Shadow on the wall cast by an Abrikosov vortex

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.     

Circuit theory of unconventional superconductor junctions

We extend the circuit theory of superconductivity to cover transport and proximity effect in mesoscopic systems that contain unconventional superconductor junctions. The approach fully accounts for zero-energy Andreev bound states forming at the surface of unconventional superconductors. As a simple application, we investigate the transport properties of a diffusive normal metal in series with a d-wave superconductor junction. We reveal the competition between the formation of Andreev bound states and proximity effect that depends on the crystal orientation of the junction interface.     

Spin-dependent quasiparticle reflection and bound States at interfaces with itinerant antiferromagnets

We find a novel channel of quasiparticle reflection from the simplest two-sublattice antiferromagnet (AF) on a bipartite lattice. Low-energy quasiparticles in a normal metal (N) experience spin-dependent retroreflection at AF/N interfaces. As a combined effect of antiferromagnetic and Andreev reflections, subgap Andreev states arise at an AF/superconductor (SC) interface. When the antiferromagnetic reflection dominates the specular one, Andreev bound states have almost zero energy on AF/s-wave superconductor (sSC) interfaces, whereas there are no low-energy subgap states on AF/d-wave superconductor (dSC) boundaries. For an sSC/AF/sSC junction, the bound states are found to split, due to the finite width of the AF interlayer, and carry the supercurrent. The theory developed in the present Letter is based on a novel quasiclassical approach, which applies to interfaces involving itinerant antiferromagnets.     

Tunneling spectroscopy and order parameter symmetry of hole- and electron-doped cuprate superconductors

In tunneling spectroscopy of superconductors the density of states close to the surface or the interface to an insulating tunneling barrier is probed. For d-wave superconductors the particle–hole coherence results in interesting new phenomena at surfaces such as the formation of bound surface states at the Fermi level by Andreev reflection due to a sign change of the order parameter field in different k -directions. The probing of these states represents a phase-sensitive experiment allowing the determination of the order parameter symmetry in superconductors. We summarize the present experimental status with respect to the study of high-temperature superconductors (HTS). We discuss theoretically predicted consequences of a dominating d-wave order parameter in the hole-doped HTS on their tunneling spectra as well as on the physics of high-temperature superconductor Josephson junctions. A comparison of the tunneling spectra obtained for hole- and electron-doped HTS leads to the conclusion that the former have a d-wave, whereas the latter most likely have an anisotropic s-wave order parameter. We also address some unsettled questions related to the presence of a state with broken time-reversal symmetry at surfaces and interfaces of d-wave HTS and discuss specific features of d-wave tunnel junctions that have been predicted theoretically but still not been confirmed in experiments.     

Evidence of a d- to s-wave pairing symmetry transition in the electron-doped cuprate superconductor Pr(2-x)CexCuO4

We present point contact spectroscopy (PCS) data for junctions between a normal metal and the electron-doped cuprate superconductor Pr(2-x)CexCuO4 (PCCO). For the underdoped compositions of this cuprate ( x approximately 0.13) we observe a peak in the conductance-voltage characteristics of the point contact junctions. The shape and magnitude of this peak suggest the presence of Andreev bound states at the surface of underdoped PCCO which is evidence for a d-wave pairing symmetry. For overdoped PCCO ( x approximately 0.17) the PCS data do not show any evidence of Andreev bound states at the surface suggesting an s-wave pairing symmetry.     

The vortex physics which comes from the vortex core

A theoretical view of vortex core states and of their effects on physics of vortices in clean s- and d-wave-type II superconductors is presented based on a semi-classical picture of a vortex core as an Andreev potential well containing many quasiparticle states. We discuss the density of states, the vortex dissipation, Hall effect, and the vortex mass. The dynamic characteristics are determined by relaxation of core excitations driven by a moving vortex. In a d-wave superconductor, gap nodes make the core states more extended and introduce novel features into thermodynamics and kinetics of vortices.     

Effect of the surface roughness on Bean-Livingston surface barrier

Bean-Livingston barrier for a single Abrikosov vortex interacting with the rough surface is calculated as a function of the random characteristics of the surface roughness. It has been shown that even a respectively smooth surface roughness results in an essential decrease of the Bean-Livingston surface barrier.     

Andreev reflection and bound states in topological insulator based planar and step Josephson junctions

A superconductor-topological insulator-superconductor (S/TI/S) junction having normal region at angle θ is studied theoretically to investigate the junction angle dependency of the Andreev reflection and the formation of the Andreev bound states in the step and planar S/TI/S structures. It is found that the Andreev reflection becomes θ dependent only in the presence of the potential barrier at the TI/S interface. In particular, the step and planar TI/S junction have totally different conductive behavior with bias voltage and potential barrier in the regime of retro and specular Andreev reflection. Interestingly, we find that the elliptical cross section of Dirac cone, an important feature of topological insulator with step surface defect, affects the Fabry-Perot resonance of the Andreev reflection induced Andreev bound states (which become Majorana zero energy states at low chemical potential) in the step S/TI/S structure. Unlike the usual planar S/TI/S structures, we find these ellipticity affected Andreev bound states lead to non-monotonic Josephson super-current in the step S/TI/S structure whose non-monotonicity can be controlled with the use of the potential barrier, which may find applications in nanoelectronics.     

Tunneling transport in topological insulator normal metal/insulator/d-wave superconductor junctions

We investigate the tunneling conductance in a normal metal/insulator/d-wave superconductor (NM/I/d-wave SC) junction with a barrier of thickness d and with an arbitrary gate voltage V(0) applied across the barrier region, formed on the surface of a topological insulator, using the Dirac-Bogoliubov-de Gennes equation and Blonder-Tinkham-Klapwijk?(BTK) formalism. We find that the tunneling conductance as a function of both d and V(0) displays an oscillatory behavior whose amplitude decreases with increase of V(0). We also find that when the Andreev resonant condition is met, the tunneling conductance approaches a maximum value of 2G(0), independent of the gate voltage V(0).     

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.     

Conductance of SIN and SIS junctions with chiral superconductors

Low-temperature conductance peaks due to the surface Andreev bound states in SIN and SIS junctions with chiral superconductors are considered. It is shown that, in SIN junctions, the conductance as a function of voltage, G(V), is highly sensitive to the dependence of the barrier transparency on the direction of the quasiparticle momentum. A weak magnetic field applied to the junction shifts the conductance peaks. In symmetric SIS junctions, the presence of chiral levels of Andreev bound states on both sides of the barrier gives rise to a conductance peak at V=0.     

Oscillations of Andreev states in clean ferromagnetic films

We investigate the influence of the exchange field on the Andreev bound states in a ferromagnetic ( F) film backed on one side by a superconductor ( S). Our model accounts for diffusive reflection at the outer surface and possible backscattering at the FS interface. Phase shifting of the Andreev level by the exchange field results in an oscillatory behavior of the density of states of F as a function of the layer thickness. We show that our results agree quantitatively with recent experiments.     

Majorana fermions and exotic surface Andreev bound states in topological superconductors: application to Cu(x)Bi2Se3

The recently discovered superconductor Cu(x)Bi2Se3 is a candidate for three-dimensional time-reversal-invariant topological superconductors, which are predicted to have robust surface Andreev bound states hosting massless Majorana fermions. In this work, we analytically and numerically find the linearly dispersing Majorana fermions at k=0, which smoothly evolve into a new branch of gapless surface Andreev bound states near the Fermi momentum. The latter is a new type of Andreev bound states resulting from both the nontrivial band structure and the odd-parity pairing symmetry. The tunneling spectra of these surface Andreev bound states agree well with a recent point-contact spectroscopy experiment [S. Sasaki et al., Phys. Rev. Lett. 107, 217001 (2011)] and yield additional predictions for low temperature tunneling and photoemission experiments.     

Singular current response from isolated impurities in d-wave superconductors

The current response of a d-wave superconductor containing a single impurity is calculated and shown to be singular in the low-temperature limit, leading in the case of strong scattering to a 1/T term in the penetration depth lambda(T) similar to that induced by Andreev surface bound states. For a small number of such impurities, we argue this low-T upturn could be observable in cuprate superconductors.     

Surface bound states and spin currents in noncentrosymmetric superconductors

We investigate the ground state properties of a noncentrosymmetric superconductor near a surface. We determine the spectrum of Andreev bound states due to surface-induced mixing of bands with opposite spin helicities for a Rashba-type spin-orbit coupling. We find that the order parameter suppression qualitatively changes the bound state spectrum. The spin structure of Andreev states leads to a spin supercurrent along the interface, which is strongly enhanced compared to the normal state spin current. Particle and hole coherence amplitudes show Faraday-like rotations of the spin along quasiparticle trajectories.     

Andreev reflection in strong magnetic fields

We have studied the interplay of Andreev reflection and cyclotron motion of quasiparticles at a superconductor-normal-metal interface with a strong magnetic field applied parallel to the interface. Bound states are formed due to the confinement introduced by both the external magnetic field and the superconducting gap. These bound states are a coherent superposition of electron and hole edge excitations similar to those realized in finite quantum-Hall samples. We find the energy spectrum for these Andreev edge states and calculate transport properties.     

Fano effect and Andreev bound states in T-shape double quantum dots

In this Letter, we investigate the transport through a T-shaped double quantum dot coupled to two normal metal leads left and right and a superconducting lead. Analytical expressions of Andreev transmission and local density of states of the system at zero temperature have been obtained. We study the role of the superconducting lead in the quantum interferometric features of the double quantum dot. We report for first time the Fano effect produced by Andreev bound states in a side quantum dot. Our results show that as a consequence of quantum interference and proximity effect, the transmission from normal to normal lead exhibits Fano resonances due to Andreev bound states. We find that this interference effect allows us to study the Andreev bound states in the changes in the conductance between two normal leads.     

Spectrum of Andreev bound states in a molecule embedded inside a microwave-excited superconducting junction

Nondissipative Josephson current through nanoscale superconducting constrictions is carried by spectroscopically sharp energy states, the so-called Andreev states. Although theoretically predicted almost 40 years ago, no direct spectroscopic evidence of these Andreev bound states exists to date. We propose a novel type of spectroscopy based on embedding a superconducting constriction, formed by a single-level molecule junction, in a microwave QED cavity environment. In the electron-dressed cavity spectrum we find a polariton excitation at twice the Andreev bound state energy, and a superconducting-phase-dependent ac Stark shift of the cavity frequency. Dispersive measurement of this frequency shift can be used for Andreev bound state spectroscopy.     

Smearing origin of zero-bias conductance peak in Ag-SiO-Bi2Sr2CaCu2O8+δ planar tunnel junctions: influence of diffusive normal metal verified with the circuit theory

We propose a new approach of smearing origins of a zero-bias conductance peak (ZBCP) in high-T_c superconductor tunnel junctions through the analysis based on the circuit theory for a d-wave pairing symmetry. The circuit theory has been recently developed from conventional superconductors to unconventional superconductors. The ZBCP frequently appears in line shapes for this theory, in which the total resistance was constructed by taking account of the effects between a d-wave superconductor and a diffusive normal metal (DN) at a junction interface, including the midgap Andreev resonant states (MARS), the coherent Andreev reflection (CAR) and the proximity effect. Therefore, we have analyzed experimental spectra with the ZBCP of Ag-SiO-Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) planar tunnel junctions for the {110}-oriented direction by using a simplified formula of the circuit theory for d-wave superconductors. The fitting results reveal that the spectral features of the ZBCP are well explained by the circuit theory not only excluding the Dynes's broadening factor but also considering only the MARS and the DN resistance. Thus, the ZBCP behaviors are understood to be consistent with those of recent studies on the circuit theory extended to the systems containing d-wave superconductor tunnel junctions.     

Josephson Current in Superconductor-Ferromagnet/Insulator/d-Wave Superconductor Junctions

Solving the Bogoliubov-de Gennes equation, the energy levels of bound states are obtained in the ferromagnetic superconductor. The Josephson currents in a ferromagnetic superconductor/Insulator/d-wave superconductor junction are calculated as a function of the exchange field, temperature, and insulating barrier strength. It is found that the Josephson critical current is always suppressed by the presence of exchange field h and depends on crystalline axis orientation of d-wave superconductor.