Spectral footprints of impurity scattering in graphene nanoribbons

We report a detailed investigation of the interplay between size quantization and local scattering centers in graphene nanoribbons, as seen in the local density of states. The spectral signatures, obtained after Fourier transformation of the local density of states, include characteristic peaks that can be related to the transverse modes of the nanoribbon. In armchair ribbons, the Fourier transformed density of states of one of the two inequivalent sublattices takes a form similar to that of a quantum channel in a two-dimensional electron gas, modified according to the differences in bandstructure. After addition of the second sublattice contribution, a characteristic modulation of the pattern due to superposition is obtained, similar to what has been obtained in spectra due to single impurity scattering in large-area graphene. We present analytic results for the electron propagator in armchair nanoribbons in the Dirac approximation, including a single scattering center within a T-matrix formulation. For comparison, we have extended the investigation with numerics obtained with an atomistic recursive Green's function approach. The spectral signatures of the atomistic approach include the effects of trigonal warping. The impurity induced oscillations in the local density of states are not decaying at large distance in few-mode nanoribbons.Comment: 21 pages, 12 figure

Large Thermoelectric Effects and Inelastic Scattering in Unconventional Superconductors

The thermoelectric coefficient $\eta(T)$ in unconventional superconductors is enhanced below $T_c$ by intermediate strength impurity scattering that is intrinsically particle-hole asymmetric. We compute $\eta(T)$ for a strong-coupling d-wave superconductor and investigate the effects of inelastic scattering originating from electron-boson interactions. We show that $\eta(T)$ is severely suppressed at temperatures just below $T_c$ by a particle-hole symmetric inelastic scattering rate. At lower temperatures inelastic scattering is frozen out and $\eta(T)$ recovers and regains its large amplitude. In the limit $T\to 0$, we have $\eta(T)\sim \eta_{0} T+{\cal O}[T^3]$, where the slope $\eta_{0}$ contains information about the Drude plasma frequency, the details of impurity scattering, and the change in effective mass by electron-boson interactions. In this limit $\eta(T)$ can be used as a probe, complementary to the universal heat and charge conductivities, in investigations of the nature of nodal quasiparticles.Comment: 2 pages, 1 figure, submitted to 24th International Conference on Low Temperature Physic

Large Thermoelectric Effects in Unconventional Superconductors

We present analytic and numerical results for the thermoelectric effect in unconventional superconductors with a dilute random distribution of impurities, each scattering isotropically but with a phase shift intermediate between the Born and unitary limits. The thermoelectric response function has a linear temperature dependence at low temperatures, with a slope that depends on the impurity concentration and phase shift. Although the thermoelectric effect vanishes identically in the strict Born and unitary limits, even a small deviation of the phase shift from these limits leads to a large response, especially in clean systems. We also discuss possibilities of measuring counter-flowing supercurrents in a SQUID-setup. The non-quantized thermoelectrically induced flux can easily be of the order of a percent of the flux quantum in clean systems at 4He temperatures.Comment: 9 pages, 7 figure

Destroyed quantum Hall effect in graphene with [0001] tilt grain boundaries

The reason why the half-integer quantum Hall effect (QHE) is suppressed in graphene grown by chemical vapor deposition (CVD) is unclear. We propose that it might be connected to extended defects in the material and present results for the quantum Hall effect in graphene with [0001] tilt grain boundaries connecting opposite sides of Hall bar devices. Such grain boundaries contain 5-7 ring complexes that host defect states that hybridize to form bands with varying degree of metallicity depending on grain boundary defect density. In a magnetic field, edge states on opposite sides of the Hall bar can be connected by the defect states along the grain boundary. This destroys Hall resistance quantization and leads to non-zero longitudinal resistance. Anderson disorder can partly recover quantization, where current instead flows along returning paths along the grain boundary depending on defect density in the grain boundary and on disorder strength. Since grain sizes in graphene made by chemical vapor deposition are usually small, this may help explain why the quantum Hall effect is usually poorly developed in devices made of this material.Comment: 5 pages, 4 figure

Shot noise in a harmonically driven ballistic graphene transistor

We study time-dependent electron transport and quantum noise in a ballistic graphene field effect transistor driven by an ac gate potential. The non-linear response to the ac signal is computed through Floquet theory for scattering states and Landauer-B\"uttiker theory for charge current and its fluctuations. Photon-assisted excitation of a quasibound state in the top-gate barrier leads to resonances in transmission that strongly influence the noise properties. For strong doping of graphene under source and drain contacts, when electrons are transmitted through the channel via evanescent waves, the resonance leads to a substantial suppression of noise. The Fano factor is then reduced well below the pseudo-diffusive value, $F<1/3$, also for strong ac drive. The good signal-to-noise ratio (small Fano factor) on resonance suggests that the device is a good candidate for high-frequency (THz) radiation detection. We show analytically that Klein tunneling (total suppression of back-reflection) persists for perpendicular incidence also when the barrier is driven harmonically. Although the transmission is inelastic and distributed among sideband energies, a sum rule leads to total suppression of shot noise.Comment: 12 pages, 7 figure

Quantum Hall effect in graphene with twisted bilayer stripe defects

We analyze the quantum Hall effect in single layer graphene with bilayer stripe defects. Such defects are often encountered at steps in the substrate of graphene grown on silicon carbide. We show that AB or AA stacked bilayer stripes result in large Hall conductivity fluctuations that destroy the quantum Hall plateaux. The fluctuations are a result of the coupling of edge states at opposite edges through currents traversing the stripe. Upon rotation of the second layer with respect to the continuous monolayer (a twisted-bilayer stripe defect), such currents decouple from the extended edge states and develop into long-lived discrete quasi bound states circulating around the perimeter of the stripe. Backscattering of edge modes then occurs only at precise resonant energies, and hence the quantum Hall plateaux are recovered as twist angle grows.Comment: 8 pages, 7 figures, published versio

Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.Peer ReviewedPostprint (published version

A finite element method for the quasiclassical theory of superconductivity

The Eilenberger-Larkin-Ovchinnikov-Eliashberg quasiclassical theory of superconductivity is a powerful method enabling studies of a wide range of equilibrium and non-equilibrium phenomena in conventional and unconventional superconductors. We introduce here a finite element method, based on a discontinuous Galerkin approach, to self-consistently solve the underlying transport equations for general device geometries, arbitrary mean free path and symmetry of the superconducting order parameter. We present exemplary results on i) the influence of scalar impurity scattering on phase crystals in $d$-wave superconducting grains at low temperatures and ii) the current flow and focusing in $d$-wave superconducting weak links, modeling recent experimental realizations of grooved high-temperature superconducting Dayem bridges. The high adaptability of this finite element method for quasiclassical theory paves the way for future investigations of superconducting devices and new physical phenomena in unconventional superconductors.Comment: 13 pages, 11 figure

Disorder-robust phase crystal in high-temperature superconductors stabilized by strong correlations

The simultaneous interplay of strong electron-electron correlations, topological zero-energy states, and disorder is yet an unexplored territory but of immense interest due to their inevitable presence in many materials. Copper oxide high-temperature superconductors (cuprates) with pair breaking edges host a flat band of topological zero-energy states, making them an ideal playground where strong correlations, topology, and disorder are strongly intertwined. Here we show that this interplay in cuprates generates a fully gapped 'phase crystal' state that breaks both translational and time-reversal invariance, characterized by a modulation of the d-wave superconducting phase co-existing with a modulating extended s-wave superconducting order. In contrast to conventional wisdom, we find that this phase crystal state is remarkably robust to omnipresent disorder, but only in the presence of strong correlations, thus giving a clear route to its experimental realization