Topological pumping in class-D superconducting wires

We study adiabatic pumping at a normal metal/class-D superconductor hybrid interface when superconductivity is induced through the proximity effect in a spin-orbit coupled nanowire in the presence of a tilted Zeeman field. When the induced order parameter in the nanowire is non-uniform, the phase diagram has isolated trivial regions surrounded by topological ones. We show that in this case the pumped charge is quantized in units of the elementary charge $e$ and has a topological nature.Comment: 7 pages, 6 figures. Published versio

Spin-resolved optical conductivity of two-dimensional group-VIB transition-metal dichalcogenides

We present an ab-initio study of the spin-resolved optical conductivity of two-dimensional (2D) group-VIB transition-metal dichalcogenides (TMDs). We carry out fully-relativistic density-functional-theory calculations combined with maximally localized Wannier functions to obtain band manifolds at extremely high resolutions and focus on the photo-response of 2D TMDs to circularly-polarized light in a wide frequency range. We present extensive numerical results for monolayer TMDs involving molybdenum and tungsten combined with sulphur and selenium. Our numerical approach allows us to locate with a high degree of accuracy the positions of the points in the Brillouin zone that are responsible for van Hove singularities in the optical response. Surprisingly, some of the saddle points do not occur exactly along high-symmetry directions in the Brillouin zone, although they happen to be in their close proximity.Comment: 9 pages, 5 figure

Electron density distribution and screening in rippled graphene sheets

Single-layer graphene sheets are typically characterized by long-wavelength corrugations (ripples) which can be shown to be at the origin of rather strong potentials with both scalar and vector components. We present an extensive microscopic study, based on a self-consistent Kohn-Sham-Dirac density-functional method, of the carrier density distribution in the presence of these ripple-induced external fields. We find that spatial density fluctuations are essentially controlled by the scalar component, especially in nearly-neutral graphene sheets, and that in-plane atomic displacements are as important as out-of-plane ones. The latter fact is at the origin of a complicated spatial distribution of electron-hole puddles which has no evident correlation with the out-of-plane topographic corrugations. In the range of parameters we have explored, exchange and correlation contributions to the Kohn-Sham potential seem to play a minor role.Comment: 13 pages, 13 figures, submitted. High-quality figures can be requested to the author

Electron-hole puddles in the absence of charged impurities

It is widely believed that carrier-density inhomogeneities ("electron-hole puddles") in single-layer graphene on a substrate like quartz are due to charged impurities located close to the graphene sheet. Here we demonstrate by using a Kohn-Sham-Dirac density-functional scheme that corrugations in a real sample are sufficient to determine electron-hole puddles on length scales that are larger than the spatial resolution of state-of-the-art scanning tunneling microscopy.Comment: 5 pages, 3 figures, published versio

Local density of states in metal - topological superconductor hybrid systems

We study by means of the recursive Green's function technique the local density-of-states of (finite and semi-infinite) multi-band spin-orbit coupled semiconducting nanowires in proximity to an s-wave superconductor and attached to normal-metal electrodes. When the nanowire is coupled to a normal electrode, the zero-energy peak, corresponding to the Majorana state in the topological phase, broadens with increasing transmission between the wire and the leads, eventually disappearing for ideal interfaces. Interestingly, for a finite transmission a peak is present also in the normal electrode, even though it has a smaller amplitude and broadens more rapidly with the strength of the coupling. Unpaired Majorana states can survive close to a topological phase transition even when the number of open channels (defined in the absence of superconductivity) is even. We finally study the Andreev-bound-state spectrum in superconductor-normal metal-superconductor junctions and find that in multi-band nanowires the distinction between topologically trivial and non-trivial systems based on the number of zero-energy crossings is preserved.Comment: 11 pages, 12 figures, published versio

Josephson-Majorana cycle in topological single-electron hybrid transistors

Charge transport through a small topological superconducting island in contact with a normal and a superconducting electrode occurs through a cycle that involves coherent oscillations of Cooper pairs and tunneling in/out the normal electrode through a Majorana bound state, the Josephson-Majorana cycle. We illustrate this mechanism by studying the current-voltage characteristics of a superconductor-topological superconductor-normal metal single-electron transistor. At low bias and temperature the Josephson-Majorana cycle is the dominant mechanism for transport. We discuss a three-terminal configuration where the non-local character of the Majorana bound states is emergent.Comment: 6 pages, 4 figure

Engineering polar discontinuities in honeycomb lattices

Unprecedented and fascinating phenomena have been recently observed at oxide interfaces between centrosymmetric cubic materials, such as LaAlO$_3$ and SrTiO$_3$, where a polar discontinuity across the boundary gives rise to polarization charges and electric fields that drive a metal-insulator transition, with the appearance of free carriers at the interface. Two-dimensional analogues of these systems are possible, and honeycomb lattices could offer a fertile playground, thanks to their versatility and the extensive on-going experimental efforts in graphene and related materials. Here we suggest different realistic pathways to engineer polar discontinuities across interfaces between honeycomb lattices, and support these suggestions with extensive first-principles calculations. Two broad approaches are discussed, that are based on (i) nanoribbons, where a polar discontinuity against the vacuum emerges, and (ii) selective functionalizations, where covalent ligands are used to engineer polar discontinuities by selective or total functionalization of the parent system. All the cases considered have the potential to deliver innovative applications in ultra-thin and flexible solar-energy devices and in micro- and nano-electronics.Comment: 12+epsilon pages, 6 figure

Ground-state properties of inhomogeneous graphene sheets

Graphene is a two-dimensional (2D) system of Carbon atoms packed in a honeycomb lattice. The recent isolation of this one-atom thick crystal has attracted considerable attention, both for the new physics which it exhibits and because it may pave the way for carbon-based electronics. In the absence of doping, graphene is a gapless semiconductor in which the conduction and valence bands touch at two inequivalent points, called Dirac points, at the corners of the hexagonal Brillouin zone. Near either of these points the energy bands are conical and the electronic states are described by a massless Dirac equation, in which the spin degree-of-freedom is replaced by a sublattice degree-of-freedom, referred to in the literature as \emph{pseudospin}. Most importantly, this implies that the eigenstates are endowed with a definite chirality, i.e. a well defined projection of the pseudospin along the momentum direction. Recent experiments have demonstrated that close to charge neutrality the system is highly inhomogeneous and breaks up into electron and hole puddles. One key challenge for graphene research has been the identification of the main source of scattering which induces these density modulations and limits the mobility of current samples. Even though the problem is not yet fully understood, it has been recognized that the approximately linear dependence of conductivity on carrier density suggests that charged impurities trapped close to the graphene sheet could play a very important role in limiting graphene's mobility, partly obscuring the intrinsic properties of graphene's massless Dirac fermions (MDFs). In this Thesis we discuss two different issues related to disorder in current graphene samples. On the one hand, we propose to engineer artificially systems of MDFs in standard parabolic-band 2D electron gases by employing suitable periodic external potentials. This route to create "artificial graphene" offers potentially unprecedented opportunities to study fundamental interactions of MDFs in high-mobility semiconductor structures. On the other hand, we provide a microscopic study (accounting for electron-electron interactions) of the impact of charged impurities on the density profiles and local density-of-states of ordinary exfoliated graphene sheets deposited on substrates such as Silicon dioxide. In the first Chapter we review some fundamental aspects concerning the quantum theory of the electron liquid. Particular attention is given to linear response theory, Landau theory of normal Fermi liquids, and density functional theory. Chapter 2 is devoted to the properties of graphene in the absence of disorder, i.e. to "homogeneous" graphene. We first review the electronic single-particle band structure of graphene and then comment on the impact of electron-electron interactions at the level of the random phase approximation. In the last section we present the main original result of this Chapter (Gibertini et al. arXiv:0904.4191v1 and Phys. Rev. B 79 (R), in press): we show that modulating a standard 2D electron gas with a long-wavelength external periodic potential with hexagonal symmetry can lead to the creation of isolated massless Dirac points with tunable Fermi velocity. We provide detailed theoretical estimates to realize such artificial graphene-like system and discuss an experimental realization in a modulation-doped GaAs quantum well. In the last Chapter we consider the effects of disorder on standard exfoliated graphene samples on Silicon dioxide substrates. After a brief introduction to the main experimental results, we first review a Kohn-Sham-Dirac (KSD) density-functional-theory scheme [Polini et al., Phys. Rev. B 78, 115426 (2008)] that treats slowly-varying external potentials and electron-electron interactions on an equal footing. We then report on original continuum-model electronic structure calculations based on the KSD scheme for graphene sheets under the influence of local scatterers distributed in space in the same way as in the sample studied experimentally by Zhang et. al. (arXiv:0902.4793v1). We first verify the reliability of the spectroscopic method used by Zhang et. al. to measure density and then assess what can be learned about the nature of these scatterers based on the detailed comparison between theory and experiment (Gibertini et. al., in preparation)

Band-like Electron Transport with Record-High Mobility in the TCNQ family

In highest quality organic single-crystal field-effect transistors, electron transport occurs in the band-like regime, with the carrier mobility increasing upon lowering temperature. Neither the microscopic nature of this regime, nor why it occurs only in a small number of materials is currently understood. Here, comparative studies of closely related materials, exhibiting high-quality reproducible transport properties are needed. We performed a study of electron transport in single-crystals of different TCNQ (tetracyanoquinodimethane) molecules, combined with band structure calculations. We show that F2-TCNQ devices exhibit very high electron mobility and an unprecedented increase in mobility upon cooling, whereas in TCNQ and F4-TCNQ the mobility is substantially lower and decreases upon cooling. We analyze the crystal and electronic structures of these materials and find that F2-TCNQ crystals are indeed ideal to achieve outstanding transport properties. Our analysis also shows that to understand the difference between the three materials, studying their band structure is not sufficient, and that the electron-phonon coupling needs to be investigated as well. Besides the outstanding transport properties of F2-TCNQ, a key result of our work is the identification of the Fx-TCNQ family as a paradigm to investigate the most fundamental aspects of electronic transport in organic crystals

Accurate prediction of Hall mobilities in two-dimensional materials through gauge-covariant quadrupolar contributions

Despite considerable efforts, accurate computations of electron-phonon and carrier transport properties of low-dimensional materials from first principles have remained elusive. By building on recent advances in the description of long-range electrostatics, we develop a general approach to the calculation of electron-phonon couplings in two-dimensional materials. We show that the nonanalytic behavior of the electron-phonon matrix elements depends on the Wannier gauge, but that a missing Berry connection restores invariance to quadrupolar order. We showcase these contributions in a MoS$_2$ monolayer, calculating intrinsic drift and Hall mobilities with precise Wannier interpolations. We also find that the contributions of dynamical quadrupoles to the scattering potential are essential, and that their neglect leads to errors of 23% and 76% in the room temperature electron and hole Hall mobilities, respectively.Comment: 6 pages and 2 figure