Edge mode dynamics of quenched topological wires.

The fermionic and Majorana edge mode dynamics of various topological systems are compared, after a sudden global quench of the Hamiltonian parameters takes place. Attention is focused on the regimes where the survival probability of an edge state has oscillations either due to critical or off-critical quenches. The nature of the wave functions and the overlaps between the eigenstates of different points in parameter space determine the various types of behaviors, and the distinction due to the Majorana nature of the excitations plays a lesser role. Performing a sequence of quenches, it is shown that the edge states, including Majorana modes, may be switched off and on. Also, the generation of Majoranas due to quenching from a trivial phase is discussed.

Fermi points and topological quantum phase transitions in a multi-band superconductor.

The importance of models with an exact solution for the study of materials with non-trivial topological properties has been extensively demonstrated. The Kitaev model plays a guiding role in the search for Majorana modes in condensed matter systems. Also, the sp-chain with an anti-symmetric mixing among the s and p bands is a paradigmatic example of a topological insulator with well understood properties. Interestingly, these models share the same universality class for their topological quantum phase transitions. In this work we study a two-band model of spinless fermions with attractive inter-band interactions. We obtain its zero temperature phase diagram, which presents a rich variety of phases including a Weyl superconductor and a topological insulator. The transition from the topological to the trivial superconducting phase has critical exponents different from those of Kitaev's model.

Magnetic chains on a triplet superconductor.

The topological state of a two-dimensional triplet superconductor may be changed by an appropriate addition of magnetic impurities. A ferromagnetic magnetic chain at the surface of a superconductor with spin-orbit coupling may eliminate the edge states of a finite system giving rise to localized zero modes at the edges of the chain. The coexistence/competition between the two types of zero modes is considered. The reduction of the system to an effective 1d system gives partial information on the topological properties but the study of the two sets of zero modes requires a two-dimensional treatment. Increasing the impurity density from a magnetic chain to magnetic islands leads to a finite Chern number. At half-filling small concentrations are enough to induce chiral modes.

Singularities of the dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field.

We study the longitudinal and transverse spin dynamical structure factors of the spin-1/2 XXX chain at finite magnetic field h, focusing in particular on the singularities at excitation energies in the vicinity of the lower thresholds. While the static properties of the model can be studied within a Fermi-liquid like description in terms of pseudoparticles, our derivation of the dynamical properties relies on the introduction of a form of the 'pseudofermion dynamical theory' (PDT) of the 1D Hubbard model suitably modified for the spin-only XXX chain and other models with two pseudoparticle Fermi points. Specifically, we derive the exact momentum and spin-density dependences of the exponents ζ(τ)(k) controlling the singularities for both the longitudinal (τ = l) and transverse (τ = t) dynamical structure factors for the whole momentum range k ∈ ]0,π[, in the thermodynamic limit. This requires the numerical solution of the integral equations that define the phase shifts in these exponents expressions. We discuss the relation to neutron scattering and suggest new experiments on spin-chain compounds using a carefully oriented crystal to test our predictions.

Fate of Majorana fermions and Chern numbers after a quantum quench.

In the sequence of quenches to either nontopological phases or other topological phases, we study the stability of Majorana fermions at the edges of a two-dimensional topological superconductor with spin-orbit coupling and in the presence of a Zeeman term. Both instantaneous and slow quenches are considered. In the case of instantaneous quenches, the Majorana modes generally decay, but for a finite system there is a revival time that scales to infinity as the system size grows. Exceptions to this decaying behavior are found in some cases due to the presence of edge states with the same momentum in the final state. Quenches to a topological Z(2) phase reveal some robustness of the Majorana fermions in the sense that even though the survival probability of the Majorana state is small, it does not vanish. If the pairing is not aligned with the spin-orbit Rashba coupling, it is found that the Majorana fermions are fairly robust with a finite survival probability. It is also shown that the Chern number remains invariant after the quench, until the propagation of the mode along the transverse direction reaches the middle point, beyond which the Chern number fluctuates between increasing values. The effect of varying the rate of change in slow quenches is also analyzed. It is found that the defect production is nonuniversal and does not follow the Kibble-Zurek scaling with the quench rate, as obtained before for other systems with topological edge states.

Entanglement entropy and entanglement spectrum of triplet topological superconductors.

We analyze the entanglement entropy properties of a 2D p-wave superconductor with Rashba spin-orbit coupling, which displays a rich phase-space that supports non-trivial topological phases, as the chemical potential and the Zeeman term are varied. We show that the entanglement entropy and its derivatives clearly signal the topological transitions and we find numerical evidence that for this model the derivative with respect to the magnetization provides a sensible signature of each topological phase. Following the area law for the entanglement entropy, we systematically analyze the contributions that are proportional to or independent of the perimeter of the system, as a function of the Hamiltonian coupling constants and the geometry of the finite subsystem. For this model, we show that even though the topological entanglement entropy vanishes, it signals the topological phase transitions in a finite system. We also observe a relationship between a topological contribution to the entanglement entropy in a half-cylinder geometry and the number of edge states, and that the entanglement spectrum has robust modes associated with each edge state, as in other topological systems.

Correlated magnetic impurities in a superconductor: electron density profiles and robustness of superconductivity.

The insertion of magnetic impurities in a conventional superconductor leads to various effects. In this work we show that the electron density is affected by the spins (considered as classical) both locally and globally. The charge accumulation is solved self-consistently. This affects the transport properties along magnetic domain walls. Also, we show that superconductivity is more robust if the spin locations are not random but correlated.

Superconductivity in the Anderson lattice: a finite-U slave boson description.

Using the Kotliar and Ruckenstein slave boson formalism we consider the finite-U Anderson lattice. We study the appearance of superconductivity as a function of the Coulomb repulsion, density and f-level location for s-wave and d-wave pairing symmetries. The results extend previous studies where the infinite-U limit was considered, confirming that superconductivity remains as the Coulomb coupling increases, if the attractive interaction is not weak. Superconductivity disappears for large U as the filling of the heavy particles approaches one, as expected. Since U is finite, superconductivity occurs, in general, for any band-filling being depressed near half-filling, particularly for d-wave symmetry.