93 research outputs found
Extended topological group structure due to average reflection symmetry
We extend the single-particle topological classification of insulators and
superconductors to include systems in which disorder preserves average
reflection symmetry. We show that the topological group structure of bulk
Hamiltonians and topological defects is exponentially extended when this
additional condition is met, and examine some of its physical consequences.
Those include localization-delocalization transitions between topological
phases with the same boundary conductance, as well as gapless topological
defects stabilized by average reflection symmetry.Comment: 8 pages, 5 figures, 1 table; improved section 4 "Extended topological
classification" incl. example of stacked QSH layer
Twisted Fermi surface of a thin-film Weyl semimetal
The Fermi surface of a conventional two-dimensional electron gas is
equivalent to a circle, up to smooth deformations that preserve the orientation
of the equi-energy contour. Here we show that a Weyl semimetal confined to a
thin film with an in-plane magnetization and broken spatial inversion symmetry
can have a topologically distinct Fermi surface that is twisted into a
\mbox{figure-8} opposite orientations are coupled at a crossing which is
protected up to an exponentially small gap. The twisted spectral response to a
perpendicular magnetic field is distinct from that of a deformed Fermi
circle, because the two lobes of a \mbox{figure-8} cyclotron orbit give
opposite contributions to the Aharonov-Bohm phase. The magnetic edge channels
come in two counterpropagating types, a wide channel of width and a narrow channel of width (with
the magnetic length and the momentum separation
of the Weyl points). Only one of the two is transmitted into a metallic
contact, providing unique magnetotransport signatures.Comment: V4: 10 pages, 14 figures. Added figure and discussion about
"uncrossing deformations" of oriented contours, plus minor corrections.
Published in NJ
Minimal conductivity in bilayer graphene
Using the Landauer formula approach, it is proven that minimal conductivity
of order of found experimentally in bilayer graphene is its intrinsic
property. For the case of ideal crystals, the conductivity turns our to be
equal to per valley per spin. A zero-temperature shot noise in
bilayer graphene is considered and the Fano factor is calculated. Its value
is close to the value 1/3 found earlier for the single-layer
graphene.Comment: 3 pages, 1 figur
How spin-orbit interaction can cause electronic shot noise
The shot noise in the electrical current through a ballistic chaotic quantum
dot with N-channel point contacts is suppressed for N --> infinity, because of
the transition from stochastic scattering of quantum wave packets to
deterministic dynamics of classical trajectories. The dynamics of the electron
spin remains quantum mechanical in this transition, and can affect the
electrical current via spin-orbit interaction. We explain how the role of the
channel number N in determining the shot noise is taken over by the ratio
l_{so}/lambda_F of spin precession length l_{so} and Fermi wave length
lambda_F, and present computer simulations in a two-dimensional billiard
geometry (Lyapunov exponent alpha, mean dwell time tau_{dwell}, point contact
width W) to demonstrate the scaling (lambda_F/l_{so})^{1/alpha tau_{dwell}} of
the shot noise in the regime lambda_F << l_{so} << W.Comment: 4 pages, 3 figure
Bimodal conductance distribution of Kitaev edge modes in topological superconductors
A two-dimensional superconductor with spin-triplet p-wave pairing supports
chiral or helical Majorana edge modes with a quantized (length -independent)
thermal conductance. Sufficiently strong anisotropy removes both chirality and
helicity, doubling the conductance in the clean system and imposing a
super-Ohmic decay in the presence of disorder. We explain the
absence of localization in the framework of the Kitaev Hamiltonian, contrasting
the edge modes of the two-dimensional system with the one-dimensional Kitaev
chain. While the disordered Kitaev chain has a log-normal conductance
distribution peaked at an exponentially small value, the Kitaev edge has a
bimodal distribution with a second peak near the conductance quantum. Shot
noise provides an alternative, purely electrical method of detection of these
charge-neutral edge modes.Comment: 11 pages, 13 figure
Absence of a metallic phase in charge-neutral graphene with a random gap
It is known that fluctuations in the electrostatic potential allow for
metallic conduction (nonzero conductivity in the limit of an infinite system)
if the carriers form a single species of massless two-dimensional Dirac
fermions. A nonzero uniform mass opens up an excitation gap,
localizing all states at the Dirac point of charge neutrality. Here we
investigate numerically whether fluctuations in
the mass can have a similar effect as potential fluctuations, allowing for
metallic conduction at the Dirac point. Our negative conclusion confirms
earlier expectations, but does not support the recently predicted metallic
phase in a random-gap model of graphene.Comment: 3 pages, 3 figure
Solid rocket booster internal flow analysis by highly accurate adaptive computational methods
The primary objective of this project was to develop an adaptive finite element flow solver for simulating internal flows in the solid rocket booster. Described here is a unique flow simulator code for analyzing highly complex flow phenomena in the solid rocket booster. New methodologies and features incorporated into this analysis tool are described
Quantum Hall effect in a one-dimensional dynamical system
We construct a periodically time-dependent Hamiltonian with a phase
transition in the quantum Hall universality class. One spatial dimension can be
eliminated by introducing a second incommensurate driving frequency, so that we
can study the quantum Hall effect in a one-dimensional (1D) system. This
reduction to 1D is very efficient computationally and would make it possible to
perform experiments on the 2D quantum Hall effect using cold atoms in a 1D
optical lattice.Comment: 8 pages, 6 figure
H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows
The commitment to develop the National Aerospace Plane and Maneuvering Reentry Vehicles has generated resurgent interest in the technology required to design structures for hypersonic flight. The principal objective of this research and development effort has been to formulate and implement a new class of computational methodologies for accurately predicting fine scale phenomena associated with this class of problems. The initial focus of this effort was to develop optimal h-refinement and p-enrichment adaptive finite element methods which utilize a-posteriori estimates of the local errors to drive the adaptive methodology. Over the past year this work has specifically focused on two issues which are related to overall performance of a flow solver. These issues include the formulation and implementation (in two dimensions) of an implicit/explicit flow solver compatible with the hp-adaptive methodology, and the design and implementation of computational algorithm for automatically selecting optimal directions in which to enrich the mesh. These concepts and algorithms have been implemented in a two-dimensional finite element code and used to solve three hypersonic flow benchmark problems (Holden Mach 14.1, Edney shock on shock interaction Mach 8.03, and the viscous backstep Mach 4.08)
Tangent fermions: Dirac or Majorana fermions on a lattice without fermion doubling
I. Introduction
II. Two-dimensional lattice fermions
III. Methods to avoid fermion doubling (sine dispersion, sine plus cosine
dispersion, staggered lattice dispersion, linear sawtooth dispersion, tangent
dispersion)
IV. Topologically protected Dirac cone
V. Application: Klein tunneling (tangent fermions on a space-time lattice,
wave packet propagation)
VI. Application: Strong antilocalization (transfer matrix of tangent
fermions, topological insulator versus graphene)
VII. Application: Anomalous quantum Hall effect (gauge invariant tangent
fermions, topologically protected zeroth Landau level)
VIII. Application: Majorana metal (Dirac versus Majorana fermions, phase
diagram)
IX. OutlookComment: review article, 26 pages, 13 figures; V2: added three appendices, and
provided code for the various implementation
- …