♦ A one-channel conductor coupled to a quantum of resistance: exact ac conductance and finite-frequency noise
Collaborators: I. Safi and R. Zamoum

We consider a one-channel coherent conductor with intermediate or good transmission embedded into an ohmic environment whose resistance is equal the quantum of resistance. Our choice is motivated by the mapping of this problem to a Tomonaga-Luttinger liquid whose interaction parameter corresponds to the specific value K=1/2 which allows a refermionization procedure. The new fermions have an energy-dependent transmission, which determines the exact dc current and zero-frequency noise through expressions similar to those of the scattering approach. We recall and discuss these results for our present purpose. Then we compute, for the first time, the finite-frequency conductance and the non-symmetrized finite-frequency noise. Surprisingly, both cannot be expressed within the scattering approach for the new fermions, even though they are still determined by the transmission functions. Besides, the dissipative ac conductance is shown to be related exactly to the dc current: the relation is similar to that initially derived within the Tien-Gordon theory for photo-assisted-tunneling, extended recently to arbitrary strongly interacting systems in the weak tunneling regime (at arbitrary dimension and for weak backscattering as well in one dimension). Its validity in the present non-perturbative regime is unique. We also show that the emission excess noise vanishes exactly above eV, which is surprising as the underlying Tomonaga-Luttinger liquid model corresponds to a many-body correlated system. Our results apply for all ranges of temperature, voltages and frequencies below the RC frequency, and allow to explore fully the quantum regime.

♦ Enhanced thermopower under a time-dependent gate voltage
Collaborator: F. Michelini

We derive formal expressions of time-dependent energy and heat currents through a nanoscopic device using the Keldysh nonequilibrium Green function technique. Numerical results are reported for a metal/dot/metal junction where the dot level energy is abruptly changed by a step-shaped voltage pulse. Analytical linear responses are obtained for the time-dependent thermoelectric coefficients. We show that the Seebeck coefficient can be enhanced in the transient regime up to an amount (here rising 40%) controlled by both the dot energy and the height of the voltage step.

♦ Non-symmetrized noise in quantum wires
Collaborators: C. Bena and I. Safi

We calculate the ac conductance and the finite-frequency non-symmetrized noise in interacting quantum wires and single-wall carbon nanotubes in the presence of an impurity. We observe a strong asymmetry in the frequency spectrum of the non-symmetrized excess noise, even in the presence of the metallic leads. We find that this asymmetry is proportional to the differential ac conductance of the system. The asymmetry disappears for a linear system (in the absence of interactions). In the quantum regime, for temperatures much smaller than the frequency and the applied voltage, we find that the emission noise is exactly equal to the impurity partition noise. Moreover the noise exhibits oscillations with respect to frequency, whose period is inversely proportional to the value of the interaction parameter g, and whose envelope is given by the noise in an infinite Luttinger liquid with the same value of g.

♦ Finite frequency noise cross-correlations
Collaborators: T. Martin, E. Paladino, A. Zazunov and M. Creux

The measurement of finite frequency noise cross-correlations represents an experimental challenge in mesoscopic physics. Here we propose a generalisation of the resonant LC circuit setup of Lesovik and Loosen which allow to probe directly such cross-correlations by measuring the charge fluctuations on the plates of a capacitor. The measuring circuit collects noise contributions at the resonant frequency of the LC circuit. Auto-correlation noise can be canceled out by switching the wires and making two distinct measurements. The measured cross-correlations then depend of four non-symmetrized correlators. This detection method is applied to a normal metal three terminal device. We subsequently discuss to what extent the measurement circuit can detect electron-antibunching and what singularities appear in the spectral density of noise cross-correlations.

Next, we consider the measurement of higher current moments with a dissipative resonant circuit, which is coupled inductively to a mesoscopic device in the coherent regime. Information about the higher current moments is coded in the histograms of the charge on the capacitor plates of the resonant circuit. Dissipation is included via the Caldeira-Leggett model, and it is essential to include it in order for the charge fluctuations (or the measured noise) to remain finite. We identify which combination of current correlators enter the measurement of the third moment. The latter remains stable for zero damping.

♦ Photo-assisted current and noise in the fractional quantum Hall effect
Collaborators: T. Martin and P. Devillard

The effect of an ac perturbation on the shot noise of a fractional quantum Hall fluid is studied both in the weak and the strong backscattering regimes. It is known that the zero-frequency current is linear in the bias voltage, while the noise derivative exhibits steps as a function of bias. In contrast, at Laughlin fractions, the backscattering current and the backscattering noise both exhibit evenly spaced singularities, which are reminiscent of the tunneling density of states singularities for quasiparticles. The spacing is determined by the quasiparticle charge e* and the ratio of the DC bias with respect to the drive frequency. Photo-assisted transport can thus be considered as a probe for effective charges at such filling factors, and could be used in the study of more complicated fractions of the Hall effect. A non-perturbative method for studying photo-assisted transport at half filling is developed, using a refermionization procedure.

♦ Electron injection in a nanotube: noise correlations and entanglement
Collaborators: A. Lebedev, T. Martin, P. Devillard and R. Guyon

Transport through a metallic carbon nanotube is considered, where electrons are injected in the bulk by an STM tip. The charge current and noise are computed both in the absence and in the presence of one dimensional Fermi liquid leads. For an infinite homogeneous nanotube, the shot noise exhibits effective charges different from the electron charge. Noise correlations between both ends of the nanotube are positive, and occur to second order only in the tunneling amplitude. The positive correlations are symptomatic of an entanglement phenomenon between quasiparticles moving right and left from the tip. This entanglement involves many body states of the boson operators which describe the collective excitations of the Luttinger liquid. In the presence of one dimensional Fermi contacts, all quantities express the transfer of electrons only. A perturbative scheme is introduced to compute the next correction in the applied voltage, which contains both the nanotube and lead parameters.

♦ Theory of the anomalous Hall effect
Collaborators: P. Bruno, V. Dugaev and J. Wunderlich

A model to treat the anomalous Hall effect has been developed. Based on the Kubo formalism and on the Dirac equation, this model allows the simultaneous calculation of the skew-scattering and side-jump contributions to the anomalous Hall conductivity. The continuity and the consistency with the weak-relativistic limit described by the Pauli Hamiltonian is shown. For both approaches, Dirac and Pauli, the Feynman diagrams, which lead to the skew-scattering and the side-jump contributions, are underlined. In order to illustrate this method, we apply it to a particular case: a ferromagnetic bulk compound in the limit of weak-scattering and free-electrons approximation. Explicit expressions for the anomalous Hall conductivity for both skew-scattering and sidejump mechanisms are obtained. Within this model, the recently predicted spin Hall effect appears naturally.