Pair-density wave states through spin-orbit coupling in multilayer superconductors

Abstract

Spin singlet superconductors with quasi-two dimensional multilayer structure are studied in high magnetic fields. Specifically we concentrate on bi-and tri-layer systems whose layers by symmetry are subject Rashba-type spin-orbit coupling. The combination of magnetic field and spin-orbit coupling leads to a first order phase transition between different states of layer-dependent superconducting order parameters upon rising the magnetic field. In this context we distinguish the low-field Bardeen-Cooper-Schrieffer state where all layers have order parameters of the same sign and the high-field pair-density wave state where the layer-dependent order parameters change the sign at the center layer. We also show that progressive paramagnetic limiting effects yield additional features in the H-T phase diagram. As possible realizations of such unusual superconducting phases we consider artificial superlattices of CeCoIn5, as well as some multilayer high-Tc cuprates.

Local Magnetization in Pair-Density Wave State

“…Although CeCoIn 5 and high-T c cuprates are believed to be a d-wave superconductor and would have a small odd-parity component admixed with the local non-centrosymmetricity, the features found below are independent of the pairing symmetry as long as the spin-singlet pairing is predominant. In fact, we have confirmed that the model for dwave superconductivity gives the qualitatively same results [8]. Hence, for the sake of numerical accuracy, we restrict ourselves to the simpler s-wave state.…”

“…Interestingly, the order parameter configuration with a sign change, (∆ 1 , ∆ 2 ) = (∆, −∆), becomes more stable at high magnetic fields, as shown in Ref. 8. This state is called the pair-density wave (PDW) state in Fig.…”

“…In the multilayer systems the mirror symmetry is broken for each layer except in the center layer, and therefore, a layer-dependent Rashba spin-orbit coupling emerges [5]. Our previous study reveals that the pairdensity wave (PDW) state, where the layer-dependent order parameter switches sign between layers, is stabilized in a magnetic field perpendicular to the conducting planes [8]. The stability of the PDW state can be understood on the basis of the spin susceptibility.…”

“…In a number of theoretical studies, unusual features are predicted for systems that conserve inversion symmetry globally but not locally [3][4][5][6][7][8][9]. One simple crystal structure displaying local noncentrosymmetricity is realized in various multilayer systems, such as the recently fabricated artificial superlattices of CeCoIn 5 [10] and the multilayer high-T c cuprates [11][12][13].…”

Electric Octupole Order in Bilayer Rashba System

“…A sublattice-dependent antisymmetric spin-orbit coupling (ASOC) arises from the local parity violation in crystal structures. Previous studies of superconductivity in multilayers, [1][2][3][4] magnetic quadrupole order in zigzag chains, 5,6) toroidal order in a honeycomb lattice, 7,8) and electric octupole (EO) order in bilayer systems 9) have revealed exotic quantum states of matter induced by the ASOC. On the basis of the generalized multipole expansion, 10) some of them are classified into odd-parity multipole states beyond the paradigm of even-parity multipole order studied in d-and f -electron systems.…”