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Surfaces of $d$-wave superconductors may host a substantial density of zero-energy Andreev states. The zero-energy flat band appears due to a topological constraint, but comes with a cost in free energy. We have recently found that an adjustment of the surface states can drive a phase transition into a phase with finite superflow that breaks time-reversal symmetry and translational symmetry along the surface. The associated Doppler shifts of Andreev states to finite energies lower the free energy. Direct experimental verification of such a phase is still technically difficult and controversial, however. To aid further experimental efforts, we use the quasiclassical theory of superconductivity to investigate how the realization and the observability of such a phase are influenced by sample geometry and surface ruggedness. Phase diagrams are produced for relevant geometric parameters. In particular, critical sizes and shapes are identified, providing quantitative guidelines for sample fabrication in the experimental hunt for symmetry-breaking phases., Comment: 9 pages, 7 figures

We investigate equilibrium properties, including structure of the order parameter, superflow patterns, and thermodynamics of low-temperature surface phases of layered d_{x^2-y^2}-wave superconductors in magnetic field. At zero external magnetic field, time-reversal symmetry and continuous translational symmetry along the edge are broken spontaneously in a second order phase transition at a temperature $T^*\approx 0.18 T_c$, where $T_c$ is the superconducting transition temperature. At the phase transition there is a jump in the specific heat that scales with the ratio between the edge length $D$ and layer area ${\cal A}$ as $(D\xi_0/{\cal A})\Delta C_d$, where $\Delta C_d$ is the jump in the specific heat at the d-wave superconducting transition and $\xi_0$ is the superconducting coherence length. The phase with broken symmetry is characterized by a gauge invariant superfluid momentum ${\bf p}_s$ that forms a non-trivial planar vector field with a chain of sources and sinks along the edges with a period of approximately $12\xi_0$, and saddle point disclinations in the interior. To find out the relative importance of time-reversal and translational symmetry breaking we apply an external field that breaks time-reversal symmetry explicitly. We find that the phase transition into the state with the non-trivial ${\bf p}_s$ vector field keeps its main signatures, and is still of second order. In the external field, the saddle point disclinations are pushed towards the edges, and thereby a chain of edge motifs are formed, where each motif contains a source, a sink, and a saddle point. Due to a competing paramagnetic response at the edges, the phase transition temperature $T^*$ is slowly suppressed with increasing magnetic field strength, but the phase with broken symmetry survives into the mixed state., Comment: 12 pages, 9 figures

We present results for non-adiabatic single-parameter pumping in a ballistic graphene field-effect transistor. We investigate how scattering from an ac-driven top gate results in dc charge current from source to drain in an asymmetric setup caused either by geometry of the device or different doping of leads. Charge current is computed using Floquet scattering matrix approach in Landauer-B\"uttiker operator formalism. We single out two mechanisms contributing to the pumped current: Fabry-P\'erot interference in open channels and quasibound state resonant scattering through closed channels. We identify two distinct parameter regimes based on the quasibound state scattering mechanism: high and low doping of contacts compared to the frequency of the ac drive. We show that the latter regime results in a stronger peak pump current. We discuss how back gate potential and temperature dependence can be used to change the direction of the pumped current, operating the device as a switch., Comment: 7 pages, 6 figures

We report a theoretical study of time-dependent transport in a ballistic graphene field effect transistor. We develop a model based on Floquet theory describing Dirac electron transmission through a harmonically driven potential barrier. Photon-assisted tunneling results in excitation of quasibound states at the barrier. Under resonance condition, the excitation of the quasibound states leads to promotion of higher-order sidebands and enhanced higher harmonics of the source-drain conductance. The resonances in the main transmission channel are of the Fano form, while they are of the Breit-Wigner form for sidebands. We discuss the possibility of utilizing the resonances in prospective ballistic high-frequency devices, in particular frequency multipliers., Comment: 14 pages, 5 figures

We present atomistic calculations of quantum coherent electron transport through fulleropyrrolidine terminated molecules bridging a graphene nanogap. We predict that three difficult problems in molecular electronics with single molecules may be solved by utilizing graphene contacts: (1) a back gate modulating the Fermi level in the graphene leads facilitate control of the device conductance in a transistor effect with high on/off current ratio; (2) the size mismatch between leads and molecule is avoided, in contrast to the traditional metal contacts; (3) as a consequence, distinct features in charge flow patterns throughout the device are directly detectable by scanning techniques. We show that moderate graphene edge disorder is unimportant for the transistor function., Comment: 8 pages, 6 figures

Using selection rules imposed by the Pauli principle, we classify pairing correlations according to their symmetry properties with respect to spin, momentum, and energy. We observe that inhomogeneity always leads to mixing of even- and odd-energy pairing components. We investigate the superconducting pairing correlations present near interfaces between superconductors and ferromagnets, with focus on clean systems consisting of singlet superconductors and either weak or half-metallic ferromagnets. Spin-active scattering in the interface region induces all of the possible symmetry components. In particular, the long-range equal-spin pairing correlations have odd-frequency s-wave and even-frequency p-wave components of comparable magnitudes. We also analyze the Josephson current through a half-metal. We find analytic expressions and an interesting universality in the temperature dependence of the critical current in the tunneling limit., Comment: 20 pages, 5 figures, added citations, corrected typos

We report complementary studies of the critical temperature and the critical current in ferromagnet (Ni) - superconductor (Nb) multilayers. The observed oscillatory behavior of both quantities upon variation of the thickness of the ferromagnetic layer is found to be in good agreement with theory. The length scale of oscillations is identical for both quantities and is set by the magnetic length corresponding to an exchange field of 200 meV in Ni. The consistency between the behavior of the two quantities provides strong evidence for periodic pi- phase shifts in these devices., Comment: 4 pages, 3 figures

We discuss how life-time broadening of quasiparticle states influences single- and two-particle current transport through zero-energy states at normal metal/d-wave superconductor junctions. We distinguish between intrinsic broadening (imaginary part $\eta$ of the energy), which couples the bound states with the superconducting reservoir, and broadening due to leakage through the junction barrier, which couples the bound states with the normal metal reservoir. We show that shot noise is highly sensitive to the mechanism of broadening, while the conductance is not. In the limit of small but finite intrinsic broadening, compared to the junction transparency $D$, $\eta/\Delta_0\ll D$, the low-voltage shot noise at zero frequency and zero temperature becomes proportional to the magnitude $\eta$ of intrinsic broadening ($\Delta_0$ is the maximum d-wave gap)., Comment: 6 pages, 4 figures; presented at the SDP2001 conference in Tokyo

The formation of bound states at surfaces of materials with an energy gap in the bulk electron spectrum is a well known physical phenomenon. At superconductor surfaces, quasiparticles with energies inside the superconducting gap $\Delta$ may be trapped in bound states in quantum wells, formed by total reflection against the vacuum and total Andreev reflection against the superconductor. Since an electron reflects as a hole and sends a Cooper pair into the superconductor, the surface states give rise to resonant transport of quasiparticle and Cooper pair currents, and may be observed in tunneling spectra. In superconducting junctions, these surface states may hybridize and form bound Andreev states, trapped between the superconducting electrodes. In d-wave superconductors, the order parameter changes sign under $90^o$ rotation and, as a consequence, Andreev reflection may lead to the formation of zero energy quasiparticle bound states, midgap states (MGS). The formation of MGS is a robust feature of d-wave superconductivity and provides a unified framework for many important effects which will be reviewed: large Josephson current, low-temperature anomaly of the critical Josephson current, $\pi$-junction behavior, $0\to \pi$ junction crossover with temperature, zero-bias conductance peaks, paramagnetic currents, time reversal symmetry breaking, spontaneous interface currents, and resonance features in subgap currents. Taken together these effects, when observed in experiments, provide proof for d-wave superconductivity in the cuprates., Comment: 52 pages, 20 figures. Review article under consideration for publication in Superconductor Science and Technology

We study spontaneous time-reversal symmetry breaking at Josephson tunnel junctions of d-wave superconductors in the absence of subdominant components of the order parameter. For tunnel junctions, when the orientation is close to 0/45 (for which a gap lobe points towards the junction on one side and a gap node on the other), the mechanism of the symmetry breaking is the splitting of midgap states (MGS) by spontaneous establishment of a phase difference $\phi=\pm \pi/2$ across the junction. This occurs for transparencies $D\gg\xi_0/\lambda$ and temperatures $k_BT\ll D\Delta_0$, where $\xi_0$ is the coherence length, $\lambda$ is the penetration depth, and $\Delta_0$ is the maximum energy gap. On the other hand. tunnel junctions with $D\ll\xi_0/\lambda$ effectively behave as surfaces, for which the mechanism of symmetry breaking is self-induced Doppler shifts of MGS. For this instability, we calculate the phase transition temperature $k_BT_{TRSB}=(1/6)(\xi_0/\lambda)\Delta_0$ and show that the spatial shape of the gap is unimportant., Comment: 5 pages, 2 figures embedded; rewritten introduction

We investigate the dc current-voltage characteristics of d-wave Josephson junctions, where the barrier at the interface may have arbitrary strength. Dividing the current into n-particle currents $I_n$ (n integer), we can explicitly show which physical processes are responsible for the subharmonic gap structure (SGS). For orientations where midgap states (MGS) exist, the resonances in the n-particle processes are drastically changed, giving rise to a strongly modified SGS. Introducing broadening in a phenomenological way, we show that MGS may produce a current peak near zero bias and we explain which physical processes are contributing to this peak. The agreement of our theory with recent experiments is discussed., Comment: 5 pages, (will appear in Journal of Low Temperature Physics, MOS-99 proceedings)

We study theoretically the ac Josephson effect in voltage biased planar junctions of d-wave superconductors. For some orientations of the superconductors a current peak is found at finite voltage in the current-voltage characteristics. We pick out the relevant physical processes and write down an analytical formula for the current which clearly shows how the midgap state acts as a resonance and produces the peak. We present a possible explanation for the zero-bias conductance peak, recently found in experiments on grain boundary junctions of high-temperature superconductors, in terms of resonant transmission through midgap state of quasiparticles undergoing multiple Andreev reflections. We note that within our framework the zero-bias conductance peak appears in rather transparent Josephson junctions of d-wave superconductors., Comment: 10 pages, 5 figures, Submitted to a special volume of "Superlattices and Microstructures"