arXiv subjects

Christophe Mora

Publications and source records attributed to Christophe Mora.

72 records · Page 4Linked to original sources

arXiv2012

Fermi liquid approach to the quantum RC circuit: renormalization-group analysis of the Anderson and Coulomb blockade models

We formulate a general approach for studying the low-frequency response of an interacting quantum dot connected to leads in the presence of oscillating gate voltages. The energy dissipated is characterized by the charge relaxation resistance, which under the loose assumption of Fermi liquid behavior at low energy, is shown to depend only on static charge susceptibilities. The predictions of the scattering theory are recovered in the noninteracting limit while the effect of interactions is simply to replace densities of states by charge susceptibilities in formulas. In order to substantiate the Fermi liquid picture in the case of a quantum RC geometry, we apply a renormalization group analysis and derive the low-energy Hamiltonian for two specific models: the Anderson and the Coulomb blockade models. The Anderson model is shown, using a field theoretical approach based on Barnes slave bosons, to map onto the Kondo model. We recover the well-known expression of the Kondo temperature for the asymmetric Anderson model and compute the charge susceptibility. The Barnes slave bosons are extended to the Coulomb blockade model where the renormalization-group analysis can be carried out perturbatively up to zero energy. All calculations agree with the Fermi liquid nature of the low-energy fixed point and satisfy the Friedel sum rule.

cond-mat.mes-hall↗

arXiv2012

Giant Charge Relaxation Resistance in the Anderson Model

We investigate the dynamical charge response of the Anderson model viewed as a quantum RC circuit. Applying a low-energy effective Fermi liquid theory, a generalized Korringa-Shiba formula is derived at zero temperature, and the charge relaxation resistance is expressed solely in terms of static susceptibilities which are accessible by Bethe ansatz. We identify a giant charge relaxation resistance at intermediate magnetic fields related to the destruction of the Kondo singlet. The scaling properties of this peak are computed analytically in the Kondo regime. We also show that the resistance peak fades away at the particle-hole symmetric point.

cond-mat.mes-hall↗

arXiv2011

Mesoscopic admittance of a double quantum dot

We calculate the mesoscopic admittance $G(ω)$ of a double quantum dot (DQD),which can be measured directly using microwave techniques. This quantity reveals spectroscopic information on the DQD and is also directly sensitive to a Pauli spin blockade effect. We then discuss the problem of a DQD coupled to a high quality photonic resonator. When the photon correlation functions can be developed along a random-phase-approximation-like scheme, the response of the resonator gives an access to $G(ω)$.

cond-mat.mes-hall↗

arXiv2010

Ultra-cold Polarized Fermi Gases

Recent experiments with ultra-cold atoms have demonstrated the possibility of realizing experimentally fermionic superfluids with imbalanced spin populations. We discuss how these developments have shed a new light on a half- century old open problem in condensed matter physics, and raised new interrogations of their own.

cond-mat.quant-gas↗

arXiv2010

Exact solution of the three-boson problem at vanishing energy

A zero range approach is used to model resonant two-body interactions between three identical bosons. A dimensionless phase parametrizes the three-body boundary condition while the scattering length enters the Bethe-Peierls boundary condition. The model is solved exactly at zero energy for any value of the scattering length, positive or negative. From this solution, an analytical expression for the rate of three-body recombination to the universal shallow dimer is extracted.

cond-mat.quant-gas↗

arXiv2010

Four-body Efimov effect

We study three same spin state fermions of mass M interacting with a distinguishable particle of mass m in the unitary limit where the interaction has a zero range and an infinite s-wave scattering length. We predict an interval of mass ratio 13.384 < M/m < 13.607 where there exists a purely four-body Efimov effect, leading to the occurrence of weakly bound tetramers without Efimov trimers.

cond-mat.quant-gas↗

arXiv2010

The normal phase of an imbalanced Fermi gas

Recent experiments on imbalanced Fermi gases have raised interest in the physics of an impurity immersed in a Fermi sea, the so-called Fermi polaron. In this letter, a simple theory is devised to describe dilute Fermi-polaron ensembles corresponding to the normal phase of an imbalanced Fermi gas. An exact formula is obtained for the dominant interaction between polarons, expressed solely in terms of a single polaron parameter. The physics of this interaction is identified as a signature of the Pauli exclusion principle.

cond-mat.quant-gas↗

arXiv2009

Universal Resistances of the Quantum RC circuit

We examine the concept of universal quantized resistance in the AC regime through the fully coherent quantum RC circuit comprising a cavity (dot) capacitively coupled to a gate and connected via a single spin-polarized channel to a reservoir lead. As a result of quantum effects such as the Coulomb interaction in the cavity and global phase coherence, we show that the charge relaxation resistance $R_q$ is identical for weak and large transmissions and it changes from $h/2e^2$ to $h/e^2$ when the frequency (times $\hbar$) exceeds the level spacing of the cavity; $h$ is the Planck constant and $e$ the electron charge. For large cavities, we formulate a correspondence between the charge relaxation resistance $h/e^2$ and the Korringa-Shiba relation of the Kondo model. Furthermore, we introduce a general class of models, for which the charge relaxation resistance is universal. Our results emphasize that the charge relaxation resistance is a key observable to understand the dynamics of strongly correlated systems.

cond-mat.mes-hall↗

arXiv2009

Theory of non-equilibrium transport in the SU(N) Kondo regime

Using a Fermi liquid approach, we provide a comprehensive treatment of the current and current noise through a quantum dot whose low-energy behaviour corresponds to an SU($N$) Kondo model, focusing on the case N=4 relevant to carbon nanotube dots. We show that for general $N$, one needs to consider the effects of higher-order Fermi liquid corrections even to describe low-voltage current and noise. We also show that the noise exhibits complex behaviour due to the interplay between coherent shot noise, and noise arising from interaction-induced scattering events. We treat various imperfections relevant to experiments, such as the effects of asymmetric dot-lead couplings.

cond-mat.mes-hall↗

arXiv2009

Fermi liquid theory for SU(N) Kondo model

We extend the Fermi liquid theory of Nozières by introducing the next-to-leading order corrections to the Fermi liquid fixed point. For a general SU(N) Kondo impurity away from half-filling, this extension is necessary to compute observables (resistivity, current or noise) at low energy. Three additional contributions are identified and their coupling constants are related using an original (and more complete) formulation of the Kondo resonance {\it floating}. In the conformal field theory language, a single cubic operator is proposed that produces the same three contributions with the same coupling constants. Comparison with an exact free energy expansion further relates the leading and next-to-leading order corrections so that a single energy scale, the Kondo temperature, eventually governs the low energy regime. We compare our results at large $N$ with the approach of Read and Newns and find analytical agreement.

cond-mat.str-el↗

arXiv2009

Ground state of a tightly bound composite dimer immersed in a Fermi Sea

In this paper we present a theoretical investigation for the ground state of an impurity immersed in a Fermi sea. The molecular regime is considered where a two-body bound state between the impurity and one of the fermions is formed. Both interaction and exchange of the bound fermion take place between the dimer and the Fermi sea. We develop a formalism based on a two channel model allowing us to expand systematically the ground state energy of this immersed dimer with the scattering length $a$. Working up to order $a^3$, associated to the creation of two particle-hole pairs, reveals the first signature of the composite nature of the bosonic dimer. Finally, a complementary variational study provides an accurate estimate of the dimer energy even at large scattering length.

cond-mat.quant-gas↗

arXiv2009

Ground state energy of the two-dimensional weakly interacting Bose gas: First correction beyond Bogoliubov theory

We consider the grand potential $Ω$ of a two-dimensional weakly interacting homogeneous Bose gas at zero temperature. Building on a number-conserving Bogoliubov method for a lattice model in the grand canonical ensemble, we calculate the next order term as compared to the Bogoliubov prediction, in a systematic expansion of $Ω$ in powers of the parameter measuring the weakness of the interaction. Our prediction is in very good agreement with recent Monte Carlo calculations.

cond-mat.stat-mech↗

arXiv2008

Analytical solution of the bosonic three-body problem

We revisit the problem of three identical bosons in free space, which exhibits a universal hierarchy of bound states (Efimov trimers). Modelling a narrow Feshbach resonance within a two-channel description, we map the integral equation for the three-body scattering amplitude to a one-dimensional Schrödinger-type single-particle equation, where an analytical solution of exponential accuracy is obtained. We give exact results for the trimer binding energies, the three-body parameter, the threshold to the three-atom continuum, and the recombination rate.

cond-mat.other↗

arXiv2008

Current noise through a Kondo quantum dot in a SU(N) Fermi liquid state

The current noise through a mesoscopic quantum dot is calculated and analyzed in the Fermi liquid regime of the SU(N) Kondo model. Results connect the Johnson-Nyquist noise to the shot noise for an arbitrary ratio of voltage and temperature, and show that temperature corrections are sizeable in usual experiments. For the experimentally relevant SU(4) case, quasiparticle interactions are shown to increase the shot noise.

cond-mat.mes-hall↗

arXiv2007

Variational wave functions, ground state and their overlap

An intrinsic measure of the quality of a variational wave function is given by its overlap with the ground state of the system. We derive a general formula to compute this overlap when quantum dynamics in imaginary time is accessible. The overlap is simply related to the area under the $E(τ)$ curve, i.e. the energy as a function of imaginary time. This has important applications to, for example, quantum Monte-Carlo algorithms where the overlap becomes as a simple byproduct of routine simulations. As a result, we find that the practical definition of a good variational wave function for quantum Monte-Carlo simulations, {\it i.e.} fast convergence to the ground state, is equivalent to a good overlap with the actual ground state of the system.

cond-mat.stat-mech↗

arXiv2007

Quantum melting of a crystal of dipolar bosons

We investigate the behaviour of dipolar bosons in two dimensions. We describe the large density crystalline limit analytically while we use quantum Monte-Carlo to study the melting toward the Bose-Einstein condensate. We find strong evidence for a first order transition. We characterize the window of experimentally accessible parameters in the context of ultracold bosons and show that observing the quantum melting should be within grasp once one is able to form cold heteronuclear molecules. Close to the melting, we can not conclude on the existence of a supersolid phase due to an insufficient overlap of our variational Bijl-Jastrow Ansatz with the actual ground state.

cond-mat.stat-mech↗

arXiv2006

From Luttinger liquid to Altshuler-Aronov anomaly in multi-channel quantum wires

A crossover theory connecting Altshuler-Aronov electron-electron interaction corrections and Luttinger liquid behavior in quasi-1D disordered conductors has been formulated. Based on an interacting non-linear sigma model, we compute the tunneling density of states and the interaction correction to the conductivity, covering the full crossover.

cond-mat.mes-hall↗

arXiv2003

Extension of Bogoliubov theory to quasi-condensates

We present an extension of the well-known Bogoliubov theory to treat low dimensional degenerate Bose gases in the limit of weak interactions and low density fluctuations. We use a density-phase representation and show that a precise definition of the phase operator requires a space discretisation in cells of size $l$. We perform a systematic expansion of the Hamiltonian in terms of two small parameters, the relative density fluctuations inside a cell and the phase change over a cell. The resulting macroscopic observables can be computed in one, two and three dimensions with no ultraviolet or infrared divergence. Furthermore this approach exactly matches Bogoliubov's approach when there is a true condensate. We give the resulting expressions for the equation of state of the gas, the ground state energy, the first order and second order correlations functions of the field. Explicit calculations are done for homogeneous systems.

cond-mat.stat-mech↗