Observation of broken time-reversal symmetry with Andreev bound state tunneling spectroscopy

Quasiparticle (QP) planar tunneling spectroscopy is used to investigate the density of states (DoS) of YBa₂Cu₃O₇ (YBCO). Temperature, crystallographic orientation, doping, damage and magnetic field dependencies confirm that the observed zero-bias conductance peak (ZBCP) is an Andreev bound state (ABS), an intrinsic property of a d-wave superconducting order parameter (OP) at an interface. In zero applied field, the splitting of the ZBCP below 8 K confirms a near-surface phase transition into a superconducting state with spontaneously broken time-reversal symmetry (BTRS). Tunneling into the ABS provides a phase-sensitive spectroscopy that can be used to measure a variety of DoS properties in an unconventional superconductor.     

The emergence of bound states in a superconducting gap at the topological insulator edge

We consider the edge of a superconducting topological insulator with the impurity in the presence of the Zeeman field. We analytically prove that in the trivial phase two Andreev bound states (ABSs) arise with energies moving from the superconducting gap edges to zero forming two Majorana-like bound states, as the impurity strength varies from 0 to ±2. When the Zeeman field is locally perturbed, ABSs arise both in the trivial and topological phases, but in the topological phase ABSs with energy near the gap edges cannot transform into Majorana bound states and vice versa.     

Andreev bound states in high temperature superconductors

Andreev bound states at the surface of superconductors are expected for any pair potential showing a sign change in different k-directions with their spectral weight depending on the relative orientation of the surface and the pair potential. We report on the observation of Andreev bound states in high temperature superconductors (HTS) employing tunneling spectroscopy on bicrystal grain boundary Josephson junctions (GBJs). The tunneling spectra were studied as a function of temperature and applied magnetic field. The tunneling spectra of GBJ formed by YBa₂Cu₃O (YBCO), Bi₂Sr₂CaCu₂O(BSCCO), and La_1.85Sr_0.15CuO₄ (LSCO) show a pronounced zero bias conductance peak that can be interpreted in terms of Andreev bound states at zero energy that are expected at the surface of HTS having a d-wave symmetry of the order parameter. In contrast, for the most likely s-wave HTS Nd_1.85Ce_0.15CuO_4-y (NCCO) no zero bias conductance peak was observed. Applying a magnetic field results in a shift of spectral weight from zero to finite energy. This shift is found to depend nonlinearly on the applied magnetic field. Further consequences of the Andreev bound states are discussed and experimental evidence for anomalous Meissner currents is presented. Received: 17 February 1998 / Revised: 27 April 1998 / Accepted: 23 June 1998     

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.     

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.     

Spin-symmetric solution of an interacting quantum dot attached to superconducting leads: Andreev states and the 0-<Emphasis Type="Italic">π</Emphasis> transition

Behavior of Andreev gap states in a quantum dot with Coulomb repulsion symmetricallyattached to superconducting leads is studied via the perturbation expansion in theinteraction strength. We find the exact asymptotic form of the spin-symmetric solution forthe Andreev states continuously approaching the Fermi level. We thereby derive a criticalinteraction at which the Andreev states at zero temperature merge at the Fermi energy,being the upper bound for the 0-π transition. We show that the spin-symmetricsolution becomes degenerate beyond this interaction, in the π phase, and the Andreevstates do not split unless the degeneracy is lifted. We further demonstrate that thedegeneracy of the spin-symmetric state extends also into the 0 phase in which the solutions with zero andnon-zero frequencies of the Andreev states may coexist.     

Phase modulated thermal conductance of Josephson weak links

We present a theory for quasiparticle heat transport through superconducting weak links. The thermal conductance depends on the phase difference (phi) of the superconducting leads. Branch-conversion processes, low-energy Andreev bound states near the contact, and the suppression of the local density of states near the gap edge are related to phase-sensitive transport processes. Theoretical results for the influence of junction transparency, temperature, and disorder, on the conductance, are reported. For high-transmission weak links, D-->1, the formation of an Andreev bound state leads to suppression of the density of states for the continuum excitations, and thus, to a reduction in the conductance for phi approximately pi. For low-transmission (D<1) barriers resonant scattering leads to an increase in the thermal conductance as T drops below T(c) (for phase differences near phi=pi).     

Spectroscopic evidence for unconventional superconductivity in UBe13

We report on measurements of the differential conductivity G of UBe13-Au contacts, which reveal the existence of low-energy Andreev surface bound states. These bound states are identified via huge conductance peaks at zero bias that may form only in superconductors with nontrivial energy-gap functions. From the voltage dependence of G at T6.7, much in excess of the weak coupling BCS value of 3.5, and directly indicating strong coupling effects in superconducting UBe13.     

Topological Superconductivity in Cu(x)Bi(2)Se(3)

A topological superconductor (TSC) is characterized by the topologically protected gapless surface state that is essentially an Andreev bound state consisting of Majorana fermions. While a TSC has not yet been discovered, the doped topological insulator Cu(x)Bi(2)Se(3), which superconducts below ～3 K, has been predicted to possess a topological superconducting state. We report that the point-contact spectra on the cleaved surface of superconducting Cu(x)Bi(2)Se(3) present a zero-bias conductance peak (ZBCP) which signifies unconventional superconductivity. Theoretical considerations of all possible superconducting states help us conclude that this ZBCP is due to Majorana fermions and gives evidence for a topological superconductivity in Cu(x)Bi(2)Se(3). In addition, we found an unusual pseudogap that develops below ～20 K and coexists with the topological superconducting state.     

Superconductivity and field-induced magnetism in Pr2-xCexCuO4 single crystals

We report muon-spin rotation and relaxation (muSR) measurements on single crystals of the electron-doped high-T(c) superconductor Pr2-xCexCuO4. In a zero external magnetic field, superconductivity is found to coexist with dilute Cu spins that are static on the muSR time scale. In an applied field, we observe a mu(+)-Knight shift that is primarily due to the magnetic moment induced on the Pr ions. Below the superconducting transition temperature T(c), an additional source of local magnetic field appears throughout the volume of the sample. This finding is shown to be consistent with field-induced antiferromagnetic ordering of the Cu spins. Measurements of the temperature dependence of the in-plane magnetic penetration depth lambda(ab) in the vortex state are also presented.     

Josephson transport in complex mesoscopic structures

A universal spectral equation is derived for Andreev bound states in superconducting quantum junctions, relating bound state energies with the normal electron scattering amplitudes. The equation is applied to calculation of d.c. Josephson effect in mesoscopic S-2DEG-S junctions.     

Commensurate spin dynamics in the superconducting state of an electron-doped cuprate superconductor

We report neutron scattering studies on two single crystal samples of the electron-doped (n-type) superconducting (SC) cuprate Nd2-xCexCuO4 (x=0.15) with T(c)=18 and 25 K. Unlike the hole-doped (p-type) SC cuprates, where incommensurate magnetic fluctuations commonly exist, the n-type cuprate shows commensurate magnetic fluctuations at the tetragonal (1/2 1/2 0) reciprocal points both in the SC and in the normal state. A spin gap opens up when the n-type cuprate becomes SC, as in the optimally doped p-type La2-xSrxCuO4. The gap energy, however, increases gradually up to about 4 meV as T decreases from T(c) to 2 K, which contrasts with the spin pseudogap behavior with a T-independent gap energy in the SC state of p-type cuprates.     

Superconducting atomic contacts under microwave irradiation

We have measured the effect of microwave irradiation on the dc current-voltage characteristics of superconducting atomic contacts. The interaction of the external field with the ac supercurrents leads to replicas of the supercurrent peak, the well-known Shapiro resonances. The observation of supplementary fractional resonances for contacts containing highly transmitting conduction channels reveals their nonsinusoidal current-phase relation. The resonances sit on a background current which is itself deeply modified, as a result of photon-assisted multiple Andreev reflections. The results provide firm support for the full quantum theory of transport between two superconductors based on the concept of Andreev bound states.     

Large magnetic field-induced spectral weight enhancement of high-energy spin excitations in La1.88Sr0.12CuO4

We report electronic Raman scattering experiments on a superconducting La(1.88)Sr(0.12)CuO(4) single crystal in a magnetic field. At low temperatures, the spectral weight of the high-energy two-magnon peak increases linearly with field and is amplified by a factor of more than two at 14 T. The effect disappears at elevated temperatures and is not present in undoped La(2)CuO(4). This observation is discussed in terms of an electronically inhomogeneous state in which the field enhances the volume fraction of a phase with local antiferromagnetic order at the expense of the superconducting phase.     

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.     

Coherent transmission of nodal Dirac fermions through a graphene-based superconducting double barrier junction

Transport characteristics of relativistic electrons through graphene-based d-wave superconducting double barrier junction and ferromagnet/d-wave superconductor/normal metal double junction have been investigated based on the Dirac–Bogoliubov–de Gennes equation. We have first presented the results of superconducting double barrier junction. In the subgap regime, both the crossed Andreev and nonlocal tunneling conductance all oscillate with the bias voltage due to the formation of Andreev bound states in the normal metal region. Moreover, the critical voltage beyond which the crossed Andreev conductance becomes to zero decreases with increasing value of superconducting pair potential α. In the presence of the ferromagnetism, the MR through graphene-based ferromagnet/ d-wave superconductor/normal metal double junction has been investigated. It is shown that the MR increases from exchange splitting h ₀=0 to h ₀=E _F (Fermi energy), and then it goes down. At h ₀=E _F, MR reaches its maximum 100. In contrast to the case of a single superconducting barrier, Andreev bound states also manifest itself in the zero bias MR, which result in a series of peaks except the maximum one at h ₀=E _F. Besides, the resonance peak of the MR can appear at certain bias voltage and structure parameter. Those phenomena mean that the coherent transmission can be tuned by superconducting pair potential, structure parameter, and external bias voltage, which benefits the spin-polarized electron device based on the graphene materials.     

Adiabatic pumping in a superconductor-normal-superconductor weak link

We present a formalism to study adiabatic pumping through a superconductor-normal-superconductor weak link. At zero temperature, the pumped charge is related to the Berry phase accumulated, in a pumping cycle, by the Andreev bound states. We analyze in detail the case when the normal region is short compared to the superconducting coherence length. The pumped charge turns out to be an even function of the superconducting phase difference. Hence, it can be distinguished from the charge transferred due to the standard Josephson effect.     

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.     

Point-contact tunneling spectroscopy between a Nb tip and an ideal topological insulator Sn-doped Bi_(1.1)Sb_(0.9)Te_2S

The lightly Sn-doped Bi_(1.1)Sb_(0.9)Te_2S is a good material to investigate the pure topological surface state because the bulk bands are far away from the Fermi level. By measuring point-contact tunneling spectra on the topological insulator Bi_(1.08)Sn_(0.02)Sb_(0.9)Te_2S samples with a superconducting Nb tip, we observed the suppression of differential conductance near zero bias, instead of the enhancement due to Andreev reflection on the spectra. The fitting to the measured spectrum results in a superconducting gap of more than 4 meV, and this value is much larger than the superconducting gap of the bulk Nb. The gaped feature exists at temperatures even above the critical temperature of bulk Nb, and is visible when the magnetic field is as large as 9 T at 3 K. We argue that such behaviors may be related to the pressure induced superconductivity by the tip in the junction area, or just some novel phenomena arising from the junction between an s-wave superconductor and an ideal topological insulator.