Christian Iniotakis

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.Tunneling spectroscopy at surfaces of unconventional supe rconductors has proven an invaluable tool for obtaining information abo ut 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 conduct ance peak is a signature for a non-trivial pair potential that exhibits different si gns on different regions of the Fermi surface. Here, we review recent theoretical resul ts on the spectrum of Andreev bound states near interfaces and surfaces in non-ce ntrosymmetric superconductors. We introduce a theoretical scheme to calculate the nergy spectrum of a non-centrosymmetric superconductor. Then, we discuss th e interplay between the spin orbit vector field on the Fermi surface and the order para meter symmetry. The Andreev states carry a spin supercurrent and represent a hel ic l edge mode along the interface. We study the topological nature of the resulting ed e currents. If the triplet component of the order parameter dominates, then the helica l dge mode exists. If, on the other hand, the singlet component dominates, the heli cal dge mode is absent. A quantum phase transition occurs for equal spin singlet and triplet order parameter components. We discuss the tunneling conductance and the An dreev point contact conductance between a normal metal and a non-centrosymmetr ic superconductor. Matthias Eschrig (a) Fachbereich Physik, Universität Konstanz, D-78464 Ko nstanz, Germany, and (b) Institut für Theoretische Festkörperphysik and DFGCenter for Functional Nanostructures, Karlsruhe Institute of Technology D-76128 Karlsruhe, Germ any, e-mail:Matthias.Eschrig@kit.de Christian Iniotakis Institute for Theoretical Physics, ETH Zurich, 8093 Zurich , Switzerland, e-mail:iniotaki@phys.ethz.ch Yukio Tanaka Department of Applied Physics, Nagoya University, Nagoya, 464-8603, Japan e-mail:ytanaka@nuap.nagoya-u.ac.jp

Andreev bound states and tunneling characteristics of a noncentrosymmetric superconductor

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.

Fractional Flux Quanta at Intrinsic Metallic Interfaces of Noncentrosymmetric Superconductors

We examine intrinsic interfaces separating crystalline twin domains of opposite spin–orbit coupling in a noncentrosymmetric superconductor such as CePt 3 Si. 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.

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.

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.

Josephson effect between conventional and Rashba superconductors

Abstract We study the Josephson effect between a conventional s-wave superconductor and a non-centrosymmetric superconductor with Rashba spin–orbit coupling. Rashba spin–orbit coupling affects the Josephson pair tunneling in a characteristic way. The Josephson coupling can be decomposed into two parts, a ‘spin-singlet-like’ and a ‘spin-triplet-like’ component. The latter component can lead to a shift of the Josephson phase by π relative to the former coupling. This has important implications on interference effects and may explain some recent experimental results for the Al/CePt 3 Si junction.

Functional superconductor interfaces from broken time-reversal symmetry.

The breaking of time-reversal symmetry in a triplet superconductor Josephson junction is shown to cause a magnetic instability of the tunneling barrier. Using a Ginzburg-Landau analysis of the free energy, we predict that this novel functional behavior reflects the formation of an exotic Josephson state, distinguished by the existence of fractional flux quanta at the barrier. The crucial role of the orbital pairing state is demonstrated by studying complementary microscopic models of the junction. Signatures of the magnetic instability are found in the critical current of the junction.

Properties of Interfaces and Surfaces in Non-centrosymmetric Superconductors

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 themselves as zero-bias conductance peaks 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.

Consequences of broken time-reversal symmetry in triplet Josephson junctions

We examine a triplet Josephson junction where time-reversal symmetry is broken by the misalignment of the d-vectors of the triplet superconductors on either side of the junction. We demonstrate that a spontaneous magnetization of the tunneling barrier can be stabilized, with moment aligned along the direction mutually perpendicular to the two d-vectors. We then find that the free energy minimum lies at a phase difference intermediate between O and π, permitting the existence of fractional flux quanta at the junction barrier.

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.