Doping and magnetic field dependence of in-plane tunneling into YBa(2)Cu(3)O(7-x): possible evidence for the existence of a quantum critical point

Self-consistent theory of current injection intodandd + issuperconductors

We present results for the steady-state nonlinear response of adx2-y2superconducting film connected to normal-metal reservoirs under voltage bias, allowing for a subdominants-wave component appearing near the interfaces. Our investigation is based on a current-conserving theory that self-consistently includes the non-equilibrium distribution functions, charge imbalance, and the voltage-dependencies of order parameters and scalar impurity self-energies. For a pured-wave superconductor with [110] orientation of the interfaces to the contacts, the conductance contains a zero-bias peak reflecting the large density of zero-energy interface Andreev bound states. Including a subdominants-wave pairing channel, it is in equilibrium energetically favorable for ans-wave order parameter componentΔsto appear near the interfaces in the time-reversal symmetry breaking combinationd + is. The Andreev states then shift to finite energies in the density of states. Under voltage bias, we find that the non-equilibrium distribution in the contact area causes a rapid suppression of thes-wave component to zero as the voltageeV→Δs. The resulting spectral rearrangements and voltage-dependent scattering amplitudes lead to a pronounced non-thermally broadened split of the zero-bias conductance peak that is not seen in a non-selfconsistent Landauer-Büttiker scattering approach.

What can Andreev bound states tell us about superconductors?

Zero-energy Andreev bound states, which manifest themselves in the tunnelling spectra as zero-bias conductance peaks (ZBCPs), are abundant at interfaces between superconductors and other materials and on the nodal surface of high-temperature superconductors. In this review, we focus on the information such excitations can provide on the properties of superconductor systems. First, a general introduction to the physics of Andreev bound states in superconductor/normal metal interfaces is given with a particular emphasis on why they appear at zero energy in d-wave superconductors. Then, specific spectroscopic tunnelling studies of thin films, bilayers and junctions are described, focusing on the corresponding ZBCP features. Scanning tunnelling spectroscopy (STS) studies show that the ZBCPs on the c-axis YBa₂Cu₃O_7-δ (YBCO) films are correlated with the surface morphology and appear only in proximity to (110) facets. STS on c-axis La_1.88Sr_0.12CuO₄ (LSCO) films exhibiting the 1/8 anomaly shows spatially modulated peaks near zero bias associated with the anti-phase ordering of the d-wave order parameter predicted at this doping level. ZBCPs were also found in micrometre-size edge junctions of YBCO/SrRuO₃/YBCO, where SrRuO₃ is ferromagnetic. Here, the results are consistent with a crossed Andreev reflection effect (CARE) at the narrow domain walls of the SrRuO₃ ZBCPs measured in STS studies of manganite/cuprate bilayers could not be attributed to CARE because the manganite's domain wall is much larger than the coherence length in YBCO, and instead are attributed to proximity-induced triplet-pairing superconductivity with non-conventional symmetry. And finally, ZBCPs found in junctions of non-intentionally doped topological insulator films of Bi₂Se₃ and the s-wave superconductor NbN are attributed to proximity-induced p_x+ ip_y triplet order parameter in the topological material.This article is part of the theme issue 'Andreev bound states'.

Broken translational symmetry at edges of high-temperature superconductors

Flat bands of zero-energy states at the edges of quantum materials have a topological origin. However, their presence is energetically unfavorable. If there is a mechanism to shift the band to finite energies, a phase transition can occur. Here we study high-temperature superconductors hosting flat bands of midgap Andreev surface states. In a second-order phase transition at roughly a fifth of the superconducting transition temperature, time-reversal symmetry and continuous translational symmetry along the edge are spontaneously broken. In an external magnetic field, only translational symmetry is broken. We identify the order parameter as the superfluid momentum ps, that forms a planar vector field with defects, including edge sources and sinks. The critical points of the vector field satisfy a generalized Poincaré-Hopf theorem, relating the sum of Poincaré indices to the Euler characteristic of the system.

New anomaly in the transverse acoustic impedance of superfluid 3He-B with a wall coated by several layers of 4He

We measured the transverse acoustic impedance of superfluid 3He-B with a wall coated by several layers of 4He. The coating is known to enhance the specularity in quasiparticle scattering by the wall. We found a new anomaly, a bump and a peak, in the temperature dependence of the transverse acoustic impedance. This agrees with a theoretical calculation using a partially specular wall boundary condition. The new anomaly is shown to arise from a change in the surface density of states by coating and the scattering of thermally occupied surface bound states to other states. The change is towards the density of states of Majorana cone in the specular limit.

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.

Nodeless d-wave superconducting pairing due to residual antiferromagnetism in underdoped Pr2-xCexCuO4-delta

We investigate the doping dependence of the penetration depth versus temperature in electron-doped Pr(2-x)Ce(x)CuO(4-delta) using a model which assumes the uniform coexistence of (mean-field) antiferromagnetism and superconductivity. Despite the presence of a d(x2-y2) pairing gap in the underlying spectrum, we find nodeless behavior of the low-T penetration depth in the underdoped case, in accord with experimental results. As doping increases, a linear-in-T behavior of the penetration depth, characteristic of d-wave pairing, emerges as the lower magnetic band crosses the Fermi level and creates a nodal Fermi surface pocket.

Transition from a mixed to a pure d-wave symmetry in superconducting optimally doped YBa2Cu3O7-x thin films under applied fields

We have probed the Landau levels of nodal quasiparticles by tunneling along a nodal direction of (110) oriented YBa2Cu3O7-x thin films with a magnetic field applied perpendicular to the CuO2 planes, and parallel to the film's surface. In optimally doped films and at low temperature, finite energy nodal states are clearly observed in films thinner than the London penetration depth. Above a well defined temperature, the order parameter reverts to a pure d-wave symmetry.

Quantum Hall effects in layered disordered superconductors

Layered singlet paired superconductors with disorder and broken time reversal symmetry are studied, demonstrating a phase diagram with charge-spin separation in transport. In terms of the average intergrain transmission and the interlayer tunneling we find quantum Hall phases with spin Hall coefficients of sigma(spin)(xy)=0,2 separated by a spin metal phase. We identify a spin metal-insulator localization exponent as well as a spin conductivity exponent of approximately 0.96. In the presence of a Zeeman term an additional sigma(spin)(xy)=1 phase appears.

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.

Robust dx2-y2 pairing symmetry in hole-doped cuprate superconductors

Although initially quite controversial, it is now widely accepted that the Cooper pairs in optimally doped cuprate superconductors have predominantly dx2-y2 wave function symmetry, and the controversy has now shifted to whether the pairing symmetry changes away from optimal doping. Here we present phase-sensitive tricrystal experiments on three cuprate systems: Y(0.7)Ca(0.3)Ba(2)Cu(3)O(7-delta) (Ca-doped Y-123), La2-xSrxCuO4 (La-214), and Bi(2)Sr(2)CaCu(2)O(8+delta) (Bi-2212), with doping levels covering the underdoped, optimal, and overdoped regions. Our work implies that predominantly d x2-y2 pairing symmetry is robust over a large variation in doping.

Metal-to-insulator crossover in YBa2Cu3Oy probed by low-temperature quasiparticle heat transport

It was recently demonstrated that in La2-xSrxCuO4 the magnetic-field (H) dependence of the low-temperature thermal conductivity kappa up to 16 T reflects whether the normal state under high magnetic field is a metal or an insulator. We measure the H dependence of kappa in YBa(2)Cu(3)O(y) (YBCO) at subkelvin temperatures for a wide doping range, and find that at low doping the kappa(H) behavior signifies the change in the ground state in this system as well. Surprisingly, the critical doping is found to be located deeply inside the underdoped region, about the hole doping of 0.07 hole/Cu; this critical doping is apparently related to the stripe correlations as revealed by the in-plane resistivity anisotropy.

Elasticity-driven nanoscale electronic structure in superconductors

The effects of long-range anisotropic elastic deformations on electronic structure in superconductors are analyzed within the framework of the Bogoliubov-de Gennes equations. Cases of twin boundaries and isolated defects are considered as illustrations. We find that the superconducting order parameter is depressed in the regions where pronounced lattice-deformation occurs. The calculated local density of states suggests that the electronic structure is strongly modulated in response to lattice deformations, and propagates to longer distances. In particular, this allows the trapping of low-lying quasiparticle states around defects. Some of our predictions can be directly tested by scanning tunneling microscopy experiments.

Andreev reflections on Y(1-x)Ca(x)Ba(2)Cu(3)O(7-delta): evidence for an unusual proximity effect

We have measured Andreev reflections between an Au tip and Y(1-x)Ca(x)Ba(2)Cu(3)O(7-delta) thin films in the in-plane orientation. The conductance spectra are best fitted with a pair potential having the d(x2-y2)+is symmetry. We find that the amplitude of the is component is enhanced as the contact transparency is increased. This is an indication for an unusual proximity effect that modifies the pair potential in the superconductor near the surface with the normal metal.

Heat transport in a strongly overdoped cuprate: Fermi liquid and a pure d-wave BCS superconductor

The transport of heat and charge in the overdoped cuprate superconductor Tl(2)Ba2CuO(6+delta) was measured down to low temperature. In the normal state, obtained by applying a magnetic field greater than the upper critical field, the Wiedemann-Franz law is verified to hold perfectly. In the superconducting state, a large residual linear term is observed in the thermal conductivity, in quantitative agreement with BCS theory for a d-wave superconductor. This is compelling evidence that the electrons in overdoped cuprates form a Fermi liquid, with no indication of spin-charge separation.

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.