On localization of Dirac fermions by disorder

This thesis is devoted to the effects of disorder on two-dimensional systems of Dirac fermions. Disorder localizes the usual electron system governed by the Schroedinger equation. The influence of disorder on Dirac fermions is qualitevely different. We concentrate on a random mass term in the Dirac equation. We have discovered that Dirac fermions in graphene are localized by a random mass, without any transition into metallic state. The situation is entirely different for Dirac fermions in a p-wave superconductor. There electrostatic disorder appears in the Dirac equation as a random mass, which localizes the excitation, but only if the disorder is relatively weak. For large mass fluctuations a transition into metallic state appears. This qualitatively different response to disorder in graphene and in p-wave superconductors is explained by the appearance of Majorana bound states, which allow for resonant tunneling and metallic state. Electrostatic disorder in a d-wave superconductor represented as random vector potential in the Dirac equation. We look at the transmission of Dirac fermions for electrostatic potential with long- and short-range fluctuations. We study the interplay of electrical and mechanical properties of suspended graphene by calculating the correction to the conductivity due to its deformation by a gate electrode.Foundation for Fundamental Research of MatterUBL - phd migration 201

Effects of disorder on the transmission of nodal fermions through a d-wave superconductor

APR 26Theoretical Physic

Scaling determination of the nonlinear I-V characteristics for 2D superconducting networks

It is shown from computer simulations that the current-voltage ($I$-$V$) characteristics for the two-dimensional XY model with resistively-shunted Josephson junction dynamics and Monte Carlo dynamics obeys a finite-size scaling form from which the nonlinear $I$-$V$ exponent $a$ can be determined to good precision. This determination supports the conclusion $a=z+1$, where $z$ is the dynamic critical exponent. The results are discussed in the light of the contrary conclusion reached by Tang and Chen [Phys. Rev. B {\bf 67}, 024508 (2003)] and the possibility of a breakdown of scaling suggested by Bormann [Phys. Rev. Lett. {\bf 78}, 4324 (1997)].Comment: 6 pages, to appear in PR

Dynamical symmetry breaking in a 2D electron gas with a spectral node

We study a disordered 2D electron gas with a spectral node in a vicinity of the node. After identifying the fundamental dynamical symmetries of this system, the spontaneous breaking of the latter by a Grassmann field is studied within a nonlinear sigma model approach. This allows us to reduce the average two-particle Green's function to a diffusion propagator with a random diffusion coefficient. The latter has non-degenerate saddle points and is treated by the conventional self-consistent Born approximation. This leads to a renormalized chemical potential and a renormalized diffusion coefficient, where the DC conductivity increases linearly with the density of quasiparticles. Applied to the special case of Dirac fermions, our approach provides a comprehensive description of the minimal conductivity at the Dirac node as well as for the V-shape conductivity inside the bands.Comment: 13 pages, 4 figures, extended versio

Eigenfrequencies of the randomly pinned drum and conductivity of graphene

Graphene is a convenient material for nanomechanical applications since high-frequency oscillations are easily accessible. In this article, we consider graphene on a rough substrate attached to imperfections at random locations. We explore the statistics of low-lying phonon modes, which exert most influence on the conductivity of graphene. Our numerics suggest the hypothesis that the nearest-neighbor spacings of low-lying eigenfrequencies have the Wigner-Dyson probability distribution after averaging over the random configurations of disorder. Due to interaction of electrons with the oscillations of the membrane, an electron can be transferred to higher or lower energies, which is a manifestation of the phonon-assisted Tien-Gordon effect. The Tien-Gordon effect suppresses the conductivity of graphene. In the regime of low Fermi energies and small sizes of the sample an increase of conductivity is observed which we refer to as Klein tunneling and electron-hole pair creation. Eventually, when the increase of the transmission becomes too prominent, the pair creation changes the ground state of the system, signalizing the limit of applicability of the single-particle Dirac equation used in this article.QN/Quantum NanoscienceApplied Science