16,192 research outputs found
Optical third harmonic generation in black phosphorus
We present a calculation of Third Harmonic Generation (THG) for two-band
systems using the length gauge that avoids unphysical divergences otherwise
present in the evaluation of the third order current density response. The
calculation is applied to bulk and monolayer black Phosphorus (bP) using a
non-orthogonal tight-binding model. Results show that the low energy response
is dominated by mixed inter-intraband processes and estimates of the magnitude
of THG susceptibility are comparable to recent experimental reports for bulk bP
samples.Comment: 9 pages, 5 figure
Iterative approach to arbitrary nonlinear optical response functions of graphene
Two-dimensional materials constitute an exciting platform for nonlinear
optics with large nonlinearities that are tunable by gating. Hence,
gate-tunable harmonic generation and intensity-dependent refraction have been
observed in e.g. graphene and transition-metal dichalcogenides, whose
electronic structures are accurately modelled by the (massive) Dirac equation.
We exploit on the simplicity of this model and demonstrate here that arbitrary
nonlinear response functions follow from a simple iterative approach. The power
of this approach is illustrated by analytical expressions for harmonic
generation and intensity-dependent refraction, both computed up to ninth order
in the pump field. Moreover, the results allow for arbitrary band gaps and
gating potentials. As illustrative applications, we consider (i)
gate-dependence of third- and fifth-harmonic generation in gapped and gapless
graphene, (ii) intensity-dependent refractive index of graphene up to ninth
order, and (iii) intensity-dependence of high-harmonic generation.Comment: 6 pages, 5 figures. Supplemental material: 6 pages, 2 figure
Linear and nonlinear optical response of crystals using length and velocity gauges: Effect of basis truncation
We study the effects of a truncated band structure on the linear and
nonlinear optical response of crystals using four methods. These are
constructed by (i) choosing either length or velocity gauge for the
perturbation and (ii) computing the current density either directly or via the
time-derivative of the polarization density. In the infinite band limit, the
results of all four methods are identical, but basis truncation breaks their
equivalence. In particular, certain response functions vanish identically and
unphysical low-frequency divergences are observed for few-band models in the
velocity gauge. Using hexagonal boron nitride (hBN) monolayer as a case study,
we analyze the problems associated with all methods and identify the optimal
one. Our results show that the length gauge calculations provide the fastest
convergence rates as well as the most accurate spectra for any basis size and,
moreover, that low-frequency divergences are eliminated.Comment: 11 pages, 7 figure
Nonperturbative Quantum Physics from Low-Order Perturbation Theory
The Stark effect in hydrogen and the cubic anharmonic oscillator furnish
examples of quantum systems where the perturbation results in a certain
ionization probability by tunneling processes. Accordingly, the perturbed
ground-state energy is shifted and broadened, thus acquiring an imaginary part
which is considered to be a paradigm of nonperturbative behavior. Here we
demonstrate how the low order coefficients of a divergent perturbation series
can be used to obtain excellent approximations to both real and imaginary parts
of the perturbed ground state eigenenergy. The key is to use analytic
continuation functions with a built in analytic structure within the complex
plane of the coupling constant, which is tailored by means of Bender-Wu
dispersion relations. In the examples discussed the analytic continuation
functions are Gauss hypergeometric functions, which take as input fourth order
perturbation theory and return excellent approximations to the complex
perturbed eigenvalue. These functions are Borel-consistent and dramatically
outperform widely used Pad\'e and Borel-Pad\'e approaches, even for rather
large values of the coupling constant.Comment: 5 pages, 3 figures, PDFLaTe
Dirac model of electronic transport in graphene antidot barriers
In order to use graphene for semiconductor applications, such as transistors
with high on/off ratios, a band gap must be introduced into this otherwise
semimetallic material. A promising method of achieving a band gap is by
introducing nanoscale perforations (antidots) in a periodic pattern, known as a
graphene antidot lattice (GAL). A graphene antidot barrier (GAB) can be made by
introducing a 1D GAL strip in an otherwise pristine sheet of graphene. In this
paper, we will use the Dirac equation (DE) with a spatially varying mass term
to calculate the electronic transport through such structures. Our approach is
much more general than previous attempts to use the Dirac equation to calculate
scattering of Dirac electrons on antidots. The advantage of using the DE is
that the computational time is scale invariant and our method may therefore be
used to calculate properties of arbitrarily large structures. We show that the
results of our Dirac model are in quantitative agreement with tight-binding for
hexagonal antidots with armchair edges. Furthermore, for a wide range of
structures, we verify that a relatively narrow GAB, with only a few antidots in
the unit cell, is sufficient to give rise to a transport gap
Optical second harmonic generation from Wannier excitons
Excitonic effects in the linear optical response of semiconductors are
well-known and the subject of countless experimental and theoretical studies.
For the technologically important second order nonlinear response, however,
description of excitonic effects has proved to be difficult. In this work, a
simplified three-band Wannier exciton model of cubic semiconductors is applied
and a closed form expression for the complex second harmonic response function
including broadening is derived. Our calculated spectra are found to be in
excellent agreement with the measured response near the band edge. In addition,
a very substantial enhancement of the nonlinear response is predicted for the
transparency region
Electronic and optical properties of graphene antidot lattices: Comparison of Dirac and tight-binding models
The electronic properties of graphene may be changed from semimetallic to
semiconducting by introducing perforations (antidots) in a periodic pattern.
The properties of such graphene antidot lattices (GALs) have previously been
studied using atomistic models, which are very time consuming for large
structures. We present a continuum model that uses the Dirac equation (DE) to
describe the electronic and optical properties of GALs. The advantages of the
Dirac model are that the calculation time does not depend on the size of the
structures and that the results are scalable. In addition, an approximation of
the band gap using the DE is presented. The Dirac model is compared with
nearest-neighbour tight-binding (TB) in order to assess its accuracy. Extended
zigzag regions give rise to localized edge states, whereas armchair edges do
not. We find that the Dirac model is in quantitative agreement with TB for GALs
without edge states, but deviates for antidots with large zigzag regions.Comment: 15 pages, 7 figures. Accepted by Journal of Physics: Condensed matte
A library of ab initio Raman spectra for automated identification of 2D materials
Raman spectroscopy is frequently used to identify composition, structure and
layer thickness of 2D materials. Here, we describe an efficient
first-principles workflow for calculating resonant first-order Raman spectra of
solids within third-order perturbation theory employing a localized atomic
orbital basis set. The method is used to obtain the Raman spectra of 733
different monolayers selected from the computational 2D materials database
(C2DB). We benchmark the computational scheme against available experimental
data for 15 known monolayers. Furthermore, we propose an automatic procedure
for identifying a material based on an input experimental Raman spectrum and
illustrate it for the cases of MoS (H-phase) and WTe
(T-phase). The Raman spectra of all materials at different excitation
frequencies and polarization configurations are freely available from the C2DB.
Our comprehensive and easily accessible library of \textit{ab initio} Raman
spectra should be valuable for both theoreticians and experimentalists in the
field of 2D materialsComment: 17 pages, 7 figure
Scaling behavior of spin transport in hydrogenated graphene
We calculate the spin transport of hydrogenated graphene using the
Landauer-B\"uttiker formalism with a spin-dependent tight-binding Hamiltonian.
The advantages of using this method is that it simultaneously gives information
on sheet resistance and localization length as well as spin relaxation length.
Furthermore, the Landauer-B\"uttiker formula can be computed very efficiently
using the recursive Green's function technique. Previous theoretical results on
spin relaxation time in hydrogenated graphene have not been in agreement with
experiments. Here, we study magnetic defects in graphene with randomly aligned
magnetic moments, where interference between spin-channels is explicitly
included. We show that the spin relaxation length and sheet resistance scale
nearly linearly with the impurity concentration. Moreover, the spin relaxation
mechanism in hydrogenated graphene is Markovian only near the charge neutrality
point or in the highly dilute impurity limit
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