92 research outputs found
On the proof of the -inextendibility of the Schwarzschild spacetime
This article presents a streamlined version of the author's original proof of
the -inextendibility of the maximal analytic Schwarzschild spacetime.
Firstly, we deviate from the original proof by using the result, recently
established in collaboration with Galloway and Ling, that given a
-extension of a globally hyperbolic spacetime, one can find a timelike
geodesic that leaves this spacetime. This result much simplifies the proof of
the inextendibility through the exterior region of the Schwarzschild spacetime.
Secondly, we give a more flexible and shorter argument for the inextendibility
through the interior region. Furthermore, we present a small new structural
result for the boundary of a globally hyperbolic spacetime within a
-extension which serves as a new and simpler starting point for the proof.Comment: Prepared for submission to the proceedings of the meeting
"Non-Regular Spacetime Geometry", Florence, 20.6.-22.6.2017. Based on
arXiv:1507.00601, v2: minor changes, version accepted for publicatio
Transversal magnetotransport in Weyl semimetals: Exact numerical approach
Magnetotransport experiments on Weyl semimetals are essential for
investigating the intriguing topological and low-energy properties of Weyl
nodes. If the transport direction is perpendicular to the applied magnetic
field, experiments have shown a large positive magnetoresistance. In this work,
we present a theoretical scattering matrix approach to transversal
magnetotransport in a Weyl node. Our numerical method confirms and goes beyond
the existing perturbative analytical approach by treating disorder exactly. It
is formulated in real space and is applicable to mesoscopic samples as well as
in the bulk limit. In particular, we study the case of clean and strongly
disordered samples.Comment: 10 pages, 4 figure
Twisted-light-induced intersubband transitions in quantum wells at normal incidence
We examine theoretically the intersubband transitions induced by laser beams
of light with orbital angular momentum (twisted light) in semiconductor quantum
wells at normal incidence. These transitions become possible in the absence of
gratings thanks to the fact that collimated laser beams present a component of
the light's electric field in the propagation direction. We derive the matrix
elements of the light-matter interaction for a Bessel-type twisted-light beam
represented by its vector potential in the paraxial approximation. Then, we
consider the dynamics of photo-excited electrons making intersubband
transitions between the first and second subbands of a standard semiconductor
quantum well. Finally, we analyze the light-matter matrix elements in order to
evaluate which transitions are more favorable for given orbital angular
momentum of the light beam in the case of small semiconductor structures.Comment: 9 pages, 2 figure
Quantum Critical Exponents for a Disordered Three-Dimensional Weyl Node
Three-dimensional Dirac and Weyl semimetals exhibit a disorder-induced
quantum phase transition between a semimetallic phase at weak disorder and a
diffusive-metallic phase at strong disorder. Despite considerable effort, both
numerically and analytically, the critical exponents and of this
phase transition are not known precisely. Here we report a numerical
calculation of the critical exponent using a minimal
single-Weyl node model and a finite-size scaling analysis of conductance. Our
high-precision numerical value for is incompatible with previous
numerical studies on tight-binding models and with one- and two-loop
calculations in an -expansion scheme. We further obtain
from the scaling of the conductivity with chemical potential
Weyl node with random vector potential
We study Weyl semimetals in the presence of generic disorder, consisting of a
random vector potential as well as a random scalar potential. We derive
renormalization group flow equations to second order in the disorder strength.
These flow equations predict a disorder-induced phase transition between a
pseudo-ballistic weak-disorder phase and a diffusive strong-disorder phase for
sufficiently strong random scalar potential or for a pure three-component
random vector potential. We verify these predictions using a numerical study of
the density of states near the Weyl point and of quantum transport properties
at the Weyl point. In contrast, for a pure single-component random vector
potential the diffusive strong-disorder phase is absent.Comment: published version with minor change
Functional renormalization-group approach
We present a functional renormalization-group approach to interacting topological Green's function invariants with a focus on the nature of transitions. The method is applied to chiral symmetric fermion chains in the Mott limit that can be driven into a Haldane phase. We explicitly show that the transition to this phase is accompanied by a zero of the fermion Green's function. Our results for the phase boundary are quantitatively benchmarked against density matrix renormalization-group data
Quantum transport of disordered Weyl semimetals at the nodal point
Weyl semimetals are paradigmatic topological gapless phases in three
dimensions. We here address the effect of disorder on charge transport in Weyl
semimetals. For a single Weyl node with energy at the degeneracy point and
without interactions, theory predicts the existence of a critical disorder
strength beyond which the density of states takes on a nonzero value.
Predictions for the conductivity are divergent, however. In this work, we
present a numerical study of transport properties for a disordered Weyl cone at
zero energy. For weak disorder our results are consistent with a
renormalization group flow towards an attractive pseudoballistic fixed point
with zero conductivity and a scale-independent conductance; for stronger
disorder diffusive behavior is reached. We identify the Fano factor as a
signature that discriminates between these two regimes
- …