We combine scanning-tunneling-spectroscopy experiments probing magnetic impurities on a superconducting surface with a theoretical analysis of the tunneling processes between (superconducting) tip and substrate. We show that the current is carried by single-electron tunneling at large tip-substrate distances and Andreev reflections at smaller distances. The single-electron current requires relaxation processes between the impurity-induced Shiba bound state and the quasiparticle continuum, allowing us to extract information on such relaxation processes from our analysis.
We present a microscopic theory of transport through quantum dot set-ups coupled to superconducting leads. We derive a master equation for the reduced density matrix to lowest order in the tunneling Hamiltonian and focus on quasiparticle tunneling. For high enough temperatures transport occurs in the subgap region due to thermally excited quasiparticles, which can be used to observe excited states of the system for low bias voltages. On the example of a double quantum dot we show how subgap transport spectroscopy can be done. Moreover, we use the single level quantum dot coupled to a normal an…
Photon-assisted tunneling frequently provides detailed information on the underlying charge-transfer process. In particular, the Tien-Gordon approach and its extensions predict that the sideband spacing in bias voltage is a direct fingerprint of the number of electrons transferred in a single tunneling event. Here, we analyze photon-assisted tunneling into subgap states in superconductors in the limit of small temperatures and bias voltages where tunneling is dominated by resonant Andreev processes and does not conform to the predictions of simple Tien-Gordon theory. Our analysis is based on a…
We study influence of the phonon modes on a subgap spectrum and Andreev conductance for the double quantum dot vertically coupled between a metallic and superconducting lead. For the monochromatic phonon reservoir we obtain replicas of the interferometric Fano-type structures appearing simultaneously in the particle and hole channels. We furthermore confront the induced on-dot pairing with the electron correlations and investigate how the phonon modes affect the zero-bias signature of the Kondo effect in Andreev conductance.
We report thermally activated transport resonances for biases below the superconducting energy gap in a carbon nanotube (CNT) quantum dot (QD) device with a superconducting Pb and a normal metal contact. These resonances are due to the superconductor's finite quasi-particle population at elevated temperatures and can only be observed when the QD life-time broadening is considerably smaller than the gap. This condition is fulfilled in our QD devices with optimized Pd/Pb/In multi-layer contacts, which result in reproducibly large and "clean" superconducting transport gaps with a strong conductan…
A recent experiment [Nadj-Perge et al., Science 346, 602 (2014)] provides evidence for Majorana zero modes in iron (Fe) chains on the superconducting Pb(110) surface. Here, we study this system by scanning tunneling microscopy using superconducting tips. This high-resolution technique resolves a rich subgap structure, including zero-energy excitations in some chains. We compare the symmetry properties of the data under voltage reversal against theoretical expectations and provide evidence that the putative Majorana signature overlaps with a previously unresolved low-energy resonance. Interpret…
There is strong support in favor of an unusual $s_{\pm}$ superconducting state in the new iron-based superconductors, in which the gap parameter has opposite signs in different bands. In this case scattering between different bands by impurities has a pair-breaking effect and introduces states inside the gap. We studied the statistics of disorder-induced subgap states in $s_{\pm}$ superconductors due to collective effects of impurities. Numerically solving the two-band Bogolyubov equations, we explored the behavior of the density of states and localization length. We located the mobility edge …
One-dimensional p-wave superconductors are known to harbor Majorana bound states at their ends. Superconducting wires with a finite width W may have fermionic subgap states in addition to possible Majorana end states. While they do not necessarily inhibit the use of Majorana end states for topological computation, these subgap states can obscure the identification of a topological phase through a density-of-states measurement. We present two simple models to describe low-energy fermionic subgap states. If the wire's width W is much smaller than the superconductor coherence length ξ, the releva…
In s-wave systems, it has been theoretically shown that a ferromagnetic film hosting a skyrmion can induce a bound state embedded in the opposite-spin continuum. In this work, we consider a case of skyrmion-induced state in a p-wave superconductor. We find that the skyrmion induces a bound state that generally resides \emph{within} the spectral gap and is isolated from all other states, in contrast to the case of conventional superconductors. To this end, we derive an approximate expression for the $T$-matrix, through which we calculate the spin-polarized local density of states which is obser…
We investigate the subgap transport properties of a S-F-Ne structure. Here S (Ne) is a superconducting (normal) electrode, and F is either a ferromagnet or a normal wire in the presence of an exchange or a spin- splitting Zeeman field respectively. By solving the quasiclassical equations we first analyze the behavior of the subgap current, known as the Andreev current, as a function of the field strength for different values of the voltage, temperature and length of the junction. We show that there is a critical value of the bias voltage V * above which the Andreev current is enhanced by the s…
We have investigated the intrinsic Josephson properties in slightly underdoped (Hg,Re)Ba2Ca2Cu3Oy [Hg(Re)1223] intrinsic Josephson junctions (IJJs) with a dimension of 1.0x1.5x0.11 um^3. The current-voltage characteristics of the IJJs exhibit clear multiple branches with subgap structures similar to those of other cuprate superconductors. The switching current distributions P(I) from the zero-voltage to the nonzero-voltage state in the current-biased IJJs agree well with the theoretical curves of the thermally assisted escape model at temperatures above ~5 K. The plasma frequency fp of the IJJ…
We report direct detection of charge-tunneling between a quantum dot and a superconducting island through radio-frequency gate sensing. We are able to resolve spin-dependent quasiparticle tunneling as well as two-particle tunneling involving Cooper pairs. The quantum dot can act as an RF-only sensor to characterize the superconductor addition spectrum, enabling us to access subgap states without transport. Our results provide guidance for future dispersive parity measurements of Majorana modes, which can be realized by detecting the parity-dependent tunneling between dots and islands.
Motivated by recent scanning tunneling microscopy experiments on single magnetic impurities on superconducting surfaces, we present here a comprehensive theoretical study of the interplay between Yu-Shiba-Rusinov bound states and (multiple) Andreev reflections. Our theory is based on a combination of an Anderson model with broken spin degeneracy and nonequilibrium Green's function techniques that allows us to describe the electronic transport through a magnetic impurity coupled to superconducting leads for arbitrary junction transparency. Using this combination we are able to elucidate the dif…
We develop a quasiclassical theory of Andreev interferometers with three superconducting electrodes. Provided tunneling interface resistance between one superconducting electrode and the normal metal strongly exceeds two others, significant current sensitivity to the external magnetic flux is observed only at subgap voltages. If all barrier conductances are comparable, multiple Andreev reflection comes into play and substantial current modulation can be achieved in both subgap and overgap voltage regimes. Our analysis reveals a large variety of interesting features which can be used for perfor…
We study a Cooper-pair transistor realized by two Josephson weak links that enclose a superconducting island in an InSb-Al hybrid nanowire. When the nanowire is subject to a magnetic field, isolated subgap levels arise in the superconducting island and, due to the Coulomb blockade,mediate a supercurrent by coherent co-tunneling of Cooper pairs. We show that the supercurrent resulting from such co-tunneling events exhibits, for low to moderate magnetic fields, a phase offset that discriminates even and odd charge ground states on the superconducting island. Notably,this phase offset persists wh…
We present an extensive experimental and theoretical study of the proximity effect in InAs nanowires connected to superconducting electrodes. We fabricate and investigate devices with suspended gate-controlled nanowires and nonsuspended nanowires, with a broad range of lengths and normal-state resistances. We analyze the main features of the current-voltage characteristics: the Josephson current, excess current, and subgap current as functions of length, temperature, magnetic field, and gate voltage, and compare them with theory. The Josephson critical current for a short-length device, L = 30…
We discuss the nonlinear Andreev current of an interacting quantum dot coupled to spin-polarized and superconducting reservoirs when voltage and temperature biases are applied across the nanostructure. Due to the particle-hole symmetry introduced by the superconducting (S) lead, the subgap spin current vanishes identically. Nevertheless, the Andreev charge current depends on the degree of polarization in the ferromagnetic (F) contact since the shift of electrostatic internal potential of the conductor depends on spin orientation of the charge carrier. This spin-dependent potential shift charac…
The tunneling conductance in the half-metal/conical magnet/superconductor (HM/CM/SC) is investigated by the use of the combined Blonder-Tinkham-Klapwijk (BTK) formalism and the Bogoliubov-de Gennes (BdG) equations. We show that the conductance calculated self-consistently differs significantly from the one calculated in the non-self-consistent framework. The use of the self-consistent procedure ensures that the charge conservation is satisfied. Due to the spin band separation in the HM, the conductance in the subgap region is mainly determined by the anomalous Andreev reflection the probabilit…
We consider a voltage-biased Normal metal-Insulator-Superconductor (NIS) tunnel junction, connected to a high-temperature external electromagnetic environment. This model system features the commonly observed subgap leakage current in NIS junctions through photon-assisted tunneling which is detrimental for applications. We first consider a NIS junction directly coupled to the environment and analyze the subgap leakage current both analytically and numerically; we discuss the link with the phenomenological Dynes parameter. Then we focus on a circuit where a low-temperature lossy transmission li…
We study the low energy spectrum of a correlated quantum dot embedded between the normal conducting and superconducting reservoirs and hybridized with the topological superconducting nanowire, hosting the Majorana end-modes. We investigate the leaking Majorana quasiparticle and inspect its interplay with the proximity induced on-dot pairing and correlations. In particular, we focus on the subgap Kondo effect near the quantum phase transition/crossover from the spinfull (doublet) to the spinless (BCS-type singlet) configurations. Treating the correlations perturbatively and within the NRG appro…
Magnetic molecules adsorbed on a superconductor give rise to a local competition of Cooper pair and Kondo singlet formation inducing subgap bound states. For Manganese-phthalocyanine molecules on a Pb(111) substrate, scanning tunneling spectroscopy resolves pairs of subgap bound states and two Kondo screening channels. We show in a combined approach of scaling and numerical renormalization group calculations that the intriguing relation between Kondo screening and superconducting pairing is solely determined by the hybridization strength with the substrate. We demonstrate that an effective one…
A graphene superlattice is formed by a one-dimensional periodic potential and is characterized by the emergence of new Dirac points in the electronic structure. The group velocity of graphene's massless Dirac fermions at the new points is drastically reduced, resulting in a measurable effect in the conductance spectroscopy. We show here that tunnel spectroscopy using a superconducting hybrid junction is more sensitive to the formation of Dirac points in the spectrum of graphene superlattices due to the additional contribution of Andreev processes. We examine the transport properties of a graph…
We develop a theory for the proximity effect in superconductor-semiconductor-normal metal tunneling structures, which have recently been extensively studied experimentally, leading to the observation of transport signatures consistent with the predicted zero-energy Majorana bound states. We show that our model for the semiconductor nanowire having multiple occupied subbands with different transmission probabilities through the barrier reproduces the observed "soft-gap" behavior associated with substantial subgap tunneling conductance. We study the manifestations of the soft gap phenomenon both…
Multimode spinless p-wave superconducting wires with a width W much smaller than the superconducting coherence length ξare known to have multiple low-energy subgap states localized near the wire's ends. Here we compare the typical energies of such endstates for various terminations of the wire: A superconducting wire coupled to a normal-metal stub, a weakly disordered superconductor wire and a wire with smooth confinement. Depending on the termination, we find that the energies of the subgap states can be higher or lower than for the case of a rectangular wire with hard-wall boundaries.
We study the electronic transport in a graphene-based superconductor-normal(graphene)-superconductor (SNS) junction by use of the Dirac-Bogoliubov-de Gennes equation. We consider the properties of tunneling conductance through an undoped strip of graphene with heavily doped superconducting electrodes in the dirty limit. We find that spectrum of Andreev bound states are modified in the presence of single localized defect in the bulk. The minimum tunneling conductance remains the same and this result doesn't depend on the actual location of the imperfection.
We present a method capable of calculating elastic scanning tunneling microscopy (STM) currents from localized atomic orbital density functional theory (DFT). To overcome the poor accuracy of the localized orbital description of the wave functions far away from the atoms, we propagate the wave functions, using the total DFT potential. From the propagated wave functions, the Bardeen's perturbative approach provides the tunneling current. To illustrate the method we investigate carbon monoxide adsorbed on a Cu(111) surface and recover the depression/protrusion observed experimentally with normal…
A single static magnetic impurity in a fully-gapped superconductor leads to formation of an intragap quasiparticle bound state. At temperatures much below the superconducting transition, the energy relaxation and spin dephasing of the state are expected to be exponentially suppressed. The presence of such a state can be detected in electron tunneling experiments as a pair of conductance peaks at positive and negative biases. Here we show, that for an arbitrarily weak tunneling strength, the peaks have to be symmetric with respect to the applied bias. This is in contrast to the standard result …
Local electronic structures of nanometer-sized patches of epitaxial graphene and its interface layer with SiC(0001) have been studied by atomically resolved scanning tunneling microscopy and spectroscopy. Localized states belonging to the interface layer of a graphene/SiC system show to have an essential influence on the electronic structure of graphene. Giant enhancement of inelastic tunneling, reaching 50% of the total tunneling current, has been observed at the localized states on a nanometer-sized graphene monolayer surrounded by defects.
We discuss the nonlinear current of an interacting quantum dot coupled to normal and superconducting reservoirs with applied voltage and temperature differences. Due to the particle-hole symmetry introduced by the superconducting lead, the pure (subgap) thermoelectric response vanishes. However, we show that the Andreev bound states shift as the thermal gradient increases. As a consequence, the $I$--$V$ characteristic can be tuned with a temperature bias if the system is simultaneously voltage biased. This is a cross effect that occurs beyond linear response only. Furthermore, we emphasize the…
We study resonant tunneling through a superconducting double barrier structure in graphene as a function of the system parameters. At each barrier, due to the proximity effect, an incident electron can either reflect as an electron or a hole (specular as well as retro Andreev reflection in graphene). Similarly, transport across the barriers can occur via electrons as well as via the crossed (specular and/or retro) Andreev channel, where a hole is transmitted nonlocally to the other lead. In this geometry, in the subgap regime, we find resonant suppression of Andreev reflection at certain energ…
We present a theoretical investigation for the full counting statistics of the Andreev tunneling through a quantum dot (QD) embedded between superconducting (SC) and normal leads in the presence of a strong on-site electron-phonon interaction using nonequilibrium Green function method. For this purpose, we generalize the dressed tunneling approximation (DTA) recently developed in dealing with inelastic tunneling in a normal QD system to the Andreev transport issue, which takes account of vibrational effect in evaluation of electronic tunneling self energy in comparison with other simple approa…
In transition metal dichalcogenides, defects have been found to play an important role, affecting doping, spin-valley relaxation dynamics, and assisting in proximity effects of spin-orbit coupling. Here, we study localized states in $\mathrm{WS}_2$ and how they affect tunneling through van der Waals heterostructures of h-BN/graphene/$\mathrm{WS}_2$/metal. The obtained conductance maps as a function of bias and gate voltage reveal single-electron transistor behavior (Coulomb blockade) with a rich set of transport features including excited states and negative differential resistance regimes. Ap…
The Floquet topological superconducting state is a nonequilibrium time-periodic state hosting Majorana fermions. We study its transport properties by using the Kitaev model with time-periodic incommensurate potentials, which experiences phase transition from the Floquet topological superconducting phase to the Anderson localized phase with increasing driving strength. We study both the real time dynamics of the current and the non-analytic behavior of the tunneling conductance at the transition. Especially, we find that the tunneling conductance changes continuously at the transition, being a …
Injection and detection of spin accumulation in a semiconductor having localized states at the interface is evaluated. Spin transport from a ferromagnetic contact by sequential, two-step tunneling via interface states is treated not in itself, but in parallel with direct tunneling. The spin accumulation induced in the semiconductor channel is not suppressed, as previously argued, but genuinely enhanced by the additional spin current via interface states. Spin detection with a ferromagnetic contact yields a weighted average of the spin accumulation in the channel and in the localized states. In…
Interplay between changes of energy levels and tunneling amplitudes caused by localized electrons on-site Coulomb interaction depending on non-equilibrium electron filling numbers is analyzed. Specific features of local tunneling conductivity spectra for different positions of localized states energy relative to the Fermi level have been investigated by means of self-consistent mean field approximation in the presence of non-equilibrium effects. The conditions when modifications of tunneling transfer amplitude due to changes of electron filling numbers in the presence of on-site Coulomb intera…
Many present and future applications of superconductivity would benefit from electrostatic control of carrier density and tunneling rates, the hallmark of semiconductor devices. One particularly exciting application is the realization of topological superconductivity as a basis for quantum information processing. Proposals in this direction based on proximity effect in semiconductor nanowires are appealing because the key ingredients are currently in hand. However, previous instances of proximitized semiconductors show significant tunneling conductance below the superconducting gap, suggesting…
Majorana zero modes can appear at the wire ends of a 1D topological superconductor and manifest themselves as a quantized zero-bias conductance peak in the tunneling spectroscopy of normal-superconductor junctions. However, in superconductor-semiconductor hybrid nanowires, zero-bias conductance peaks may arise owing to topologically trivial mechanisms as well, mimicking the Majorana-induced topological peak in many aspects. In this work, we systematically investigate the characteristics of zero-bias conductance peaks for topological Majorana bound states, trivial quasi-Majorana bound states an…
Quantum system abruptly driven from its stationary phase can reveal nontrivial dynamics upon approaching a new final state. We investigate here such dynamics for a correlated quantum dot sandwiched between the metallic and superconducting leads, considering two types of quenches feasible experimentally. In particular, we examine an interplay between the proximity induced electron pairing with correlations caused by the on-dot Coulomb repulsion. We discuss the time-dependent charge occupancy, complex order parameter, transient currents, and analyze evolution of the subgap quasiparticles which c…
We study the tunneling density of states (TDOS) of a disordered electronic system with Coulomb interaction on the insulating side of the Anderson localization transition. The average TDOS shows a critical behavior at high energies, with a crossover to a soft Coulomb gap $Δ$ at low energies. We demonstrate that the single-particle excitations experience a localization transition (which belongs to the noninteracting universality class) at an energy $E=\pm E_c$. The mobility edge $E_c$ scales with the distance $μ_c-μ$ from the interacting critical point according to $E_c\propto (μ_c-μ)^{νz}$, whe…
Imperfections change essentially the electronic transport properties of graphene. Motivated by a recent experiment reporting on the possible application of graphene as junctions, we study transport properties in graphene-based junctions with single localized defect. We solve the Dirac-Bogoliubov-de-Gennes equation with a single localized defect superconductor-normal(graphene)-superconductor (SNS) junction. We consider the properties of tunneling conductance and Josephson current through an undoped strip of graphene with heavily doped s-wave superconducting electrodes in the dirty limit. We fin…
