Nanomechanical characterization of quantum interference in a topological insulator nanowire

The discovery of two-dimensional gapless Dirac fermions in graphene and topological insulators (TI) has sparked extensive ongoing research toward applications of their unique electronic properties. The gapless surface states in three-dimensional insulators indicate a distinct topological phase of matter with a non-trivial Z2 invariant that can be verified by angle-resolved photoemission spectroscopy or magnetoresistance quantum oscillation. In TI nanowires, the gapless surface states exhibit Aharonov-Bohm (AB) oscillations in conductance, with this quantum interference effect accompanying a change in the number of transverse one-dimensional modes in transport. Thus, while the density of states (DOS) of such nanowires is expected to show such AB oscillation, this effect has yet to be observed. Here, we adopt nanomechanical measurements that reveal AB oscillations in the DOS of a topological insulator. The TI nanowire under study is an electromechanical resonator embedded in an electrical circuit, and quantum capacitance effects from DOS oscillation modulate the circuit capacitance thereby altering the spring constant to generate mechanical resonant frequency shifts. Detection of the quantum capacitance effects from surface-state DOS is facilitated by the small effective capacitances and high quality factors of nanomechanical resonators, and as such the present technique could be extended to study diverse quantum materials at nanoscale.Comment: 15+16 pages, 4+11 figure

The self-consistent quantum-electrostatic problem in strongly non-linear regime

The self-consistent quantum-electrostatic (also known as Poisson-Schr\"odinger) problem is notoriously difficult in situations where the density of states varies rapidly with energy. At low temperatures, these fluctuations make the problem highly non-linear which renders iterative schemes deeply unstable. We present a stable algorithm that provides a solution to this problem with controlled accuracy. The technique is intrinsically convergent including in highly non-linear regimes. We illustrate our approach with (i) a calculation of the compressible and incompressible stripes in the integer quantum Hall regime and (ii) a calculation of the differential conductance of a quantum point contact geometry. Our technique provides a viable route for the predictive modeling of the transport properties of quantum nanoelectronics devices.Comment: 28 pages. 14 figures. Added solution to a potential failure mode of the algorith

Eigenmode-based capacitance calculations with applications in passivation layer design

The design of high-speed metallic interconnects such as microstrips requires the correct characterization of both the conductors and the surrounding dielectric environment, in order to accurately predict their propagation characteristics. A fast boundary integral equation approach is obtained by modeling all materials as equivalent surface charge densities in free space. The capacitive behavior of a finite dielectric environment can then be determined by means of a transformation matrix, relating these charge densities to the boundary value of the electric potential. In this paper, a new calculation method is presented for the important case that the dielectric environment is composed of homogeneous rectangles. The method, based on a surface charge expansion in terms of the Robin eigenfunctions of the considered rectangles, is not only more efficient than traditional methods, but is also more accurate, as shown in some numerical experiments. As an application, the design and behavior of a microstrip passivation layer is treated in some detail

Nanoscale Dielectric Capacitors Composed of Graphene and Boron Nitride Layers: A First Principles Study of High-Capacitance at Nanoscale

We investigate a nanoscale dielectric capacitor model consisting of two-dimensional, hexagonal h-BN layers placed between two commensurate and metallic graphene layers using self-consistent field density functional theory. The separation of equal amounts of electric charge of different sign in different graphene layers is achieved by applying electric field perpendicular to the layers. The stored charge, energy, and the electric potential difference generated between the metallic layers are calculated from the first-principles for the relaxed structures. Predicted high-capacitance values exhibit the characteristics of supercapacitors. The capacitive behavior of the present nanoscale model is compared with that of the classical Helmholtz model, which reveals crucial quantum size effects at small separations, which in turn recede as the separation between metallic planes increases.Comment: Published version in The Journal of Physical Chemistry: http://pubs.acs.org/doi/abs/10.1021/jp403706