirmed by experiments [25][26][27] indicating that the critical temperature of pairing states transforming under a nontrivial representation of the point group might only be weakly suppressed in the presence of spin-orbit coupling-even when l becomes smaller than ξ (or even of the order of the Fermi wavelength). The basic reason for this protection mechanism is that matrix elements of an impurity potential between certain pairs (k 1 , k 2 ) of momenta can be suppressed due to spin-orbit mixing and that only certain scattering processes are pair breaking.…”

Lifshitz transition in dirty nematic superconductor

“…Nematic superconductivity is suppressed by the large disorder that confirms results of Refs. [27][28][29]. The critical temperature depends on the parameter ζ that determines both the critical temperature in a clean case and robustness against the disorder according to Eqs.…”

“…In Refs. [26][27][28][29] effects of the disorder on critical temperature of nematic superconductor was studied. It was found that density disorder decreases critical temperature for the nematic order parameter.…”