Andreev bound states in rounded corners of d-wave superconductors

Andreev bound states at boundaries of d-wave superconductors are strongly influenced by the boundary geometry itself. In this work, the zero-energy spectral weight of the local quasiparticle density of states is presented for the case of wedge-shaped boundaries with rounded corners. Generally, both orientation of the d-wave and the specific local reflection properties of the rounded wedges determine, whether Andreev bound states exist or not. For the bisecting line of the wedge being parallel to the nodal direction of the d-wave gap function, strong zero-energy Andreev bound states are expected at the round part of the boundary

Theoretical aspects of Andreev spectroscopy and tunneling spectroscopy in non-centrosymmetric superconductors: a topical review

Tunneling spectroscopy at surfaces of unconventional superconductors has proven an invaluable tool for obtaining information about the pairing symmetry. It is known that mid gap Andreev bound states manifest itself as a zero bias conductance peak in tunneling spectroscopy. The zero bias conductance peak is a signature for a non-trivial pair potential that exhibits different signs on different regions of the Fermi surface. Here, we review recent theoretical results on the spectrum of Andreev bound states near interfaces and surfaces in non-centrosymmetric superconductors. We introduce a theoretical scheme to calculate the energy spectrum of a non-centrosymmetric superconductor. Then, we discuss the interplay between the spin orbit vector field on the Fermi surface and the order parameter symmetry. The Andreev states carry a spin supercurrent and represent a helical edge mode along the interface. We study the topological nature of the resulting edge currents. If the triplet component of the order parameter dominates, then the helical edge mode exists. If, on the other hand, the singlet component dominates, the helical edge mode is absent. A quantum phase transition occurs for equal spin singlet and triplet order parameter components. We discuss the tunneling conductance and the Andreev point contact conductance between a normal metal and a non-centrosymmetric superconductor.Comment: 42 pages, 11 figure

Coherent single atom shuttle between two Bose-Einstein condensates

We study an atomic quantum dot representing a single hyperfine "impurity" atom which is coherently coupled to two well-separated Bose-Einstein condensates, in the limit when the coupling between the dot and the condensates dominates the inter-condensate tunneling coupling. It is demonstrated that the quantum dot by itself can induce large-amplitude Josephson-like oscillations of the particle imbalance between the condensates, which display a two-frequency behavior. For noninteracting condensates, we provide an approximate solution to the coupled nonlinear equations of motion which allows us to obtain these two frequencies analytically.Comment: 4 pages of RevTex4, 4 figures; Rapid Communication in Physical Review

Chirality sensitive effect on surface states in chiral p-wave superconductors

We study the local density of states at the surface of a chiral p-wave superconductor in the presence of a weak magnetic field. As a result, the formation of low-energy Andreev bound states is either suppressed or enhanced by an applied magnetic field, depending on its orientation with respect to the chirality of the p-wave superconductor. Similarly, an Abrikosov vortex, which is situated not too far from the surface, leads to a zero-energy peak of the density of states, if its chirality is the same as that of the superconductor, and to a gap structure for the opposite case. We explain the underlying principle of this effect and propose a chirality sensitive test on unconventional superconductors.Comment: 4 pages, 2 figure

Andreev bound states in d-wave superconductors: influence of boundary geometry and vortices

An geraden Grenzflächen von d-Wellen-Supraleitern können starke gebundene Andreev-Zustände lokalisiert sein. Dieser bekannte Effekt hängt auf charakteristische Weise von der Orientierung der Grenzfläche zur Gapfunktion der d-Welle ab und kann experimentell in Form von zero-bias conductance peaks nachgewiesen werden. Die vorliegende Arbeit geht der theoretischen Frage nach, wie sich die gebundenen Zustände und damit auch das lokale Quasiteilchen-Spektrum verändern, wenn der betrachtete d-Wellen-Supraleiter eine nichttriviale Grenzflächengeometrie besitzt. Es zeigt sich, dass eine Fülle interessanter und exotischer Effekte auftritt, die sich sämtlich auf das klassische optische Reflexionsverhalten der Grenzflächengeometrie zurückführen lassen. Als konkrete Beispiele werden in der Arbeit supraleitende Keile, polygonale Grenzflächen und gelochte Supraleiter untersucht, dazu noch eine Reihe weiterer nichttrivialer Grenzflächengeometrien. Für einige Geometrien wird zudem der zusätzliche Einfluss durch einen Abrikosov-Vortex sowie ein äußeres Magnetfeld auf die gebundenen Andreev-Zustände untersucht.Zero-energy Andreev bound states may be localised at a straight flat surface of a d-wave superconductor. This well-known effect strongly depends on the orientation between the boundary and the d-wave gap function. Its existence is well confirmed experimentally, for example by the measurement of zero-bias conductance peaks. This dissertation goes further into the question of how the bound states and thus the local quasiparticle spectra are changed, if the superconductor under consideration exhibits a nontrivial boundary geometry. As a result, there is a variety of interesting and exotic effects, all of which can be explained by taking into account the reflection properties of the boundary geometry according to classical optics. The superconductors examined in this work are for example wedge-shaped or exhibit polygonal boundaries, or they have got holes inside. However, many more nontrivial boundary geometries are also considered. Furthermore, for some of the geometries the additional influence of both an Abrikosov-vortex and an applied magnetic field on the Andreev bound states is also examined

The chiral superconductor-ferromagnet-chiral superconductor Josephson junction

We study a Josephson junction between two chiral p-wave superconductors separated by a magnetically active tunneling barrier. We find that the interaction of the barrier magnetic moment with the spin of the tunneling triplet Cooper pairs is responsible for a number of unconventional Josephson effects. For example, we show that the critical current depends on the orientation of the moment, and that a finite spin current is possible in the ground state of the junction. In the case where the two superconductors have opposite chirality, we have also calculated the chiral Andreev bound state spectrum and the associated interface currents at the barrier, which have similar dependence on the magnetic moment to the Josephson currents.ISSN:1367-263