Self-consistent theory of current injection into d and d plus is superconductors

We present results for the steady-state nonlinear response of a dx2-y2 Delta s <i . 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-Buttiker scattering approach

Thermopower and thermophase in a d -wave superconductor

In an unconventional superconductor, the interplay of scattering off impurities and Andreev processes may lead to different scattering times for electronlike and holelike quasiparticles. Such electron-hole asymmetry appears when the impurity scattering phase shift is intermediate between the Born and unitary limits and leads to an expectation for large thermoelectric effects. Here, we examine the thermoelectric response of a d-wave superconductor connected to normal-metal reservoirs under a temperature bias using a fully self-consistent quasiclassical theory. The thermoelectrically induced quasiparticle current is cancelled by superflow in an open circuit setup, but at the cost of a charge imbalance induced at the contacts and extending across the structure. We investigate the resulting thermopower and thermophase and their dependencies on scattering phase shift, mean free path, and interface transparency. For crystal-axis orientations such that surface-bound zero-energy Andreev states are formed, the thermoelectric effect is reduced as a result of locally reduced electron-hole asymmetry. For a semiballistic superconductor with good contacts, we find thermopowers of order several μV/K, suggesting a thermovoltage measurement as a promising path to investigate thermoelectricity in unconventional superconductors

Spontaneous generation of fractional vortex-Antivortex pairs at single edges of high-Tc superconductors

Unconventional d-wave superconductors with pair-breaking edges are predicted to have ground states with spontaneously broken time-reversal and translational symmetries. We use the quasiclassical theory of superconductivity to demonstrate that such phases can exist at any single pair-breaking facet. This implies that a greater variety of systems, not necessarily mesoscopic in size, should be unstable to such symmetry breaking. The density of states averaged over the facet displays a broad peak centered at zero energy, which is consistent with experimental findings of a broad zero-bias conductance peak with a temperature-independent width at low temperatures

SuperConga: An open-source framework for mesoscopic superconductivity

We present SuperConga, an open-source framework for simulating equilibrium properties of unconventional and ballistic singlet superconductors, confined to two-dimensional (2D) mesoscopic grains in a perpendicular external magnetic field, at arbitrary low temperatures. It aims at being both fast and easy to use, enabling research without access to a computer cluster, and visualization in real-time with OpenGL. The core is written in C++ and CUDA, exploiting the embarrassingly parallel nature of the quasiclassical theory of superconductivity by utilizing the parallel computational power of modern graphics processing units. The framework self-consistently computes both the superconducting order-parameter and the induced vector potential and finds the current density, free energy, induced flux density, local density of states (LDOS), and the magnetic moment. A user-friendly Python frontend is provided, enabling simulation parameters to be defined via intuitive configuration files, or via the command-line interface, without requiring a deep understanding of implementation details. For example, complicated geometries can be created with relative ease. The framework ships with simple tools for analyzing and visualizing the results, including an interactive plotter for spectroscopy. An overview of the theory is presented, as well as examples showcasing the framework\u27s capabilities and ease of use. The framework is free to download from https://gitlab.com/superconga/superconga, which also links to the extensive user manual, containing even more examples, tutorials, and guides. To demonstrate and benchmark SuperConga, we study the magnetostatics, thermodynamics, and spectroscopy of various phenomena. In particular, we study flux quantization in solenoids, vortex physics, surface Andreev bound-states, and a "phase crystal."We compare our numeric results with analytics and present experimental observables, e.g., the magnetic moment and LDOS, measurable with, for example, scanning probes, STM, and magnetometry

Transport Properties of Superconducting d-wave junctions

At surfaces and interfaces of d-wave superconductors, quasiparticle bound states with zero energy, midgap states (MGS), are necessarily formed as a consequence of the sign change of the d-wave order parameter upon 90\ub0 rotation. The MGS can never exist at s-wave superconductor surfaces and are therefore true fingerprints of unconventional superconductivity. In this thesis we have studied the basic properties of d-wave superconducting junctions, the central issue being the role of midgap states. Within a scattering theory of transport, we calculate both the dc Josephson current in phase-biased junctions and the current-voltage characteristics (IVC) and ac current components in voltage-biased junctions. We have studied the role of MGS in spontaneous time-reversal symmetry breaking at Josphson tunnel junctions of purely d-wave superconductors. For junction transparencies , where is the superconducting coherence length and is the penetration depth, the driving mechanism of the instability is the splitting of MGS by spontaneous establishment of a phase difference across the junction. For tunnel junctions with , the mechanism is instead self-induced Dopplershifts of MGS. For the particular orientation when a lobe points towards the junction at one side and a node at the other, we find that the odd ac components disapper, which results in a doubling of the Josephson frequency for this orientation. We present a detailed study of the IVC of voltage-biased junctions. For low transparency junctions we derive analytical results for the MGS resonances. We also elaborate on how intrinsic broadening of MGS may determine the nature of resonant tranport through MGS: either via single particle tunneling for large broadening or via pair tunneling for negligible broadening. We argue that it may be possible to distinguish between these types of transport by a measurement of either the low-voltage IVC of Josephson junctions or the zero-voltage zero-frequency shot noise in normal metal-superconductor junctions

Transport Properties of Superconducting d-wave junctions

At surfaces and interfaces of d-wave superconductors, quasiparticle bound states with zero energy, midgap states (MGS), are necessarily formed as a consequence of the sign change of the d-wave order parameter upon 90\ub0 rotation. The MGS can never exist at s-wave superconductor surfaces and are therefore true fingerprints of unconventional superconductivity. In this thesis we have studied the basic properties of d-wave superconducting junctions, the central issue being the role of midgap states. Within a scattering theory of transport, we calculate both the dc Josephson current in phase-biased junctions and the current-voltage characteristics (IVC) and ac current components in voltage-biased junctions. We have studied the role of MGS in spontaneous time-reversal symmetry breaking at Josphson tunnel junctions of purely d-wave superconductors. For junction transparencies , where is the superconducting coherence length and is the penetration depth, the driving mechanism of the instability is the splitting of MGS by spontaneous establishment of a phase difference across the junction. For tunnel junctions with , the mechanism is instead self-induced Dopplershifts of MGS. For the particular orientation when a lobe points towards the junction at one side and a node at the other, we find that the odd ac components disapper, which results in a doubling of the Josephson frequency for this orientation. We present a detailed study of the IVC of voltage-biased junctions. For low transparency junctions we derive analytical results for the MGS resonances. We also elaborate on how intrinsic broadening of MGS may determine the nature of resonant tranport through MGS: either via single particle tunneling for large broadening or via pair tunneling for negligible broadening. We argue that it may be possible to distinguish between these types of transport by a measurement of either the low-voltage IVC of Josephson junctions or the zero-voltage zero-frequency shot noise in normal metal-superconductor junctions

Quasiclassical Theory of Spin Imbalance in a Normal Metal-Superconductor Heterostructure with a Spin-Active Interface

Non-equilibrium phenomena in superconductors have attracted much attention since the first experiments on charge imbalance in the early 1970\u27s. Nowadays a new promising line of research lies at an intersection between superconductivity and spintronics. Here we develop a quasiclassical theory of a single junction between a normal metal and a superconductor with a spin-active interface at finite bias voltages. Due to spin-mixing and spin-filtering effects of the interface a non-equilibrium magnetization (or spin imbalance) is induced at the superconducting side of the junction, which relaxes to zero in the bulk. A peculiar feature of the system is the presence of interface-induced Andreev bound states, which influence the magnitude and the decay length of spin imbalance. Recent experiments on spin and charge density separation in superconducting wires required external magnetic field for observing a spin signal via non-local measurements. Here, we propose an alternative way to observe spin imbalance without applying magnetic field

Triplet supercurrents in clean and disordered half-metallic ferromagnets

Interfaces between materials with differently ordered phases present unique opportunities to study fundamental problems in physics. One example is the interface between a singlet superconductor and a half-metallic ferromagnet, where Cooper pairing occurs between electrons with opposite spin on the superconducting side, whereas the other exhibits 100% spin polarization. The recent surprising observation of a supercurrent through half-metallic CrO2 therefore requires a mechanism for conversion between unpolarized and completely spin-polarized supercurrents. Here, we suggest a conversion mechanism based on electron spin precession together with triplet-pair rotation at interfaces with broken spin-rotation symmetry. In the diffusive limit (short mean free path), the triplet supercurrent is dominated by inter-related odd-frequency s-wave and even-frequency p-wave pairs. In the crossover to the ballistic limit, further symmetry components become relevant. The interface region exhibits a superconducting state of mixed-spin pairs with highly unusual symmetry properties that open up new perspectives for exotic Josephson devices