Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2412.13220

Relativistic particles in super-periodic potentials: exploring graphene and fractal systems

Sudhanshu Shekhar·Bhabani Prasad Mandal·Anirban Dutta
View original source ↗Read source document ↗Export metadata ↓

Abstract

In this article, we employ the transfer matrix method to investigate relativistic particles in super-periodic potentials (SPPs) of arbitrary order $n \in I^{+}$. We calculate the reflection and transmission probabilities for spinless Klein particles encountering rectangular potential barriers with super-periodic repetition. It is found that spinless relativistic particles exhibit Klein tunneling and a significantly higher degree of reflection compared to their non-relativistic counterparts. Additionally, we analytically explore the behavior of experimentally realizable massless Dirac electrons as they encounter rectangular potential barriers with a super-periodic pattern in a monolayer of graphene. In this system, the transmission probability, conductance, and Fano factor are evaluated as functions of the number of barriers, the order of super-periodicity, and the angle of incidence. Our findings reveal that the transmission probability shows a series of resonances that depend on the number of barriers and the order of super-periodicity. We extend our analysis to specific cases within the Unified Cantor Potentials (UCPs)-$\gamma$ system ($\gamma$ is a scaling parameter greater than $1$), focusing on the General Cantor fractal system and the General Smith-Volterra-Cantor (GSVC) system. For the General Cantor fractal system, we calculate the tunneling probability, which reveals sharp transmission peaks and progressively thinner unit cell potentials as $G$ increases. In the GSVC system, we analyze the potential segment length and tunneling probability, observing nearly unity tunneling coefficients when $\gamma \approx 1$, as well as saturation behavior in transmission coefficients at higher stages $G$.

Explore related subjects

cond-mat.mes-hallquant-ph

Keep this discovery

BibTeXRIS

Sudhanshu Shekhar, Bhabani Prasad Mandal, Anirban Dutta. 2024-12-16. Relativistic particles in super-periodic potentials: exploring graphene and fractal systems. https://doi.org/10.1103/s82p-5sxv

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Emergence of spin-orbit coupling among spin, atomic orbital, and Bloch dynamics in Janus double-transition-metal MXenes

We found a spin-orbit coupling to cause a simultaneous correlation among three degrees of freedom, the electronic spin, orbital, and Bloch dynamics in an investigation into the electronic structure of Janus double-transition-metal MXenes, Mo$_2$HfC$_2$OS and W$_2$HfC$_2$OS. In this paper, it is also revealed that the spin-orbit coupling causes a staggered spin configuration with a trigonal pattern around the $\Gamma$ point near the insulating gap. We developed a reduced Hamiltonian describing the electronic states and show that the spin-orbit coupling cannot be equated with conventional forms for a single electron in solids, LS, Rashba, and Dresselhaus couplings, even in the approximation under the low-energy and small wave number condition. Because of the intrinsic shape of the conduction band, a trigonally alternating spin-momentum locking emerges with the spin axis perpendicular to the layer plane. The theoretical analysis shows that these Janus materials can provide a platform for exploring the spin-related phenomena due to the trigonal spin-momentum locking other than Rashba and Dresselhaus types.

cond-mat.mes-hall↗
arXiv2026

A substrate booster for P-type 2D ferromagnetic semiconductor

Spin transistors with its both charge and spin properties tuned via electrostatic gating are believed capable for widespread use, which however have proven challenging due to the extreme rareness of their physical base -- magnetic semiconductors. The latter are limited within very few systems including diluted magnetic semiconductors (DMS) and two-dimensional ferromagnetic semiconductors (2D-FMS), and known to suffer from inadequate gate-tunability of their electric and/or magnetic properties. Here, we show a substrate engineering paradigm by interfacing few-layered Cr$_{2}$Ge$_{2}$Te$_{6}$ (FL-CGT) with an antiferromagnetic insulator CrOCl. Owing to the subtle interfacial charge transfer couplings, CGT can be drastically turned from an ambipolar semiconductor into a high performance P-type semiconductor. When cooled below the Curie temperature, the ON-OFF ratio in such substrate-boosted FMS field-effect transistor (FET) reaches 10$^{5}$ with its coercive field $H_{c}$ of magnetic hysteresis loop tunable by a factor of more than 200$\%$, enabling {gate-assisted magnetic switching in the prototype semiconducting spin transistor architecture}. A crossover from critical power-law scaling to a dual power-law behaviour under heavy hole doping was further observed. Our findings {signify} an efficient interfacial charge transfer and electrically modulated magnetic anisotropy energy supported by calculations. This high performance P-type FMS-FET system suggests that active substrate-boosting paradigm might be a powerful path for the investigation of future gate-tunable spintronic devices.

cond-mat.mes-hall↗
arXiv2026

In-plane magnetic field control of anomalous Hall response enabled by magnetic anisotropy engineering

Engineering magnetic anisotropy provides a powerful route to control magnetization orientation and unlock emerging functionalities in opto-spintronic and current-driven devices. Beyond its role in magnetization reversal, the effective anisotropy can strongly influence the magnetotransport response, offering an additional degree of freedom to tune new device functionalities. In this work, we report a magnetotransport study of a ferrimagnetic [Tb/Co]$_{\times 5}$ multilayer grown with a Tb thickness gradient, whose wedge-shaped tilts the uniaxial anisotropy axis slightly away from the film normal. Anomalous Hall resistivity measurements from 80 K to 300 K reveal a spin reorientation transition, while the angular dependence of the magnetotransport responses exposes the crucial role of the tilted anisotropy. A simplified macrospin model reproduces the full angular response across the transition and shows that the observed anomalous Hall effect when the in-plane magnetic field is applied originates from the tilt of the uniaxial anisotropy axis, which supplies a built-in symmetry-breaking mechanism, enabling in-plane field control over the out-of-plane anomalous Hall response, sign included. These findings establish tilted magnetic anisotropy as a promising route toward Hall effect-based sensor applications and highlight Tb/Co multilayers as a versatile platform for anisotropy-engineered spintronic devices.

cond-mat.mes-hall↗