Abstract: Electron transport through multiterminal rectangular arrays of quantum rings is studied in the presence of Rashba-type spin-orbit interaction (SOI) and of a perpendicular magnetic field. Using the analytic expressions for the transmission and reflection coefficients for single rings we obtain the conductance through such arrays as a function of the SOI strength, of the magnetic flux, and of the wave vector k of the incident electron. Due to destructive or constructive spin interferences caused by the SOI, the array can be totally opaque for certain ranges of k, while there are parameter values where it is completely transparent. Spin resolved transmission probabilities show nontrivial spin transformations at the outputs of the arrays. When pointlike random scattering centers are placed between the rings, the Aharonov-Bohm peaks split, and an oscillatory behavior of the conductance emerges as a function of the SOI strength.

Abstract: Nanoscale corrugation is a fundamental property of graphene arising from its low-dimensional nature. It places a fundamental limit to the conductivity of graphene and influences its properties. However the degree of the influence of the corrugation has not been well established because of the little knowledge about its spectrum in suspended graphene. We present a transmission electron microscopy technique that enables us to measure the average corrugation height and length. We applied the technique also to measure the temperature dependence of the corrugation. The difference in corrugation between suspended and supported graphene has been illustrated.

Abstract: The strain-induced pseudomagnetic field in supported graphene deposited on top of a nanostructured substrate is investigated by using atomistic simulations. A step, an elongated trench, a one-dimensional barrier, a spherical bubble, a Gaussian bump, and a Gaussian depression are considered as support structures for graphene. From the obtained optimum configurations we found very strong induced pseudomagnetic fields which can reach up to similar to 1000 T due to the strain-induced deformations in the supported graphene. Different magnetic confinements with controllable geometries are found by tuning the pattern of the substrate. The resulting induced magnetic fields for graphene on top of a step, barrier, and trench are calculated. In contrast to the step and trench the middle part of graphene on top of a barrier has zero pseudomagnetic field. This study provides a theoretical background for designing magnetic structures in graphene by nanostructuring substrates. We found that altering the radial symmetry of the deformation changes the sixfold symmetry of the induced pseudomagnetic field.

Abstract: Monte Carlo (MC) methods have a long-standing history as partners of molecular dynamics (MD) to simulate the evolution of materials at the atomic scale. Among these techniques, the uniform-acceptance force-bias Monte Carlo (UFMC) method [ G. Dereli Mol. Simul. 8 351 (1992)] has recently attracted attention [ M. Timonova et al. Phys. Rev. B 81 144107 (2010)] thanks to its apparent capacity of being able to simulate physical processes in a reduced number of iterations compared to classical MD methods. The origin of this efficiency remains, however, unclear. In this work we derive a UFMC method starting from basic thermodynamic principles, which leads to an intuitive and unambiguous formalism. The approach includes a statistically relevant time step per Monte Carlo iteration, showing a significant speed-up compared to MD simulations. This time-stamped force-bias Monte Carlo (tfMC) formalism is tested on both simple one-dimensional and three-dimensional systems. Both test-cases give excellent results in agreement with analytical solutions and literature reports. The inclusion of a time scale, the simplicity of the method, and the enhancement of the time step compared to classical MD methods make this method very appealing for studying the dynamics of many-particle systems.

Abstract: The effective Hamiltonian for an electron in a quasi-one-dimensional quantum ring in the presence of spin-orbit interactions is derived. We demonstrate that, when both coupling types are simultaneously present, the effective Hamiltonian derived by the lowest-radial-state approximation produces energy spectra and charge densities which deviate strongly from the exact ones. For equal Rashba and Dresselhaus coupling constants the lowest-radial-state approximation opens artifactal avoided crossings in the energy spectra and deforms the circular symmetry of the confined charge densities. In this case, there does not exist a ring thin enough to justify the restriction to the lowest radially quantized energy state. We derive the effective Hamiltonian accounting for both the lowest and the first excited radial states, and show that the inclusion of the latter restores the correct features of the exact solution. Relation of this result to the states of a quantum wire is also discussed.

Abstract: We investigate low-temperature magnetotransport of high-mobility two-dimensional electron gases subjected to one-dimensional periodic magnetic and electric modulations. Our previous quantum perturbation theory is extended to lower temperatures and the energy broadening due to impurity scattering is incorporated. Numerical calculations are made for situations where several Landau bands overlap. We find that the Shubnikov-de Haas (SdH) oscillations are dominated by collisional resistance. The amplitudes of the SdH oscillations are strongly modulated and the positions of the SdH minima switch between even and odd Landau-level filling factors, in the resistance both parallel and perpendicular to the one-dimensional modulation. This is a consequence of the internal structure (i.e., smeared out van Hove singularities) of overlapping Landau bands. Our theoretical results are in good agreement with recent experiments.

Abstract: A microscopic theory for the coupling of molecular orientations with acoustic lattice displacements is proposed. The relevant interaction is quadratic in the orientational-order-parameter variables and linear in longitudinal strains. The coupling is evaluated for a complex molecular structure. The intermolecular potential is obtained from interaction centers placed at nuclei and at the centers of interatomic bonds. The free energy is derived and the experimental consequences of the theory are studied. The Clausius-Clapeyron equation for orientational melting is obtained. The theory explains the decrease of the lattice constant at the first-order phase transition and the increase of the transition temperature with applied pressure.