Eigen spectra and wave functions of the massless Dirac fermions under the nonuniform magnetic fields in graphene

Eshghi, Mahdi; Mehraban, Hossein; Azar, I. Ahmadi

doi:10.1016/j.physe.2017.07.024

Cited by 20 publications

(20 citation statements)

References 43 publications

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“…In this stage, to solve Eq. 53, one can use the generalized series method by Eshghi et al [99,112,113], and the parameters a 0 , a 1 , a 2 , a −1 and a −2 are given in Eq. 54, and by a little algebraic calculation, one can evaluate eigenvalues of the problem.…”

Section: Scalar Particle With Linear and Coulomb-type Scalar Potentiamentioning

confidence: 99%

Linear confinement of a scalar and spin-0 particle in a topologically trivial flat Gödel-type space-time

Ahmed

2019

Eur. Phys. J. C

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In the previous work (Ahmed, Eur Phys J C 78(7):598, 2018), we investigated the relativistic quantum effects on a scalar and spin-half particles in a topologically trivial flat Gödel-type space-time. We have found that the energy eigenvalues of the system are influenced by the vorticity parameter characterizing the space-time. In the present work, we investigate the linear confinement of a scalar particle on the Klein-Gordon equation with a linear and Coulombtype scalar potential in this flat Gödel-type solution. The energy eigenvalues of the system get modifies due to the presence of scalar potentials, and the vorticity parameter. In addition, we study the relativistic quantum motion of spin-0 particles with vector and scalar potentials of Coulomb-type and analyze the effects on the energy eigenvalues.

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Section: Scalar Particle With Linear and Coulomb-type Scalar Potentiamentioning

confidence: 99%

Linear confinement of a scalar and spin-0 particle in a topologically trivial flat Gödel-type space-time

Ahmed

2019

Eur. Phys. J. C

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“…Thus, present-day technology allows for the theoretical and experimental study of a massless particle, with states that are eigenstate of the helicity operator and that can interact with electromagnetic fields through its charge. Analytical solutions of the Dirac equations are very scarce, and it is remarkable that graphene in few cases permits solutions in a closed form that can be used as benchmarks for approximated or numerical calculations in complex problems [6][7][8][9][10][11]. These properties, together with a wealth of new effects, make the study of graphene very attractive.…”

Section: Introductionmentioning

confidence: 99%

“…This might look like an artificial model, since the symmetry that is required for treating the electron as a massless particle requires an infinite lattice. Besides, the manufacture of a graphene annulus is rather difficult, and the Klein paradox obstructs the design of a potential trap [16]; several magnetic schemes have been proposed to bypass these drawbacks [4,6,7,[17][18][19]. In our model, we adopt a very large annulus that should make the use of a massless electron in a finite piece of graphene acceptable; as a reward, analytical solutions are found.…”

Section: Introductionmentioning

confidence: 99%

Laser Assisted Dirac Electron in a Magnetized Annulus

Fiordilino

2021

Symmetry

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We study the behaviour of a charge bound on a graphene annulus under the assumption that the particle can be treated as a massless Dirac electron. The eigenstates and relative energy are found in closed analytical form. Subsequently, we consider a large annulus with radius ρ∈[5000,10,000]a0 in the presence of a static magnetic field orthogonal to its plane and again the eigenstates and eigenenergies of the Dirac electron are found in both analytical and numerical form. The possibility of designing filiform currents by controlling the orbital angular momentum and the magnetic field is shown. The currents can be of interest in optoelectronic devices that are controlled by electromagnetic radiation. Moreover, a small radial force acts upon the annulus with a stretching effect. A linearly polarized electromagnetic field propagating in the orthogonal direction is added; the time evolution of the operators show that the acceleration of the electron is proportional to the rate of change of the spin of the particle.

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“…[37][38][39] However, a large number of potentials of physical importance used into the Schrödinger equation or the perturbations into Dirac and Dirac-Weyl equations may be transformed into the form of the biconfluent Heun function (BHF). [40][41][42][43][44][45][46][47][48] Moreover, from a century ago, the Schrödinger equation can be reduced to the BHF known in mathematics for harmonium. 49,50 Although, some of the authors have submitted different solvable traditional models as analytically, [51][52][53][54][55] and there are a few works about of the geometric model in these areas.…”

Section: Introductionmentioning

confidence: 99%

Schrödinger equation based analytic assessment of thermal properties of confined electrons under vector and scalar fields

Eshghi

Azar

Soudi

2021

Math Methods in App Sciences

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In this research, we have extracted the covariant form of the Schrödinger equation in the Riemannian manifold 0.25emscriptM0.25em= ℝ3 with a position‐dependent mass (PDM) distribution in the presence of magnetic fields for each point p∈scriptM. Then, we have solved the extracted nonrelativistic equation for a charged particle with a PDM in quantum system under the magnetic and Aharonov–Bohm (AB) flux fields and Yukawa‐like potential using the Frobenius series method. It is interesting that the obtained analytical solutions of the nonrelativistic equation have been expressed in terms of the biconfluent Heun function (BHF). Then, we have expanded the BHF as the power series and obtained a three‐term recurrence relation between the successive coefficients of the power expansion. To investigate the nontrivial solution of the power expansion, we need to apply an explicit continued fraction equation for the coefficients of the recurrence relation. This relation must be satisfied in order to assure the series convergence. At the continuation, we have found two different conditions using the submitted lemmas. Then, using the obtained conditions, we have calculated the eigenvalues and eigenfunctions of the particle in the arbitrary point of the manifold. Finally, the canonical formalism is applied to compute different thermodynamic variables for the case of the higher temperatures. Also, we have discussed the special states on the obtained results.

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Eigen spectra and wave functions of the massless Dirac fermions under the nonuniform magnetic fields in graphene

Cited by 20 publications

References 43 publications

Linear confinement of a scalar and spin-0 particle in a topologically trivial flat Gödel-type space-time

Linear confinement of a scalar and spin-0 particle in a topologically trivial flat Gödel-type space-time

Laser Assisted Dirac Electron in a Magnetized Annulus

Schrödinger equation based analytic assessment of thermal properties of confined electrons under vector and scalar fields

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