arXiv subjects

Pedro Pereyra

Publications and source records attributed to Pedro Pereyra.

12 recordsLinked to original sources

arXiv2026

Unified Integer and Fractional Quantum Hall Effects from Boundary-Induced Edge-State Quantization

Despite the success of Landau-level theory and edge-state transport formalisms, a direct microscopic link between bulk quantization and the observed hierarchy of quantum Hall plateaus has not been established. In particular, no unified microscopic mechanism accounting simultaneously for integer and fractional sequences has been derived within standard quantum mechanics. Here we show that boundary-induced quantization of edge states provides this missing bridge. Starting from the Landau problem in laterally confined two-dimensional electron systems, we demonstrate that the imposition of Dirichlet, Neumann, and mixed (Robin) boundary conditions discretizes both the guiding-center coordinate and the longitudinal momentum of chiral edge states. The resulting boundary-dependent spectra generate families of edge channels with well-defined multiplicities that couple to electronic transport. When incorporated into an edge-state transport description, this boundary quantization reproduces the integer Hall sequence and simultaneously yields a structured hierarchy of fractional filling factors without invoking separate microscopic mechanisms. We further show that a weak Hall-induced parity-breaking contribution reorganizes the low-energy edge spectrum while leaving the bulk Landau levels intact. This controlled symmetry breaking enhances edge-state multiplicities at small Landau indices and stabilizes the fractional plateaus observed at strong magnetic fields. The quantized Hall response thus emerges from the interplay between Landau quantization and boundary-induced guiding-center discretization, which together determine the spectrum and occupation of chiral edge channels. These results establish boundary-induced quantization as the microscopic origin of quantum Hall transport and provide a unified description of both integer and fractional regimes within conventional quantum mechanics.

cond-mat.mes-hall↗

arXiv2025

Transition from MOS to Ideal Capacitor Behavior Triggered by Tunneling in the Inversion Population Regime

An analytical solution to the nonlinear Poisson equation governing the inversion layer in metal-oxide-semiconductor (MOS) structures has recently been obtained, resolving a fundamental challenge in semiconductor theory first identified in 1955. This breakthrough enables the derivation of explicit expressions for relevant physical quantities, such as the inversion-layer width, electric potential, and charge distribution, as functions of gate voltage $V_G$, distance from oxide-semiconductor interface and impurity concentration. These quantities exhibit rapid variation during early-stage inversion but saturate once the gate voltage exceeds the threshold voltage by a few tenths of a volt signaling a transition in the MOS response to $V_G$. The onset of tunneling through the Esaki barrier leads to increased charge accumulation near the interface, reshaping the charge distribution into a two-dimensional profile and shifting the potential drop from the semiconductor to the oxide layer. This reconfiguration resembles the behavior of an ideal parallel-plate capacitor, with charge confined at the interface and the voltage drop localized across the oxide. We analyze this mechanism in detail and demonstrate, through explicit calculations, that the tunneling current through the Esaki-like barrier formed during inversion becomes dominant, effectively superseding classical inversion behavior. These results offer a new analytical foundation for quantum-aware device modeling and inform the design of next-generation MOSFET and tunneling FET architectures.

cond-mat.mtrl-sci↗

arXiv2025

Quantum Hall Resistance and Quantum Hall Plateaus from Edge State Quantization

Despite the extensive literature on the quantum Hall effect (QHE), a direct derivation of the phenomenological formula $ρ_{xy} = h/e^2ν$ from first principles has remained elusive. In this work, we revisit the Landau and Landauer-Büttiker formalisms and impose hard-wall boundary conditions on the wavefunction, an essential but often overlooked constraint. This condition quantizes the guiding center position and the longitudinal wave number $k_x$, leading naturally to a discrete number of edge states without invoking energy bending. We derive the Hall resistance directly and recover the standard result $ρ_{xy} = h/e^2ν$, along with an explicit expression for the filling factor $ν$ in terms of the Fermi energy and magnetic field. The resulting resistance steps reproduce the observed QHE plateaus and match experimental data without fitting parameters.

cond-mat.mes-hall↗

arXiv2021

The Transfer Matrix Method and The Theory of Finite Periodic Systems. From Heterostructures to Superlattices

Long-period systems and superlattices, with additional periodicity, have new effects on the energy spectrum and wave functions. Most approaches adjust theories for infinite systems, which is acceptable for large but not small number of unit cells $n$. In the past 30 years, a theory based entirely on transfer matrices was developed, where the finiteness of $n$ is an essential condition. The theory of finite periodic systems (TFPS) is also valid for any number of propagating modes, and arbitrary potential profiles (or refractive indices). We review this theory, the transfer matrix definition, symmetry properties, group representations, and relations with the scattering amplitudes. We summarize the derivation of multichannel matrix polynomials (which reduce to Chebyshev polynomials in the one-propagating mode limit), the analytical formulas for resonant states, energy eigenvalues, eigenfunctions, parity symmetries, and discrete dispersion relations, for superlattices with different confinement characteristics. After showing the inconsistencies and limitations of hybrid approaches that combine the transfer-matrix method with Floquet's theorem, we review some applications of the TFPS to multichannel negative resistance, ballistic transistors, channel coupling, spintronics, superluminal, and optical antimatter effects. We review two high-resolution experiments using superlattices: tunneling time in photonic band-gap and optical response of blue-emitting diodes, and show extremely accurate theoretical predictions.

cond-mat.mtrl-sci↗

arXiv2020

On the transmittance of metallic superlattices in the optical regime and the true refraction angle

Recently, an approach for metallic superlattices based on the finite periodic systems theory was introduced \cite{Pereyra2020}. Unlike most, if not all, of the published approaches that are valid in the $n \rightarrow \infty $ limit, the finite periodic approach is valid for any natural number $n$ and allows one to determine analytical expressions for scattering amplitudes and dispersion relations. It was shown, for frequencies below $ω_{p}$ and large metallic-layer thickness, that under the common assumption that fields inside conductors move along the so-called "true" angle that defines the orientation of the constant-phase planes, anomalous results appear with an apparent parity effect. This issue is addressed here and it is shown that those results are due to the lack of unitarity and the underlying phenomena of absorption and loss of energy. Two compatible approaches are presented here to solve the lack of unitarity and to account for the absorption phenomenon. We show that by keeping the complex angles, the principle of flux conservation is fully satisfied, above and below $ω_p$. This approach, free of assumptions, gives us light to improve the formalism when the real angle assumption is made. We show that by taking into account the induced currents and the requirement of flux conservation, we end up with an improved approach, with new Fresnel and transmission coefficients, fully compatible with those of the complex-angle approach.

cond-mat.mtrl-sci↗

arXiv2020

Photonic transmittance in metallic and metamaterial Superlattices

We present here the transmission of electromagnetic waves through layered structures of metallic and left-handed media. Based on the theory of finite periodic systems, we show that besides the strong influence of the incidence angle, the low transmission characteristic of a single conductor slab, for frequencies $ω$ below the plasma frequency $ω_p$, becomes in this domain highly oscillating. Similarly, the well-established transmission coefficient of a single left-handed slab becomes highly resonant with superluminal effects in superlattices with more than one unit cell. We determine the space-time evolution of a wave packet through the $λ/4$ photonic superlattice whose transmission coefficient is a sequence of isolated and equidistant peaks with negative phase times. We show that the space-time evolution of a Gaussian wave packet, with centroid at any of these peaks, agrees with the theoretical predictions, and no violation of the causality principle occurs. We show that besides the strong influence of the incidence angle, the coherent coupling of the bulk plasmon modes and the interface surface plasmon polaritons lead to oscillating transmission coefficients, and depending on the parity of the number of unit cells $n$ of the superlattice, the transmission vanishes or amplifies as the conductor width increases. We determine the space-time evolution of a wave packet through the $λ/4$ photonic superlattice whose bandwidth becomes negligible, and the transmission coefficient becomes a sequence of isolated and equidistant peaks with negative phase times. We show that the space-time evolution of a Gaussian wave packet, with the centroid at any of these peaks, agrees with the theoretical predictions, and no violation of the causality principle occurs.

physics.optics↗

arXiv2018

Why the effective-mass approximation works so well for nano-structures

The reason why the effective-mass approximation, derived for wave packets constructed from infinite-periodic-systems' wave functions, works so well with nanoscopic structures, has been an enigma and a challenge for theorists. To explain and clarify this issue, we re-derive the effective-mass approximation in the framework of the theory of finite periodic systems, i.e., using energy eigenvalues and fast-varying eigenfunctions, obtained with analytical methods where the finiteness of the number of primitive cells per layer, in the direction of growth, is a prerequisite and an essential condition. This derivation justifies and explains why the effective-mass approximation works so well for nano-structures. We show also with explicit optical-response calculations that the rapidly varying eigenfunctions $Φ_{ε_0,η_0}(z)$ of the one-band wave functions $Ψ^{ε_0,η_0}_{μ,ν}(z)= Ψ^{ε_0}_{μ,ν}(z) Φ_{ε_0,η_0}(z)$, can be safely dropped out for the calculation of inter-band transition matrix elements.

cond-mat.mtrl-sci↗

arXiv2017

Charge polarization effects on the optical response of blue-emitting superlattices

In the new approach to study the optical response of periodic structures, successfully applied to study the optical properties of blue-emitting InGaN/GaN superlattices, the spontaneous charge polarization was neglected. To search the effect of this quantum confined Stark phenomenon we study the optical response, assuming parabolic band edge modulations in the conduction and valence bands. We discuss the consequences on the eigenfunction symmetries and the ensuing optical transition selection rules. Using the new approach in the WKB approximation of the finite periodic systems theory, we determine the energy eigenvalues, their corresponding eigenfunctions and the subband structures in the conduction and valence bands. We calculate the photoluminescence as a function of the charge localization strength, and compare with the experimental result. We show that for subbands close to the barrier edge the optical response and the surface states are sensitive to charge polarization strength.

cond-mat.mtrl-sci↗

arXiv2016

New approach to study light-emission of periodic structures. Unveiling novel surface-states effects

An accurate approach to calculate the optical response of periodic structures is proposed. Using the genuine superlattice eigenfunctions and energy eigenvalues, the eigenfunctions parity symmetries, the subband symmetries and the detached surface energy levels, we report new optical-transition selection rules and explicit optical-response calculations. Observed transitions that were considered forbidden, become allowed and interesting optical-spectra effects emerge as fingerprints of intra-subband and surface states. The unexplained groups and isolated narrow peaks observed in high resolution blue-laser spectra, by Nakamura et al., are now fully explained and faithfully reproduced

cond-mat.mtrl-sci↗

arXiv2016

Improved optical transitions theory for superlattices and periodic systems; new selection rules

Using the superlattice (SL) eigenvalues $E_{μ,ν}^{c,v}$ and eigenfunctions $φ_{μν}^{c,v}(z) $, obtained within the theory of finite periodic systems, where $μ$ indicates the subbands and $ν$ the intra-subband levels, we calculate optical transitions in SLs and periodic systems. Based on the eigenfunction parity symmetries, studied in the previous paper, new symmetry selection rules (SSR) are derived and photoluminescence and infrared spectra for different types of SLs are calculated. The narrow peaks clustered in groups that couldn't be explained before in Nakamura's et al. for blue emitting devices, are now fully understood. Among the various properties and differences that we discuss in the paper, we notice that many transitions that were experimentally observed but theoretically forbidden, are now perfectly possible. Since the number of matrix-elements allowed by the SSR is generally too large, we devote the second part of this paper to show that one can obtain the same spectra when, besides the SSR, other leading order selection rules closely related to intra-subband symmetries are introduced. These rules reduce the number of matrix evaluations from $\sim n^2$$n_cn_v/2$ to $\sim n$$n_cn_v/2$, i.e., depending on the SL, from about 1000 to 100. We comment also on a third rule, that picks up the contributions of the surface and edge states, and show that it reduces further the number of transitions to $N_s\leq n_cn_v$. With these rules, the main peaks are conserved and their number practically matches with that of the actual spectrum. Excellent agreements with experimental results are found.

cond-mat.mtrl-sci↗

arXiv2016

Theory of finite periodic systems: The eigenfunctions symmetries

Using the analytical expressions for the genuine eigenfunctions $φ_{μν}(z)$ and eigenvalues $E_{μ,ν}$, of open, bounded and quasi-bounded finite periodic systems, we derive the eigenfunctions space-inversion symmetry relations. The superlattice eigenfunctions symmetries, closely related with the symmetries and zeros of the Chebyshev polynomials of the second kind $U_n$, are fully written in terms of the number of unit cells $n$, the subband index $μ$ and the intra-subband index $ν$.

cond-mat.mtrl-sci↗

arXiv2000

On Eigenvalues and Eigenfunctions Absent in the Actual Solid State Theory

In this letter new, closed and compact analytic expressions for the evaluation of resonant energies, resonant bound-states, eigenvalues and eigenfunctions for both scattering and bounded $n$-cell systems are reported. It is shown that for (scattering and bounded) 1-D systems the eigenfunctions $Ψ_{μ,ν}(z)$ are simple and well defined functions of the Chebyshev polynomials of the second kind $U_{n}$, and the energy eigenvalues $E_{μ,ν}$ (in the $μ$-th band) are determined by the zeros of these polynomials. New insights on the energy gap and the localization effect induced by phase coherence are shown.

cond-mat.soft↗