Anomalous surface states at interfaces in p -wave superconductors

We study theoretically the spontaneous edge current in a small chiral superconductor with surface roughness. We obtained self-consistent solutions of the pair potential and the vector potential by solving the quasiclassical Eilenberger equation and the Maxwell equation simultaneously. We then employed them to calculate numerically the spatial distribution of the chiral edge current in a small superconductor. The characteristic behavior of the spontaneous edge current depends strongly on the symmetries of the order parameters such as chiral p-, chiral d-, and chiral f -wave pairing. The edge current is robust under the surface roughness in the chiral p-and chiral d-wave superconductors. In the chiral d-wave case, the surface roughness tends to flip the direction of the chiral current. On the other hand, the edge current in a chiral f -wave superconductor is fragile when there is surface roughness. We also discuss the temperature dependence of a spontaneous magnetization, which is a measurable value in standard experiments.

Section: Introductionmentioning

confidence: 99%

Spontaneous edge current in a small chiral superconductor with a rough surface

Suzuki

Asano

2016

“…The finite voltage current is thus helpful to distinguish chiral p-wave symmetry from d-wave or higher, which is qualitatively similar to trivial superconductors. The main effect of impurity scattering on chiral superconductors is to soften the dip at eV ∼ b , where the presence of continuum bands makes jĝ j (E ∼ b ,x = 0)τ j θ diverge [15,58]. As a consequence, the self-energy is acutely increased in the Born limit, while it is suppressed in the unitary limit; cf., Eq.…”

Section: B Effect Of Impurities At Finite Biasmentioning

confidence: 99%

Current fluctuations in unconventional superconductor junctions with impurity scattering

Burset

Tamura

et al. 2017

The order parameter of bulk two-dimensional superconductors is classified as nodal if it vanishes for a direction in momentum space, or gapful if it does not. Each class can be topologically nontrivial if Andreev bound states are formed at the edges of the superconductor. Nonmagnetic impurities in the superconductor affect the formation of Andreev bound states and can drastically change the tunneling spectra for small voltages. Here, we investigate the mean current and its fluctuations for two-dimensional tunnel junctions between normal-metal and unconventional superconductors by solving the quasiclassical Eilenberger equation self-consistently, including the presence of nonmagnetic impurities in the superconductor. As the impurity strength increases, we find that superconductivity is suppressed for almost all order parameters since (i) at zero applied bias, the effective transferred charge calculated from the noise-current ratio tends to the electron charge e, and (ii) for finite bias, the current-voltage characteristics follows that of a normal-state junction. There are notable exceptions to this trend. First, gapful nontrivial (chiral) superconductors are very robust against impurity scattering due to the linear dispersion relation of their surface Andreev bound states. Second, for nodal nontrivial superconductors, only p x -wave pairing is almost immune to the presence of impurities due to the emergence of odd-frequency s-wave Cooper pairs near the interface. Due to their anisotropic dependence on the wave vector, impurity scattering is an effective pair-breaking mechanism for the remaining nodal superconductors. All these behaviors are neatly captured by the noise-current ratio, providing a useful guide to find experimental signatures for unconventional superconductivity.

“…The one-dimensional Brillouin zone is ill defined with the disordered potential breaking the translational symmetry. Therefore, the winding number W (k) can no longer use to predict the number of ZESs at a dirty surface [29][30][31][32]. In other words, the potential disorder may lift the high degeneracy in the surface ZESs and may wash out the characteristic transport properties.…”

Section: Introductionmentioning

confidence: 99%

Stability of flat zero-energy states at the dirty surface of a nodal superconductor

Ikegaya¹,

Asano²

2017

We discuss the stability of highly degenerate zero-energy states that appear at the surface of a nodal superconductor preserving time-reversal symmetry. The existence of such surface states is a direct consequence of the nontrivial topological numbers defined in the restricted Brillouin zones in the clean limit. In experiments, however, potential disorder is inevitable near the surface of a real superconductor, which may lift the high degeneracy at zero energy. We show that an index defined in terms of the chiral eigenvalues of the zero-energy states can be used to measure the degree of degeneracy at zero energy in the presence of potential disorder. We also discuss the relationship between the index and the topological numbers.