Serge Florens

Self-consistent description of Andreev bound states in Josephson quantum dot devices

We develop a general perturbative framework based on a superconducting atomic limit for the description of Andreev bound states (ABS) in interacting quantum dots connected to superconducting leads. A local effective Hamiltonian for dressed ABS, including both the atomic (or molecular) levels and the induced proximity effect on the dot is argued to be a natural starting point. A self-consistent expansion in single-particle tunneling events is shown to provide accurate results even in regimes where the superconducting gap is smaller than the atomic energies, as demonstrated by a comparison to recent numerical renormalization group calculations. This simple formulation may have bearings for interpreting Andreev spectroscopic experiments in superconducting devices, such as scanning tunnel microscope measurements on carbon nanotubes or radiative emission in optical quantum dots.

Observation of the Underscreened Kondo Effect in a Molecular Transistor

We present the first quantitative experimental evidence for the underscreened Kondo effect, an incomplete compensation of a quantized magnetic moment by conduction electrons, as originally proposed by Nozières and Blandin. The device consists of an even charge spin S=1 molecular quantum dot, obtained by electromigration of C60 molecules into gold nanogaps and operated in a dilution fridge. The persistence of logarithmic singularities in the low temperature conductance is demonstrated by a comparison to the fully screened configuration obtained in odd charge spin S=1/2 Coulomb diamonds. We also discover an extreme sensitivity of the underscreened Kondo resonance to the magnetic field that we confirm on the basis of numerical renormalization group calculations.

Mott transition at large orbital degeneracy: Dynamical mean-field theory

We study analytically the Mott transition of the N-orbital Hubbard model using dynamical mean-field theory and a low-energy projection onto an effective Kondo model. It is demonstrated that the critical interaction at which the insulator appears (U c 1 ) and the one at which the metal becomes unstable (U c 2 ) have a different dependence on the number of orbitals as the latter becomes large: U c 1 N while U c 2 N. An exact analytical determination of the critical coupling U c 2 IN is obtained in the large-N limit. The metallic solution close to this critical coupling has many similarities at low-energy with the results of slave boson approximations, to which a comparison is made. We also discuss how the critical temperature associated with the Mott critical endpoint depends on the number of orbitals.

Spectroscopic signatures of a bandwidth-controlled Mott transition at the surface of 1T-TaSe2.

High-resolution angle-resolved photoemission data show that a metal-insulator Mott transition occurs at the surface of the quasi-two-dimensional compound 1T-TaSe2. The transition is driven by the narrowing of the Ta 5d band induced by a temperature-dependent modulation of the atomic positions. A dynamical mean-field theory calculation of the spectral function of the half-filled Hubbard model captures the main qualitative feature of the data, namely, the rapid transfer of spectral weight from the observed quasiparticle peak at the Fermi surface to the Hubbard bands, as the correlation gap opens up.

Observation of Majorana quantum critical behaviour in a resonant level coupled to a dissipative environment

A quantum critical point associated with a carbon nanotube quantum dot that is in contact with dissipative leads exhibits striking non-Fermi-liquid properties and anomalous scaling. The dissipative environment enables the comparison of the system under thermal- and non-equilibrium conditions.

Generalized multipolaron expansion for the spin-boson model: Environmental entanglement and the biased two-state system

We develop a systematic variational coherent-state expansion for themany-body ground state of the spin-boson model, in which a quantum two-level system is coupled to a continuum of harmonic oscillators. Energetic constraints at the heart of this technique are rationalized in terms of polarons (displacements of the bath states in agreement with classical expectations) and antipolarons (counterdisplacements due to quantum tunneling effects). We present a comprehensive study of the ground-state two-level system population and coherence as a function of tunneling amplitude, dissipation strength, and bias (akin to asymmetry of the double-well potential defining the two-state system). The entanglement among the different environmental modes is investigated by looking at spectroscopic signatures of the bipartite entanglement entropy between a given environmental mode and all the other modes. We observe a drastic change in behavior of this entropy for increasing dissipation, indicative of the entangled nature of the environmental states. In addition, the entropy spreads over a large energy range at strong dissipation, a testimony to the wide entanglement window characterizing the underlying Kondo state. Finally, comparisons to accurate numerical renormalization-group calculations and to the exact Bethe ansatz solution of the model demonstrate the rapid convergence of our variationally optimized multipolaron expansion, suggesting that it should also be a useful tool for dissipative models of greater complexity, as relevant for numerous systems of interest in quantum physics and chemistry.

Quantum impurity solvers using a slave rotor representation

We introduce a representation of electron operators as a product of a spin-carrying fermion and of a phase variable dual to the total charge (slave quantum rotor). Based on this representation, a method is proposed for solving multiorbital Anderson quantum impurity models at finite interaction strength U. It consists in a set of coupled integral equations for the auxiliary field Greens functions, which can be derived from a controlled saddle point in the limit of a large number of field components. In contrast to some finite-U extensions of the noncrossing approximation, the method provides a smooth interpolation between the atomic limit and the weak-coupling limit, and does not display violation of causality at low frequency. We demonstrate that this impurity solver can be applied in the context of dynamical mean-field theory, at or close to half-filling. Good agreement with established results on the Mott transition is found, and large values of the orbital degeneracy can be investigated at low computational cost.

Robust nodal structure of Landau level wave functions revealed by Fourier transform scanning tunneling spectroscopy.

Scanning tunneling spectroscopy is used to study the real-space local density of states of a two-dimensional electron system in a magnetic field, in particular within higher Landau levels. By Fourier transforming the local density of states, we find a set of n radial minima at fixed momenta for the nth Landau levels. The momenta of the minima depend only on the inverse magnetic length. By comparison with analytical theory and numerical simulations, we attribute the minima to the nodes of the quantum cyclotron orbits, which decouple in a Fourier representation from the random guiding center motion due to disorder. Adequate Fourier filtering reveals the nodal structure in real space in some areas of the sample with relatively smooth potential disorder.

Gate-Tuned High Frequency Response of Carbon Nanotube Josephson Junctions

Carbon nanotube Josephson junctions in the open quantum dot limit are fabricated using Pd/Al bilayer electrodes, and exhibit gate-controlled superconducting switching currents. Shapiro voltage steps can be observed under radio frequency current excitations, with a damping of the phase dynamics that strongly depends on the gate voltage. These measurements are described by a standard resistively and capacitively shunted junction model showing that the switching currents from the superconducting to the normal state are close to the critical current of the junction. The effective dynamical capacitance of the nanotube junction is found to be strongly gate dependent, suggesting a diffusive contact of the nanotube.

Non-Fermi-liquid behavior from two-dimensional antiferromagnetic fluctuations: A renormalization-group and large- N analysis

We analyze the Hertz-Moriya-Millis theory of an antiferromagnetic quantum critical point, in the marginal case of two dimensions