Missing derivative discontinuity of the exchange-correlation energy for attractive interactions: the charge Kondo effect

We show that the energy functional of ensemble Density Functional Theory (DFT) [Perdew et al., Phys. Rev. Lett. 49, 1691 (1982)] in systems with attractive interactions is a convex function of the fractional particle number N and is given by a series of straight lines joining a subset of ground-state energies. As a consequence the exchange-correlation (XC) potential is not discontinuous for all N. We highlight the importance of this exact result in the ensemble-DFT description of the negative-U Anderson model. In the atomic limit the discontinuity of the XC potential is missing for odd N while for finite hybridizations the discontinuity at even N is broadened. We demonstrate that the inclusion of these properties in any approximate XC potential is crucial to reproduce the characteristic signatures of the charge-Kondo effect in the conductance and charge susceptibility.Comment: 5 pages, 5 eps figure. Phys. Rev. B 86, 081409(R) (2012

Dynamical formation and manipulation of Majorana fermions in driven quantum wires

Controlling the dynamics of Majorana fermions (MF) subject to time-varying driving fields is of fundamental importance for the practical realization of topological quantum computing. In this work we study how it is possible to dynamically generate and maintain the topological phase in one-dimensional superconducting nanowires after the temporal variation of the Hamiltonian parameters. Remarkably we show that for a sudden quench the system can never relax towards a state exhibiting fully developed MF, independently of the initial and final Hamiltonians. Only for sufficiently slow protocols the system behaves adiabatically, and the topological phase can be reached. Finally we address the crucial question of how "adiabatic" a protocol must be in order to manipulate the MF inside the topological phase without deteriorating their Majorana character.Comment: 5 pages, 4 eps figure

The dissection algorithm for the second-Born self-energy

We describe an algorithm to efficiently compute the second-Born self-energy of many-body perurbation theory. The core idea consists in dissecting the set of all four-index Coulomb integrals into properly chosen subsets, thus avoiding to loop over those indices for which the Coulomb integrals are zero or negligible. The scaling properties of the algorithm with the number of basis functions is discussed. The computational gain is demonstrated in the case of one-particle Kohn-Sham basis for organic molecules.Comment: 6 pages, contribution to the proceedings of the workshop "Progress in Nonequilibrium Green's Function VII

A theory of superconductivity in multi-walled carbon nanotubes

We devise an approach to describe the electronic instabilities of doped multi-walled nanotubes, where each shell has in general a manifold of Fermi points. Our analysis relies on the scale dependence of the different scattering processes, showing that a pairing instability arises for a large enough number of Fermi points as a consequence of their particular geometric arrangement. The instability is enhanced by the tunneling of Cooper pairs between nearest shells, giving rise to a transition from the Luttinger liquid to a superconducting state in a wide region of the phase diagram.Comment: 4 pages, 2 figures, replaced with revised versio

Transient dynamics in the Anderson-Holstein model with interfacial screening

We study the combined effects of electron-phonon coupling and dot-lead repulsion in the transport properties of the Anderson-Holstein model. We employ a recently proposed nonperturbative method to calculate the transient response of the system. By varying the initial conditions for the time propagation the current exhibits transient oscillations of different nature. We are able to disentangle two dynamical processes, namely the local charge rearrangement due to the dot-lead contacting and the establishment of the nonequilbrium many-body state due to the application of the external bias. These processes involve either Franck-Condon excitations or transitions between the resonant level and the Fermi energy of the leads.Comment: 6 pages, 6 figure

CHEERS: A tool for Correlated Hole-Electron Evolution from Real-time Simulations

We put forward a practical nonequilibrium Green's function (NEGF) scheme to perform real-time evolutions of many-body interacting systems driven out of equilibrium by external fields. CHEERS is a computational tool to solve the NEGF equation of motion in the so called generalized Kadanoff-Baym ansatz and it can be used for model systems as well as first-principles Hamiltonians. Dynamical correlation (or memory) effects are added to the Hartree-Fock dynamics through a many-body self-energy. Applications to time-dependent quantum transport, time-resolved photoabsorption and other ultrafast phenomena are discussed.Comment: 15 pages, 6 figures, to be published, J. Phys.: Condens. Matter (2018

Time-dependent transport in graphene nanoribbons

We theoretically investigate the time-dependent ballistic transport in metallic graphene nanoribbons after the sudden switch-on of a bias voltage $V$. The ribbon is divided in three different regions, namely two semi-infinite graphenic leads and a central part of length $L$, across which the bias drops linearly and where the current is calculated. We show that during the early transient time the system behaves like a graphene bulk under the influence of a uniform electric field $E=V/L$. In the undoped system the current does not grow linearly in time but remarkably reaches a temporary plateau with dc conductivity $\sigma_{1}=\pi e^{2}/2h$, which coincides with the minimal conductivity of two-dimensional graphene. After a time of order $L/v_{F}$ ($v_{F}$ being the Fermi velocity) the current departs from the first plateau and saturates at its final steady state value with conductivity $\sigma_{2}=2e^{2}/h$ typical of metallic nanoribbons of finite width.Comment: 5 pages, 5 figure

Unconventional quasiparticle lifetime in undoped graphene

We address the question of how small can the quasiparticle decay rate be at low energies in undoped graphene, where kinematical constraints are known to prevent the decay into particle-hole excitations. For this purpose, we study the renormalization of the phonon dispersion by many-body effects, which turns out to be very strong in the case of the out-of-plane phonons at the K point of the spectrum. We show that these evolve into a branch of very soft modes that provide the relevant channel for quasiparticle decay, at energies below the scale of the optical phonon modes. In this regime, we find that the decay rate is proportional to the cube of the quasiparticle energy. This implies that a crossover should be observed in transport properties from the linear dependence characteristic of the high-energy regime to the much slower decay rate due to the soft phonon modes.Comment: 5 pages, 1 figur