Quasiparticle States near the Surface and the Domain Wall in ap_x±ip_y-Wave Superconductor

Abstract

The electronic states near a surface or a domain wall in the p-wave superconductor are studied for the order parameter of the form p x ±ip y -wave, which is a unitary odd-parity state with broken time-reversal symmetry. This state has been recently suggested as the superconducting state of Sr 2 RuO 4 . The spatial variation of the order parameter and vector potential is determined selfconsistently within the quasi-classical approximation. The local density of states at the surface is constant and does not show any peak-like or gap-like structure within the superconducting energy gap, in contrast to the case of the d-wave superconductors. The influence of an external magnetic field is mainly observable in the energy range above the bulk gap. On the other hand, there is a small energy gap in the local density of states at the domain wall between domains of the two degenerate p x +ip y -wave and p x −ip y -wave states.KEYWORDS: Sr2RuO4, p-wave superconductor, unitary state, time-reversal breaking state, boundary effect, surface, domain wall, quasi-classical theory, Ginzburg-Landau free energy §1. Introduction Sr 2 RuO 4 is the first superconductor with layered perovskite structure, which does not contain copper. 1) Although the structure is identical to that of some of the high-temperature superconductors, the transition temperature is rather low, T C =1.5K. There is a clear difference in the electronic structure, since Sr 2 RuO 4 is a good metal and even a Fermi liquid in its stoichiometric composition.Band structure calculations in good agreement with the de Haas-van Alphen measurements show that this compound has three Fermi surfaces originating from the three 4d-t 2g -orbitals of Ru 4+ . 2,3,4) There is growing experimental evidence that the superconducting state is unconventional (non-swave). Examples are the absence of a Hebel-Slichter peak in 1/T 1 T of NQR-measurements 5) and the sensitivity of T C on non-magnetic impurities. 6) It was suggested that the superconducting state has odd-parity (spin triplet) pairing. 7,8,10,9,11) There is a certain similarity with 3 He considering the correlation effects (superfluid 3 He has pwave pairing). 7) Furthermore, there is a series of related compounds such as SrRuO 3 which are 1 ferromagnetic suggesting that ferromagnetic spin fluctuations are probably enhanced in Sr 2 RuO 4 and mediate odd-parity, spin triplet pairing. 12,7,13) The recent discovery of intrinsic magnetism in the superconducting phase by µSR experiments indicates a pairing state with broken time reversal symmetry. 14) Symmetry considerations lead to the conclusion that this would only be possible for an odd-parity state. 15) A very strong support for odd-parity pairing comes also from the Knight shift data in the 17 O-NMR measurements which demonstrate the absence of any reduction of the spin susceptibility in the superconducting state. 16) The superconducting state compatible with all of these experiments is given by d(k)=ẑ(k x ±ik y ). 15) The presence of three electron bands forming the Fermi liqui...

Suppression of spontaneous currents inSr2RuO4by surface disorder

“…The energetic cost of the domain boundaries would be small, due to the very weak dispersion of the electronic band structure along the c direction, and symmetry requires that no spontaneous current would flow at these boundaries. The measurements of Hicks et al 10 place an upper bound of 20 − 400nm on the height of such domains, depending on microscopic domain details, and again assuming Matsumoto-Sigrist predictions for edge currents 12 (similar bounds have not been estimated for the experimental geometries of refs. 5 and 11).…”

“…The assumption of specular surface scattering as employed in [12][13][14][15][16] requires an atomically smooth surface. ab faces of Sr 2 RuO 4 can be cleaved, but ac and bc faces are typically polished to a smoothness of several nm 9 , on the order of ten lattice constants.…”

“…However, the magnitude of these currents is determined by microscopic details -they are neither quantized nor universal. The reason that the null result of the scanning magnetometry experiments poses such a challenge to the chiral p-wave hypothesis is quantitative -spontaneous currents of size comparable to theoretical estimates [12][13][14][15][16] would give a magnetic signal more than two orders of magnitude greater than the experimental resolution. Magnetometry measurements on mesoscopic samples 5 also see no signs of these currents.…”

Tunneling spectroscopy and Josephson current of superconductor-ferromagnet hybrids on the surface of a 3D TI

“…The asymmetry becomes prominent when magnetization is along z axis (Figs.3(a), (c) and (e)). We know that ρ e (x, E) and ρ h (x, E) are symmetric functions of E for chiral p-wave superconductor when ∆ 0 is much smaller than µ [61]. In that case, the time-reversal symmetry is already broken in the bulk states of p-wave superconductor.…”

Evidence from tunneling spectroscopy for a quasi-one-dimensional origin of superconductivity in Sr2RuO4

“…Exotic phenomena, such as topologically protected Majorana edge modes, which are currently the subject of much speculation, [13][14][15][16] might then be possible in Sr 2 RuO 4 . Issues with this OP identification, however, include the apparent absence of the anticipated edge currents, [17][18][19][20] the absence of a splitting of the transition near T c by an in-plane magnetic field, 21 and the strong evidence [22][23][24][25][26][27][28][29][30] for lines of gap nodes, or near nodes, that are nongeneric in the presence of time-reversal symmetry breaking. We here follow the bulk of the literature and take a chiral p-wave order parameter as a working assumption.…”