The Microscopic Approach in the Theory of Superconductors With a Many-Component Order Parameter

Abstract

In terms of the generalized Bardeen-Cooper-Schrieffer model for a superconductor with degenerate orbital electron states, we derive a Ginzburg-Landau energy functional with a microscopic deciphering of the coefficients involved. The superconducting order parameter is separated out by expanding the wave function of a Cooper pair in the basis functions of crystal point group irreducible representations. It is shown that a many-component superconducting order parameter may arise from the degeneracy of the electron states on the Fermi surface—either owing to the degeneracy of the orbital states or owing to the degeneracy over the arms of the star, or as a result of both degeneracies simultaneously. Allowance for the orbital degeneracy extends the physical basis on which superconducting modes are realized and perturbs the classification of singlet and triplet states according to even and odd point group representations. It is also shown that allowance for the orbital degeneracy may alter the conditions for the superconducting gap to go to zero in individual Fermi surface points or lines as compared with the conditions that follow from arm degeneracy alone.

Unconventional superconducting gap structure protected by space group symmetry

“…Finally, we reduce P k into irreducible representations (IRs) of the original crystal point group. The gap functions should be zero, and thus, the gap nodes appear, if the corresponding IRs do not exist in the results of reductions [7,9,35]. Otherwise, the superconducting gap will open in general.…”

Space-Group Approach to the Nodal Structure of the Superconducting Order Parameter in UPt3

“…Izyumov et al [13] proposed to use IRs of space groups for the description of oneelectron states coupled in a Cooper pair and showed that the above-mentioned direct connection between multiplicity and parity of a Copper pair may be violated if oneelectron states are characterize by the wave vector in symmetrical directions in a Brillouin zone. The space-group approach to the wavefunction of a Copper pair was further developed [14 to 16] by making use of the Pauli exclusion principle and of the Mackey theorem [17,18].…”

Symmetry-Protected Line Nodes in Non-symmorphic Magnetic Space Groups: Applications to UCoGe and UPd2Al3

“…In both planes, there are four IRs, A g , B g , A u , and B u since the coset group M k /T is isomorphic to the point group C 2h [33]. The results are summarized in Table III. Note that the gap functions should be zero, which means the appearance of gap nodes, if the corresponding IRs do not exist in the reduction ofP k [21][22][23]. The absence of A u in PP corresponds to the emergent horizontal line node of the recently proposed E 2u state in UPt 3 superconductors [24,[34][35][36].…”

“…Such classification provides useful information in analyzing the nodal structure of various unconventional superconductors [20]. Also, another development of gap classification based on the space group symmetry [21][22][23][24] gives us the correct way to take into account small representations at Brillouin zone (BZ) boundary in non-symmorphic space groups [25,26]. T. Micklitz and M. R. Norman [24] demonstrated in the pioneering work that new types of * nomoto.takuya@scphys.kyoto-u.ac.jp symmetry-protected nodes can appear at the BZ boundary.…”