arXiv subjects

Régis Mélin

Publications and source records attributed to Régis Mélin.

At least 19 recordsLinked to original sources

arXiv2026

Floquet-Multiple Andreev Reflections

Floquet theory describes quantum systems governed by time-periodic Hamiltonians, much as Bloch theory describes spatially periodic solids. In voltage-biased multiterminal Josephson junctions, the Josephson relation causes superconducting phase differences to evolve periodically in time, thereby providing an intrinsic Floquet drive. In this Letter, we consider three-terminal Josephson junctions formed on a ballistic two-dimensional normal conductor with a continuum of electronic states. We show that the quartet and higher-order multipair processes yield characteristic Floquet-multiple Andreev reflection (Floquet-MAR) finite-bias conductance and noise resonances that are parameterized by the bias voltage and electrochemical potential. This microscopic picture opens a route toward implementing and probing Floquet-MAR physics in ballistic multiterminal Josephson junctions.

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arXiv2026

Revisiting the adiabatic limit in ballistic multiterminal Josephson junctions

Motivated by recent experiments on multiterminal Josephson junctions (MJJs) that probe different ranges of the size and bias voltage parameters, we explore the regime of increasing bias voltage in large-scale devices, where the electrochemical potential becomes comparable to the 1D energy level spacing. We find that the relative number of quantum-correlated pairs formed by colliding Floquet--Kulik quartet levels is equal to the inverse of the number of channels. This observation motivates a model for the intermediate regime in which the ballistic central two-dimensional normal metal is treated as a continuum under the adiabatic approximation, while Andreev modes propagate in a background of voltage- and flux-tunable nonequilibrium electronic populations. The model predicts characteristic voltage scales that govern the mesoscopic oscillations of the critical current, and these scales are at the crossroads of interpreting experiments in all sectors of the MJJs: quartets, topology, and Floquet theory. Our model is specifically inspired by the recent Harvard and Penn State group experiments.

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arXiv2026

Hybridization of topologically distinct quartet modes in three-terminal graphene Josephson junctions

Multiterminal Josephson junctions offer a powerful playground for exploring exotic superconducting and topological phenomena beyond the reach of conventional two-terminal devices. In this work, we present the direct spectroscopic observation of Cooper quartet resonances, a signature of correlated tunneling of two Cooper pairs across the device, in a graphene three-terminal Josephson junction (3TJJ). Using tunneling spectroscopy, we visualize how Andreev bound states (ABS) evolve across a two-dimensional superconducting phase space, controlled by the two independent phase differences in the 3TJJ. These measurements reveal sharp local minima in the differential conductance spectra locked in a specific phase condition of superconducting phase variables. The resulting quantized trajectories around the compact torus of the superconducting phase variables reveal an underlying topological winding in the multipair transport. To interpret our results, we develop a theoretical model that connects the observed quartet resonances to the coherent hybridization of multiple ABS branches, a hallmark of the rich pairing process enabled by multiterminal geometries. Our results highlight the potential of multiterminal superconducting devices to host engineered superconducting states and pave the way for new approaches to topological band structure design based on phase-controlled, higher-order superconducting transport.

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arXiv2025

Nonequilibrium Andreev resonances in ballistic graphene Andreev interferometers

We study nonequilibrium Andreev resonances in a voltage-biased graphene three-terminal Josephson junction (JJ). We observe periodic oscillations of resistance with maxima at multiples of the magnetic flux quantum (noninversion regime). As we increase the bias voltage, we further observe a transition point beyond which oscillations exhibit a $π$ phase shift (inversion regime) with maxima of resistance occuring at multiples of half-flux quantum. At this transition point, the frequency of the oscillations is doubled. We develop a model based on the coupling of the static Andreev bound states (ABSs) to the nonequilibrium Fermi surface of graphene to explain the observed noninversion to inversion crossovers. Our model associates these crossovers to microscopic phase-sensitive Andreev reflections which couple the normal and superfluid components of the current. Our findings show that multiterminal JJs can be used to engineer unconventional energy-phase relations such as those expected in the $π$-shifted ABSs without relying on quartet and Floquet physics. These nonequilibrium ABSs could potentially find applications in superconducting $π$ qubits.

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arXiv2025

Ballistic Andreev interferometers

A Josephson junction, formed between two phase-biased superconductors and a normal metal, hosts a discrete spectrum of Andreev bound states (ABS). In this paper, we develop a theory for long ballistic Andreev interferometers in two-dimensional metals. We consider three frameworks in our theoretical analysis: (i) perturbation theory in the tunneling amplitudes; (ii) non-perturbative transport theory; and (iii) physically motivated approximations to visualize the conductance maps in the (flux, voltage) plane. We find a non-standard phase-sensitive Andreev reflection process in ballistic interferometers that couples the supercurrent to the non-equilibrium populations of the ABS in the normal region. Furthermore, our model shows that conductance spectroscopy follows the spectrum of the ABS in long junctions. We also discuss our results in terms of the semiclassical theory, the classical orbits being the one-dimensional Andreev tubes. Our theoretical analysis captures the results of recent experiments by the Penn State and Harvard groups.

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arXiv2024

Evidence for $π$-shifted Cooper quartets and few-mode transport in PbTe nanowire three-terminal Josephson junctions

Josephson junctions are typically characterized by a single phase difference across two superconductors. This conventional two-terminal Josephson junction can be generalized to a multi-terminal device where the Josephson energy contains terms with contributions from multiple independent phase variables. Such multi-terminal Josephson junctions (MTJJs) are being considered as platforms for engineering effective Hamiltonians with non-trivial topologies, such as Weyl crossings and higher-order Chern numbers. These prospects rely on the ability to create MTJJs with non-classical multi-terminal couplings in which only a few quantum modes are populated. Here, we demonstrate these requirements in a three-terminal Josephson junction fabricated on selective-area-grown (SAG) PbTe nanowires. We observe signatures of a $π$-shifted Josephson effect, consistent with inter-terminal couplings mediated by four-particle quantum states called Cooper quartets. We further observe supercurrent co-existent with a non-monotonic evolution of the conductance with gate voltage, indicating transport mediated by a few quantum modes in both two- and three-terminal devices.

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arXiv2024

Magnetointerferometry of multiterminal Josephson junctions

We report a theoretical study of multiterminal Josephson junctions under the influence of a magnetic field $B$. We consider a ballistic rectangular two-dimensional metal $N_0$ connected by the edges to the left, right, top and bottom superconductors $S_L$, $S_R$, $S_T$ and $S_B$, respectively. We numerically calculate in the large-gap approximation the critical current $I_c$ versus $B$ between the left and right $S_L$ and $S_R$ for various aspect ratios, with the top and bottom $S_T$ and $S_B$ playing the role of superconducting mirrors. We find the critical current $I_c$ to be enhanced by orders of magnitude, especially at long distance, due to the phase rigidity provided by the mirrors. We obtain superconducting quantum interference device-like magnetic oscillations. With symmetric couplings, the self-consistent superconducting phase variables of the top and bottom mirrors take the values $0$ or $π$, as for emerging Ising degrees of freedom. We propose a simple effective Josephson junction circuit model that is compatible with these microscopic numerical calculations. From the $I_c(B)$ patterns we infer where the supercurrent flows in various device geometries. In particular in the elongated geometry, we show that the supercurrent flows between all pairs of contacts, which allows exploring the full phase space of the relevant phase differences.

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arXiv2023

Proposal for detecting the $π-$shifted Cooper quartet supercurrent

The multiterminal Josephson effect aroused considerable interest recently, in connection with theoretical and experimental evidence for correlations among Cooper pairs, that is, the so-called Cooper quartets. It was further predicted that the spectrum of Andreev bound states in such devices could host Weyl-point singularities. However, the relative phase between the Cooper pair and quartet supercurrents has not yet been addressed experimentally. Here, we propose an experiment involving four-terminal Josephson junctions with two independent orthogonal supercurrents, and calculate the critical current contours (CCCs) from a multiterminal Josephson junction circuit theory. We predict a generically $π$-shifted contribution of both the local or nonlocal second-order Josephson harmonics. Furthermore, we show that these lead to marked nonconvex shapes for the CCCs in zero magnetic field, where the dissipative state reenters into the superconducting one. Eventually, we discuss distinctive features of the non-local Josephson processes in the CCCs. The experimental observation of the latter could allow providing firm evidence of the $π$-shifted Cooper quartet current-phase relation.

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arXiv2023

A quantum interferometer for quartets in superconducting three-terminal Josephson junctions

An interferometric device is proposed in order to analyze the quartet mode in biased three-terminal Josephson junctions (TTJs), and to provide experimental evidence for emergence of a single stationary phase, the so-called quartet phase. In such a quartet-Superconducting Quantum Interference Device (quartet-SQUID), the flux sensitivity exhibits period ${hc}/{4e}$, which is the fingerprint of a transient intermediate state involving two entangled Cooper pairs. The quartet-SQUID provides two informations: an amplitude that measures a total ``quartet critical current'', and a phase lapse coming from the superposition of the following two current components: the quartet supercurrent that is odd in the quartet phase, and the phase-sensitive multiple Andreev reflection (phase-MAR) quasiparticle current, that is even in the quartet phase. This makes a TTJ a generically "$θ$-junction". Evidence for phase-MARs plays against conservative scenarii involving synchronization of AC Josephson currents, based on ``adiabatic'' phase dynamics and RSJ-like models.

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arXiv2022

Evidence for 4e charge of Cooper quartets in a biased multi-terminal graphene-based Josephson junction

In a Josephson junction (JJ), Cooper pairs are transported via Andreev bound states (ABSs) between superconductors. The ABSs in the weak link of multi-terminal (MT) JJs can coherently hybridize two Cooper pairs among different superconducting electrodes, resulting in the Cooper quartet (CQ) involving four fermions entanglement. The energy spectrum of these CQ-ABS can be controlled by biasing MT-JJs due to the AC Josephson effect. Here, using gate tunable four-terminal graphene JJs complemented with a flux loop, we construct CQs with a tunable spectrum. The critical quartet supercurrent exhibits magneto-oscillation associated with a charge of 4e; thereby presenting the evidence for interference between entangled CQ-ABS. At a finite bias voltage, we find the DC quartet supercurrent shows non-monotonic bias dependent behavior, attributed to Landau-Zener transitions between different Floquet bands. Our experimental demonstration of coherent non-equilibrium CQ-ABS sets a path for design of artificial topological materials based on MT-JJs.

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arXiv2022

Multiterminal ballistic Josephson junctions coupled to normal leads

Multiterminal Josephson junctions have aroused considerable theoretical interest recently and numerous works aim at putting the predictions of correlations among Coopers (i.e. the so-called quartets) and simulation of topological matter to the test of experiments. The present paper is motivated by recent experimental investigation from the Harvard group reporting $h/4e$-periodic quartet signal in a four-terminal configuration containing a loop pierced by magnetic flux, together with inversion controlled by the bias voltage, i.e. the quartet signal can be larger at half-flux quantum than in zero magnetic field. Here, we theoretically focus on devices consisting of finite-size quantum dots connected to four superconducting and to a normal lead. In addition to presenting numerical calculations of the quartet signal within a simplified modeling, we reduce the device to a non-Hermitian Hamiltonian in the infinite-gap limit. Then, relaxation has the surprising effect of producing sharp peaks and log-normal variations in the voltage-sensitivity of the quartet signal in spite of the expected moderate fluctuations in the two-terminal DC-Josephson current. The phenomenon is reminiscent of a resonantly driven harmonic oscillator having amplitude inverse proportional to the damping rate, and of the thermal noise of a superconducting weak link, inverse proportional to the Dynes parameter. Perspectives involve quantum bath engineering multiterminal Josephson junctions in the circuits of cavity quantum electrodynamics.

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arXiv2021

Ultralong-distance quantum correlations in three-terminal Josephson junctions

The production of entangled pairs of electrons in ferromagnet-superconductor-ferromagnet or normal metal-superconductor-normal metal three-terminal structures has aroused considerable interest in the last twenty years. In these studies, the distance between the contacts is limited by the zero-energy superconducting coherence length. Here, we demonstrate nonlocality and quantum correlations in voltage-biased three-terminal Josephson junctions over the ultralong distance that exceeds the superconducting coherence length by orders of magnitude. The effect relies on} the interplay between the time-periodic Floquet-Josephson dynamics, Cooper pair splitting and long-range coupling similar to the two-terminal Tomasch effect. We find cross-over between the ``Floquet-Andreev quartets'' (if the spatial separation is smaller than the superconducting coherence length), and the ``ultralong-distance Floquet-Tomasch clusters of Cooper pairs'' if the separation exceeds the superconducting coherence length, possibly reaching the same $\simeq 30\,μ$m as in the Tomasch experiments. The effect can be detected with DC-transport and zero-frequency quantum current-noise cross-correlation experiments, and it can be used for fundamental studies of superconducting quasiparticle quantum coherence in the circuits of quantum engineering.

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arXiv2021

The dc-Josephson effect with more than four superconducting leads

By definition, the $p$-terminal dc-Josephson current is sensitive to the superconducting phase variables of $p$ terminals. In the paper, we establish protocol for direct detection of the $p$-terminal dc-Josephson effect with $p\ge 3$ in a device containing $N$ superconducting leads $S_1,\,S_2,\,...,\,S_N$ having the phase variables $φ_1,\,φ_2,\,...,\,φ_N$. The calculated signal $χ^{(N)}$ can be probed in microwave experiments, and it corresponds to the higher-order nonlocal inverse inductance obtained from differentiating the current $I_1$ through $S_1$ with respect to the remaining $N-2$ independent phase differences $φ_2-φ_N,\,φ_3-φ_N,\, ...,φ_{N-1}-φ_N$. We find that the values $p\le N-2$ do not contribute to $χ^{(N)}$, and that $χ^{(N)}\ne 0$ implies evidence for the $p=N-1$ or the $p=N$-terminal dc-Josephson currents. For $N=4$ superconducting leads, we demonstrate that $χ^{(4)}\ne 0$ implies evidence for the $p=3$ or $p=4$ dc-Josephson effect, irrespective of the $p=2$-terminal dc-Josephson current. Thus, we provide a way to demonstrate the dc-Josephson effect with more than three terminals (i.e. with $p\ge 3$) in a device containing more than four superconducting leads (i.e. with $N\ge 4$). The predicted $χ^{(4)}$ is "yes or no" answer to the $p\ge 3$ dc-Josephson effect, i.e. for $N=4$, nonvanishingly small $χ^{(4)}\ne 0$ implies the $p=3$ or $p=4$-terminal dc-Josephson effect and vanishingly small $χ^{(4)}=0$ implies absence of the $p=3$ and $p=4$-terminal dc-Josephson effect. The paper can be viewed as generalizing the recently considered $φ$-junctions in Andreev molecules to arbitrary number $N$ of the superconducting leads, and it relies on basic properties of the dc-Josephson effect that are not directly related to nontrivial topology and Weyl point singularities.

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arXiv2020

Berry phase in superconducting multiterminal quantum dots

We report on the study of the non-trivial Berry phase in superconducting multiterminal quantum dots biased at commensurate voltages. Starting with the time-periodic Bogoliubov-de Gennes equations, we obtain a tight binding model in the Floquet space, and we solve these equations in the semiclassical limit. We observe that the parameter space defined by the contact transparencies and quartet phase splits into two components with a non-trivial Berry phase. We use the Bohr-Sommerfeld quantization to calculate the Berry phase. We find that if the quantum dot level sits at zero energy, then the Berry phase takes the values $φ_B=0$ or $φ_B=π$. We demonstrate that this non-trivial Berry phase can be observed by tunneling spectroscopy in the Floquet spectra. Consequently, the Floquet-Wannier-Stark ladder spectra of superconducting multiterminal quantum dots are shifted by half-a-period if $φ_B=π$. Our numerical calculations based on Keldysh Green's functions show that this Berry phase spectral shift can be observed from the quantum dot tunneling density of states.

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arXiv2020

Inversion in a four-terminal superconducting device on the quartet line: I. Two-dimensional metal and the quartet beam splitter

In connection with the recent Harvard group experiment on graphene-based four-terminal Josephson junctions containing a grounded loop, we consider biasing at opposite voltages on the quartet line and establish lowest-order perturbation theory in the tunnel amplitudes between a two-dimensional (2D) metal and four superconducting leads in the dirty limit. We present in addition general nonperturbative and nonadiabatic results. The critical current on the quartet line $I_c(Φ/Φ_0)$ depends on the reduced flux $Φ/Φ_0$ via interference between the three-terminal quartets (3TQ) and the nonstandard four-terminal split quartets (4TSQ). The 4TSQ result from synchronizing two Josephson junctions by exchange of two quasiparticles "surfing" on the 2D quantum wake, and this mechanism is already operational at equilibrium. Perturbation theory in the tunnel amplitudes shows that the 3TQ are $π$-shifted but the 4TSQ are $0$-shifted if the contacts have linear dimension which is large compared to the elastic mean free path. We establish the gate voltage dependence of the quartet critical current oscillations $I_c(Φ/Φ_0)$. It is argued that "Observation of $I_c(0)\ne I_c(1/2)$" implies "Evidence for the four-terminal 4TSQ" for finite bias voltage on the quartet line and arbitrary interface transparencies. This statement relies on physically-motivated approximations leading to the Ambegaokar-Baratoff-type formula for the quartet critical current-flux relation. It is concluded that the recent experiment mentioned above finds evidence for the four-terminal 4TSQ.

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arXiv2020

Inversion in a four terminal superconducting device on the quartet line: II. Quantum dot and Floquet theory

In this paper, we consider a quantum dot connected to four superconducting terminals biased at opposite voltages on the quartet line. The grounded superconductor contains a loop threaded by the magnetic flux $Φ$. We provide Keldysh microscopic calculations and physical pictures for the voltage-$V$ dependence of the quartet current. Superconductivity is expected to be stronger at $Φ/Φ_0=0$ than at $Φ/Φ_0=1/2$. However, inversion $I_{q,c}(V,0)<I_{q,c}(V,1/2)$ is obtained in the critical current $I_{q,c}(V,Φ/Φ_0)$ on the quartet line in the voltage-$V$ ranges which match avoided crossings in the Floquet spectrum at $(V,Φ/Φ_0=0)$ but not at $(V,1/2)$. A reduction in $I_{q,c}$ appears in the vicinity of those avoided crossings, where Landau-Zener tunneling produces dynamical quantum mechanical superpositions of the Andreev bound states. In addition, $π$-$0$ and $0$-$π$ cross-overs emerge in the current-phase relations as $V$ is further increased. The voltage-induced $π$-shift is interpreted as originating from the nonequilibrium Floquet populations produced by voltage biasing. The numerical calculations reveal that the inversion is robust against strong Landau-Zener tunneling and many levels in the quantum dot. Our theory provides a simple ``Floquet level and population'' mechanism for inversion tuned by the bias voltage $V$, which paves the way towards more realistic models for the recent Harvard group experiment where the inversion is observed.

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arXiv2019

Engineering the Floquet spectrum of superconducting multiterminal quantum dots

Here we present a theoretical investigation of the Floquet spectrum in multiterminal quantum dot Josephson junctions biased with commensurate voltages. We first draw an analogy between the electronic band theory and superconductivity which enlightens the time-periodic dynamics of the Andreev bound states. We then show that the equivalent of the Wannier-Stark ladders observed in semiconducting superlattices via photocurrent measurements, appears as specific peaks in the finite frequency current fluctuations of superconducting multiterminal quantum dots. In order to probe the Floquet-Wannier-Stark ladder spectra, we have developed an analytical model relying on the sharpness of the resonances. The charge-charge correlation function is obtained as a factorized form of the Floquet wave-function on the dot and the superconducting reservoir populations. We confirm these findings by Keldysh Green's function calculations, in particular regarding the voltage and frequency dependence of the resonance peaks in the current-current correlations. Our results open up a road-map to quantum correlations and coherence in the Floquet dynamics of superconducting devices.

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arXiv2017

Non-local Supercurrent of Quartets in a Three-Terminal Josephson Junction

We report an observation of a new, non dissipative and non local supercurrent, carried by quartets; each consisting of four entangled electrons. The supercurrent is a result of a novel Andreev bound state (ABS), formed among three superconducting terminals. While in a two-terminal Josephson junction the usual ABS, and thus the DC Josephson current, exist only in equilibrium, in the present realization the ABS exists also in the strongly nonlinear regime (biased terminals). The presence of supercurrent carried by quartets was established by performing non-local conductance and cross-correlation of current fluctuations measurements, in different devices made of aluminum-InAs nanowire junctions. An extensive and detailed theoretical study is intertwined with the experimental results.

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