Inertial and topological effects on a 2D electron gas

Brandão, Julio; Filgueiras, Cleverson; Rojas, M.; Moraes, Fernando

doi:10.1088/2399-6528/aa8aa3

Cited by 6 publications

(5 citation statements)

References 22 publications

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“…Similar to the electromagnetic interactions, the investigation of noninertial effects in the context of the conical geometry has attracted attention, and curious theoretical predictions have been achieved. These characteristics are found, for example, in the study of the relativistic quantum motion of scalar bosons [49], in the description of the two-dimensional electron gas model [50], in the relativistic Landau quantization [51], and problems involving the Dirac oscillator [52][53][54].…”

Section: Introductionmentioning

confidence: 95%

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Self-Adjoint Extension Approach to Motion of Spin-1/2 Particle in the Presence of External Magnetic Fields in the Spinning Cosmic String Spacetime

Cunha

Silva

2020

Universe

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In this work, we study the relativistic quantum motion of an electron in the presence of external magnetic fields in the spinning cosmic string spacetime. The approach takes into account the terms that explicitly depend on the particle spin in the Dirac equation. The inclusion of the spin element in the solution of the problem reveals that the energy spectrum is modified. We determine the energies and wave functions using the self-adjoint extension method. The technique used is based on boundary conditions allowed by the system. We investigate the profiles of the energies found. We also investigate some particular cases for the energies and compare them with the results in the literature.

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Section: Introductionmentioning

confidence: 95%

“…The above energies present some curious characteristics. When we compare the energies E 70) and ( 71) can be compared with the energies (47) and (50) of Ref. [55], respectively, for the particular case when the cyclotron frequency plays the role of the Dirac oscillator frequency.…”

mentioning

confidence: 99%

Self-Adjoint Extension Approach to Motion of Spin-1/2 Particle in the Presence of External Magnetic Fields in the Spinning Cosmic String Spacetime

Cunha

Silva

2020

Universe

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“…In fact, inertial effects on the quantum Hall effect have already been examined in Refs. [12][13][14][15][16][17][18]. By solving the corresponding Schrödinger equation, it was found that the energy spectrum of the charge carriers of the sample is affected in a nontrivial way.…”

Section: Introductionmentioning

confidence: 99%

The Quantum Hall Effect under the Influence of Gravity and Inertia: A Unified Approach

Landry,

Hammad,

Saadati

2024

Universe

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The quantum Hall effect under the influence of gravity and inertia is studied in a unified way. We make use of an algebraic approach, as opposed to an analytic approach. We examine how both the integer and the fractional quantum Hall effects behave under a combined influence of gravity and inertia using a unified Hamiltonian. For that purpose, we first re-derive, using the purely algebraic method, the energy spectrum of charged particles moving in a plane perpendicular to a constant and uniform magnetic field either (i) under the influence of a nonlinear gravitational potential or (ii) under the influence of a constant rotation. The general Hamiltonian for describing the combined effect of gravity, rotation and inertia on the electrons of a Hall sample is then built and the eigenstates are obtained. The electrons mutual Coulomb interaction that gives rise to the familiar fractional quantum Hall effect is also discussed within such a combination.

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“…For example, from a relativistic point of view, this combination of the two effects has already been applied in the study of the Dirac and Klein-Gordon oscillators [131][132][133], Aharonov-Casher effect [134], Aharonov-Bohm quantum rings [135], scalar bosons [136], geometric quantum phases [137], etc. Now, from a nonrelativistic point of view, the combination of these two effects has already been applied in the study of quantum dots [138], scattering [139], bound states for neutral particles with AMM and electric dipole moment [140], and in the QHE [141]. Recently, the Dirac, Klein-Gordon, and DKP-like oscillators have been studied under the influence of the noncommutativity and noninertial effects in a cosmic string spacetime [142][143][144].…”

Section: Introductionmentioning

confidence: 99%

The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios

Oliveira¹,

Alencar²,

Landim³

2022

Preprint

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In the present paper, we investigate the bound-state solutions of the noncommutative quantum Hall effect (NCQHE) with anomalous magnetic moment (AMM) in three different relativistic scenarios, namely: the Minkowski spacetime (inertial flat case), the spinning cosmic string (CS) spacetime (inertial curved case), and the spinning CS spacetime with noninertial effects (noninertial curved case). In particular, in the first two scenarios, we have an inertial frame, while in the third, we have a rotating frame. With respect to bound-state solutions, we focus primarily on eigenfunctions (Dirac spinor and wave function) and on energy eigenvalues (Landau levels), where we use the flat and curved Dirac equation in polar coordinates to reach such solutions. However, unlike the literature, here we consider a CS with an angular momentum non-null and also the NC of the positions, and therefore, we seek a more general description for the QHE. Once the solutions are obtained, we discuss the influence of all parameters and physical quantities on relativistic energy levels. Finally, we analyze the nonrelativistic limit, and we also compared our problem with other works, where we verified that our results generalize some particular cases of the literature.

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Inertial and topological effects on a 2D electron gas

Cited by 6 publications

References 22 publications

Self-Adjoint Extension Approach to Motion of Spin-1/2 Particle in the Presence of External Magnetic Fields in the Spinning Cosmic String Spacetime

Self-Adjoint Extension Approach to Motion of Spin-1/2 Particle in the Presence of External Magnetic Fields in the Spinning Cosmic String Spacetime

The Quantum Hall Effect under the Influence of Gravity and Inertia: A Unified Approach

The noncommutative quantum Hall effect with anomalous magnetic moment in three different relativistic scenarios

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