Kondo screening by the surface modes of a strong topological insulator

We consider a magnetic impurity deposited on the surface of a strong topological insulator and interacting with the surface modes by a Kondo exchange interaction. Taking into account the warping of the Fermi line of the surface modes, we derive a mapping to an effective one dimensional model and show that the impurity is fully screened by the surface electrons except when the Fermi level lies exactly at the Dirac point. Using an Abrikosov fermion mean-field theory, we calculate the shape of the electronic density Friedel oscillation resulting from the presence of the Kondo screening cloud. We analyze quantitatively the observability of a six-fold symmetry in the Friedel oscillations for two prototype compounds: Bi$_2$Se$_3$ and Bi$_2$Te$_3$.Comment: 22 pages, 6 figure

Superfluidity and Anderson localisation for a weakly interacting Bose gas in a quasiperiodic potential

Using exact diagonalisation and Density Matrix Renormalisation group (DMRG) approach, we analyse the transition to a localised state of a weakly interacting quasi-1D Bose gas subjected to a quasiperiodic potential. The analysis is performed by calculating the superfluid fraction, density profile, momentum distribution and visibility for different periodicities of the second lattice and in the presence (or not) of a weak repulsive interaction. It is shown that the transition is sharper towards the maximally incommensurate ratio between the two lattice periodicities, and shifted to higher values of the second lattice strength by weak repulsive interactions. We also relate our results to recent experiments.Comment: 12 pages, 9 figures, RevTeX

Polar bosons in one-dimensional disordered optical lattices

We analyze the effects of disorder and quasi-disorder on the ground-state properties of ultra-cold polar bosons in optical lattices. We show that the interplay between disorder and inter-site interactions leads to rich phase diagrams. A uniform disorder leads to a Haldane-insulator phase with finite parity order, whereas the density-wave phase becomes a Bose-glass at very weak disorder. For quasi-disorder, the Haldane insulator connects with a gapped generalized incommesurate density wave without an intermediate critical region.Comment: 5 pages + 2 pages, 8 figure

Spectral functions of two-band spinless fermion and single-band spin-1/2 fermion models

We examine zero-temperature one-particle spectral functions for the one-dimensional two-band spinless fermions with different velocities and general forward-scattering interactions. By using the bosonization technique and diagonalizing the model to two Tomonaga-Luttinger-liquid Hamiltonians, we obtain general expressions for the spectral functions which are given in terms of the Appell hypergeometric functions. For the case of identical two-band fermions, corresponding to the SU(2) symmetric spin-1/2 fermions with repulsive interactions,the spectral functions can be expressed in terms of the Gauss hypergeometric functions and are shown to recover the double-peak structure suggesting the well-known "spin-charge" separation. By tuning the difference in velocities for the two-band fermions, we clarify the crossover in spectral functions from the "spin-charge" separation to the decoupled fermions. We discuss the relevance of our results to the spin-1/2 Hubbard model under a magnetic field which can be mapped onto two-band spinless fermions.Comment: RevTeX 4, 18 pages, 11 Encapsulated Postscript figures (v2) fig. 9 replaced for compatibility with PDF generation (v3) new references adde

Effect of disorder on 2D topological merging transition from a Dirac semi-metal to a normal insulator

We study the influence of disorder on the topological transition from a two-dimensional Dirac semi-metal to an insulating state. This transition is described as a continuous merging of two Dirac points leading to a semi-Dirac spectrum at the critical point. The latter is characterized by a dispersion relation linear in one direction and quadratic in the orthogonal one. Using the self-consistent Born approximation and renormalization group we calculate the density of states above, below and in the vicinity of the transition in the presence of different types of disorder. Beyond the expected disorder smearing of the transition we find an intermediate disordered semi-Dirac phase. On one side this phase is separated from the insulating state by a continuous transition while on the other side it evolves through a crossover to the disordered Dirac phase.Comment: 6 pages, 5 figure

Disorder in low dimensions : localisation effects in spin glass wires and cold atoms

In this paper, we review the recent activity of our group on the study of disorder effects on systems displaying phase coherence. These studies have focused on both the electronic transport through mesoscopic metallic spin glasses, and cold atomic gases trapped in a disordered potential

Incommensurate phases of a bosonic two-leg ladder under a flux

A boson two--leg ladder in the presence of a synthetic magnetic flux is investigated by means of bosonization techniques and Density Matrix Renormalization Group (DMRG). We follow the quantum phase transition from the commensurate Meissner to the incommensurate vortex phase with increasing flux at different fillings. When the applied flux is $\rho \pi$ and close to it, where $\rho$ is the filling per rung, we find a second incommensuration in the vortex state that affects physical observables such as the momentum distribution, the rung-rung correlation function and the spin-spin and charge-charge static structure factors.Comment: 19 pages, 9 EPS figures, RevTeX 4 (v1); 20 pages, 10 EPS figures, improved section on mean-field theory (v2

Persisting Meissner state and incommensurate phases of hard-core boson ladders in a flux

The phase diagram of a half-filled hard core boson two-leg ladder in a flux is investigated by means of numerical simulations based on the Density Matrix Renormalization Group (DMRG) algorithm and bosonization. We calculate experimentally accessible observables such as the momentum distribution, as well as rung current, density wave and bond-order wave correlation functions, allowing us to identify the Mott Meissner and Mott Vortex states. We follow the transition from commensurate Meissner to incommensurate Vortex state at increasing interchain hopping till the critical value [Piraud et al. Phys. Rev. B v. 91, p. 140406 (2015)] above which the Meissner state is stable at any flux. For flux close to $\pi$, and below the critical hopping, we observe the formation of a second incommensuration in the Mott Vortex state that could be detectable in current experiments.Comment: RevTeX 4, 5 pages + 8 pages supplemental, 6 EPS figures; (v2) references added, corrected the discussion of the Meissner state at high interchain hoppin

Ground-state properties of the one-dimensional Hubbard model with pairing potential

We consider a modification of the one-dimensional Hubbard model by including an external pairing potential. Guided by analytic bosonization results, we quantitatively determine the grand-canonical zero-temperature phase diagram using both finite and infinite density matrix renormalization group algorithm based on the formalism of matrix product states and matrix product operator, respectively. By computing various local quantities as well as the half-system entanglement, we are able to distinguish between Mott, metallic and superconducting phases. We point out the compressible nature of the Mott phase and the fully gapped nature of the many-body spectrum of the superconducting phase, in the presence of explicit U(1)-charge symmetry breaking.Comment: 26 pages, 8 figure