Enhancement of critical temperatures in disordered bipartite lattices

We study the strong enhancement, induced by random hopping, of the critical temperatures characterizing the transitions to superconductivity, charge-density wave and antiferromagnetism, which can occur in bipartite lattice models at half-filling, like graphene, by means of an extended Finkel'stein non-linear $\sigma$-model renormalization group approach. We show that, if Cooper channel interaction dominates, superconducting critical temperature can be enhanced at will, since superconductivity cannot be broken by entering any Anderson insulating phase. If, instead, staggered interactions are relevant, antiferromagnetic order is generated by disorder at a temperature well above that expected for a clean system.Comment: 7 pages, 4 figures, final versio

Two-mode dipolar bosonic junctions

We consider a two-mode atomic Josephson junction realized with dilute dipolar bosons confined by a double-well. We employ the two-site extended Bose-Hubbard Hamiltonian and characterize the ground-state of this system by the Fisher information, coherence visibility, and entanglement entropy. These quantities are studied as functions of the interaction between bosons in different wells. The emergence of Schroedinger-cat like state with a loss of coherence is also commented.Comment: 9 pages, 1 figur

Extended Kitaev chain with longer-range hopping and pairing

We consider the Kitaev chain model with finite and infinite range in the hopping and pairing parameters, looking in particular at the appearance of Majorana zero energy modes and massive edge modes. We study the system both in the presence and in the absence of time reversal symmetry, by means of topological invariants and exact diagonalization, disclosing very rich phase diagrams. In particular, for extended hopping and pairing terms, we can get as many Majorana modes at each end of the chain as the neighbors involved in the couplings. Finally we generalize the transfer matrix approach useful to calculate the zero-energy Majorana modes at the edges for a generic number of coupled neighbors.Comment: 14 pages, 16 figure

Self-consistent Keldysh approach to quenches in weakly interacting Bose-Hubbard model

We present a non-equilibrium Green's functional approach to study the dynamics following a quench in weakly interacting Bose Hubbard model (BHM). The technique is based on the self-consistent solution of a set of equations which represents a particular case of the most general set of Hedin's equations for the interacting single-particle Green's function. We use the ladder approximation as a skeleton diagram for the two-particle scattering amplitude useful, through the self-energy in the Dyson equation, for finding the interacting single-particle Green's function. This scheme is then implemented numerically by a parallelized code. We exploit this approach to study the correlation propagation after a quench in the interaction parameter, for one (1D) and two (2D) dimensions. In particular, we show how our approach is able to recover the crossover from ballistic to diffusive regime by increasing the boson-boson interaction. Finally we also discuss the role of a thermal initial state on the dynamics both for 1D and 2D Bose Hubbard models, finding that surprisingly at high temperature a ballistic evolution is restored.Comment: 13 figure

Long-range topological insulators and weakened bulk-boundary correspondence

We formalize the appearance of new types of insulators in long-range (LR) fermionic systems. These phases are not included in the "ten-fold way classification" (TWC) for the short-range (SR) topological insulators. This conclusion is obtained studying at first specific one-dimensional LR examples, in particular their phase diagrams and contents in symmetries and entanglement. The purely long-range phases (LRP) are signaled by the violation of the area-law for the Von Neumann entropy and by corresponding peculiar distributions for the entanglement spectrum (ES). The origin of the deviations from the TWC is analyzed from a more general point of view and in any dimension. In particular, it is found related with a particular type of divergences occurring in the spectrum, due to the LR couplings. A satisfying characterization for the LRP can be achieved at least for one-dimensional systems, as well as the connected definition of a nontrivial topology, provided a careful evaluation of the LR contributions. Our results lead to reconsider the definition of correlation length in LR systems. The same analysis also allows to infer, at least for one-dimensional models, the weakening of the bulk-boundary correspondence, due to the important correlations between bulk and edges, and consequently to clarify the nature of the massive edge states appearing in the topological LR. The emergence of this peculiar edge structure is signaled by the bulk ES. The stability of the LRP against finite-size effects, relevant in current experiments, and against local disorder is discussed, showing that the latter ingredient can even strengthen the effect of the LR couplings. Finally, we analyze the entanglement content of the paradigmatic LR Ising spin chain, inferring again important deviations from the SR regime, and the limitations of bulk-boundary (tensor-network based) approaches to classify LR spin models

Wavevector-dependent spin filtering and spin transport through magnetic barriers in graphene

We study the spin-resolved transport through magnetic nanostructures in monolayer and bilayer graphene. We take into account both the orbital effect of the inhomogeneous perpendicular magnetic field as well as the in-plane spin splitting due to the Zeeman interaction and to the exchange coupling possibly induced by the proximity of a ferromagnetic insulator. We find that a single barrier exhibits a wavevector-dependent spin filtering effect at energies close to the transmission threshold. This effect is significantly enhanced in a resonant double barrier configuration, where the spin polarization of the outgoing current can be increased up to 100% by increasing the distance between the barriers

Spreading of correlations and Loschmidt echo after quantum quenches of a Bose gas in the Aubry-Andr\'e potential

We study the spreading of density-density correlations and the Loschmidt echo, after different sudden quenches in an interacting one dimensional Bose gas on a lattice, also in the presence of a superimposed aperiodic potential. We use a time dependent Bogoliubov approach to calculate the evolution of the correlation functions and employ the linked cluster expansion to derive the Loschmidt echo.Comment: 10 pages, 14 figures, a section on momentum distribution function is include

Quasiparticle conductivities in disordered d-wave superconductors

We study the quasiparticle transport coefficients in disordered d-wave superconductors. We find that spin and charge excitations are generally localized unless magnetic impurities are present. If the system is close to a nesting point in the impurity-scattering unitary limit, the tendency towards localization is reduced while the quasiparticle density of states gets enhanced by disorder. We also show that the residual repulsive interaction among quasiparticles has a delocalizing effect and increases the density of states.Comment: 13 pages, no figure

Magnetic confinement of massless Dirac fermions in graphene

Due to Klein tunneling, electrostatic potentials are unable to confine Dirac electrons. We show that it is possible to confine massless Dirac fermions in a monolayer graphene sheet by inhomogeneous magnetic fields. This allows one to design mesoscopic structures in graphene by magnetic barriers, e.g. quantum dots or quantum point contacts.Comment: 4 pages, 3 figures, version to appear in PR