Transport & Nanostructures Group

Our first paper of 2023 “Lévy flight for electrons in graphene: Superdiffusive-to-diffusive transport transition”  has just appeared in the Physical Review B.

In this work we propose an electronic Lévy glass, analogous to a recent optical realization. To that end, we investigate the transmission of electrons in graphene nanoribbons in the presence of circular electrostatic clusters, whose diameter follow a power-law distribution. We analyze the effect of the electrostatic clusters on the electronic transport regime of the nanoribbons, in terms of its diffusion behavior. Our numerical calculations show that the presence of circular electrostatic clusters induces a transition from Lévy (superdiffusive) to diffusive transport as the energy increases. Furthermore, we argue that in our electronic Lévy glass, superdiffusive transport is an exclusive feature of the low-energy quantum regime, while diffusive transport is a feature of the semiclassical regime. We thus attribute the observed transition to the chiral symmetry breaking, once the energy moves away from the Dirac point of graphene.

The results stem from Diego B. Fonseca mater’s thesis, which is supervised by Anderson L. R. Barbosa at UFRPE.

Our latest publication of 2022 “Wave transmission and its universal fluctuations in one-dimensional systems with Lévy-like disorder: Schrödinger, Klein-Gordon, and Dirac equations”  has just appeared in the Physical Review E.

In this publication we investigate the propagation of electronic waves in one-dimensional systems with Lévy-type disorder. We perform a complete analysis of nonrelativistic and relativistic wave transmission submitted to potential barriers whose width, separation, or both follow Lévy distributions characterized by an exponent 0<α<1. For the first two cases, where one of the parameters is fixed, nonrelativistic and relativistic waves present anomalous localization. However, for the latter case, in which both parameters follow a Lévy distribution, nonrelativistic and relativistic waves present a transition between anomalous and standard localization as the incidence energy increases relative to the barrier height. Moreover, we obtain the localization diagram delimiting anomalous and standard localization regimes, in terms of incidence angle and energy. Finally, we verify that transmission fluctuations, characterized by its standard deviation, are universal, independent of barrier architecture, wave equation type, incidence energy, and angle, further extending earlier studies on electronic localization. We believe that our predictions can be verified in graphene nanoribbons, where Dirac electrons are the main charge carriers.

This publication was done in collaboration with Jonas R.F. Lima and Anderson L. R. Barbosa, both at UFRPE, and we began it before the covid-19 pandemic hit the world! We are all glad to finally see it out there.

Our latest publication of 2022 “Localization effects in graphene nanoribbons with quasiperiodic hopping modulation”  has just appeared in Micro and Nanostructures (formerly know as Superlattices and Microstructures).

Graphene nanoribbons present remarkable electronic transport properties which can be tailored to specific applications. We consider a quasiperiodic modulation in the electronic hopping of metallic armchair and zigzag graphene nanoribbons, originating a Fibonacci superlattice with two possible hopping parameters. The electronic conductance for various Fibonacci generations is calculated via the recursive Green’s function method. We observe that a quasiperiodic hopping modulation opens a conductance gap at the Fermi level of armchair nanoribbons, leading to a strong electronic localization regime. The localization length initially increases with Fibonacci generation and saturates for high order generations. Considering an energy slightly above the Fermi level, we obtain similar results for the armchair nanoribbon, while the zigzag nanoribbon eventually enters the localization regime for high order Fibonacci generations. Our results demonstrate that a quasiperiodic hopping modulation is a viable way to control the electronic transport in graphene nanoribbons, widening its range of possible application in nanoelectronic devices.

This publication stems from José Roberto’s PhD dissertation at UFRN, which has been co-supervised by Anderson L. R. Barbosa at UFRPE.

Our second publication of 2022 “A direct approach to calculate the temperature dependence of the electronic relaxation time in 2D semiconductors from Boltzmann transport theory”  has just been published in the Journal of Applied Physics.

In this publication we present a simple heuristic method to obtain the relaxation time and the temperature dependence of the electrical conductivity in 2D semiconductors. The approach is computationally straightforward, and relies on the BoltzTraP algorithm, on a direct fitting procedure, and on a scaling at a reference temperature. The approach provides a good estimate for the thermoelectric figure of merit ZT. We demonstrate our approach in nitrogenated holey graphene (NHG), boron-doped NHG, and tungsten disulfide 2D-WS2. In all these cases, our results agree with computationally expensive calculations available in the literature at a fraction of the computing time.

This publication was led by former postdoc Raphael Tromer at UFRN, in collaboration with Mauro S. Ferreira at Trinity College Dublin and Marcos G. E. da Luz at Universidade Federal do Paraná. Computational support was provided by the supercomputing center at UFRN (NPAD).

Our first publication of 2022 “Thermal conductivity of Thue–Morse and double-period quasiperiodic graphene-hBN superlattices”  has just been published in the International Journal of Heat and Mass Transfer.

Nanostructured superlattices are promising materials for novel electronic devices due to their adjustable physical properties. Periodic superlattices facilitate coherent phonon thermal transport due to constructive wave interference at the boundaries between the materials. However, it is possible to induce a crossover from coherent to incoherent transport regimes by adjusting the superlattice period. In 2018 we observed such crossover in periodic graphene-boron nitride nanoribbons as the length of individual domains was increased. In general, transport properties are dominated by translational symmetry and the presence of unconventional symmetries leads to unusual transport characteristics. In 2020 we showed that the quasiperiodicity can suppress coherent phonon thermal transport in superlattices following the Fibonacci quasiperiodic sequence, which lie between periodic and disordered structures. Finally, in our latest publication we perform non-equilibrium molecular dynamics simulations to investigate phonon heat transport in graphene-hBN superlattices following the Thue-Morse and double-period quasiperiodic sequences, and show that coherent transport is indeed suppressed due to phonon localization caused by increase in superlattice period. We also obtain a general expression for conductivity as a function of quasiperiodic generation and supercell size, which might be useful for superlattice following other sequences.

This is the latest publication, but hopefully not the last, from Isaac’s PhD dissertation. It was completely carried out within our research group at UFRN and UFPE, and we are grateful for the computational support provided by the supercomputing center at UFRN (NPAD).

Encontro de Física do Norte e Nordeste (North and northeast physics meeting) promoted by the Brazilian Physical Society is the second largest Physics meeting in Brazil, gathering more than 500 researchers from the north and northeast regions of Brazil. In 2021, the event takes place online, hosted by Universidade Federal de Pernambuco, from 18 to 20 of October.

I contributed to the local organization of the event, but also presented a talk entitled “Electronic structure, elastic properties and thermal conductivity of pentadiamond: First-principles calculations and machine-trained potentials“, in which I present some of our results recently published in Carbon Trends.