The tunneling characteristics of planar junctions between a normal metal and a non-centrosymmetric superconductor like CePt3Si are examined. It is shown that the superconducting phase with mixed parity can give rise to characteristic zero-bias anomalies in certain junction directions. The origin of these zero-bias anomalies are Andreev bound states at the interface. The tunneling characteristics for different directions allow to test the structure of the parity-mixed pairing state.
We present a detailed comparison of numerical solutions of the quasiclassical Eilenberger equations with several approximation schemes for the density of states of s-and d-wave superconductors in the vortex state, which have been used recently. In particular, we critically examine the use of the Doppler shift method, which has been claimed to give good results for d-wave superconductors. Studying the single vortex case we show that there are important contributions coming from core states, which extend far from the vortex cores into the nodal directions and are not present in the Doppler shift method, but significantly affect the density of states at low energies. This leads to sizeable corrections to Volovik's law, which we expect to be sensitive to impurity scattering. For a vortex lattice we also show comparisons with the method due to Brandt, Pesch, and Tewordt and an approximate analytical method, generalizing a method due to Pesch. These are high field approximations strictly valid close to the upper critical field Bc2. At low energies the approximate analytical method turns out to give impressively good results over a broad field range and we recommend the use of this method for studies of the vortex state at not too low magnetic fields.
At the surface of a d-wave superconductor, a zero-energy peak in the quasiparticle spectrum can be observed. This peak appears due to Andreev bound states and is maximal if the nodal direction of the d-wave pairing potential is perpendicular to the boundary. We examine the effect of a single Abrikosov vortex in front of a reflecting boundary on the zero-energy density of states. We can clearly see a splitting of the low-energy peak and therefore a suppression of the zero-energy density of states in a shadowlike region extending from the vortex to the boundary. This effect is stable for different models of the single Abrikosov vortex, for different mean free paths and also for different distances between the vortex center and the boundary. This observation promises to have also a substantial influence on the differential conductance and the tunneling characteristics for low excitation energies.
We study the influence of surface Andreev bound states in d-wave superconductors on the Bean-Livingston surface barrier for entry of a vortex line into a strongly type-II superconductor. Starting from Eilenberger theory, we derive a generalization of London theory to incorporate the anomalous surface currents arising from the Andreev bound states. This allows us to find an analytical expression for the modification of the Bean-Livingston barrier in terms of a single parameter describing the influence of the Andreev bound states. We find that the field of first vortex entry is significantly enhanced. Also, the depinning field for vortices near the surface is renormalized. Both effects are temperature dependent and depend on the orientation of the surface relative to the d-wave gap.
We examine intrinsic interfaces separating crystalline twin domains of opposite spin-orbit coupling in a noncentrosymmetric superconductor such as CePt3Si. At these interfaces, low-energy Andreev bound states occur as a consequence of parity-mixed Cooper pairing, and a superconducting phase which violates time reversal symmetry can be realized. This provides an environment allowing flux lines with fractional flux quanta to be formed at the interface. Their presence could have strong implications on the flux creep behavior in such superconductors. PACS numbers: 74.20.Rp, 74.50.+r, 74.70.Tx Symmetry is a decisive factor for many properties of materials. Lowering a symmetry can yield new couplings between physical observables and causes intriguing phenomena. The recently discovered noncentrosymmetric superconductors CePt 3 Si, CeRhSi 3 , CeIrSi 3 , and Li 2 (Pt x Pd 1−x ) 3 B provide such examples [1,2,3,4]. In these materials, the absence of an inversion center generates antisymmetric spin-orbit interaction and leads, in the superconducting state, to parity-mixing of Cooper pairs, magnetoelectric effects, and many other interesting features [5,6,7,8]. In many cases, such crystal structures permit the existence of twin domains exhibiting opposite inversion symmetry breaking within a single crystal. Actually, in the crystal growth processes of noncentrosymmetric materials, the formation of such twin domains is inevitable. The existence of twin domains in noncentrosymmetric superconductors is also suggested by a recent experiment, which revealed that a high quality single crystal sample of CePt 3 Si exhibits a lower transition temperature than polycrystal ones [9]. Since the origin of this behavior cannot be understood in terms of conventional impurity effects [10], possibly twin boundaries could enhance the trend to superconductivity. Furthermore, recent NMR measurements of the single crystal sample are ingeniously interpreted by assuming the existence of twin domains [11]. Motivated by these observations, in this letter, we investigate effects of intrinsic interfaces between twin domains on the parity-mixed superconducting state. Our central finding is, that superconducting states with broken time-reversal symmetry can occur at the interfaces, allowing for fractional vortices.We consider a noncentrosymmetric superconductor such as CePt 3 Si and assume for simplicity a spherical Fermi surface parametrized by the unit vectork = (cos ϕ sin θ, sin ϕ sin θ, cos θ). The presence of a Rashbatype spin-orbit coupling, α(ẑ×k)·s, induces a splitting of the electron bands and the Fermi surface into sheets, each exhibiting a specific spin structure. The superconducting phase displays a mixed parity [5,6,7], and the state compatible with experiments consists of an s-and a p-wave component, being of s ± p-character on the two Fermi sheets. Moreover, there is experimental evidence for a nodal gap structure, which suggests a dominant spintriplet p-wave component with q = ∆ s /∆ p < 1, where ∆ s and ∆ p denote the magnitudes of th...
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