43 research outputs found
Strong disorder in nodal semimetals: Schwinger-Dyson–Ward approach
The self-consistent Born approximation quantitatively fails to capture disorder effects in semimetals. We present an alternative, simple-to-use nonperturbative approach to calculate the disorder-induced self-energy. It requires a sufficient broadening of the quasiparticle pole and the solution of a differential equation on the imaginary frequency axis. We demonstrate the performance of our method for various paradigmatic semimetal Hamiltonians and compare our results to exact numerical reference data. For intermediate and strong disorder, our approach yields quantitatively correct momentum-resolved results. It is thus complementary to existing renormalization group treatments of weak disorder in semimetals
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
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
Second order functional renormalization group approach to one-dimensional systems in real and momentum space
We devise a functional renormalization group treatment for a chain of
interacting spinless fermions which is correct up to second order in
interaction strength. We treat both inhomogeneous systems in real space as
well as the translationally invariant case in a k-space formalism. The
strengths and shortcomings of the different schemes as well as technical
details of their implementation are discussed. We use the method to study two
proof-of-principle problems in the realm of Luttinger liquid physics, namely,
reflection at interfaces and power laws in the occupation number as a function
of crystal momentum
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