Larkin-Ovchinnikov state of superconducting Weyl metals: Fundamental differences between restricted and extended pairings in k -space

Abstract

Two common approaches of studying theoretically the property of a superconductor are shown to have significant differences, when they are applied to the Larkin-Ovchinnikov state of Weyl metals. In the first approach the pairing term is restricted by a cutoff energy to the neighborhood of the Fermi surface, whereas in the second approach the pairing term is extended to the whole Brillouin zone. We explore their difference by considering two minimal models for the Weyl metal. For a model giving a single pair of Weyl pockets, both two approaches give a partly-gapped (fully-gapped) bulk spectrum for small (large) pairing amplitude. However, for very small cutoff energy, a portion of the Fermi surface can be completely unaffected by the pairing term in the first approach. For the other model giving two pairs of Weyl pockets, while the bulk spectrum for the first approach can be fully gapped, the one from the second approach has a robust line node, and the surface states are also changed qualitatively by the pairing. We elucidate the above differences by topological arguments and analytical analyses. A factor common to both of the two models is the tilting of the Weyl cones which leads to asymmetric normal state band structure with respect to the Weyl nodes. For the Weyl metal with two pairs of Weyl pockets, the band folding leads to a double degeneracy in the effective model, which distinguishes the pairing of the second approach from all others.

Fractional Quantum Hall Effect in Weyl Semimetals

“…However, due to the effective doubling of degrees of freedom, induced by pairing, which is corrected by the factor of 1/2 in Eq. ( 6), the Fermi arc get copied to the part of the BZ outside of the Weyl points, and occupies the range of 4Q, which always coincides with the size of the new BZ, reduced by the translational symmetry breaking in the FFLO state [40]. When Q = G/4, however, this range is identical to the size of the original BZ, which is another way to see why the FFLO state does not break translational symmetry when and only when the Weyl node separation is exactly half the size of the BZ [15].…”

Bereziskii-Kosterlitz-Thouless transition in the Weyl system PtBi2

“…This may lead to unconventional superconducting states, such as a mixed singlet and triplet superconductivity [35][36][37] , or a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) finite momentum pairing [38][39][40][41][42][43] . It can also enable the realization of a Weyl semimetal phase, which, coupled to superconductivity, constitutes an ideal platform to study unconventional superconducting states or topological superconductivity [44][45][46][47][48][49][50][51] .…”

Pairing-dependent superconductivity gap and nonholonomic Andreev reflection in Weyl semimetal/Weyl superconductor heterojunctions

“…The superconducting transition temperature is about 0.5 K. However, a recent study showed that it is a superconducting Weyl semimetal with nodal points [7]. The superconductivity in doped WSMs [1][2][3][8][9][10][11][12][13] has become a topic of interest in unconventional superconductivity. Theoretically, for the lightly doped Weyl semimetal, the Fermi energy is sufficiently close to the Weyl nodes such that the Fermi surface consists of an even number of disconnected Fermi sheets around the Weyl nodes.…”