Magnetic-field-induced helical and stripe phases in Rashba superconductors

Abstract

Due to the lack of both parity and time-reversal symmetries, the Rashba superconductors CePt 3 Si, CeRhSi 3 , and CeIrSi 3 , in the presence of a magnetic field, are unstable to helical ͑single plane wave͒ order. We develop a microscopic theory for such superconductors and examine the stability of this helical phase. We show that the helical phase typically occupies most of the magnetic field-temperature phase diagram. However, we also find that this phase is sometimes unstable to a multiple-q phase ͑loosely called a stripe phase͒, in which both the magnitude and the phase of the order parameter are spatially varying. We find the position of this helical to multiple-q phase transition. We further examine the density of states and identify features unique to the helical phase.

Complex-Stripe Phases Induced by Staggered Rashba Spin–Orbit Coupling

“…It has been found by Agterberg and Kaur that an inhomogeneous superconducting phase similar to the complex-stripe phase could be realized in non-centrosymmetric superconductors, but the spin-orbit coupling turns out to be rather detrimental for this type of phase. 12) In contrast, the complexstripe phase in the locally non-centrosymmetric superconductors is favored by the strong staggered antisymmetric spinorbit coupling. As mentioned in Sect.…”

“…2) Examples are the mixing of spin-singlet and triplet Cooper pairings, 3,4) magnetoelectric effect, [5][6][7][8] helical superconducting phase, 3,[9][10][11][12][13][14][15] and topological superconductivity. 16,17) These unconventional features result from an antisymmetric spinorbit coupling, which can be classified in various categories such as Rashba-type, Dresselhaus-type, and cubic-type.…”

Transverse Magnetic Field Distribution in the Vortex State of Noncentrosymmetric Superconductor with O Symmetry

“…1, 2,3,4,5,6,7,8,9 The lack of inversion symmetry of background crystal causes an unconventional pairing in the superconducting state and a number of consequences are predicted. 10,11,12,13 It is commonly believed that in the normal state the Fermi surface is split by the spin-orbital coupling as a result of the broken inversion symmetry, and the pairing wavefunction is in a mixture of singlet and triplet pseudospin state. 10 Suggested by the low temperature measurements of penetration depths, the family of Li 2 B(Pd 1−x Pt x ) 3 with point group symmetry O demonstrates a trend from a conventional gap to a nodal gap caused by mixing with a stronger triplet pairing as the composition x varies from 0 to 1.…”

Magnetoelectric effect and the upper critical field in superconductors without inversion center

“…First predicted by Levitov, Nazarov, and Eliashberg [1], the magnetoelectric effect was studied microscopically by several authors [2][3][4][5][6]. In this context several observable effects have been predicted: (i) the existence of a helically twisted superconducting order parameter in a magnetic field in two and three dimensional cases and spontaneous supercurrents in a 2D geometry [4][5][6][7][8][9] and near the superconductor surface [10] as well as along junctions of two superconductors with opposite directions of polarization [11], (ii) the augmentation of the upper critical field oriented perpendicular to the direction of the space parity breaking [6,8], (iii) magnetic interference patterns of the Josephson critical current for a magnetic field applied perpendicular to the junction [8].…”