Conductance fluctuations in graphene in the presence of long-range disorder.

The fluctuations in the conductance of graphene that arise from a long-range disorder potential induced by random impurities are investigated with an atomic tight-binding lattice. The screened impurities lead to a slow variation of the background potential and this varies the overall potential landscape as the Fermi energy or an applied magnetic field is varied. As a result, the phase interference varies randomly and leads to fluctuations in the conductance. Recently, experiments have shown that an applied magnetic field produces a remarkable reduction in the amplitude of these conductance fluctuations. We find qualitative agreement with these experiments, and it appears that the reduction in magnetic field of the fluctuations arises from a field induced smoothing of the conductance landscape.

Relativistic quantum scars.

The concentrations of wave functions about classical periodic orbits, or quantum scars, are a fundamental phenomenon in physics. An open question is whether scarring can occur in relativistic quantum systems. To address this question, we investigate confinements made of graphene whose classical dynamics are chaotic and find unequivocal evidence of relativistic quantum scars. The scarred states can lead to strong conductance fluctuations in the corresponding open quantum dots via the mechanism of resonant transmission.

Rigid ion model of high field transport in GaN.

Here we report on high field transport in GaN based on the rigid ion model of the electron-phonon interaction within the cellular Monte Carlo (CMC) approach. Using the rigid pseudo-ion method for the cubic zinc-blende and hexagonal wurtzite structures, the anisotropic deformation potentials are derived from the electronic structure, the atomic pseudopotential and the full phonon dispersion and eigenvectors for both acoustic and optical modes. Several different electronic structure and lattice dynamics models are compared, as well as different models for the interpolation of the atomic pseudopotentials required in the rigid pseudo-ion method. Piezoelectric as well as anisotropic polar optical phonon scattering is accounted for as well. In terms of high field transport, the peak velocity is primarily determined by deformation potential scattering described through the rigid pseudo-ion model. The calculated velocity is compared with experimental data from pulsed I-V measurements. Good agreement is found using the rigid ion model to the measured velocity-field characteristics with the inclusion of dislocation and ionized impurity scattering. The crystal orientation of the electric field is investigated, where very little difference is observed in the velocity-field characteristics. We simulate the effects of nonequilibrium hot phonons on the energy relaxation as well, using a detailed balance between emission and absorption during the simulation, and an anharmonic decay of LO phonons to acoustic phonons, as reported previously. Nonequilibrium phonons are shown to result in a significant degradation of the velocity-field characteristics for high carrier densities, such as those encountered at the AlGaN/GaN interface due to polarization effects.

Transmission and scarring in graphene quantum dots.

We study electronic transport in quantum-dot structures made of graphene. Focusing on the rectangular dot geometry and utilizing the non-equilibrium Green's function to calculate the transmission in the tight-binding framework, we find significant fluctuations in the transmission as a function of the electron energy. The fluctuations are correlated with the formation of quantum scarring states, or pointer states in the dot. Both enhancement and suppression of transmission have been observed. As the size of the quantum dot is increased, more scarring states can be formed, leading to stronger transmission or conductance fluctuations.

Tunneling and nonhyperbolicity in quantum dots.

We argue that many major features in electronic transport in realistic quantum dots are not explainable by the usual semiclassical approach, due to the contributions of the quantum-mechanical tunneling of the electrons through the Kolmogorov-Arnol'd-Moser islands. We show that dynamical tunneling gives rise to a set of resonances characterized by two quantum numbers, which leads to conductance oscillations and concentration of wave functions near stable and unstable periodic orbits. Experimental results agree very well with our theoretical predictions, indicating that tunneling has to be taken into account to understand the physics of transport in generic nanostructures.