Transport in spinless superconducting wires

Journal of Physics: Conference Series, 2010

We present results on the microscopic dynamics of electrons in nanoscale systems coupled to superconducting leads. By solving the time-dependent Bogoliubov-deGennes equations for the Nambu-Gorkov Keldysh Green's function we are able to calculate the current and the charge density when the system is perturbed by bias voltages. For scattering of electrons across a normal-superconducting surface we provide a time-dependent picture of the Andreev reflections. When the nanoscale system is contacted to two DC biased superconducting leads the amplitude of the current oscillations at even multiple of the bias can be extracted by Fourier transforming the time-dependent results. In the transient regime the dwelling time is inversely proportional to the bias in agreement with the occurrence of multiple Andreev reflections.

Physical Review B, 2007

Motivated by recent findings of unconventional superconductors exhibiting multiple broken symmetries, we consider a general Hamiltonian describing coexistence of itinerant ferromagnetism, spin-orbit coupling and mixed spin-singlet/triplet superconducting pairing in the context of mean-field theory. The Hamiltonian is diagonalized and exact eigenvalues are obtained, thus allowing us to write down the coupled gap equations for the different order parameters. Our results may then be applied to any model describing coexistence of any combination of these three phenomena. As a specific application of our results, we consider tunneling between a normal metal and a noncentrosymmetric superconductor with mixed singlet and triplet gaps. The conductance spectrum reveals information about these gaps in addition to how the influence of spin-orbit coupling is manifested. Explicitly, we find well-pronounced peaks and bumps in the spectrum at voltages corresponding to the sum and the difference of the magnitude of the singlet and triplet components. Our results may thus be helpful in determining the relative sizes of the singlet and triplet gaps in noncentrosymmetric superconductors. We also consider the coexistence of itinerant ferromagnetism and triplet superconductivity as a model for recently discovered ferromagnetic superconductors. The coupled gap equations are solved self-consistently, and we study the conditions necessary to obtain the coexistent regime of ferromagnetism and superconductivity. Analytical expressions are presented for the order parameters, and we provide an analysis of the free energy to identify the preferred system state. It is found that the uniform coexistence of ferromagnetism and superconductivity is energetically favored compared to both the purely ferromagnetic state and the unitary superconducting state with zero magnetization. Moreover, we make specific predictions concerning the heat capacity for a ferromagnetic superconductor. In particular, we report a nonuniversal relative jump in the specific heat, depending on the magnetization of the system, at the uppermost superconducting phase transition. We propose that this may be exploited to obtain information about both the superconducting pairing symmetry realized in ferromagnetic superconductors in addition to the magnitude of the exchange splitting between majority and minority spin bands.

Physical Review B, 2008

We investigate transport properties of a superconducting junction of many ($N \ge 2$) one-dimensional quantum wires. We include the effectofelectron-electron interaction within the one-dimensional quantum wire using a weak interaction renormalization group procedure. Due to the proximity effect, transport across the junction occurs via direct tunneling as well as via the crossed Andreev channel. We find that the fixed point structure of this system is far more rich than the fixed point structure of a normal metal$-$superconductor junction ($N = 1$), where we only have two fixed points - the fully insulating fixed point or the Andreev fixed point. Even a two wire (N=2)system with a superconducting junction i.e. a normalmetal$-$superconductor$-$normal metal structure, has non-trivialfixed points with intermediate transmissions and reflections. We also include electron-electron interaction induced back-scattering in the quantum wires in our study and hence obtain non-Luttinger liquid behaviour. It is interesting to note that {\textsl{(a)}} effects due to inclusion of electron-electron interaction induced back-scattering in the wire, and {\textsl{(b)}} competition between the charge transport via the electron and hole channels across the junction, give rise to a non-monotonic behavior of conductance as a functionof temperature. We also find that transport across the junction depends on two independent interaction parameters. The first one is due to the usual correlations coming from Friedel oscillations for spin-full electrons giving rise to the well-known interaction parameter (${{\alpha = (g_2-2g_1)/2 \pi \hbar v_F}}$). The second one arises due to the scattering induced by the proximity of the superconductor and is given by(${{\alpha^\prime = (g_2 + g_1)/2 \pi \hbar v_F}}$).

New Journal of Physics, 2021

One-dimensional nanowires with strong spin-orbit coupling and proximity-induced superconductivity are predicted to exhibit topological superconductivity with condensed-matter analogues to Majorana fermions. Here, the nonequilibrium Green's function approach with the generalized Kadanoff-Baym ansatz is employed to study the electron-correlation effects and their role in the topological superconducting phase in and out of equilibrium. Electron-correlation effects are found to affect the transient signatures regarding the zero-energy Majorana states, when the superconducting nanowire is subjected to external perturbations such as magnetic-field quenching, laser-pulse excitation, and coupling to biased normal-metal leads.

We discuss an extension of our earlier work on the time-dependent Landauer– Büttiker formalism for noninteracting electronic transport. The formalism can without complication be extended to superconducting central regions since the Green's functions in the Nambu representation satisfy the same equations of motion which, in turn, leads to the same closed expression for the equal-time lesser Green's function, i.e., for the time-dependent reduced one-particle density matrix. We further write the finite-temperature frequency integrals in terms of known special functions thereby considerably speeding up the computation. Simulations in simple normal metal – superconductor – normal metal junctions are also presented.

Physical Review B

We present a theoretical study of the interplay between topological p-wave superconductivity, orbital magnetic fields and quantum Hall phases in coupled wire systems. First, we calculate the phase diagram and physical observables of a fermionic ladder made of two coupled Kitaev chains, and discuss the presence of two and four Majorana zero modes. Second, we analyze hybrid systems consisting of a Kitaev chain coupled to a Luttinger liquid. By tuning the magnetic field and the carrier density, we identify quantum Hall and charge density wave phases, as well as regimes in which superconductivity is induced in the second chain by proximity effect. Finally, we consider two-dimensional systems made of weakly coupled ladders. There, we engineer a p+ip superconductor and describe a generalization of the ν = 1/2 fractional quantum Hall phase. These phases might be realized in solid-state or cold-atom nanowires.

Physical Review B, 2021

We present exact analytical results for the differential conductance of a finite Kitaev chain in an N-S-N configuration, where the topological superconductor is contacted on both sides with normal leads. Our results are obtained with the Keldysh non-equilibrium Green's functions technique, using the full spectrum of the Kitaev chain without resorting to minimal models. A closed formula for the linear conductance is given, and the analytical procedure to obtain the differential conductance for the transport mediated by higher excitations is described. The linear conductance attains the maximum value of e 2 /h only for the exact zero energy states. Also the differential conductance exhibits a complex pattern created by numerous crossings and anticrossings in the excitation spectrum. We reveal the crossings to be protected by the inversion symmetry, while the anticrossings result from a pairing-induced hybridization of particle-like and hole-like solutions with the same inversion character. Our comprehensive treatment of the Kitaev chain allows us also to identify the contributions of both local and non-local transmission processes to transport at arbitrary bias voltage. Local Andreev reflection processes dominate the transport within the bulk gap and diminish for higher excited states, but reemerge when the bias voltage probes the avoided crossings. The non-local direct transmission is enhanced above the bulk gap, but contributes also to the transport mediated by the topological states.

Theoretical and Mathematical Physics, 1991

In a model with intra-atomic interaction of electrons and interatomic correlated hopping of the electrons (model of Hubbard-Hirsch type), Bose condensation is obtained, and the temperature T c of the superconducting transition is calculated. Investigations are made of the limiting cases of the superconducting transition for noninteracting electrons with 4-fermion tunneling for different values of the hopping integrals and for the case of correlated electrons. It is shown that the general expression for the coupling constants obtained on the basis of the kinematic mechanism of high-temperature superconductivity is identical in the considered special cases to the expressions found earlier for the superconducting transition in the Hubbard and Hirsch models.

physica status solidi (c), 2008

Physical Review Letters, 2011

We study the nonlinear cotunneling current through a spinful quantum dot contacted by two superconducting leads. Applying a general nonequilibrium Green function formalism to an effective Kondo model, we study the rich variation in the IV-characteristics with varying asymmetry in the tunnel coupling to source and drain electrodes. The current is found to be carried respectively by multiple Andreev reflections in the symmetric limit, and by spin-induced Yu-Shiba-Russinov bound states in the strongly asymmetric limit. The interplay between these two mechanisms leads to qualitatively different IV-characteristics in the cross-over regime of intermediate symmetry, consistent with recent experimental observations of negative differential conductance and re-positioned conductance peaks in sub-gap cotunneling spectroscopy.

Physical review, 2023

We study two-terminal configurations in junctions between a topological superconducting wire with spinorbit coupling and magnetic field, and an ordinary conductor with an embedded quantum dot. One of the signatures of the Majorana zero modes in the topological phase is a quantization of the zero-bias conductance at G(V = 0) = 2e 2 /h. However, the finite size of the wires and the presence of the quantum dot in the junction generate more complicated features which lead to deviations from this simple picture. Here, we analyze the behavior of the conductance at zero and finite bias, G(V), as a function of a gate voltage applied at the quantum dot in the case of a finite-length wire. We analyze the effect of the angle between the magnetic field and the orientation associated to the spin-orbit coupling. We provide a detailed description of the spectral features of the quantum wire weakly and also strongly coupled to the quantum dot and describe the conditions to have zero-energy states in these two regimes for both the topological and non-topological phases. We also analyze the concomitant behavior of the noise. We identify qualitative features that are useful to distinguish between the topological and non-topological phases. We show that in a strongly coupled quantum dot the simultaneous hybridization with the topological modes and the supragap states of the wire mask the signatures of the Majorana bound states in both the conductance and the Fano factor.

Japanese Journal of Applied Physics, 2008

We derive the nonequilibrium transport property formulas for a three-site quantum wire model using Keldysh formalism. Some rigorous formulas in the case of noninteraction are provided for direct calculations. On the basis of the numerical calculations, we investigate the differential and total conductances, transport current, and on-site electronic charges of a wire in some special cases. For a uniform-ingredient wire, if the temperature T ¼ 0 K, it shows that, when site-site couplings in the wire are stronger than wire-electrode couplings, resonant tunneling transport takes place and the phenomenon of conductance quantization can be easily observed. In the opposite case, these quantum effects on transport disappear gradually with the increase in the strength of wire-electrode couplings. We also discuss the charge distributions in the three sites of the wire and the characteristics of the charge barrier (Schottky barrier) regardless of Coulomb interaction. If T > 0 K, all the line shapes of the transport properties become smoother than those at T ¼ 0 K owing to thermal fluctuations. For a wire containing impurities, the line shapes of the transport properties change because of the change of system electronic states.

Physical Review B

Recent findings of superconductors that simultaneously exhibit multiple spontaneously broken symmetries, such as ferromagnetic order or lack of an inversion center and even combinations of such broken symmetries, have led to much theoretical and experimental research. We consider quantum transport in a junction consisting of a ferromagnetic metal and a non-unitary ferromagnetic superconductor. It is shown that the conductance spectra provides detailed information about the superconducting gaps, and is thus helpful in determining the pairing symmetry of the Cooper pairs in ferromagnetic superconductor.

Eprint Arxiv Cond Mat 9810023, 1998

We investigate the electronic transport coefficients in unconventional superconductors at low temperatures, where charge and heat transport are dominated by electron scattering from random lattice defects. We discuss the features of the pairing symmetry, Fermi surface, and excitation spectrum which are reflected in the low temperature heat transport. For temperatures $k_B T \la \gamma \ll \Delta_0$, where $\gamma$ is the bandwidth of impurity induced Andreev states, certain eigenvalues become {\it universal}, i.e., independent of the impurity concentration and phase shift. Deep in the superconducting phase ($k_B T \la \gamma$) the Wiedemann-Franz law, with Sommerfeld's value of the Lorenz number, is recovered. We compare our results for theoretical models of unconventional superconductivity in high-T$_c$ and heavy fermion superconductors with experiment. Our findings show that impurities are a sensitive probe of the low-energy excitation spectrum, and that the zero-temperature limit of the transport coefficients provides an important test of the order parameter symmetry.

Physical Review B, 2013

We study transport across a line junction lying between two orthogonal topological insulator surfaces and a superconductor which can have either s-wave (spin-singlet) or p-wave (spin-triplet) pairing symmetry. We present a formalism for studying the effect of a general time-reversal invariant barrier at the junction and show that such a barrier can be completely described by three arbitrary parameters. We compute the charge and the spin conductance across such a junction and study their behaviors as a function of the bias voltage applied across the junction and the three parameters used to characterize the barrier. We find that the presence of topological insulators and a superconductor leads to both Dirac and Schrödinger-like features in charge and spin conductances. We discuss the effect of bound states on the superconducting side of the barrier on the conductance; in particular, we show that for triplet p-wave superconductors such a junction may be used to determine the spin state of its Cooper pairs. Our study reveals that there is a non-zero spin conductance for some particular spin states of the triplet Cooper pairs; this is an effect of the topological insulators which break the spin rotation symmetry. Finally, we find an unusual satellite peak (in addition to the usual zero bias peak) in the spin conductance for p-wave symmetry of the superconductor order parameter.