arXiv subjects

Régis Mélin

Publications and source records attributed to Régis Mélin.

28 records · Page 2Linked to original sources

arXiv2017

Simple Floquet-Wannier-Stark-Andreev viewpoint and emergence of low-energy scales in a voltage-biased three-terminal Josephson junction

A three-terminal Josephson junction consists of three superconductors coupled coherently to a small nonsuperconducting island, such as a diffusive metal, a single or double quantum dot. A specific resonant single quantum dot three-terminal Josephson junction $(S_a,S_b,S_c)$ biased with voltages $(V,-V,0)$ is considered, but the conclusions hold more generally for resonant semi-conducting quantum wire set-ups. A simple physical picture of the steady state is developed, using Floquet theory. It is shown that the equilibrium Andreev bound states (for $V=0$) evolve into nonequilibrium Floquet-Wannier-Stark-Andreev (FWS-Andreev) ladders of resonances (for $V\ne 0$). These resonances acquire a finite width due to multiple Andreev reflection (MAR) processes. We also consider the effect of an extrinsic line-width broadening on the quantum dot, introduced through a Dynes phenomenological parameter. The DC-quartet current manifests a cross-over between the extrinsic relaxation dominated regime at low voltage to an intrinsic relaxation due to MAR processes at higher voltage. Finally, we study the coupling between the two FWS-Andreev ladders due to Landau-Zener-Stückelberg transitions, and its effect on the cross-over in the relaxation mechanism. Three important low-energy scales are identified, and a perspective is to relate those low-energy scales to a recent noise cross-correlation experiment [Y. Cohen {\it et al.}, arXiv:1606.08436].

cond-mat.mes-hall↗

arXiv2016

Gate-tunable zero-frequency current cross-correlations of the quartet mode in a voltage-biased three-terminal Josephson junction

A three-terminal Josephson junction biased at opposite voltages can sustain a phase-sensitive dc-current carrying three-body static phase coherence, known as the "quartet current". We calculate the zero-frequency current noise cross-correlations and answer the question of whether this current is noisy (like a normal current in response to a voltage drop) or noiseless (like an equilibrium supercurrent in response to a phase drop). A quantum dot with a level at energy $ε_0$ is connected to three superconductors $S_a$, $S_b$ and $S_c$ with gap $Δ$, biased at $V_a=V$, $V_b=-V$ and $V_c=0$, and with intermediate contact transparencies. At zero temperature, nonlocal quartets (in the sense of four-fermion correlations) are noiseless at subgap voltage in the nonresonant dot regime $ε_0/Δ\gg 1$, which is demonstrated with a semi-analytical perturbative expansion of the cross-correlations. Noise reveals the absence of granularity of the superflow splitting from $S_c$ towards $(S_a,S_b)$ in the nonresonant dot regime, in spite of finite voltage. In the resonant dot regime $ε_0/Δ< 1$, cross-correlations measured in the $(V_a,V_b)$ plane should reveal an "anomaly" in the vicinity of the quartet line $V_a+V_b=0$, related to an additional contribution to the noise, manifesting the phase sensitivity of cross-correlations under the appearance of a three-body phase variable. Phase-dependent effective Fano factors $F_φ$ are introduced, defined as the ratio between the amplitudes of phase modulations of the noise and the currents. At low bias, the Fano factors $F_φ$ are of order unity in the resonant dot regime $ε_0/Δ< 1$, and they are vanishingly small in the nonresonant dot regime $ε_0/Δ\gg 1$.

cond-mat.mes-hall↗

arXiv2016

Partially resummed perturbation theory for multiple Andreev reflections in a short three-terminal Josephson junction

In a transparent three-terminal Josephson junction, modeling nonequilibrium transport is numerically challenging, owing to the interplay between multiple Andreev reflection (MAR) thresholds and multipair resonances in the pair current. An approximate method, coined as "partially resummed perturbation theory in the number of nonlocal Green's functions", is presented that can be operational on a standard computer and demonstrates compatibility with results existing in the literature. In a linear structure made of two neighboring interfaces (with intermediate transparency) connected by a central superconductor, tunneling through each of the interfaces separately is taken into account to all orders. On the contrary, nonlocal processes connecting the two interfaces are accounted for at the lowest relevant order. This yields logarithmically divergent contributions at the gap edges, which are sufficient as a semi-quantitative description. The method is able to describe the current in the full two-dimensional voltage range, including commensurate as well as incommensurate values. The results found for the multipair (for instance quartet) current-phase characteristics as well as the MAR thresholds are compatible with previous results. At intermediate transparency, the multipair critical current is much larger than the background MAR current, which supports an experimental observation of the quartet and multipair resonances. The paper provides a proof of principle for addressing in the future the interplay between quasiparticles and multipairs in four-terminal structures.

cond-mat.mes-hall↗

arXiv2014

Sub-Gap Structure in the Conductance of a Three-Terminal Josephson Junction

Three-terminal superconductor (S) - normal metal (N) - superconductor (S) Josephson junctions are investigated. In a geometry where a T-shape normal metal is connected to three superconducting reservoirs, new sub-gap structures appear in the differential resistance for specific combinations of the superconductor chemical potentials. Those correspond to a correlated motion of Cooper pairs within the device that persist well above the Thouless energy and is consistent with the prediction of quartets formed by two entangled Cooper pairs. A simplified nonequilibrium Keldysh Green's function calculation is presented that supports this interpretation.

cond-mat.mes-hall↗

arXiv2014

Phase-sensitive transport at a normal metal-superconductor interface close to a Josephson junction

Phase- and voltage bias-sensitive quasiparticle transport at a double $NIS_1IS_2$ interface is considered. The barriers $I$ range from tunnel to transparent, and the intermediate region $S_1$ has a width comparable to the superconducting coherence length. A phase difference $φ$ is applied to the Josephson junction $S_1IS_2$. The normal and Andreev reflections at the $NIS_1$ interface become $φ$-sensitive, and transport is governed by interferences within the narrow $S_1$ region, both in the normal and anomalous channels. The subgap conductance is separately (energy $E$)- and (phase $φ$)- symmetric. Above the superconducting gap, the conductance is in general not symmetric even if $(E,φ)$ is changed in $(-E,-φ)$, but the symmetry is restored by averaging Fermi oscillations. The Tomasch oscillations are amplified by the phase difference. The subgap conductance exhibits a resonant structure at the energy of the Andreev bound states (ABS) of the $S_1IS_2$ junction, providing a side-spectroscopy of such states. Depending on the relative transparencies of the junctions, the resonance can increase or reduce the conductance, and it can even vanish for $φ=π$, featuring total reflection of quasiparticles at $NS_1$ by the ABS at $S_1S_2$.

cond-mat.mes-hall↗

arXiv2013

Absence of split pairs in the cross-correlations of a highly transparent normal metal-superconductor-normal metal electron beam splitter

The nonlocal conductance and the current cross-correlations are investigated within scattering theory for three-terminal normal metal-superconductor-normal metal (NSN) hybrid structures. The positive cross-correlations at high transparency found by Mélin, Benjamin and Martin [Phys. Rev. B 77, 094512 (2008)] are not due to crossed Andreev reflection. On the other hand, local processes can be enhanced by reflectionless tunneling but this mechanism has little influence on nonlocal processes and on current cross-correlations. Therefore Cooper pair splitting cannot be enhanced by reflectionless tunneling. Overall, this shows that NSN structures with highly transparent or effectively highly transparent interfaces are not suited to experimentally producing entangled split pairs of electrons.

cond-mat.mes-hall↗

arXiv2012

Enhancement of Cooper pair splitting by multiple scattering

In three-terminal NSN hybrid structures the influence of additional barriers on the nonlocal conductance and on current cross-correlations is studied within a scattering theory. In metallic systems with additional barriers and phase averaging, which simulate disordered regions, local processes can be enhanced by reflectionless tunneling but this mechanism has little influence on nonlocal processes and on current cross-correlations. Therefore Cooper pair splitting cannot be enhanced by reflectionless tunneling. On the contrary, in ballistic systems, additional barriers lead to Fabry-Perot resonances and allow to separate the different contributions to the conductance and to the current cross-correlations. In particular, crossed Andreev processes can be selectively enhanced by tuning the length or the chemical potential of the interbarrier region.

cond-mat.mes-hall↗

arXiv2011

Production of non-local quartets and phase-sensitive entanglement in a superconducting beam splitter

Three BCS superconductors S_a, S_b, and S and two short normal regions N_a and N_b in a three-terminal S_aN_aSN_bS_b set-up provide a source of non-local quartets spatially separated as two correlated pairs in S_a and S_b, if the distance between the interfaces N_aS and SN_b is comparable to the coherence length in S. Low-temperature dc-transport of non-local quartets from S to S_a and S_b can occur in equilibrium, and also if S_a and S_b are biased at opposite voltages. At higher temperatures, thermal excitations result in correlated current fluctuations which depend on the superconducting phases phi_a and phi_b in S_a and S_b. Phase-sensitive entanglement is obtained at zero temperature if N_a and N_b are replaced by discrete levels.

cond-mat.supr-con↗

arXiv2010

Positive current cross-correlations in a highly transparent normal-superconducting beam splitter due to synchronized Andreev and inverse Andreev reflections

Predictions are established for linear differential current-current cross-correlations dSab/dV in a symmetrically biased three-terminal normal metal-superconductor-normal metal (NSN) device. Highly transparent contacts turn out to be especially interesting because they feature positive dSab/dV. At high transparency, processes based on Crossed Andreev Reflection (CAR) contribute only negligibly to the current and to dSab/dV. Under these circumstances, current-current cross-correlations can be plausibly interpreted as a coherent coupling between the two NS interfaces in the form of synchronized Andreev and inverse Andreev reflections, corresponding to the process where a pair of electron-like quasi-particles and a pair of hole-like quasi-particles arrive from the normal electrodes and annihilate in the superconductor. Hence, positive dSab/dV does not automatically imply CAR. For tunnel contacts, dSab/dV is positive because of CAR. In between these two extremities, at intermediate transparencies, dSab/dV is negative because both processes which cause positive correlations, occur only with small amplitude. We use scattering theory to obtain analytic expressions for current and noise, and microscopic calculation using a tight binding model in order to obtain a clear interpretation of the physical processes.

cond-mat.supr-con↗

arXiv1998

Designability, thermodynamic stability, and dynamics in protein folding: a lattice model study

In the framework of a lattice-model study of protein folding, we investigate the interplay between designability, thermodynamic stability, and kinetics. To be ``protein-like'', heteropolymers must be thermodynamically stable, stable against mutating the amino-acid sequence, and must be fast folders. We find two criteria which, together, guarantee that a sequence will be ``protein like'': i) the ground state is a highly designable stucture, i. e. the native structure is the ground state of a large number of sequences, and ii) the sequence has a large $Δ/Γ$ ratio, $Δ$ being the average energy separation between the ground state and the excited compact conformations, and $Γ$ the dispersion in energy of excited compact conformations. These two criteria are not incompatible since, on average, sequences whose ground states are highly designable structures have large $Δ/Γ$ values. These two criteria require knowledge only of the compact-state spectrum. These claims are substantiated by the study of 45 sequences, with various values of $Δ/Γ$ and various degrees of designability, by means of a Borst-Kalos-Lebowitz algorithm, and the Ferrenberg-Swendsen histogram optimization method. Finally, we report on the reasons for slow folding. A comparison between a very slow folding sequence, an average folding one and a fast folding one suggests that slow folding originates from a proliferation of nearly compact low-energy conformations, not present for fast folders.

cond-mat.stat-mech↗