arXiv subjects

Anderson L. R. Barbosa

Publications and source records attributed to Anderson L. R. Barbosa.

At least 19 recordsLinked to original sources

arXiv2026

Parametric Glassiness in Graphene-based Electronic Lévy Glass

Complex disordered conductors can display highly structured and parameter-sensitive transport even in the absence of a thermodynamically stable glass phase. Overlap distributions originally developed for replica symmetry breaking (RSB) provide a useful diagnostic of this organization, provided that their interpretation is distinguished from the equilibrium Parisi construction. In this study, we report RSB-like overlap phenomenology and parametric mesoscopic glassiness in a graphene-based electronic Lévy glass, a device that mimics optical phenomena via electronic processes. By tuning the Fermi energy, we can control the number of propagating wave modes and observe reentrant changes from narrowly centered to broad or bimodal overlap distributions. The phenomenology is observed in both graphene-based and conventional two-dimensional electron-gas electronic Lévy glasses, indicating its generality. Sample-resolved overlap distributions show that the effect is intrinsic to each disorder landscape, whereas the normalized conductance variance shows that the growth of the absolute variance is mainly caused by the increasing mean conductance. We therefore interpret the overlap as a measure of correlation among hierarchically organized transport pathways and the reentrant behavior as evidence of pinning, parameter-induced reorganizations, and mesoscopic chaos in coherent transport.

cond-mat.mes-hall↗

arXiv2026

Scaling, fractal dynamics, and critical exponents in the equilibrium phase transition

Statistical methods are essential for understanding thermodynamic systems with many degrees of freedom. For systems in equilibrium, a very useful method is that of correlation functions, which establish a correlation between a field phi(x), which depends on the spatial position x, and the same field evaluated at another position, phi(x0). Fisher [Journal of Mathematical Physics 5, 944322 (1964)] introduced the autocorrelation function for fluctuations of the order parameter, which has been an important mathematical tool for understanding second-order phase transitions in equilibrium. However, his analysis is restricted to a Euclidean space of dimension d, and an exponent eta is introduced to correct the spatial behavior of the correlation function at T = Tc. In a recent work, Lima et al. [Phys. Rev. E 110, L062107 (2024)] demonstrated that a modern fractional differential analysis is necessary for a complete description of the correlation function at Tc. In this study, we highlight the deep connection among scaling behavior, critical exponents, and fractal geometry. Our results provide a unified geometric interpretation of critical exponents and fractal dimensions, broadly applicable to thermodynamic phase transitions. However, the approach does not apply to topological phase transitions, which lack local order parameters and the associated scale-invariant fractal geometry. We verify its predictions for several cornerstone thermodynamic models: the Ising, Potts, XY, and Heisenberg systems.

cond-mat.stat-mech↗

arXiv2026

Spin Hall effect in electronic Lévy glasses: Enhanced spin current generation in the superdiffusive regime

In spintronics, both electronic charge and spin are used to process and store information. Generation, manipulation, and detection of spin currents are essential for the development of next-generation spintronic technologies. Here, we investigate the spin Hall effect in electronic Lévy glasses composed of graphene ribbons with randomly distributed circular regions of high spin-orbit coupling. These systems exhibit two transport regimes that can be tuned by adjusting the Fermi energy. The superdiffusive regime is characterized by low Fermi energy, low resistivity, and low magnetoresistivity, resulting in a long spin diffusion length, in contrast to the diffusive regime. Employing the Landauer-Büttiker approach in conjunction with numerically exact tight-binding simulations, we compute spin-resolved transmission coefficients to assess the spin Hall current and the spin Hall angle as functions of Fermi energy, spin-orbit coupling strength, and on-site electrostatic potential. Our findings reveal that, in the superdiffusive regime, a low charge current can be converted into a large spin Hall current, whereas in the diffusive regime, the same charge current generates a modest spin Hall current. Moreover, we observe that the spin Hall angle can reach 30% in the superdiffusive regime, whereas in the diffusive regime it is only 5%. These results demonstrate that electronic Lévy glasses provide a versatile platform for controlling spin transport and optimizing the spin Hall effect for spintronic applications.

cond-mat.mes-hall↗

arXiv2026

Engineering Delocalization in Graphene Nanoribbons via Quasiperiodic Edges and Electronic Interactions

We investigate localization effects in zigzag graphene nanoribbons with quasiperiodic Fibonacci-type edge extensions, accounting for electron-electron interactions. We employ a tight-binding model that includes first- and third-nearest-neighbor hoppings, in which electronic interactions are treated within a self-consistent mean-field Hubbard approximation. Charge transport properties are calculated using the Landauer-Büttiker formalism. Our results reveal that the combination of quasiperiodic geometry and electronic interactions gives rise to nontrivial transport phenomena. Specifically, the system exhibits three transport regimes: in the non-interacting case, we observe geometric localization. For weak interactions, the system shows a conductive regime with transmission oscillations, whose multiplicity increases with the Fibonacci generation order. In this regime, delocalization emerges from the interplay between geometry and interaction-induced correlations. Finally, for strong interactions, repulsion dominates, and the system returns to a localized state. Our results demonstrate that quasiperiodic edge engineering, combined with electronic interaction control, offers a promising path to modulate transport in graphene nanoribbons.

cond-mat.mes-hall↗

arXiv2026

Multifractal and Ergodic Properties of Conductance Fluctuations under Strong Disorder

Understanding the stochastic properties of conductance fluctuations in disordered mesoscopic systems is fundamental to quantum transport. In this work, we investigate the multifractal and ergodic properties of the fictitious time series of conductance in two-dimensional tight-binding models under varying Anderson disorder. Using standard multifractal analysis, we show that conductance fluctuations exhibit a transition from non-ergodic to ergodic behavior as the disorder strength increases, as evidenced by the decay of the conductance correlation function. Remarkably, multifractality persists in both regimes; however, it becomes insensitive to shuffling in the strong-disorder (ergodic) regime, suggesting that distributional effects dominate temporal organization. On the contrary, in the weakly disordered (non-ergodic) regime, long-range correlations play a significant role. These findings are robust against changes in lead geometry (asymmetric vs. symmetric). Our results provide new insights into the interplay between ergodicity, multifractality, and rare events in disordered quantum transport.

cond-mat.mes-hall↗

arXiv2025

Extrinsic Orbital Hall Effect and Orbital Relaxation in Mesoscopic Devices

Despite recent advances in orbitronics, the influence of disorder on the orbital Hall effect and orbital relaxation mechanisms remains poorly understood. In this work, we numerically investigate the role of disorder in orbital transport within mesoscopic devices using a real-space tight-binding model on a two-dimensional square lattice that hosts atomic orbitals capable of carrying atomic orbital angular momentum. By considering devices with varying geometries--square and rectangular--and systematically tuning disorder strength, we examine the disorder effect on orbital Hall current (OHC) generation, and orbital relaxation. Our results reveal a strong dependence of the OHC and orbital Hall angle on disorder strength. In square devices, we demonstrate that the orbital Hall response can be strongly enhanced by disorder and its dependence on the disorder strength indicates the dominance of skew-scattering mechanism in the diffusive regime. In rectangular geometries, the orbital current decays exponentially with increasing device width, from which the orbital relaxation length is extracted. These findings provide critical insights into disorder-driven orbital transport phenomena and lay the foundation for designing next-generation orbitronic devices.

cond-mat.mes-hall↗

arXiv2025

Coexistent multifractal mesoscopic fluctuations in Integer Quantum Hall Transition and in Orbital Hall Transition

We show that the integer quantum Hall transition in a disordered nanowire with orbital momentum-space texture connected to four terminals is accompanied by an orbital Hall transition. We applied a multifractal detrended fluctuation analysis and found that both conductance fluctuations in the integer quantum Hall transition (IQHT) and orbital-conductance fluctuations in the orbital Hall transition (OHT) display multifractal behavior. We argue that this multifractality is primarily related to disorder, which gives rise to the strong fluctuations that are fingerprints of IQHT and OHT, but is also a consequence of the fact that the nanowire has finite size, which causes a weakening of the multifractality in a certain range of values of disorder strength followed by a new regime of increasing multifractality with increasing disorder strength. Furthermore, our findings indicate that OHT can bring novel insights to future IQHT analysis.

cond-mat.mes-hall↗

arXiv2024

Lévy flight for electrons in graphene in the presence of regions with enhanced spin-orbit coupling

We propose an electronic Lévy glass built from graphene nanoribbons in the presence of regions with enhanced spin-orbit coupling. Although electrons in graphene nanoribbons present a low spin-orbit coupling strength, it can be increased by a proximity effect with an appropriate substrate. We consider graphene nanoribbons with different edge types, which contain circular regions with a tunable Rashba spin-orbit coupling, whose diameter follow a power-law distribution. We find that spin-orbital clusters induce a transition from superdiffusive to diffusive charge transport, similar to what we recently reported for nanoribbons with electrostatic clusters [Phys. Rev. B. 107, 155432 (2023)]. We also investigate spin polarization in the spin-orbital Lévy glasses, and show that a finite spin polarization can be found only in the superdiffusive regime. In contrast, the spin polarization vanishes in the diffusive regime, making the electronic Lévy glass a useful device whose electronic transmission and spin polarization can be controlled by its Fermi energy. Finally, we apply a multifractal analysis to charge transmission and spin polarization, and find that the transmission time series in the superdiffusive regime are multifractal, while they tend to be monofractal in the diffusive regime. In contrast, spin polarization time series are multifractal in both regimes, characterizing a marked difference between mesoscopic fluctuations of charge transport and spin polarization in the proposed electronic Lévy glass.

cond-mat.mes-hall↗

arXiv2023

Orbital Hall effect and topology on a two-dimensional triangular lattice: from bulk to edge

We investigate a generalized multi-orbital tight-binding model on a triangular lattice, a system prevalent in a wide range of two-dimensional materials, and particularly relevant for simulating transition metal dichalcogenide monolayers. We show that the interplay between spin-orbit coupling and different symmetry-breaking mechanisms leads to the emergence of four distinct topological phases [Eck, P., \textit{et al.}, Phys. Rev. B, 107 (11), 115130 (2023)]. Remarkably, this interplay also triggers the orbital Hall effect with distinguished characteristics. Furthermore, by employing the Landauer-Büttiker formula, we establish that in the orbital Hall insulating phase, the orbital angular momentum is carried by edge states present in nanoribbons with specific terminations. We also show that, as expected, they do not have topological protection against the disorder of the edge states belonging to a first-order topological insulator.

cond-mat.mes-hall↗

arXiv2023

Orbital Hall effect in mesoscopic devices

We investigate the orbital Hall effect through a mesoscopic device with momentum-space orbital texture that is connected to four semi-infinite terminals embedded in the Landauer-Büttiker configuration for quantum transport. We present analytical and numerical evidence that the orbital Hall current exhibits mesoscopic fluctuations, which can be interpreted in the framework of random matrix theory (RMT) (as with spin Hall current fluctuations). The mesoscopic fluctuations of orbital Hall current display two different amplitudes of 0.36 and 0.18 for weak and strong spin-orbit coupling, respectively. The amplitudes are obtained by analytical calculation via RMT and are supported by numerical calculations based on the tight-binding model. Furthermore, the orbital Hall current fluctuations lead to two relationships between the orbital Hall angle and conductivity. Finally, we confront the two relations with experimental data of the orbital Hall angle, which shows good concordance between theory and experiment.

cond-mat.mes-hall↗

arXiv2023

A Lévy flight for electrons in graphene: superdiffusive-to-diffusive transport transition

In this work we propose an electronic Lévy flight device, 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 flight device, superdiffusive transport is an exclusive feature of the low-energy quantum regime, while diffusive transport is a feature of the semiclassical regime. Therefore, we attribute the observed transition to the chiral symmetry breaking, once the energy moves away from the Dirac point of graphene.

cond-mat.mes-hall↗

arXiv2022

Spin Hall angle in single-layer graphene

We investigate the spin Hall effect in a single-layer graphene device with disorder and interface-induced spin-orbit coupling. Our graphene device is connected to four semi-infinite leads that are embedded in a {Landauer-Büttiker} setup for quantum transport. We show that the spin Hall angle of graphene devices exhibits mesoscopic fluctuations that are similar to metal devices. Furthermore, the product between the {maximum spin Hall angle deviation} and dimensionless longitudinal conductivity follows a universal relationship $Θ_{sH} \times σ= 0.18$. Finally, we compare the universal relation with recent experimental data and numerically exact real-space simulations from the tight-binding model.

cond-mat.mes-hall↗

arXiv2022

Wave transmission and its universal fluctuations in one-dimensional systems with Lévy-like disorder: Schrödinger, Klein-Gordon and Dirac equations

We investigate the propagation of waves in one-dimensional systems with Lévy-type disorder. We perform a complete analysis of non-relativistic 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, non-relativistic and relativistic waves present anomalous localization, $\langle T \rangle \propto L^{-α}$. However, for the latter case, in which both parameters follow a Lévy distribution, non-relativistic 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.

cond-mat.mes-hall↗

arXiv2022

Electronic transport in three-terminal chaotic systems with a tunnel barrier

We consider the problem of electronic quantum transport through ballistic mesoscopic systems with chaotic dynamics, connected to a three-terminal architecture in which one of the terminals has a tunnel barrier. Using a semiclassical approximation based on matrix integrals, we calculate several transport statistics, such as average and variance of conductance, average shot-noise power, among others, that give access to the extreme quantum regime (small channel numbers in the terminal) for broken and intact time-reversal symmetry, which the traditional random matrix approach does not access. As an application, we treat the dephasing regime.

cond-mat.mes-hall↗

arXiv2022

Turbulence Hierarchy and Multifractality in the Integer Quantum Hall Transition

We offer a new perspective to the problem of characterizing mesoscopic fluctuations in the inter-plateau region of the integer quantum Hall transition. We found that longitudinal and transverse conductance fluctuations, generated by varying the external magnetic field within a microscopic model, are multifractal and lead to distributions of conductance increments (magnetoconductance) with heavy tails (intermittency) and signatures of a hierarchical structure (a cascade) in the corresponding stochastic process, akin to Kolmogorov's theory of fluid turbulence. We confirm this picture by interpreting the stochastic process of the conductance increments in the framework of H-theory, which is a continuous-time stochastic approach that incorporates the basic features of Kolmogorov's theory. The multifractal analysis of the conductance "time series," combined with the H-theory formalism provides, strong support for the overall characterization of mesoscopic fluctuations in the quantum Hall transition as a multifractal stochastic phenomenon with multiscale hierarchy, intermittency, and cascade effects.

cond-mat.mes-hall↗

arXiv2021

Effect of proximity-induced spin-orbit coupling in graphene mesoscopic billiards

Van der Waals heterostructures based on two-dimensional materials have recently become a very active topic of research in spintronics, both aiming at a fundamental description of spin dephasing processes in nanostructures and as a potential element in spin-based information processing schemes. Here, we theoretically investigate the magnetoconductance of mesoscopic devices built from graphene proximity-coupled to a high spin-orbit coupling material. Through numerically exact tight-binding simulations, we show that the interfacial breaking of inversion symmetry generates robust weak antilocalization even when the $z\rightarrow -z$ symmetric spin-orbit coupling in the quantum dot dominates over the Bychkov--Rashba interaction. Our findings are in interpreted on the light of random matrix theory, which links the observed behavior of quantum interference corrections to a transition from circular-orthogonal to circular-sympletic ensemble.

cond-mat.mes-hall↗

arXiv2020

Global correlation matrix spectra of the surfacetemperature of the Oceans from Random MatrixTheory to Poisson fluctuations

In this work we use the random matrix theory (RMT) to correctly describethe behavior of spectral statistical properties of the sea surface temperatureof oceans. This oceanographic variable plays an important role in theglobalclimate system. The data were obtained from National Oceanic and Atmo-spheric Administration (NOAA) and delimited for the period 1982 to 2016.The results show that oceanographic systems presented specific $β$ values thatcan be used to classify each ocean according to its correlation behavior. Thenearest-neighbors spacing of correlation matrix for north, central and south ofthe three oceans get close to a RMT distribution. However, the regions delim-ited in the Antarctic pole exhibited the distribution of the nearest-neighborsspacing well described by the Poisson model, which shows astatistical changeof RMT to Poisson fluctuations.

physics.ao-ph↗

arXiv2020

Electronic transport in disordered graphene superlattices with scale-free correlated barrier spacements

A transfer matrix approach is used to study the electronic transport in graphene superlattices with long-range correlated barrier spacements. By considering the low-energy electronic excitations as massless Dirac fermions, we compute by transmission spectra of graphene superlattices with potential barriers having spacements randomly distributed with long-range correlations governed by a power-law spectral density $S(k)\propto 1/k^α$. We show that at large incidence angles, the correlations in the disorder distribution do not play a significant role in the electronic transmission. However, long-range correlations suppress the Anderson localization as normal incidence is approached and a band of transmitting modes sets up reminiscent of Klein tunneling.

cond-mat.mes-hall↗