Anapole superconductivity from $\mathcal{PT}$-symmetric mixed-parity interband pairing

Abstract

Recently, superconductivity with spontaneous time-reversal or parity symmetry breaking is attracting much attention owing to its exotic properties, such as nontrivial topology and nonreciprocal transport. Particularly fascinating phenomena are expected when the time-reversal and parity symmetry are simultaneously broken. This work shows that time-reversal symmetry-breaking mixed-parity superconducting states generally exhibit an unusual asymmetric Bogoliubov spectrum due to nonunitary interband pairing. For generic two-band models, we derive the necessary conditions for the asymmetric Bogoliubov spectrum. We also demonstrate that the asymmetric Bogoliubov quasiparticles lead to the effective anapole moment of the superconducting state, which stabilizes a nonuniform Fulde-Ferrell-Larkin-Ovchinnikov state at zero magnetic fields. The concept of anapole order employed in nuclear physics, magnetic materials science, strongly correlated electron systems, and optoelectronics is extended to superconductors by this work. Our conclusions are relevant for any multiband superconductors with competing even-and odd-parity pairing channels. Especially, we discuss the superconductivity in UTe 2 .

Nonunitary superconductivity in complex quantum materials

“…This suggests that Fe-based superconductors are promising materials for nonunitary superconductors to be identified. Interestingly, nonunitary superconductors breaking both TRS and IS (not discussed here) but invariant under the product of these symmetries, are expected to be associated with exotic phenomena such as supercurrent-induced strain or photon-induced supercurrents [36]. This suggests that transport experiments could directly probe the nonunitary character of superconductors, at least within a subclass of nonunitary superconducting states.…”

“…Recently, nonunitary superconductors started to attract special attention given its association with Bogoliubov Fermi surfaces [34,35], anapole superconductivity with asymmetric Bogoliubov spectra [36], topological classification in terms of q-helicity [37], and multiple Majorana fermion phases [38]. Theoretical works in the context of nonunitary superconductivity have explored general aspects of impurity induced density of states and residual electric and thermal transport [39], disorder-induced mixed-parity superconductivity in noncentrosymmetric monolayer transition-metal dichalcogenides [40], and field-induced mixed-parity in locally noncentrosymmetric materials [41].…”

“…Superconducting fitness analysis for effective models with two orbitals of equal parity. This table is in direct parallel to table 1 and should be read as follows: the first column corresponds to the function d ab (k) accompanied by the basis matrix [a, b] contributing to the order parameter in equation(36), while the first line specifies the h ab (k) terms in the normal state Hamiltonian in equation (35), accompanied by the corresponding basis matrix. The table entries correspond to FC (k) 2 = 4 cd (table entry) |h cd (k)| 2 /|h(k)| 2 , for each term h cd (k) in the normal-state Hamiltonian indicated in the first row as (c, d).…”

Nonunitary Superconductivity in Complex Quantum Materials

“…Most superconducting states discussed in the literature are unitary. Recently, nonunitary superconductors started to attract special attention given its association with Bogoliubov Fermi surfaces [6,7], anapole superconductivity [8], and topolgical classification in terms of q-helicity [9].…”

Intrinsic finite-energy Cooper pairing in $j=3/2$ superconductors

“…Note added.-During the preparation of this manuscript, we became aware of a related proposal of inter-band pairing away from the Fermi surface. This proposal is, however, based on different physical properties and, therefore, applies to different physical systems [69].…”