arXiv subjects

C. Morais Smith

Publications and source records attributed to C. Morais Smith.

At least 37 records · Page 2Linked to original sources

arXiv2020

Shining Light on Quantum Transport in Fractal Networks

Fractals are fascinating structures, not only for their aesthetic appeal, but also because they allow for the investigation of physical properties in non-integer dimensions. In these unconventional systems, a myriad of intrinsic features might come into play, such as the fractal dimension, the spectral dimension, or the fractal geometry. Despite abundant theoretical and numerical studies, experiments in fractal networks remain elusive. Here, we experimentally investigate quantum transport in fractal networks by performing continuous-time quantum walks in fractal photonic lattices with incremental propagation lengths. Photons act as the walkers and evolve in the lattices after being injected into one initial site. We unveil the transport properties through the photon evolution pattern at different propagation lengths and the analysis of the variance and the P'olya number, which are calculated based on the probability distribution of the patterns. Contrarily to classical fractals, we observe anomalous transport governed solely by the fractal dimension. In addition, the critical point at which there is a transition from normal to anomalous transport is highly dependent on the fractal geometry. Our experiment allows the verification of physical laws in a quantitative manner and reveals the transport dynamics with unprecedented detail, thus opening a path to the understanding of more complex quantum phenomena governed by fractality.

quant-ph↗

arXiv2020

Topological phase transitions driven by next-nearest-neighbor hopping in two-dimensional lattices

For two-dimensional lattices in a tight-binding description, the intrinsic spin-orbit coupling, acting as a complex next-nearest-neighbor hopping, opens gaps that exhibit the quantum spin Hall effect. In this paper, we study the effect of a real next-nearest-neighbor hopping term on the band structure of several Dirac systems. In our model, the spin is conserved, which allows us to analyze the spin Chern numbers. We show that in the Lieb, kagome, and T_3 lattices, variation of the amplitude of the real next-nearest-neighbor hopping term drives interesting topological phase transitions. These transitions may be experimentally realized in optical lattices under shaking, when the ratio between the nearest- and next-nearest-neighbor hopping parameters can be tuned to any possible value. Finally, we show that in the honeycomb lattice, next-nearest-neighbor hopping only drives topological phase transitions in the presence of a magnetic field, leading to the conjecture that these transitions can only occur in multigap systems.

cond-mat.mes-hall↗

arXiv2020

Thermodynamics of a Higher-Order Topological Insulator

We investigate the order of the topological quantum phase transition in a two dimensional quadrupolar topological insulator within a thermodynamic approach. Using numerical methods, we separate the bulk, edge and corner contributions to the grand potential and detect different phase transitions in the topological phase diagram. The transitions from the quadrupolar to the trivial or to the dipolar phases are well captured by the thermodynamic potential. On the other hand, we have to resort to a grand potential based on the Wannier bands to describe the transition from the trivial to the dipolar phase. The critical exponents and the order of the phase transitions are determined and discussed in the light of the Josephson hyperscaling relation.

cond-mat.stat-mech↗

arXiv2020

Projected Proca Field Theory: a One-Loop Study

The recent discovery of two-dimensional Dirac materials, such as graphene and transition-metaldichalcogenides, has raised questions about the treatment of hybrid systems, in which electrons moving in a two-dimensional plane interact via virtual photons from the three-dimensional space. In this case, a projected non-local theory, known as Pseudo-QED, or reduced QED, has shown to provide a correct framework for describing the interactions displayed by these systems. In a related situation, in planar materials exhibiting a superconducting phase, the electromagnetic field has a typical exponential decay that is interpreted as the photons having an effective mass, as a consequence of the Anderson-Higgs mechanism. Here, we use an analogous projection to that used to obtain the pseudo-QED to derive a Pseudo-Proca equivalent model. In terms of this model, we unveil the main effects of attributing a mass to the photons and to the quasi-relativistic electrons. The one-loop radiative corrections to the electron mass, to the photon and to the electron-photon vertex are computed. We calculate the quantum corrections to the electron g-factor and show that it smoothly goes to zero in the limit when the photon mass is much larger than the electron mass. In addition, we correct the results obtained for graphene within Pseudo-QED in the limit when the photon mass vanishes.

hep-th↗

arXiv2019

p-band engineering in artificial electronic lattices

Artificial electronic lattices, created atom by atom in a scanning tunneling microscope, have emerged as a highly tunable platform to realize and characterize the lowest-energy bands of novel lattice geometries. Here, we show that artificial electronic lattices can be tailored to exhibit higher-energy bands. We study p-like bands in four-fold and three-fold rotationally symmetric lattices. In addition, we show how an anisotropic design can be used to lift the degeneracy between p_x- and p_y-like bands. The experimental measurements are corroborated by muffin-tin and tight-binding calculations. The approach to engineer higher-energy electronic bands in artificial quantum systems introduced here enables the realization of complex band structures from the bottom up.

cond-mat.mes-hall↗

arXiv2019

Edge-dependent topology in Kekulé lattices

Topological states of matter are robust quantum phases, characterised by propagating or localised edge states in an insulating bulk. Topological boundary states can be triggered by various mechanisms, for example by strong spin-orbit coupling. In this case, the existence of topological states does not depend on the termination of the material. On the other hand, topological phases can also occur in systems without spin-orbit coupling, such as topological crystalline insulators. In these systems, the protection mechanism originates from the crystal symmetry. Here, we show that for topological crystalline insulators with the same bulk, different edge geometries can lead to topological or trivial states. We artificially engineer and investigate a 2D electronic dimerised honeycomb structure, known as the Kekulé lattice, on the nanoscale. The surface electrons of Cu(111) are confined into this geometry by positioning repulsive scatterers (carbon monoxide molecules) with atomic precision, using the tip of a scanning tunnelling microscope. We show experimentally and theoretically that for the same bulk, molecular zigzag and partially bearded edges lead to topological or trivial states in the opposite range of parameters, thus revealing a subtle link between topology and edge termination. Our results shed further light on the nature of topological states and might be useful for future manipulations of these states, with the aim of designing valves or other more complex devices.

cond-mat.mes-hall↗

arXiv2019

Robust zero-energy modes in an electronic higher-order topological insulator: the dimerized Kagome lattice

Quantum simulators are an essential tool for understanding complex quantum materials. Platforms based on ultracold atoms in optical lattices and photonic devices led the field so far, but electronic quantum simulators are proving to be equally relevant. Simulating topological states of matter is one of the holy grails in the field. Here, we experimentally realize a higher-order electronic topological insulator (HOTI). Specifically, we create a dimerized Kagome lattice by manipulating carbon-monoxide (CO) molecules on a Cu(111) surface using a scanning tunneling microscope (STM). We engineer alternating weak and strong bonds to show that a topological state emerges at the corner of the non-trivial configuration, while it is absent in the trivial one. Contrarily to conventional topological insulators (TIs), the topological state has two dimensions less than the bulk, denoting a HOTI. The corner mode is protected by a generalized chiral symmetry, which leads to a particular robustness against perturbations. Our versatile approach to quantum simulation with artificial lattices holds promises of revealing unexpected quantum phases of matter.

cond-mat.mes-hall↗

arXiv2018

Quantum-electrodynamical approach to the exciton spectrum in Transition-Metal Dichalcogenides

Manipulation of intrinsic electron degrees of freedom, such as charge and spin, gives rise to electronics and spintronics, respectively. Electrons in monolayer materials with a honeycomb lattice structure, such as the Transition-Metal Dichalcogenides (TMD's), can be distinguished according to the region (valley) of the Brillouin zone to which they belong. Valleytronics, the manipulation of this electron's property, is expected to set up a new era in the realm of electronic devices. In this work, we accurately determine the energy spectrum and lifetimes of exciton (electron-hole) bound-states for different TMD materials, namely WSe$_2$, WS$_2$ and MoS$_2$. For all of them, we obtain a splitting of the order of 170 meV between the exciton energies from different valleys, corresponding to an effective Zeeman magnetic field of 1400 T. Our approach, which employs quantum-field theory (QFT) techniques based on the Bethe-Salpeter equation and the Schwinger-Dyson formalism, takes into account the full electromagnetic interaction among the electrons. The valley selection mechanism operates through the dynamical breakdown of the time-reversal (TR) symmetry, which originally interconnects the two valleys. This symmetry is spontaneously broken whenever the full electromagnetic interaction vertex is used to probe the response of the system to an external field.

cond-mat.str-el↗

arXiv2018

Genesis of the Floquet Hofstadter butterfly

We investigate theoretically the spectrum of a graphene-like sample (honeycomb lattice) subjected to a perpendicular magnetic field and irradiated by circularly polarized light. This system is studied using the Floquet formalism, and the resulting Hofstadter spectrum is analyzed for different regimes of the driving frequency. For lower frequencies, resonances of various copies of the spectrum lead to intricate formations of topological gaps. In the Landau-level regime, new wing-like gaps emerge upon reducing the driving frequency, thus revealing the possibility of dynamically tuning the formation of the Hofstadter butterfly. In this regime, an effective model may be analytically derived, which allows us to retrace the energy levels that exhibit avoided crossings and ultimately lead to gap structures with a wing-like shape. At high frequencies, we find that gaps open for various fluxes at $E=0$, and upon increasing the amplitude of the driving, gaps also close and reopen at other energies. The topological invariants of these gaps are calculated and the resulting spectrum is elucidated. We suggest opportunities for experimental realization and discuss similarities with Landau-level structures in non-driven systems.

cond-mat.mes-hall↗

arXiv2018

Proposed Spontaneous Generation of Magnetic Fields by Curved Layers of a Chiral Superconductor

We demonstrate that two-dimensional chiral superconductors on curved surfaces spontaneously develop magnetic flux. This geometric Meissner effect provides an unequivocal signature of chiral super- conductivity, which could be observed in layered materials under stress. We also employ the effect to explain some puzzling questions related to the location of zero-energy Majorana modes.

cond-mat.supr-con↗

arXiv2018

Staircase to Higher-Order Topological Phase Transitions

We find a series of topological phase transitions of increasing order, beyond the more standard second-order phase transition in a one-dimensional topological superconductor. The jumps in the order of the transitions depend on the range of the pairing interaction, which is parametrized by an algebraic decay with exponent $α$. Remarkably, in the limit $α= 1$ the order of the topological transition becomes infinite. We compute the critical exponents for the series of higher-order transitions in exact form and find that they fulfill the hyperscaling relation. We also study the critical behaviour at the boundary of the system and discuss potential experimental platforms of magnetic atoms in superconductors.

cond-mat.stat-mech↗

arXiv2018

Chern-Simons theory and atypical Hall conductivity in the Varma phase

In this letter, we analyze the topological response of a fermionic model defined on the Lieb lattice in presence of an electromagnetic field. The tight-binding model is built in terms of three species of spinless fermions and supports a topological Varma phase due to the spontaneous breaking of time-reversal symmetry. In the low-energy regime, the emergent effective Hamiltonian coincides with the so-called Duffin-Kemmer-Petiau (DKP) Hamiltonian, which describes relativistic pseudospin-0 quasiparticles. By considering a minimal coupling between the DKP quasiparticles and an external Abelian gauge field, we calculate both the Landau-level spectrum and the emergent Chern-Simons theory. The corresponding Hall conductivity reveals an atypical quantum Hall effect, which can be simulated in an artificial Lieb lattice.

cond-mat.str-el↗

arXiv2017

Fermi-Bose mixture in mixed dimensions

One of the challenging goals in the studies of many-body physics with ultracold atoms is the creation of a topological $p_{x} + ip_{y}$ superfluid for identical fermions in two dimensions (2D). The expectations of reaching the critical temperature $T_c$ through p-wave Feshbach resonance in spin-polarized fermionic gases have soon faded away because on approaching the resonance, the system becomes unstable due to inelastic-collision processes. Here, we consider an alternative scenario in which a single-component degenerate gas of fermions in 2D is paired via phonon-mediated interactions provided by a 3D BEC background. Within the weak-coupling regime, we calculate the critical temperature $T_c$ for the fermionic pair formation, using Bethe-Salpeter formalism, and show that it is significantly boosted by higher-order diagramatic terms, such as phonon dressing and vertex corrections. We describe in detail an experimental scheme to implement our proposal, and show that the long-sought p-wave superfluid is at reach with state-of-the-art experiments.

cond-mat.quant-gas↗

arXiv2017

The influence of a weak magnetic field in the Renormalization-Group functions of (2+1)-dimensional Dirac systems

The experimental observation of the renormalization of the Fermi velocity $v_{F}$ as a function of doping has been a landmark for confirming the importance of electronic interactions in graphene. Although the experiments were performed in the presence of a perpendicular magnetic field $B$, the measurements are well described by a renormalization-group (RG) theory that did not include it. Here we clarify this issue, for both massive and massless Dirac systems, and show that for the weak magnetic fields at which the experiments are performed, there is no change in the renormalization-group functions. Our calculations are carried out in the framework of the Pseudo-quantum electrodynamics (PQED) formalism, which accounts for dynamical interactions. We include only the linear dependence in $B$, and solve the problem using two different parametrizations, the Feynman and the Schwinger one. We confirm the results obtained earlier within the RG procedure and show that, within linear order in the magnetic field, the only contribution to the renormalization of the Fermi velocity arises due to interactions. In addition, for gapped systems, we observe a running of the mass parameter.

cond-mat.str-el↗

arXiv2017

Spin g-factor due to electronic interactions in graphene

The gyromagnetic factor is an important physical quantity relating the magnetic-dipole moment of a particle to its spin. The electron spin g-factor in vacuo is one of the best model-based theoretical predictions ever made, showing agreement with the measured value up to ten parts per trillion. However, for electrons in a material the g-factor is modified with respect to its value in vacuo because of environment interactions. Here, we show how interaction effects lead to the spin g-factor correction in graphene by considering the full electromagnetic interaction in the framework of pseudo-QED. We compare our theoretical prediction with experiments performed on graphene deposited on SiO2 and SiC, and we find a very good agreement between them.

cond-mat.str-el↗

arXiv2017

Excitonic gap generation in thin-film topological insulators

In this work, we analyze the excitonic gap generation in the strong-coupling regime of thin films of three-dimensional time-reversal-invariant topological insulators. We start by writing down the effective gauge theory in 2+1-dimensions from the projection of the 3+1-dimensional quantum electrodynamics. Within this method, we obtain a short-range interaction, which has the form of a Thirring-like term, and a long-range one. The interaction between the two surface states of the material induces an excitonic gap. By using the large-$N$ approximation in the strong-coupling limit, we find that there is a dynamical mass generation for the excitonic states that preserves time-reversal symmetry and is related to the dynamical chiral-symmetry breaking of our model. This symmetry breaking occurs only for values of the fermion-flavor number smaller than $N_{c}\approx 11.8$. Our results show that the inclusion of the full dynamical interaction strongly modifies the critical number of flavors for the occurrence of exciton condensation, and therefore, cannot be neglected.

cond-mat.str-el↗

arXiv2017

Driving protocol for a Floquet topological phase without static counterpart

Periodically driven systems play a prominent role in optical lattices. In these ultracold atomic systems, driving is used to create a variety of interesting behaviours, of which an important example is provided by topological states of matter. Such Floquet topological phases have a richer classification that their equilibrium counterparts. Although analogues of the equilibrium topological phases exist, which are characterised by a Chern number, the corresponding Hall conductivity, and protected edge states, there is an additional possibility. This is a phase that has vanishing Chern number and no Hall conductivity, but nevertheless hosts anomalous topological edge states. Due to experimental difficulties associated with the observation of such a phase, it has not been experimentally realised so far. In this paper, we show that optical lattices prove to be a good candidate for both its realisation and subsequent observation, because they can be driven in a controlled manner. Specifically, we present a simple shaking protocol that serves to realise this special Floquet phase, discuss the specific properties that it has, and propose a method to experimentally detect this fascinating topological phase that has no counterpart in equilibrium systems.

cond-mat.quant-gas↗

arXiv2017

Quantum Valley Hall Effect in Massive Dirac Systems Coupled to a Scalar Field

We use Pseudo Quantum Electrodynamics to study massive (2+1)D Dirac systems interacting electromagnetically via a U(1) gauge field in (3+1)D. It was recently found in Ref. [1], that an interaction-induced Quantum Hall Effect (QHE) and Quantum Valley Hall Effect (QVHE) occur in these systems, when considering a two-component fermion representation. Here, we study the corrections to these effects when coupling the fermions to a (2+1)D massive scalar field via a quartic interaction. We find no correction to the QHE and a non-universal correction to the QVHE, which depends on the ratio of the fermion and scalar-field masses.

cond-mat.str-el↗