Andreev States Research Articles

Effects of measurement power on state discrimination and dynamics in a circuit-QED experiment

We explore the effects of driving a cavity at a large photon number in a circuit-QED experiment where the “matterlike” part corresponds to a unique Andreev level in a superconducting weak link. The three many-body states of the weak link, corresponding to the occupation of the Andreev level by 0, 1, or 2 quasiparticles, lead to different cavity frequency shifts. We show how the nonlinearity inherited by the cavity from its coupling to the weak link affects the state discrimination and the photon number calibration. Both effects require treating the evolution of the driven system beyond the dispersive limit. In addition, we observe how transition rates between the circuit states (quantum and parity jumps) are affected by the microwave power, and compare the measurements with a theory accounting for the “dressing” of the Andreev states by the cavity. Published by the American Physical Society 2024

Spectral and Transport Properties of Andreev Molecule Coupled to Majorana Wire

AbstractThe quasiparticle spectrum and transport properties of the double quantum dot (DQD) deposited on a superconducting substrate (Andreev molecule) and side‐coupled to a nanowire hosting Majorana zero modes (MZMs) are studied. Placing a DQD on the superconducting substrate induces the trivial Andreev‐bound states (ABSs) in quantum dots. However, coupling of DQD with a nanowire causes the leakage of the MZM from the topological nanowire into quantum dots. The relationship between the Andreev states and the Majorana mode for different values of the coupling parameters is analyzed. Additionally, it is shown that the connection point of a metallic tip, treated as an scanning tunneling microscope (STM) tip, affects the measured results of the differential conductance.

Many-body quantum dynamics of spin-orbit coupled Andreev states in a Zeeman field

Many-body quantum dynamics of spin-orbit coupled Andreev states in a Zeeman field

Andreev reflection, Andreev states, and long ballistic SNS junction

The analysis in the present paper is based on the most known concept introduced by the brilliant physicist Alexander Andreev: Andreev bound states in a normal metal sandwiched between two superconductors. The paper presents results of direct calculations of ab initio expressions for the currents in a long ballistic SNS junction. The expressions are expanded in 1/L (L is the thickness of the normal layer). The main contribution ∝1/L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\propto 1/L$$\\end{document} to the current agrees with the results obtained in the past, but the analysis suggests a new physical picture of the charge transport through the junction free from the problem with the charge conservation law. The saw-tooth current-phase relation at T=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T=0$$\\end{document} directly follows from the Galilean invariance of the Bogolyubov–de Gennes equations proved in the paper. The proof is valid for any variation of the energy gap in space if the Andreev reflection is the only scattering process. The respective roles of the contributions of bound and continuum states to the current are clarified. They depend on the junction dimensionality.

Magneto-structural phase transitions and two-dimensional spin waves in graphite

We have previously found experimental evidence for several quantum phenomena in oxygen-ion implanted of hydrogenated graphite: ferromagnetism, antiferromagnetism, paramagentism, triplet superconductivity, Andreev states, Little-Parks oscillations, Lamb shift, Casimir effect, colossal magnetoresistance, and topologically-protected flat-energy bands [1-6]. Triplet superconductivity results in the formation of Josephson junctions, thus with potential of being used for spintronics applications in the critical area of quantum computing. In this paper, we are showing new experimental evidence for the formation of two-dimensional (2D) spin waves in oxygen-ion enriched and in hydrogenated highly oriented pyrolytic graphite. The temperature evolution of the remanent magnetization M rem(T) data confirms the formation of spin waves that follow the 2D Heisenberg model with a weak uniaxial anisotropy. In addition, the step-like features also found in the temperature dependence of the electrical resistivity between insulating and metallic states suggest several outstanding possibilities, such as a structural transition, triplet superconductivity, and chiral properties.

Andreev bound states in Josephson junctions of semi-Dirac semimetals

We consider a Josephson junction built with the two-dimensional semi-Dirac semimetal, which features a hybrid of linear and quadratic dispersion around a nodal point. We model the weak link between the two superconducting regions by a Dirac delta potential because it mimics the thin-barrier-limit of a superconductor–barrier–superconductor configuration. Assuming a homogeneous pairing in each region, we set up the BdG formalism for electronlike and holelike quasiparticles propagating along the quadratic-in-momentum dispersion direction. This allows us to compute the discrete bound-state energy spectrum ɛ of the subgap Andreev states localized at the junction. In contrast with the Josephson effect investigated for propagation along linearly dispersing directions, we find a pair of doubly degenerate Andreev bound states. Using the dependence of ɛ on the superconducting phase difference ϕ, we compute the variation of Josephson current as a function of ϕ.

Microwave-induced conductance replicas in hybrid Josephson junctions without Floquet—Andreev states

Light–matter coupling allows control and engineering of complex quantum states. Here we investigate a hybrid superconducting–semiconducting Josephson junction subject to microwave irradiation by means of tunnelling spectroscopy of the Andreev bound state spectrum and measurements of the current–phase relation. For increasing microwave power, discrete levels in the tunnelling conductance develop into a series of equally spaced replicas, while the current–phase relation changes amplitude and skewness, and develops dips. Quantitative analysis of our results indicates that conductance replicas originate from photon assisted tunnelling of quasiparticles into Andreev bound states through the tunnelling barrier. Despite strong qualitative similarities with proposed signatures of Floquet–Andreev states, our study rules out this scenario. The distortion of the current–phase relation is explained by the interaction of Andreev bound states with microwave photons, including a non-equilibrium Andreev bound state occupation. The techniques outlined here establish a baseline to study light–matter coupling in hybrid nanostructures and distinguish photon assisted tunnelling from Floquet–Andreev states in mesoscopic devices.

Sign reversal of the Josephson inductance magnetochiral anisotropy and 0-π-like transitions in supercurrent diodes.

The recent discovery of the intrinsic supercurrent diode effect, and its prompt observation in a rich variety of systems, has shown that non-reciprocal supercurrents naturally emerge when both space-inversion and time-inversion symmetries are broken. In Josephson junctions, non-reciprocal supercurrent can be conveniently described in terms of spin-split Andreev states. Here we demonstrate a sign reversal of the Josephson inductance magnetochiral anisotropy, a manifestation of the supercurrent diode effect. The asymmetry of the Josephson inductance as a function of the supercurrent allows us to probe the current-phase relation near equilibrium, and to probe jumps in the junction ground state. Using a minimal theoretical model, we can then link the sign reversal of the inductance magnetochiral anisotropy to the so-called 0-π-like transition, a predicted but still elusive feature of multichannel junctions. Our results demonstrate the potential of inductance measurements as sensitive probes of the fundamental properties of unconventional Josephson junctions.

Andreev Reflection and Klein Tunneling in High-Temperature Superconductor-Graphene Junctions.

Scattering processes in quantum materials emerge as resonances in electronic transport, including confined modes, Andreev states, and Yu-Shiba-Rusinov states. However, in most instances, these resonances are driven by a single scattering mechanism. Here, we show the appearance of resonances due to the combination of two simultaneous scattering mechanisms, one from superconductivity and the other from graphene p-n junctions. These resonances stem from Andreev reflection and Klein tunneling that occur at two different interfaces of a hole-doped region of graphene formed at the boundary with superconducting graphene due to proximity effects from Bi_{2}Sr_{2}Ca_{1}Cu_{2}O_{8+δ}. The resonances persist with gating from p^{+}-p and p-n configurations. The suppression of the oscillation amplitude above the bias energy which is comparable to the induced superconducting gap indicates the contribution from Andreev reflection. Our experimental measurements are supported by quantum transport calculations in such interfaces, leading to analogous resonances. Our results put forward a hybrid scattering mechanism in graphene-high-temperature superconductor heterojunctions of potential impact for graphene-based Josephson junctions.

Control of Andreev Bound States Using Superconducting Phase Texture.

Andreev bound states with opposite phase-inversion asymmetries are observed in local tunneling spectra at the two ends of a superconductor-semiconductor-superconductor planar Josephson junction in the presence of a perpendicular magnetic field, while the nonlocal spectra remain phase symmetric. Spectral signatures agree with a theoretical model, yielding a physical picture in which phase textures in superconducting leads localize and control the position of Andreev bound states in the junction, demonstrating a simple means of controlling the position and size of Andreev states within a planar junction.

Probing Fermi Sea Topology by Andreev State Transport.

We show that the topology of the Fermi sea of a two-dimensional electron gas (2DEG) is reflected in the ballistic Landauer transport along a long and narrow Josephson π junction that proximitizes the 2DEG. The low-energy Andreev states bound to the junction are shown to exhibit a dispersion that is sensitive to the Euler characteristic of the Fermi sea (χ_{F}). We highlight two important relations: one connects the electron or hole nature of Andreev states to the convex or concave nature of Fermi surface critical points, and one relates these critical points to χ_{F}. We then argue that the transport of Andreev states leads to a quantized conductance that probes χ_{F}. An experiment is proposed to measure this effect, from which we predict an I-V characteristic that not only captures the topology of the Fermi sea in metals, but also resembles the rectification effect in diodes. Finally, we evaluate the feasibility of measuring this quantized response in graphene, InAs and HgTe 2DEGs.

Scanning tunneling spectroscopy of Majorana zero modes in a Kitaev spin liquid

The experimental detection of Majorana zero modes represents a major open problem. In topological superconductors, scanning tunneling spectroscopy provides evidence through zero-bias conductance peaks, which can however be confused with disorder-induced Andreev states. The theory here suggests that the Majorana zero modes bound to vortices in Kitaev spin liquids offer a more favorable testing ground: the Majorana-induced conductance features found are quite distinct from those of an alternative scenario based on magnons.

Long-lived Andreev states as evidence for protected hinge modes in a bismuth nanoring Josephson junction

Long-lived Andreev states as evidence for protected hinge modes in a bismuth nanoring Josephson junction

Characterizing the helical Andreev states of a second-order topological insulator

Characterizing the helical Andreev states of a second-order topological insulator

Anomalous superconducting proximity effect of planar Pb–RhPb2 heterojunctions in the clean limit

Interest in superconducting proximity effect has been revived by the exploitation of Andreev states and by the possible emergence of Majorana bound states at the interface. Spectroscopy of these states has been so far restricted to just a handful of superconductor-metal systems in the diffusion regime, whereas reports in otherwise clean superconductor-superconductor heterojunctions are scarce. Here, we realize molecular beam epitaxy growth of atomically sharp planar heterojunctions between Pb and a topological superconductor candidate RhPb2 that allows us to spectroscopically image the proximity effect in the clean limit. The measured energy spectra of RhPb2 vary with the spatial separation from proximal Pb, and exhibit unusual modifications in the pairing gap structure and size that extend over a distance far beyond the coherence length. This anomalously long-range proximity (LRP) effect breaks the rotational symmetry of Cooper pair potential in real space and largely deforms the Abrikosov vortex cores. Our work opens promising avenues for fundamental studies of the Andreev physics and extraordinary states in clean superconducting heterojunctions.

Energy distribution controlled ballistic Josephson junction

We report an experimental study on the tuning of supercurrent in a ballistic graphene-based Josephson junction by applying a control voltage to a transverse normal channel. In this four-terminal geometry, the control voltage changes the occupation of Andreev states in the Josephson junction, thereby tuning the magnitude of the supercurrent. As a function of gate voltage, we find two different regimes characterized by a double-step distribution and a hot-electron distribution, respectively. Our work opens new opportunities to design highly controllable Josephson junctions for tunable superconducting quantum circuits.

Microwave Susceptibility Observation of Interacting Many-Body Andreev States.

Electrostatic charging affects the many-body spectrum of Andreev states, yet its influence on their microwave properties has not been elucidated. We developed a circuit quantum electrodynamics probe that, in addition to transition spectroscopy, measures the microwave susceptibility of different states of a semiconductor nanowire weak link with a single dominant (spin-degenerate) Andreev level. We found that the microwave susceptibility does not exhibit a particle-hole symmetry, which we qualitatively explain as an influence of Coulomb interaction. Moreover, our state-selective measurement reveals a large, π-phase shifted contribution to the response common to all many-body states which can be interpreted as arising from a phase-dependent continuum in the superconducting density of states.

Microwave spectroscopy of Andreev states in InAs nanowire-based hybrid junctions using a flip-chip layout

Josephson junctions based on semiconductor nanowires are potential building blocks for electrically tunable qubit structures, e.g., the gatemon or the Andreev qubit. However, an actual realization requires the thorough investigation of the intrinsic excitation spectrum. Here, we demonstrate the fabrication of low-loss superconducting microwave circuits that combine high quality factors with a well-controlled gate architecture by utilizing a flip-chip approach. This platform is then used to perform single-tone and two-tone experiments on Andreev states in in-situ grown InAs/Al core/half-shell nanowires with shadow mask defined Josephson junctions. In gate-controlled and flux-biased spectroscopic measurements we find clear signatures of single quasiparticle as well as quasiparticle pair transitions between discrete Andreev bound states mediated by photon-absorption. Our experimental findings are supported by simulations that show that the junction resides in the intermediate channel length regime.

Drastic effect of weak interaction near special points in semiclassical multiterminal superconducting nanostructures

A generic semiclassical superconducting nanostructure connected to multiple superconducting terminals hosts a quasi-continuous spectrum of Andreev states. The spectrum is sensitive to the superconducting phases of the terminals. It can be either gapped or gapless depending on the point in the multi-dimensional parametric space of these phases. Special points in this space correspond to setting some terminals to the phase 0 and the rest to the phase of $\pi$. For a generic nanostructure, three distinct spectra come together in the vicinity of a special point: two gapped phases of different topology and a gapless phase separating the two by virtue of topological protection. In this paper, we show that a weak interaction manifesting as quantum fluctuations of superconducting phases drastically changes the spectrum in a narrow vicinity of a special point. We develop an interaction model and derive a universal generic quantum action that describes this situation. The action is complicated by incorporating a non-local in time matrix order parameter, and its full analysis is beyond the scope of the present paper. Here, we identify and address two limits: the semiclassical one and the quantum one, concentrating on the first-order interaction correction in the last case. In both cases, we find that the interaction squeezes the domain of the gapless phase in the narrow vicinity of the point so the gapped phases tend to contact each other immediately, defying the topological protection. We identify the domains of strong coupling where the perturbation theory does not work. In the gapless phase, we find the logarithmic divergence of the first-order corrections. This leads us to an interesting hypothesis: weak interaction might induce an exponentially small gap in the formerly gapless phase.

Andreev states in a quasi-one-dimensional superconductor on the surface of a topological insulator

Andreev states in a quasi-one-dimensional superconductor on the surface of a topological insulator