Decreasing excitation gap in Andreev billiards by disorder scattering

We investigate the distribution of the lowest-lying energy states in a disordered Andreev billiard by solving the Bogoliubov-de Gennes equation numerically. Contrary to conventional predictions we find a decrease rather than an increase of the excitation gap relative to its clean ballistic limit. We relate this finding to the eigenvalue spectrum of the Wigner-Smith time delay matrix between successive Andreev reflections. We show that the longest rather than the mean time delay determines the size of the excitation gap. With increasing disorder strength the values of the longest delay times increase, thereby, in turn, reducing the excitation gap.Comment: 6 pages, 5 figures, submitted to EP

Photovoltaic effect in an electrically tunable van der Waals heterojunction

Semiconductor heterostructures form the cornerstone of many electronic and optoelectronic devices and are traditionally fabricated using epitaxial growth techniques. More recently, heterostructures have also been obtained by vertical stacking of two-dimensional crystals, such as graphene and related two- dimensional materials. These layered designer materials are held together by van der Waals forces and contain atomically sharp interfaces. Here, we report on a type- II van der Waals heterojunction made of molybdenum disulfide and tungsten diselenide monolayers. The junction is electrically tunable and under appropriate gate bias, an atomically thin diode is realized. Upon optical illumination, charge transfer occurs across the planar interface and the device exhibits a photovoltaic effect. Advances in large-scale production of two-dimensional crystals could thus lead to a new photovoltaic solar technology.Comment: 26 pages, 14 figures, Nano Letters 201

Non-retracing orbits in Andreev billiards

The validity of the retracing approximation in the semiclassical quantization of Andreev billiards is investigated. The exact energy spectrum and the eigenstates of normal-conducting, ballistic quantum dots in contact with a superconductor are calculated by solving the Bogoliubov-de Gennes equation and compared with the semiclassical Bohr-Sommerfeld quantization for periodic orbits which result from Andreev reflections. We find deviations that are due to the assumption of exact retracing electron-hole orbits rather than the semiclassical approximation, as a concurrently performed Einstein-Brillouin-Keller quantization demonstrates. We identify three different mechanisms producing non-retracing orbits which are directly identified through differences between electron and hole wave functions.Comment: 9 pages, 12 figures, Phys. Rev. B (in print), high resolution images available upon reques

Graphene quantum dots: Beyond a Dirac billiard

We present realistic simulations of quantum confinement effects in ballistic graphene quantum dots with linear dimensions of 10 to 40 nm. We determine wavefunctions and energy level statistics in the presence of disorder resulting from edge roughness, charge impurities, or short-ranged scatterers. Marked deviations from a simple Dirac billiard for massless fermions are found. We find a remarkably stable dependence of the nearest-neighbor level spacing on edge roughness suggesting that the roughness of fabricated devices can be potentially characterized by the distribution of measured Coulomb blockade peaks.Comment: 5 figures, higher resolution available upon reques

Machine learning sparse tight-binding parameters for defects

We employ machine learning to derive tight-binding parametrizations for the electronic structure of defects. We test several machine learning methods that map the atomic and electronic structure of a defect onto a sparse tight-binding parameterization. Since Multi-layer perceptrons (i.e., feed-forward neural networks) perform best we adopt them for our further investigations. We demonstrate the accuracy of our parameterizations for a range of important electronic structure properties such as band structure, local density of states, transport and level spacing simulations for two common defects in single layer graphene. Our machine learning approach achieves results comparable to maximally localized Wannier functions (i.e., DFT accuracy) without prior knowledge about the electronic structure of the defects while also allowing for a reduced interaction range which substantially reduces calculation time. It is general and can be applied to a wide range of other materials, enabling accurate large-scale simulations of material properties in the presence of different defects

Electrostatically confined monolayer graphene quantum dots with orbital and valley splittings

The electrostatic confinement of massless charge carriers is hampered by Klein tunneling. Circumventing this problem in graphene mainly relies on carving out nanostructures or applying electric displacement fields to open a band gap in bilayer graphene. So far, these approaches suffer from edge disorder or insufficiently controlled localization of electrons. Here we realize an alternative strategy in monolayer graphene, by combining a homogeneous magnetic field and electrostatic confinement. Using the tip of a scanning tunneling microscope, we induce a confining potential in the Landau gaps of bulk graphene without the need for physical edges. Gating the localized states towards the Fermi energy leads to regular charging sequences with more than 40 Coulomb peaks exhibiting typical addition energies of 7-20 meV. Orbital splittings of 4-10 meV and a valley splitting of about 3 meV for the first orbital state can be deduced. These experimental observations are quantitatively reproduced by tight binding calculations, which include the interactions of the graphene with the aligned hexagonal boron nitride substrate. The demonstrated confinement approach appears suitable to create quantum dots with well-defined wave function properties beyond the reach of traditional techniques