We investigate the conductance statistics of a quantum-chaotic dot--a normal-metal grain--with a superconducting lead attached to it. The cases of one and two normal leads additionally attached to the dot are studied. For these two configurations the complete distribution of the conductance is calculated, within the framework of random matrix theory, as a function of the transparency parameter of the Schottky barrier formed at the interface of the normal-metal and superconducting regions. Our predictions are verified by numerical simulations.
Nonlocal currents, in devices where two normal metal terminals are contacted to a superconductor, are determined using the circuit theory of mesoscopic superconductivity. We calculate the conductance associated with crossed Andreev reflection and electron transfer between the two normal metal terminals, in addition to the conductance from direct Andreev reflection and quasiparticle tunneling. Dephasing and proximity effect are taken into account.
We study the conductance of normal-superconducting quantum dots with strong spin-orbit scattering, coupled to a source reservoir using a single-mode spin-filtering quantum point contact. The choice of the system is guided by the aim to study triplet Andreev reflection without relying on half metallic materials with specific interface properties. Focusing on the zero temperature, zero-bias regime, we show how dephasing due to the presence of a voltage probe enables the conductance, which vanishes in the quantum limit, to take nonzero values. Concentrating on chaotic quantum dots, we obtain the …
We study the excess conductance due to the superconducting proximity effect in a ballistic two-dimensional electron system subject to an in-plane magnetic field. We show that under certain conditions the interplay of the Zeeman spin splitting and the effect of a screening supercurrent gives rise to a spin-selective Andreev enhancement of the conductance and anomalies in its voltage, temperature and magnetic field characteristics. The magnetic-field influence on Andreev reflection is discussed in the context of using superconducting hybrid junctions for spin detection.
We construct a theory of coherent transport through a ballistic quantum dot coupled to a superconductor. We show that the leading-order quantum correction to the two-terminal conductance of these Andreev quantum dots may change sign depending on (i) the number of channels carried by the normal leads or (ii) the magnetic flux threading the dot. In contrast, spin-orbit interaction may affect the magnitude of the correction, but not always its sign. Experimental signatures of the effect include a non-monotonic magnetoconductance curve and a transition from an insulator-like to a metal-like temper…
At low temperatures, the transport through a superconductor-ferromagnet tunnel interface is due to tunneling of electrons in pairs. Exchange field of a monodomain ferromagnet aligns electron spins and suppresses the two electron tunneling. The presence of the domain walls at the SF interface strongly enhances the subgap current. The Andreev conductance is proven to be proportional to the total length of domain walls at the SF interface.
We investigate the transport properties through a finite dimer chain connected to two normal leads or one normal and one superconductor (SC) leads. The dimer chain is described by the Su-Schrieffer-Hegger model and can be tuned into a topologically nontrivial phase with a pair of zero-energy edge states (ZEESs). We find that if the dimer chain is of nontrivial topology, (1) it will show apparent but opposite odd-even parity of the number of sites, in comparison with the topologically trivial and plain chains, in the (Andreev) transmission probability at the Fermi energy (i.e. the conductance a…
We introduce quantum maps with particle-hole conversion (Andreev reflection) and particle-hole symmetry, which exhibit the same excitation gap as quantum dots in the proximity to a superconductor. Computationally, the Andreev maps are much more efficient than billiard models of quantum dots. This makes it possible to test analytical predictions of random-matrix theory and semiclassical chaos that were previously out of reach of computer simulations. We have observed the universal distribution of the excitation gap for large Lyapunov exponent and the logarithmic reduction of the gap when the Eh…
We report our investigation of the sample to sample fluctuation in transport properties of phase coherent normal metal-superconductor hybrid systems. Extensive numerical simulations were carried out for quasi-one dimensional and two dimensional systems in both square lattice (Fermi electron) as well as honeycomb lattice (Dirac electron). Our results show that when the Fermi energy is within the superconducting energy gap $Δ$, the Andreev conductance fluctuation exhibits a universal value (UCF) which is approximately two times larger than that in the normal systems. According to the random matr…
We examine the voltage V and magnetic field B dependent Andreev conductance of a chaotic quantum dot coupled via point contacts to a normal metal and a superconductor. In the case where the contact to the superconductor dominates, we find that the conductance is consistent with the dot itself behaving as a superconductor-- it appears as though Andreev reflections are occurring locally at the interface between the normal lead and the dot. This is contrasted against the behaviour of an integrable dot, where for a similar strong coupling to the superconductor, no such effect is seen. The voltage …
We analyze the subgap spectrum and transport properties of the quantum dot embedded between one superconducting and another metallic reservoirs and additionally coupled to an external boson mode. Emission/absorption of the bosonic quanta induces a series of the subgap Andreev states, that eventually interfere with each other. We discuss their signatures in the differential conductance both, for the linear and nonlinear regimes.
We study a strongly interacting quantum dot connected to a normal and to a superconducting lead. By means of the slave-boson technique we investigate the low temperature regime and discuss electrical transport through the dot. We find that the zero bias anomaly in the current-voltage characteristics which is associated to the occurance of the Kondo resonance in the quantum dot, is enhanced in the presence of superconductivity, due to resonant Andreev scattering.
We report measurements of the nonlinear conductance of InAs nanowire quantum dots coupled to superconducting leads. We observe a clear alternation between odd and even occupation of the dot, with sub-gap-peaks at $|V_{sd}|=Δ/e$ markedly stronger(weaker) than the quasiparticle tunneling peaks at $|V_{sd}|=2Δ/e$ for odd(even) occupation. We attribute the enhanced $Δ$-peak to an interplay between Kondo-correlations and Andreev tunneling in dots with an odd number of spins, and substantiate this interpretation by a poor man's scaling analysis.
The accurate and proper form of electron-hole excitations and corresponding Dirac-like spinors of monolayer molybdenum disulfide superconductor are exactly obtained. Andreev reflection and resulting subgap conductance in a $MoS_2$-based ferromagnetic superconducting (F/S) junction is accurately investigated in terms of dynamical characteristics of system. Due to spin-splitting energy gap in the valence band and nondegenerate $K$ and $K'$ valleys, the ferromagnetic exchange energy $σh$ can cause a distinct behavior of Andreev process between spin-up and spin-down charge carriers belonging to di…
We calculate the thermal conductance $G^T$ of diffusive Andreev interferometers, which are hybrid loops with one superconducting arm and one normal-metal arm. The presence of the superconductor suppresses $G^T$; however, unlike a conventional superconductor, $G^T/G^T_N$ does not vanish as the temperature $T\to0$, but saturates at a finite value that depends on the resistance of the normal-superconducting interfaces, and their distance from the path of the temperature gradient. The reduction of $G^T$ is determined primarily by the suppression of the density of states in the proximity-coupled no…
Andreev quantum dot (AQD) is a superconducting junction where Bogolyubov quasiparticles can be trapped in discrete Andreev levels. We investigate the feasibility of manipulating individual spin in an AQD. We show that AQD can be brought into spin-1/2 state. The coupling between spin and superconducting current facilitate manipulation and measurement of this state in comparison with common semiconductor quantum dots. We demonstrate that AQD's coupled inductively can serve as a solid-state base for universal quantum computing.
We have studied the Kondo quantum dot coupled to two superconducting leads and investigated the subgap Andreev states using the NRG method. Contrary to the recent NCA results [Clerk and Ambegaokar, Phys. Rev. B 61, 9109 (2000); Sellier et al., Phys. Rev. B 72, 174502 (2005)], we observe Andreev states both below and above the Fermi level.
We study resonant tunneling through an interacting quantum dot coupled to normal metallic and superconducting leads. We show that large Coulomb interaction gives rise to novel effects in Andreev transport. Adopting an exact relation for the Green's function, we find that at zero temperature, the linear response conductance is enhanced due to Kondo-Andreev resonance in the Kondo limit, while it is suppressed in the empty site limit. In the Coulomb blockaded region, on the other hand, the conductance is reduced more than the corresponding conductance with normal leads because large charging ener…
When coupling a superconductor to a normal conducting region the physical properties of the system are highly affected by the superconductor. We will investigate the effect of one or two superconductors on the conductance of a ballistic chaotic quantum dot to leading order in the total channel number using trajectory based semiclassics. The results show that the effect of one superconductor on the conductance is of the order of the number of channels and that the sign of the correction from the Drude conductance depends on the particular ratios of the numbers of channels of the superconducting…
The proximity effect in hybrid superconductor-semiconductor structures, crucial for realizing Majorana edge modes, is complicated to control due to its dependence on many unknown microscopic parameters. In addition, defects can spoil the induced superconductivity locally in the proximitised system which complicates measuring global properties with a local probe. We show how to use the nonlocal conductance between two spatially separated leads to probe three global properties of a proximitised system: the bulk superconducting gap, the induced gap, and the induced coherence length. Unlike local …
Trivial Andreev bound states arising from chemical potential variations could lead to zero-bias tunneling conductance peaks at finite magnetic fields in class $D$ nanowires, precisely mimicking the predicted zero-bias conductance peaks arising from the topological Majorana bound states. This finding raises a serious question on the efficacy of using zero-bias tunneling conductance peaks, by themselves, as evidence supporting the existence of topological Majorana bound states in nanowires. In the current work, we provide specific experimental protocols for tunneling spectroscopy measure- ments …
We review recent work on resonant Andreev tunneling through a strongly interacting quantum dot connected to a normal and to a superconducting lead. We derive a general expression for the current flowing in the structure and discuss the linear and non-linear transport in the nonperturbative regime. New effects associated to the Kondo resonance combined with the two-particle tunneling arise. The Kondo anomaly in the $I-V$ characteristics depends on the relative size of the gap energy and the Kondo temperature.
We study resonant Andreev tunneling through a strongly interacting quantum dot connected to a normal and to a superconducting lead. We obtain a formula for the Andreev current and apply it to discuss the linear and non-linear transport in the nonperturbative regime, where the effects of the Kondo resonance on the two particle tunneling arise. In particular we notice an enhancement of the Kondo anomaly in the $I-V$ characteristics due to the superconducting electrode.
We study the nonequilibrium transport through a quantum dot coupled to normal and superconducting leads. We use the modified second-order perturbation theory to calculate the differential conductance and the local density of states at the quantum dot. In the strong but finite Coulomb interaction regime, the differential conductance shows an anomalous peak not at a zero bias voltage but at a finite bias voltage. We also observe an additional Kondo resonance besides the normal one in the local density of states, where the former is caused by nonequilibrium Andreev tunneling via the normal Kondo …
The Majorana search is caught up in an extensive debate about the false-positive signals from non-topological Andreev bound states (ABSs). We introduce a remedy using the dissipative probe to generate electron-boson interaction. We theoretically show that the interaction-induced renormalization leads to significantly distinct universal zero-bias conductance behaviors, i.e. distinct characteristic power-law in temperature, for different types of Andreev reflections, which shows a sharp contrast to that of a Majorana zero mode. Various specific cases have been studied, including the cases that t…
In the framework of Bogoliubov-de Gennes equation, we theoretically study the Andreev reflection in normal-superconducting junctions based on semi-Dirac materials. Owing to the intrinsic anisotropy of semi-Dirac materials, the configuration of Andreev reflection and differential conductance are strongly orientation-dependent. For the transport along the linear dispersion direction, the differential conductance exhibits a clear crossover from retro Andreev reflection to specular Andreev reflection with an increasing bias-voltage, and the differential conductance oscillates without a decaying pr…
Two-terminal conductance spectroscopy of superconducting devices is a common tool for probing Andreev and Majorana bound states. Here, we study theoretically a three-terminal setup, with two normal leads coupled to a grounded superconducting terminal. Using a single-electron scattering matrix, we derive the subgap conductance matrix for the normal leads and discuss its symmetries. In particular, we show that the local and the nonlocal elements of the conductance matrix have pairwise identical antisymmetric components. Moreover, we find that the nonlocal elements are directly related to the loc…
We study transport mediated by Andreev bound states formed in InSb nanowire quantum dots. Two kinds of superconducting source and drain contacts are used: epitaxial Al/InSb devices exhibit a doubling of tunneling resonances, while in NbTiN/InSb devices Andreev spectra of the dot appear to be replicated multiple times at increasing source-drain bias voltages. In both devices, a mirage of a crowded spectrum is created. To describe the observations a model is developed that combines the effects of a soft induced gap and of additional Andreev bound states both in the quantum dot and in the finite …
Semiconductor quantum dots have proven to be a useful platform for quantum simulation in the solid state. However, implementing a superconducting coupling between quantum dots mediated by a Cooper pair has so far suffered from limited tunability and strong suppression. This has limited applications such as Cooper pair splitting and quantum dot simulation of topological Kitaev chains. In this work, we propose how to mediate tunable effective couplings via Andreev bound states in a semiconductor-superconductor nanowire connecting two quantum dots. We show that in this way it is possible to indiv…
We present a combined experimental and theoretical analysis of the low bias conductance properties of carbon nanotubes coupled to superconducting leads. In the Kondo regime the conductance exhibits a zero bias peak which can be several times larger than the unitary limit in the normal case. This zero bias peak can be understood by analyzing the dynamics of the subgap Andreev states under an applied bias voltage. It is shown that the existence of a linear regime is linked to the presence of a finite relaxation rate within the system. The theory provides a good fitting of the experimental result…
We present a theory of transport through interacting quantum dots coupled to normal and superconducting leads in the limit of weak tunnel coupling. A Josephson current between two superconducting leads, carried by first-order tunnel processes, can be established by non-equilibrium proximity effect. Both Andreev and Josephson current is suppressed for bias voltages below a threshold set by the Coulomb charging energy. A $π$-transition of the supercurrent can be driven by tuning gate or bias voltages.
We investigate Andreev reflection (AR) resonant tunneling through a precessing spin which is coupled to a normal metallic lead and a superconducting lead. The formula of the AR conductance at zero temperature is obtained as a function of chemical potential and azimuthal angle of the spin precessing by using the nonequilibrium Green function method. It is found that as the local spin precesses in a weak external magnetic field at Larmor frequency $ω_l$, the AR tunneling conductance exhibits an oscillation at the frequency $2ω_l$ alone. The amplitude of AR conductance oscillation enhances with s…
The charge character of Andreev bound states (ABSs) in a three-terminal semiconductor-superconductor hybrid nanowire was measured using local and nonlocal tunneling spectroscopy. The device is fabricated using an epitaxial InAs/Al two-dimensional heterostructure with several gate-defined side probes. ABSs are found to oscillate around zero as a function of gate voltage, with modifications of their charge consistent with theoretical expectations for the total Bardeen-Cooper- Schrieffer (BCS) charge of ABSs.
The Andreev current and the subgap conductance in a superconductor/ insulator/ ferromagnet (SIF) structure in the presence of a small spin-splitting field show novel interesting features (A. Ozaeta et al., Phys. Rev. B 86, 060509(R), 2012). For example, the Andreev current at zero temperature can be enhanced by a spin-splitting field h, smaller than the superconducting gap, as has been recently reported by the authors. Also at finite temperatures the Andreev current has a peak for values of the spin-splitting field close to the superconducting gap. Finally, the differential subgap conductance …
We investigate the correlation functions of mesoscopic electronic transport in open chaotic quantum dots with finite tunnel barriers in the crossover between Wigner-Dyson ensembles. Using an analytical stub formalism, we show the emergence of a depletion/amplification of conductance fluctuations as a function of tunnel barriers, for both parametric variations of electron energy or magnetoconductance fields. Furthermore, even for pure Dyson ensembles, correlation functions of conductance fluctuations in chaotic quantum dots can exhibit anti-correlation. Experimental support to our findings is p…
In an experimental study of Andreev reflection (AR) in normal metal/superconductor (N-S) devices featuring a superconducting topological insulator CuxBi2Se3 [arXiv:1301.1030], Peng et. al. reported the reproducible experimental observation of archetypical double-peak AR spectra for finite barrier strength in N-S junctions, which clearly indicates the absence of zero-energy peak in density of states and thus rules out theoretically predicted zero-energy Majorana fermions in CuxBi2Se3. This report casts doubt on previous claims of CuxBi2Se3 as a topological superconductor. Here we clarify an ina…
Conductance measurements cannot distinguish crossed Andreev reflection from elastic co-tunneling in normal--superconductor--normal junctions
Osipyan Institute of Solid State Physics, Russian Academy of Sciences（俄罗斯科学院奥西皮扬固体物理研究所）；Condensed-Matter Physics Laboratory, HSE University（国立高等经济学院凝聚态物理实验室）；National Research University Higher School of Economics（国立高等经济大学）
We study Andreev reflection (AR) tunneling through a quantum dot (QD) connected to a ferromagnet and a superconductor, in which the intradot spin-flip interaction is included. By using the nonequibrium-Green-function method, the formula of the linear AR conductance is derived at zero temperature. It is found that competition between the intradot spin-flip scattering and the tunneling coupling to the leads dominantes resonant behaviours of the AR conductance versus the gate voltage.A weak spin-flip scattering leads to a single peak resonance.However, with the spin-flip scattering strength incre…
Studying the interplay between superconductivity and quantum magnetotransport in two-dimensional materials has been a topic of interest in recent years. Towards such a goal it is important to understand the impact of magnetic field on the charge transport at the superconductor-normal channel (SN) interface. Here we carried out a comprehensive study of Andreev conductance under weak magnetic fields using diffusive superconductor- graphene Josephson weak links. We observe that the Andreev conductance is suppressed even in magnetic fields far below the upper critical field of the superconductor. …
Electrical conductance measurements have limited scope in identifying Andreev edge states (AESs), which form the basis for realizing various topological excitations in quantum Hall (QH) - superconductor (SC) junctions. To unambiguously detect AESs, we measure shot noise along with electrical conductance in a graphene based QH-SC junction at integer filling nu=2. Remarkably, we find that the Fano factor of shot noise approaches half when the bias energy is less than the superconducting gap, whereas it is close to zero above the superconducting gap. This is striking, given that, at the same time…
We study the transport through side-coupled double quantum dots, connected to normal and superconducting (SC) leads with a T-shape configuration. We find, using the numerical renormalization group, that the Coulomb interaction suppresses SC interference in the side dot, and enhances the conductance substantially in the Kondo regime. This behavior stands in total contrast to a wide Kondo valley seen in the normal transport. The SC proximity penetrating into the interfacial dot pushes the Kondo clouds, which screens the local moment in the side dot, towards the normal lead to make the singlet bo…
The Andreev reflection of narrow ferromagnet/superconductor point contacts is theoretically studied. We show that the conductance quantization depends on whether the contact region is superconducting or ferromagnetic as well as on the strength of the exchange field in the ferromagnet. The Andreev reflection of the ferromagnetic contact is more suppressed than that of the superconducting contact. We also show that the conductance-voltage curve has a bump at zero bias-voltage if there is no interfacial-scattering. On the contrary, the conductance-voltage curve shows a dip if the system has an in…
We consider mesoscopic four-terminal Josephson junctions and study emergent topological properties of the Andreev subgap bands. We use symmetry-constrained analysis for Wigner-Dyson classes of scattering matrices to derive band dispersions. When scattering matrix of the normal region connecting superconducting leads is energy-independent, the determinant formula for Andreev spectrum can be reduced to a palindromic equation that admits a complete analytical solution. Band topology manifests with an appearance of the Weyl nodes which serve as monopoles of finite Berry curvature. The correspondin…
In this paper, 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 …
We investigate the transport properties of a ferromagnet-superconductor interface within the framework of a modified three-dimensional Blonder-Tinkham-Klapwijk formalism. In particular, we propose that charge inhomogeneity forms via two unique transport mechanisms, namely, evanescent Andreev reflection and evanescent quasiparticle transmission. Furthermore, we take into account the influence of charge inhomogeneity on the interfacial barrier potential and calculate the conductance as a function of bias voltage. Point-contact Andreev reflection (PCAR) spectra often show dip structures, large ze…
We investigate Andreev reflection at the interface between a superconductor and a two--dimensional electron system (2DES) in an external magnetic field such that cyclotron motion is important in the latter. A finite Zeeman splitting in the 2DES and the presence of diamagnetic screening currents in the superconductor are incorporated into a microscopic theory of Andreev edge states, which is based on the Bogoliubov--de Gennes formalism. The Andreev--reflection contribution to the interface conductance is calculated. The effect of Zeeman splitting is most visible as a double--step feature in the…
Directional conductance of Andreev crystals in hybrid Josephson junction arrays
Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯·玻尔研究所量子器件中心）；Center for Quantum Information Physics, Department of Physics, New York University（纽约大学物理系量子信息物理中心）；Nordita, KTH Royal Institute of Technology and Stockholm University（诺迪塔（斯德哥尔摩皇家理工学院与斯德哥尔摩大学联合机构））；Department of Physics, Massachusetts Institute of Technology（麻省理工学院物理系）
We study the sub-gap spectrum and the transport properties of a double quantum dot coupled to metallic and superconducting leads. The coupling of both quantum dots to the superconducting lead induces a non-local pairing in both quantum dots by the Andreev reflection processes. Additionally, we obtain two channels of Cooper pair tunneling into a superconducting lead. In such a system, the direct tunneling process (by one of two dots) or the crossed tunneling process (by both quantum dots at the same time) is possible. We consider the dependence of the Andreev transmittance on an inter-dot tunne…
We show that a quantum dot connected via tunnel barriers to superconducting leads traps a continuously tunable and hence fractional charge. The fractional charge on the island is due to particle-hole symmetry breaking and can be tuned via a gate potential acting on the dot or via changes in the phase difference across the island. We determine the groundstate, equilibrium, and excitation charges and show how to identify these quantities in an experiment.
We study tunneling spectroscopy of discrete subgap Andreev states in a superconducting system. If the tunneling coupling is weak, individual levels are resolved and the conductance $G(V)$ at small temperatures is composed of a set of resonant Lorentz peaks which cannot be described within perturbation theory over tunnelling strength. We establish a general formula for their widths and heights and show that the width of any peak scales as normal-state tunnel conductance, while its height is $\lesssim 2e^2/h$ and depends only on contact geometry and the spatial profile of the resonant Andreev le…
We investigate thermoelectric transport through Andreev interferometers. We show that the ratio of the thermal and the charge conductance exhibits large oscillations with the phase difference $ϕ$ between the two superconducting contacts, and that the Wiedemann-Franz law holds only when $ϕ=π$. A large average thermopower furthermore emerges whenever there is an asymmetry in the dwell times to reach the superconducting contacts. When this is the case, the thermopower is odd in $ϕ$. In contrast, when the average times to reach either superconducting contact are the same, the average thermopower i…
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…
We calculate the differential conductance at a probe inserted in the weak link of a topological Josephson junction, consisting of a semiconducting nanowire deposited on top of two separated superconductors. Our aim is to understand how the peculiar features in the spectrum of Andreev bound states, arising due to the presence of Majorana bound states at the ends of the two topological superconducting wires defining the junction, can be determined through a measurement of the differential conductance. We find that when the probe allows a single propagating mode, the differential conductance pres…
We consider the conductance of a normal-superconductor junction in bilayer graphene in the framework of the Dirac-Bogoliubov-De-Gennes equation. A remarkable suppression of the conductance at voltages just below the superconducting gap is found. This can be understood in terms of the spinor structures of the electron and hole excitations, in particular the reflected valence band hole being orthogonal to the incoming electron at normal incidence. Minor changes in response to referee reports, references updated.
