Nuclear magnetic relaxation rate in a noncentrosymmetric superconductor

Abstract

For a noncentrosymmetric superconductor such as CePt3Si, we consider a Cooper pairing model with a two-component order parameter composed of spin-singlet and spin-triplet pairing components. We demonstrate that such a model on a qualitative level accounts for experimentally observed features of the temperature dependence of the nuclear spin-lattice relaxation rate T −1 1 , namely a peak just below Tc and a line-node gap behavior at low temperatures.Inversion symmetry is one of the key points for the formation of Cooper pairs in superconductors. Unusual properties arise in superconductors whose crystal structure does not possess an inversion center (e.g., Refs. [1,2,3,4,5], and references therein). The recent discovery of superconductivity in the noncentrosymmetric heavy Fermion compound CePt 3 Si has initiated much interest, as experimental data revealed various intriguing features [6,7,8]. The essential element in modelling noncentrosymmetric systems is the presence of antisymmetric spin-orbit coupling [9,10]. One of the characteristic features in the superconducting phase is the mixing of the spin-singlet and spin-triplet Cooper pairing channels which are otherwise distinguished by parity [2]. This is likely responsible for the surprisingly high value of the upper critical field H c2 which exceeds the paramagnetic limit [3,6,8,11,12]. CePt 3 Si displays further intriguing properties. Recent nuclear magnetic resonance (NMR) experiments found an overall anomalous temperature dependence of the nuclear spin-lattice relaxation rate T −1 1 [8,13,14]. The behavior of T −1 1 shows a (Hebel-Slichter) peak just below the superconducting critical temperature T c , and simultaneously a T 3 dependence at low temperatures indicating line nodes in the quasiparticle gap. Such a gap with line nodes is also suggested by measurements of the London penetration depth [8]. At first sight, those experimental results seem to be mutually contradicting, as the features of unconventional Cooper pairing (line nodes) and of conventional superconductivity (peak in T −1 1 due to the coherence effect) are implied at the same time by the temperature dependence of T −1 1 [8,13,14].In the present study, we demonstrate that these apparently conflicting behaviors can be reconciled by taking account of the mixing of the pairing channels with opposite parity, which naturally occurs in superconductors without inversion center. For this purpose, we consider a pairing model with a two-component order parameter consisting of spin-singlet and spin-triplet pairing components. Such a model contains the necessary ingredients to account for the observed features of T −1 1 , i.e., the linenode behavior at low temperatures and the coherence effect just below T c . At the same time, the pairing model would also explain the temperature dependence of the London penetration depth qualitatively and be consistent with earlier studies of H c2 [3,15].We base our analysis on a Hamiltonian considered in Ref. [3], in which the lack of inversion symmetry is incorporated ...

Inverse coherence effects in nuclear magnetic relaxation rates as a sign of topological superconductivity

“…In contrast, the k-integral with a spin-triplet p-wave gap leads toρ F = 0 [29]. Now, we apply the above arguments to topological superconducting insulators.…”

“…The presence of a coherence peak just below T c is determined by the second term in Eq. (2) [27,29]. The Hebel-Slichter peak appears when this term (including the minus sign in front of the spectral functions) has a positive contribution to T −1 1 .…”

“…The check symbol (ˇ) indicates a matrix in the Nambu space, whereas the hat symbol (ˆ) does that in an orbital-spin space. The NMR rate [28,29] is…”

Phase Diagrams of Noncentrosymmetric Superconductors

“…Recently, superconductors without inversion symmetry have been studied extensively owing to their unconventional features [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. A strong spin-orbit coupling results in the splitting of electronic bands, in which the direction of the electron spin depends on momentum.…”

Josephson effect between conventional and Rashba superconductors

“…We now turn to the Josephson effect between a spin-singlet s-wave superconductor (left-hand side) and a non-centrosymmetric one (right-hand side) with Rashba spin-orbit coupling ∼ λ ·σ, where λ = (−k R y , k R x , 0) [21]. The qualitative properties of such a junction can be obtained utilizing bulk Green functions as in Refs.…”