arXiv subjects

Christophe Mora

Publications and source records attributed to Christophe Mora.

At least 55 records · Page 3Linked to original sources

arXiv2018

Two-color Fermi liquid theory for transport through a multilevel Kondo impurity

We consider a quantum dot with ${\cal K}{\geq} 2$ orbital levels occupied by two electrons connected to two electric terminals. The generic model is given by a multi-level Anderson Hamiltonian. The weak-coupling theory at the particle-hole symmetric point is governed by a two-channel $S{=}1$ Kondo model characterized by intrinsic channels asymmetry. Based on a conformal field theory approach we derived an effective Hamiltonian at a strong-coupling fixed point. The Hamiltonian capturing the low-energy physics of a two-stage Kondo screening represents the quantum impurity by a two-color local Fermi-liquid. Using non-equilibrium (Keldysh) perturbation theory around the strong-coupling fixed point we analyze the transport properties of the model at finite temperature, Zeeman magnetic field and source-drain voltage applied across the quantum dot. We compute the Fermi-liquid transport constants and discuss different universality classes associated with emergent symmetries.

cond-mat.mes-hall↗

arXiv2017

Topological phases of parafermions: a model with exactly-solvable ground states

Parafermions are emergent excitations that generalize Majorana fermions and can also realize topological order. In this paper we present a non-trivial and quasi-exactly-solvable model for a chain of parafermions in a topological phase. We compute and characterize the ground-state wave-functions, which are matrix-product states and have a particularly elegant interpretation in terms of Fock parafermions, reflecting the factorized nature of the ground states. Using these wavefunctions, we demonstrate analytically several signatures of topological order. Our study provides a starting point for the non-approximate study of topological one-dimensional parafermionic chains with spatial-inversion and time-reversal symmetry in the absence of strong edge modes.

quant-ph↗

arXiv2017

Quantum Properties of the radiation emitted by a conductor in the Coulomb Blockade Regime

We present an input-output formalism describing a tunnel junction strongly coupled to its electromagnetic environment. We exploit it in order to investigate the dynamics of the radiation being emitted and scattered by the junction. We find that the non-linearity imprinted in the electronic transport by a properly designed environment generates strongly squeezed radiation. Our results show that the interaction between a quantum conductor and electromagnetic fields can be exploited as a resource to design simple sources of non-classical radiation.

cond-mat.mes-hall↗

arXiv2017

Bipartite charge fluctuations in one-dimensional $\mathbb{Z}_2$ superconductors and insulators

Bipartite charge fluctuations (BCF) have been introduced to provide an experimental indication of many-body entanglement. They have proved themselves to be a very efficient and useful tool to characterize quantum phase transitions in a variety of quantum models conserving the total number of particles (or magnetization for spin systems). In this Letter, we study the BCF in generic one-dimensional $\mathbb{Z}_2$ (topological) models including the Kitaev superconducting wire model, the Ising chain or various topological insulators such as the SSH model. The considered charge (either the fermionic number or the relative density) is no longer conserved, leading to macroscopic fluctuations of the number of particles. We demonstrate that at phase transitions characterized by a linear dispersion, the BCF probe the change in a winding number that allows one to pinpoint the transition and corresponds to the topological invariant for standard models. Additionally, we prove that a sub-dominant logarithmic contribution is still present at the exact critical point. Its quantized coefficient is universal and characterizes the critical model. Results are extended to the Rashba topological nanowires and to the XYZ model.

cond-mat.str-el↗

arXiv2017

Noise of a chargeless Fermi liquid

We construct a Fermi liquid theory to describe transport in a superconductor-quantum dot- normal metal junction close to the singlet-doublet (parity changing) transition of the dot. Though quasiparticles do not have a definite charge in this chargeless Fermi liquid, in case of particle-hole symmetry, a mapping to the Anderson model unveils a hidden U(1) symmetry and a corresponding pseudo-charge. In contrast to other correlated Fermi-liquids, the back scattering noise reveals an effective charge equal to the charge of Cooper pairs, $e^* = 2e$. In addition,we find a strong suppression of noise when the linear conductance is unitary, even for its non-linear part.

cond-mat.mes-hall↗

arXiv2016

Many-terminal Majorana island: from Topological to Multi-Channel Kondo Model

We study Kondo screening obtained by coupling Majorana bound states, located on a topological superconducting island, to interacting electronic reservoirs. At the charge degeneracy points of the island, we formulate an exact mapping onto the spin-$1/2$ multi-channel Kondo effect. The coupling to Majorana fermions transforms the tunneling terms into effective fermionic bilinear contributions with a Luttinger parameter $K$ in the leads that is effectively doubled. For strong interaction, $K=1/2$, the intermediate fixed point of the standard multi-channel Kondo model is exactly recovered. It evolves with $K$ and connects to strong coupling in non-interacting case $K=1$, with maximum conductance between the leads and robustness against channel asymmetries similarly to the topological Kondo effect. For a number of leads above four, there exists a window of Luttinger parameters in which a quantum phase transition can occur between the strong coupling topological Kondo state and the partially conducting multi-channel Kondo state.

cond-mat.mes-hall↗

arXiv2016

Electron-photon interaction in a quantum point contact coupled to a microwave resonator

We study a single-mode cavity weakly coupled to a voltage-biased quantum point contact. In a perturbative analysis, the lowest order predicts a thermal state for the cavity photons, driven by the emission noise of the conductor. The cavity is thus emptied as all transmission probabilities of the quantum point contact approach one or zero. Two-photon processes are identified at higher coupling, and pair absorption dominates over pair emission for all bias voltages. As a result, the number of cavity photons, the cavity damping rate and the second order coherence $g^{(2)}$ are all reduced and exhibit less bunching than the thermal state. These results are obtained with a Keldysh path integral formulation and reproduced with rate equations. They can be seen as a backaction of the cavity measuring the electronic noise. Extending the standard $P(E)$ theory to a steady-state situation, we compute the modified noise properties of the conductor and find quantitative agreement with the perturbative calculation.

cond-mat.mes-hall↗

arXiv2016

Phase Diagram and Entanglement of two interacting topological Kitaev chains

A superconducting wire described by a p-wave pairing and a Kitaev Hamiltonian exhibits Majorana fermions at its edges and is topologically protected by symmetry. We consider two Kitaev wires (chains) coupled by a Coulomb type interaction and study the complete phase diagram using analytical and numerical techniques. A topological superconducting phase with four Majorana fermions occurs until moderate interactions between chains. For large interactions, both repulsive and attractive, by analogy with the Hubbard model, we identify Mott phases with Ising type magnetic order. For repulsive interactions, the Ising antiferromagnetic order favors the occurrence of orbital currents spontaneously breaking time-reversal symmetry. By strongly varying the chemical potentials of the two chains, quantum phase transitions towards fully polarized (empty or full) fermionic chains occur. In the Kitaev model, the quantum critical point separating the topological superconducting phase and the polarized phase belongs to the universality class of the critical Ising model in two dimensions. When increasing the Coulomb interaction between chains, then we identify an additional phase corresponding to two critical Ising theories (or two chains of Majorana fermions). We confirm the existence of such a phase from exact mappings and from the concept of bipartite fluctuations. We show the existence of negative logarithmic corrections in the bipartite fluctuations, as a reminiscence of the quantum critical point in the Kitaev model. Other entanglement probes such as bipartite entropy and entanglement spectrum are also used to characterize the phase diagram. The limit of large interactions can be reached in an equivalent setup of ultra-cold atoms and Josephson junctions.

cond-mat.str-el↗

arXiv2016

Cavity quantum electrodynamics with an out-of-equilibrium quantum dot

We consider a superconducting microwave cavity capacitively coupled to both a quantum conductor and its electronic reservoirs. We analyze in details how the measurements of the cavity microwave field, which are related to the electronic charge susceptibility, can be used to extract information on the transport properties of the quantum conductor. We show that the asymmetry of the capacitive couplings between the electronic reservoirs and the cavity plays a crucial role in relating optical measurements to transport properties. For asymmetric capacitive couplings, photonic measurements can be used to probe the finite low frequency admittance of the quantum conductor, the real part of which being related to the differential conductance. In particular, when the quantum dot is far from resonance, the charge susceptibility is directly proportional to the admittance for a large range of frequencies and voltages. However, when the quantum conductor is near a resonance, such a relation generally holds only at low frequency and for equal tunnel coupling or low voltage. Beyond this low-energy near equilibrium regime, the charge susceptibility and thus the optical transmission offers new insights on the quantum conductors since the optical observables are not directly connected to transport quantities. For symmetric lead capacitive couplings, we show that the optical measurements can be used to reveal the Korringa-Shiba relation, connecting the reactive to the dissipative part of the susceptibility, at low frequency and low bias.

cond-mat.mes-hall↗

arXiv2015

Cavity squeezing by a quantum conductor

Hybrid architectures integrating mesoscopic electronic conductors with resonant microwave cavities have a great potential for investigating unexplored regimes of electron-photon coupling. In this context, producing nonclassical squeezed light is a key step towards quantum communication with scalable solid-state devices. Here we show that parametric driving of the electronic conductor induces a squeezed steady state in the cavity. We find that squeezing properties of the cavity are essentially determined by the electronic noise correlators of the quantum conductor. In the case of a tunnel junction, we predict that squeezing is optimized by applying a time-periodic series of quantized $δ-$peaks in the bias voltage. For an asymmetric quantum dot, we show that a sharp Leviton pulse is able to achieve perfect cavity squeezing.

cond-mat.mes-hall↗

arXiv2015

Fermi-liquid theory for the single-impurity Anderson model

We generalize Nozières' Fermi-liquid theory for the low-energy behavior of the Kondo model to that of the single-impurity Anderson model. In addition to the electrons' phase shift at the Fermi energy, the low-energy Fermi-liquid theory is characterized by four Fermi-liquid parameters: the two given by Nozières that enter to first order in the excitation energy, and two additional ones that enter to second order and are needed away from particle-hole symmetry. We express all four parameters in terms of zero-temperature physical observables, namely the local charge and spin susceptibilities and their derivatives with respect to the local level position. We determine these in terms of the bare parameters of the Anderson model using Bethe Ansatz and Numerical Renormalization Group (NRG) calculations. Our low-energy Fermi-liquid theory applies throughout the crossover from the strong-coupling Kondo regime via the mixed-valence regime to the empty-orbital regime. From the Fermi-liquid theory, we determine the conductance through a quantum dot symmetrically coupled to two leads in the regime of small magnetic field, low temperature and small bias voltage, and compute the coefficients of the $\sim B^2$, $\sim T^2$, and $\sim V^2$ terms \textit{exactly} in terms of the Fermi-liquid parameters. The coefficients of $T^2$, $V^2$ and $B^2$ are found to change sign during the Kondo to empty-orbital crossover. The crossover becomes universal in the limit that the local interaction is much larger than the level width. For completeness, we also compute the shot noise and discuss the resulting Fano factor.

cond-mat.mes-hall↗

arXiv2014

Tunneling spectroscopy of Majorana-Kondo devices

We study the local density of states (LDOS) in systems of Luttinger-liquid nanowires connected to a common mesoscopic superconducting island, in which Majorana bound states give rise to different types of topological Kondo effects. We show that electron interactions enhance the low-energy LDOS in the leads close to the island, with unusual exponents due to Kondo physics that can be probed in tunneling experiments.

cond-mat.mes-hall↗

arXiv2014

Non-Fermi liquid manifold in a Majorana device

We propose and study a setup realizing a stable manifold of non-Fermi liquid states. The device consists of a mesoscopic superconducting island hosting $N \ge 3$ Majorana bound states tunnel-coupled to normal leads, with a Josephson contact to a bulk superconductor. We find a nontrivial interplay between multi-channel Kondo and resonant Andreev reflection processes, which results in the fixed point manifold. The scaling dimension of the leading irrelevant perturbation changes continuously within the manifold and determines the power-law scaling of the temperature dependent conductance.

cond-mat.mes-hall↗

arXiv2014

The Kondo Temperature of SU(4) Symmetric Quantum Dots

A path integral approach is used to derive a closed analytical expression for the Kondo temperature of the SU(4) symmetrical Anderson model. In contrast to the SU(2) case, the prefactor of the Kondo temperature is found to display a peculiar orbital energy (gate voltage) dependence, reflecting the presence of various SU(4) mixed valence fixed points. Our analytical expressions are tested against and confirmed by numerical renormalization group computations.

cond-mat.mes-hall↗

arXiv2014

Probing dynamics of Majorana fermions in quantum impurity systems

We investigate the admittance of a metallic quantum RC circuit with a spinful single-channel lead or equally with two conducting spin-polarized channels, in which Majorana fermions play a crucial role in the charge dynamics. We address how the two-channel Kondo physics and its emergent Majoranas arise. The existence of a single unscreened Majorana mode results in non-Fermi-liquid features and we determine the universal crossover function describing the Fermi-liquid to non-Fermi-liquid region. Remarkably, the same universal form emerges both at weak transmission and large transmission. We find that the charge relaxation resistance strongly increases in the non-Fermi-liquid realm. Our findings can be measured using current technology assuming a large cavity.

cond-mat.mes-hall↗

arXiv2014

Transport properties of fully screened Kondo models

We study the non-equilibrium transport properties of fully (exactly) screened Kondo quantum dots subject to a finite bias voltage or a finite temperature. Firstly, we calculate the Fermi-liquid coefficients of the conductance for models with arbitrary spin, i.e. its leading behaviour for small bias voltages or temperatures. Secondly, we determine the low-temperature behaviour of the static susceptibility from the exactly known Bethe Ansatz results for the magnetisation. Thirdly, we study the crossover from strong to weak coupling in the spin-1/2 and the spin-1 models coupled to one or two screening channels respectively. Using a real-time renormalisation group method we calculate the static and dynamical spin-spin correlation functions for the spin-1/2 model as well as the linear and differential conductance and the static susceptibility for the spin-1 model. We define various Kondo scales and discuss their relations. We assess the validity of the renormalisation-group treatment by comparing with known results for the temperature dependence of the linear conductance and static susceptibility as well as the Fermi-liquid behaviour at low energies.

cond-mat.str-el↗

arXiv2013

Admittance of the SU(2) and SU(4) Anderson quantum RC circuits

We study the Anderson model as a description of the quantum RC circuit for spin-1/2 electrons and a single level connected to a single lead. Our analysis relies on the Fermi liquid nature of the ground state which fixes the form of the low energy effective model. The constants of this effective model are extracted from a numerical solution of the Bethe ansatz equations for the Anderson model. They allow us to compute the charge relaxation resistance Rq in different parameter regimes. In the Kondo region, the peak in Rq as a function of the magnetic field is recovered and proven to be in quantitative agreement with previous numerical renormalization group results. In the valence-fluctuation region, the peak in Rq is shown to persist, with a maximum value of h/2e^2, and an analytical expression is obtained using perturbation theory. We extend our analysis to the SU(4) Anderson model where we also derive the existence of a giant peak in the charge relaxation resistance.

cond-mat.mes-hall↗

arXiv2013

Strongly correlated dynamics in multichannel quantum RC circuits

We examine dissipation effects in a multichannel quantum RC circuit, comprising a cavity or single-electron box capacitively coupled to a gate and connected to a reservoir lead via several conducting channels. Depending on the engineering details of the quantum RC circuit, the number of channels contributing to transport vary, as do the form of the interchannel couplings. For low-frequency AC transport, the charge-relaxation resistance ($R_{q}$) is a nontrivial function of the parameters of the system. However, in the vicinity of the charge degeneracy points and for weak tunneling, we find as a result of cross-mode mixing or channel asymmetry that $R_q$ becomes universal for a metallic cavity at low temperatures, and equals the unit of quantum resistance. To prove this universality we map the system to an effective one-channel Kondo model, and construct an analogy with the Coulomb gas. Next, we probe the opposite regime of near-perfect transmission using a bosonization approach. Focussing on the two-channel case, we study the effect of backscattering at the lead-dot interface, more specifically, the role of an asymmetry in the backscattering amplitudes, and make a connection with the weak tunneling regime near the charge degeneracy points.

cond-mat.str-el↗