Régis Mélin

Transport theory of multiterminal hybrid structures

Abstract:We derive a microscopic transport theory of multiterminal hybrid structures in which a superconductor is connected to several spin-polarized electrodes. We discuss the non-perturbative physics of extended contacts, and show that such contacts can be well represented by averaging out the phase of the electronic wave function. The intercontact Andreev reflection and elastic cotunneling conductances are identical if the phase can be averaged out, namely in the presence of at least one extended contact. The maximal conductance of a two-channel contact is proportional to (e2/h)(a0/D)2exp[-D/ξ(ω*)], where D is the distance between the contacts, a0 the lattice spacing, ξ(ω) is the superconducting coherence length, and ω* is the cross-over frequency between a perturbative regime ( ω < ω*) and a non perturbative regime ( ω* < ω < Δ).

Glauber dynamics and ageing

The Glauber dynamics of various models (REM-like trap models, Brownian motion, BM model, Ising chain and SK model) is analyzed in relation with the existence of ageing. From a finite size Glauber matrix, we calculate a time τw(N) after which the system has relaxed to the equilibrium state. The case of metastability is also discussed. If the only non zero overlaps between pure states are only self-overlaps (REM-like trap models, BM model), the existence or absence of ageing depends only on the behavior of the density of eigenvalues for small eigenvalues. We have carried out a detailed numerical and analytical analysis of the density of eigenvalues of the REM-like trap models. In this case, we show that the behavior of the density of eigenvalues for typical trap realizations is related to the spectral dimension of the equivalent random walk model.

Interplay between phase defects and spin polarization in the specific heat of the spin-density-wave compound (TMTTF)2Br in a magnetic field.

Equilibrium heat relaxation experiments provide evidence that the ground state of the commensurate spin-density-wave compound (TMTTF)2Br after the application of a sufficient magnetic field is different from the conventional ground state. The experiments are interpreted on the basis of the local model of strong pinning as the deconfinement of soliton-antisoliton pairs triggered by the Zeeman coupling to spin degrees of freedom, resulting in a magnetic-field-induced density-wave glass for the spin carrying the phase configuration.

Antiferromagnetism in a doped spin-Peierls model: Classical and quantum behaviors

Abstract:We address the problem of antiferromagnetism in a two-dimensional model of doped spin-Peierls system, at the classical and quantum levels. A Bethe-Peierls solution is derived for the classical model, with an ordering temperature proportional to the doping concentration. The quantum model is treated in a cluster renormalization group showing a finite randomness behavior and an antiferromagnetic susceptibility at low temperature.

Production of nonlocal quartets and phase-sensitive entanglement in a superconducting beam splitter.

Three BCS superconductors Sa, Sb, and S and two short normal regions Na and Nb in a three-terminal SaNaSNb Sb setup provide a source of nonlocal quartets spatially separated as two correlated pairs in Sa and Sb, if the distance between the interfaces Na S and SNb is comparable to the coherence length in S. Low-temperature dc transport of nonlocal quartets from S to Sa and Sb can occur in equilibrium, and also if Sa and Sb are biased at opposite voltages. At higher temperatures, thermal excitations result in correlated current fluctuations which depend on the superconducting phases Φa and Φb in Sa and Sb. Phase-sensitive entanglement is obtained at zero temperature if Na and Nb are replaced by discrete levels.

Unconventional antiferromagnetic correlations of the doped Haldane gapsystem Y2BaNi1 - xZnxO5

Abstract:We make a new proposal to describe the very low temperature susceptibility of the doped Haldane gap compound Y2BaNi1-xZnxO5. We propose a new mean field model relevant for this compound. The ground state of this mean field model is unconventional because antiferromagnetism coexists with random dimers. We present new susceptibility experiments at very low temperature. We obtain a Curie-Weiss susceptibility χ(T) ∼C/(Θ + T) as expected for antiferromagnetic correlations but we do not obtain a direct signature of antiferromagnetic long range order. We explain how to obtain the “impurity” susceptibility (T) by subtracting the Haldane gap contribution to the total susceptibility. In the temperature range [1 K, 300 K] the experimental data are well fitted by T(T) = Cimp1 + Timp/T. In the temperature range [100 mK, 1 K] the experimental data are well fitted by T(T) = A ln(T/Tc), where Tc increases with x. This fit suggests the existence of a finite Néel temperature which is however too small to be probed directly in our experiments. We also obtain a maximum in the temperature dependence of the ac-susceptibility (T) which suggests the existence of antiferromagnetic correlations at very low temperature.

Closing the proximity gap in a metallic Josephson junction between three superconductors

We describe the proximity effect in a short disordered metallic junction between three superconducting leads. Andreev bound states in the multiterminal junction may cross the Fermi level. We reveal that for a quasicontinuous metallic density of states, crossings at the Fermi level manifest as a closing of the proximity-induced gap. We calculate the local density of states for a wide range of transport parameters using quantum circuit theory. The gap closes inside an area of the space spanned by the superconducting phase differences. We derive an approximate analytic expression for the boundary of the area and compare it to the full numerical solution. The size of the area increases with the transparency of the junction and is sensitive to asymmetry. The finite density of states at zero energy is unaffected by the electron-hole decoherence present in the junction, although decoherence is important at higher energies. Our predictions can be tested using tunneling transport spectroscopy. To encourage experiments, we calculate the current-voltage characteristic in a typical measurement setup. We show how the structure of the local density of states can be mapped out from the measurement.

Subgap structure in the conductance of a three-terminal Josephson junction

Three-terminal superconductor (S)-normalmetal (N)-superconductor (S) Josephson junctions are investigated. In a geometry where a T-shape normal metal is connected to three superconducting reservoirs, new subgap 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-Greens function calculation is presented that supports this interpretation.

Slow relaxation experiments in disordered charge and spin density waves: collective dynamics of randomly distributed solitons

Abstract:We show that the dynamics of disordered charge density waves (CDWs) and spin density waves (SDWs) is a collective phenomenon. The very low temperature specific heat relaxation experiments are characterized by: (i) “interrupted” ageing (meaning that there is a maximal relaxation time); and (ii) a broad power-law spectrum of relaxation times which is the signature of a collective phenomenon. We propose a random energy model that can reproduce these two observations and from which it is possible to obtain an estimate of the glass cross-over temperature (typically Tg≃ 100-200 mK). The broad relaxation time spectrum can also be obtained from the solutions of two microscopic models involving randomly distributed solitons. The collective behavior is similar to domain growth dynamics in the presence of disorder and can be described by the dynamical renormalization group that was proposed recently for the one dimensional random field Ising model [D.S. Fisher, P. Le Doussal, C. Monthus, Phys. Rev. Lett. 80, 3539 (1998)]. The typical relaxation time scales like ∼τexp(Tg/T). The glass cross-over temperature Tg related to correlations among solitons is equal to the average energy barrier and scales like Tg∼ 2xξΔ. x is the concentration of defects, ξ the correlation length of the CDW or SDW and Δ the charge or spin gap.

Multipair dc Josephson resonances in a biased all-superconducting bijunction

An all-superconducting bijunction consists of a central superconductor contacted to two lateral superconductors, such that nonlocal crossed Andreev reflection is operating. Then new correlated transport channels for the Cooper pairs appear in addition to those of separated conventional Josephson junctions. We study this system in a configuration where the superconductors are connected through gate-controllable quantum dots. Multipair phase-coherent resonances and phase-dependent multiple Andreev reflections are both obtained when the voltages of the lateral superconductors are commensurate, and they add to the usual local dissipative transport due to quasiparticles. The two-pair resonance (quartets) as well as some other higher order multipair resonances are π shifted at low voltage. Dot control can be used to dramatically enhance the multipair current when the voltages are resonant with the dot levels.