arXiv subjects

J. M. B. Lopes dos Santos

Publications and source records attributed to J. M. B. Lopes dos Santos.

At least 19 recordsLinked to original sources

arXiv2021

Nonlinear optical conductivity of a two-band crystal I

The structure of the electronic nonlinear optical conductivity is elucidated in a detailed study of the time-reversal symmetric two-band model. The nonlinear conductivity is decomposed as a sum of contributions related with different regions of the First Brillouin Zone, defined by single or multiphoton resonances. All contributions are written in terms of the same integrals, which contain all information specific to the particular model under study. In this way, ready-to-use formulas are provided that reduce the often tedious calculations of the second and third order optical conductivity to the evaluation of a small set of similar integrals. In the scenario where charge carriers are present prior to optical excitation, Fermi surface contributions must also be considered and are shown to have an universal frequency dependence, tunable by doping. General characteristics are made evident in this type of resonance-based analysis: the existence of step functions that determine the chemical potential dependence of electron-hole symmetric insulators; the determination of the imaginary part by Hilbert transforms, simpler than those of the nonlinear Kramers-Krönig relations; the absence of Drude peaks in the diagonal elements of the second order conductivity, among others. As examples, analytical expressions are derived for the nonlinear conductivities of some simple systems: a very basic model of direct gap semiconductors and the Dirac fermions of monolayer graphene.

cond-mat.other↗

arXiv2020

A Polynomial Approach to the Spectrum of Dirac-Weyl Polygonal Billiards

The Schrödinger equation in a square or rectangle with hard walls is solved in every introductory quantum mechanics course. Solutions for other polygonal enclosures only exist in a very restricted class of polygons, and are all based on a result obtained by Lamé in 1852. Any enclosure can, of course, be addressed by finite element methods for partial differential equations. In this paper, we present a variational method to approximate the low-energy spectrum and wave-functions for arbitrary convex polygonal enclosures, developed initially for the study of vibrational modes of plates. In view of the recent interest in the spectrum of quantum dots of two dimensional materials, described by effective models with massless electrons, we extend the method to the Dirac-Weyl equation for a spin-1/2 fermion confined in a quantum billiard of polygonal shape, with different types of boundary conditions. We illustrate the method's convergence in cases where the spectrum in known exactly and apply it to cases where no exact solution exists.

physics.comp-ph↗

arXiv2020

Second order divergence in the third order DC response of a cold semiconductor

In this work, we present the analytical expression for the second order divergence in the third order DC response of a cold semiconductor, which can be probed by different electric field setups. Results from this expression were then compared, for the response of the gapped graphene monolayer, with numerical results from a velocity gauge calculation of the third order conductivity. The good agreement between the two validates our analytical expression.

cond-mat.mes-hall↗

arXiv2020

A study of the nonlinear optical response of the plain graphene and gapped graphene monolayers beyond the Dirac approximation

In this work, we present numerical results for the second and third order conductivities of the plain graphene and gapped graphene monolayers associated with the second and third harmonic generation, the optical rectification and the optical Kerr effect. The frequencies considered here range from the microwave to the ultraviolet portion of the spectrum, the latter end of which had not yet been studied. These calculations are performed in the velocity gauge and directly address the components of the conductivity tensor. In the velocity gauge, the radiation field is represented by a power series in the vector potential, and we discuss a very efficient way of calculating its coefficients in the context of tight-binding models.

cond-mat.mes-hall↗

arXiv2019

Global Delocalization Transition in the de Moura-Lyra Model

The possibility of having a delocalization transition in the 1D de Moura-Lyra class of models (having a power-spectrum $\propto q^{-α})$ has been the object of a long standing discussion in the literature, filled with ambiguities. In this letter, we report the first numerical evidences that such a transition happens at $α=1$, where the localization length (measured from the scaling of the conductance) is shown to diverge as $(1-α)^{-1}$. The persistent finite-size scaling of the data is shown to be caused by a very slow convergence of the nearest-neighbor correlator to its infinite-size limit, and controlled by the choice of a proper scaling parameter. This last conclusion leads to the re-interpretation of the localization in these models to be caused by an effective Anderson uncorrelated model at small length-scales. Finally, the numerical results are confirmed by analytical perturbative calculations which are built on previous work.

cond-mat.dis-nn↗

arXiv2019

Spectral Functions of One-Dimensional Systems with Correlated Disorder

We investigate the spectral function of Bloch states in an one-dimensional tight-binding non-interacting chain with two different models of static correlated disorder, at zero temperature. We report numerical calculations of the single-particle spectral function based on the Kernel Polynomial Method, which has an $\mathcal{O}(N)$ computational complexity. These results are then confirmed by analytical calculations, where precise conditions were obtained for the appearance of a classical limit in a single-band lattice system. Spatial correlations in the disordered potential give rise to non-perturbative spectral functions shaped as the probability distribution of the random on-site energies, even at low disorder strengths. In the case of disordered potentials with an algebraic power-spectrum, $\propto\left|k\right|^{-α}$, we show that the spectral function is not self-averaging for $α\geq1$.

cond-mat.dis-nn↗

arXiv2018

Nonlinear optical responses of crystalline systems: Results from a velocity gauge analysis

In this work, the difficulties inherent to perturbative calculations in the velocity gauge are addressed. In particular, it is shown how calculations of nonlinear optical responses in the independent particle approximation can be done to any order and for any finite band model. The procedure and advantages of the velocity gauge in such calculations are described. The addition of a phenomenological relaxation parameter is also discussed. As an illustration, the nonlinear optical response of monolayer graphene is numerically calculated using the velocity gauge.

cond-mat.other↗

arXiv2017

Gauge covariances and nonlinear optical responses

The formalism of the reduced density matrix is pursued in both length and velocity gauges of the perturbation to the crystal Hamiltonian. The covariant derivative is introduced as a convenient representation of the position operator. This allow us to write compact expressions for the reduced density matrix in any order of the perturbation which simplifies the calculations of nonlinear optical responses; as an example, we compute the first and third order contributions of the monolayer graphene. Expressions obtained in both gauges share the same formal structure, allowing a comparison of the effects of truncation to a finite set of bands. This truncation breaks the equivalence between the two approaches: its proper implementation can be done directly in the expressions derived in the length gauge, but require a revision of the equations of motion of the reduced density matrix in the velocity gauge.

cond-mat.other↗

arXiv2013

Scattering by linear defects in graphene: a tight-binding approach

We develop an analytical scattering formalism for computing the transmittance through periodic defect lines within the tight-binding model of graphene. We first illustrate the method with a relatively simple case, the pentagon-only defect line. Afterwards, more complex defect lines are treated, namely the zz(558) and the zz(5757) ones. The formalism developed, only uses simple tight-binding concepts, reducing the problem to matrix manipulations which can be easily worked out by any computational algebraic calculator.

cond-mat.mes-hall↗

arXiv2012

Scattering by linear defects in graphene: a continuum approach

We study the low-energy electronic transport across periodic extended defects in graphene. In the continuum low-energy limit, such defects act as infinitesimally thin stripes separating two regions where Dirac Hamiltonian governs the low-energy phenomena. The behavior of these systems is defined by the boundary condition imposed by the defect on the massless Dirac fermions. We demonstrate how this low-energy boundary condition can be computed from the tight-binding model of the defect line. For simplicity we consider defect lines oriented along the zigzag direction, which requires the consideration of only one copy of Dirac equation. Three defect lines of this kind are studied and shown to be mappable between them: the pentagon-only, the zz(558) and the zz(5757) defect lines. In addition, in this same limit, we calculate the conductance across such defect lines with size L, and find it to be proportional to k_FL at low temperatures.

cond-mat.mes-hall↗

arXiv2012

Continuum Model of the Twisted Bilayer

The continuum model of the twisted graphene bilayer (Phys. Rev. Lett. 99, 256802, 2007) is extended to include all types of commensurate structures. The essential ingredient of the model, the Fourier components of the spatially modulated hopping amplitudes, can be calculated analytically, for any type of commensurate structures in the low twist angle limit. We show that the Fourier components that could give rise to a gap in the SE-even structures discussed by Mele (Phys. Rev. B 81, 161405 2010) vanish linearly with angle, whereas the amplitudes that saturate to finite values, as $θ\to0$, ensure that all low angle structures share essentially the same physics. We extend our previous calculations beyond the validity of perturbation theory, to discuss the disappearance of Dirac cone structure at angles below 1^{\circ}.

cond-mat.mtrl-sci↗

arXiv2011

Zigzag graphene nanoribbon edge reconstruction with Stone-Wales defects

In this article, we study zigzag graphene nanoribbons with edges reconstructed with Stone-Wales defects, by means of an empirical (first-neighbor) tight-binding method, with parameters determined by ab-initio calculations of very narrow ribbons. We explore the characteristics of the electronic band structure with a focus on the nature of edge states. Edge reconstruction allows the appearance of a new type of edge states. They are dispersive, with non-zero amplitudes in both sub-lattices; furthermore, the amplitudes have two components that decrease with different decay lengths with the distance from the edge; at the Dirac points one of these lengths diverges, whereas the other remains finite, of the order of the lattice parameter. We trace this curious effect to the doubling of the unit cell along the edge, brought about by the edge reconstruction. In the presence of a magnetic field, the zero-energy Landau level is no longer degenerate with edge states as in the case of pristine zigzag ribbon.

cond-mat.mes-hall↗

arXiv2011

Coulomb Drag and High Resistivity Behavior in Double Layer Graphene

We show that Coulomb drag in ultra-clean graphene double layers can be used for controlling the on/off ratio for current flow by tunning the external gate voltage. Hence, although graphene remains semi-metallic, the double layer graphene system can be tuned from conductive to a highly resistive state. We show that our results explain previous data of Coulomb drag in double layer graphene samples in disordered SiO2 substrates.

cond-mat.mes-hall↗

arXiv2010

Emergence of robust gaps in 2D antiferromagnets via additional spin-1/2 probes

We study the capacity of antiferromagnetic lattices of varying geometries to entangle two additional spin-1/2 probes. Analytical modeling of the Quantum Monte Carlo data shows the appearance of a robust gap, allowing a description of entanglement in terms of probe-only states, even in cases where the coupling to the probes is larger than the gap of the spin lattice and cannot be treated perturbatively. We find a considerable enhancement of the temperature at which probe entanglement disappears as we vary the geometry of the bus and the coupling to the probes. In particular, the square Heisenberg antiferromagnet exhibits the best thermal robustness of all systems, whereas the three-leg ladder chain shows the best performance in the natural quantum ground state.

cond-mat.mes-hall↗

arXiv2010

Electronic properties of a biased graphene bilayer

We study, within the tight-binding approximation, the electronic properties of a graphene bilayer in the presence of an external electric field applied perpendicular to the system -- \emph{biased bilayer}. The effect of the perpendicular electric field is included through a parallel plate capacitor model, with screening correction at the Hartree level. The full tight-binding description is compared with its 4-band and 2-band continuum approximations, and the 4-band model is shown to be always a suitable approximation for the conditions realized in experiments. The model is applied to real biased bilayer devices, either made out of SiC or exfoliated graphene, and good agreement with experimental results is found, indicating that the model is capturing the key ingredients, and that a finite gap is effectively being controlled externally. Analysis of experimental results regarding the electrical noise and cyclotron resonance further suggests that the model can be seen as a good starting point to understand the electronic properties of graphene bilayer. Also, we study the effect of electron-hole asymmetry terms, as the second-nearest-neighbor hopping energies $t'$ (in-plane) and $γ_{4}$ (inter-layer), and the on-site energy $Δ$.

cond-mat.mes-hall↗

arXiv2010

Bilayer graphene: gap tunability and edge properties

Bilayer graphene -- two coupled single graphene layers stacked as in graphite -- provides the only known semiconductor with a gap that can be tuned externally through electric field effect. Here we use a tight binding approach to study how the gap changes with the applied electric field. Within a parallel plate capacitor model and taking into account screening of the external field, we describe real back gated and/or chemically doped bilayer devices. We show that a gap between zero and midinfrared energies can be induced and externally tuned in these devices, making bilayer graphene very appealing from the point of view of applications. However, applications to nanotechnology require careful treatment of the effect of sample boundaries. This being particularly true in graphene, where the presence of edge states at zero energy -- the Fermi level of the undoped system -- has been extensively reported. Here we show that also bilayer graphene supports surface states localized at zigzag edges. The presence of two layers, however, allows for a new type of edge state which shows an enhanced penetration into the bulk and gives rise to band crossing phenomenon inside the gap of the biased bilayer system.

cond-mat.mes-hall↗

arXiv2010

Substitutional disorder and charge localization in manganites

In the manganites $RE_{1-x}AE_{x}$MnO$_{3}$ ($RE$ and $AE$ being rare-earth and alkaline-earth elements, respectively) the random distribution of $RE^{3+}$ and $AE^{2+}$ induces random, but correlated, shifts of site energies of charge carriers in the Mn sites. We consider a realistic model of this diagonal disorder, in addition to the double-exchange hopping disorder, and investigate the metal-insulator transition as a function of temperature, across the paramagnetic-ferromagnetic line, and as a function of doping $x$. Contrary to previous results, we find that values of parameters, estimated from the electronic structure of the manganites, are not incompatible with the possibility of a disorder induced metal to insulator transition accompanying the ferromagnetic to paramagnetic transition at intermediate doping ($x\sim0.2-0.4$). These findings indicate clearly that substitutional disorder has to be considered as an important effect when addressing the colossal magnetoresistance properties of manganites.

cond-mat.str-el↗

arXiv2009

Observation of Van Hove singularities in twisted graphene layers

Electronic instabilities at the crossing of the Fermi energy with a Van Hove singularity in the density of states often lead to new phases of matter such as superconductivity, magnetism or density waves. However, in most materials this condition is difficult to control. In the case of single-layer graphene, the singularity is too far from the Fermi energy and hence difficult to reach with standard doping and gating techniques. Here we report the observation of low-energy Van Hove singularities in twisted graphene layers seen as two pronounced peaks in the density of states measured by scanning tunneling spectroscopy. We demonstrate that a rotation between stacked graphene layers can generate Van Hove singularities, which can be brought arbitrarily close to the Fermi energy by varying the angle of rotation. This opens intriguing prospects for Van Hove singularity engineering of electronic phases.

cond-mat.mes-hall↗