Magnetic dispersion of Dirac fermions in graphene under inhomogeneous field profiles

Jahani, D.; Shahbazi, Farhad; Setare, M. R.

doi:10.1140/epjp/i2018-12137-4

Cited by 6 publications

(10 citation statements)

References 27 publications

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“…The first-order intertwining method presented here generalizes the shape invariant technique that different authors have used previously to describe the behavior of an electron near to the Dirac points in a graphene layer with applied external magnetic fields [23][24][25][26][27][28]. Similarly as Figure 7: Second intertwining for the Morse potential with k = 6α, ν 1 = − 3 2 , ν 2 = − 1 2 , 1 = − 1 2 E − 1 = − 11α 2 2 , 2 = −E − 1 = −11α 2 : (a) generated potential V 2 (x, 2 ) (continuous line) and initial oneṼ 1 (x, 1 ) (dashed line), with energy levels E n (x)| 2 for the ground state (GS, blue) and the excited states n = 1, 2, 3 (red, green, purple); (d) current density for the excited states with the same colors that in (c).…”

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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Dirac electron in graphene with magnetic fields arising from first-order intertwining operators

Castillo-Celeita

2020

J. Phys. A: Math. Theor.

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The behaviour of a Dirac electron in graphene, under magnetic fields which are orthogonal to the layer, is studied. The initial problem is reduced to an equivalent one, where two one-dimensional Schrödinger Hamiltonians H ± are intertwined by a first order differential operator. Special magnetic field are initially chosen, in order that V ± will be shape invariant exactly solvable potentials. When looking for more general first order operators, intertwining H − with a non necessarily shape invariant Hamiltonian, new magnetic fields associated also to analytic solutions will be generated. The iteration of this procedure is as well discussed. * mfcastillo@fis.cinvestav.mx † david@fis.cinvestav.mx arXiv:1905.12045v2 [quant-ph]

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Dirac electron in graphene with magnetic fields arising from first-order intertwining operators

Castillo-Celeita

2020

J. Phys. A: Math. Theor.

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“…In this work, we have studied the Dirac fermion propagator for graphene-like systems in external magnetic fields. We have constructed the Dirac fermion propagator for graphene-like systems in the presence of non-trivial and inhomogeneous external magnetic fields generated by first-order intertwining operators from the solutions to the Dirac equation for a constant magnetic field and an exponetially decaying magnetic field [27,34,[37][38][39][40]. We constructed the propagator in the basis of the eigenfunctions of the operator (γ • Π) 2 .…”

Section: Final Remarksmentioning

confidence: 99%

Ritus functions for graphene-like systems with magnetic fields generated by first-order intertwining operators

Concha-Sánchez,

Díaz-Bautista,

Raya

2022

Preprint

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In this work, we construct the propagator for Dirac fermions in graphene-like systems immersed in external magnetic fields. In these circumstances, the asymptotic fermionic states are no longer plane waves and thus the propagator in the basis of eigenstates of the momentum operator has a more cumbersome form. An alternative representation of this object is obtained on the basis of the Ritus eigenfunctions which correspond to asymptotic states of Dirac fermions in a background electromagnetic field. We construct the 2D Dirac fermion propagator in the Ritus eigenfunction basis considering external magnetic fields generated by first-order intertwining operators which are non-uniform in space, static, and directed perpendicularly to the plane of the system. Charge and current densities are found directly from the corresponding propagator.

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“…In addition, the coherent state methods have been started to be applied recently to graphene subject to static homogeneous magnetic fields [179]. As can be seen, the SUSY methods applied to Dirac materials is a very active field which surely will continue its development in the near future [151][152][153][154][155][156][157][158][159][160][161].…”

Section: Recent Applications Of Susy Qmmentioning

confidence: 99%

“…Recently, the SUSY methods started to be used also in the study of Dirac electrons in graphene and some of its allotropes, when external electric or magnetic fields are applied [151][152][153][154][155][156][157][158][159][160][161]. It is worth to mention as well some systems in optics, since there is a well-known correspondence between Schrödinger equation and Maxwell equations in the paraxial approximation, which makes that the SUSY methods can be applied directly in some areas of optics [162][163][164][165][166][167][168][169].…”

Section: Introductionmentioning

confidence: 99%

Trends in Supersymmetric Quantum Mechanics

David²

2019

Integrability, Supersymmetry and Coherent States

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Along the years, supersymmetric quantum mechanics (SUSY QM) has been used for studying solvable quantum potentials. It is the simplest method to build Hamiltonians with prescribed spectra in the spectral design. The key is to pair two Hamiltonians through a finite order differential operator. Some related subjects can be simply analyzed, as the algebras ruling both Hamiltonians and the associated coherent states. The technique has been applied also to periodic potentials, where the spectra consist of allowed and forbidden energy bands. In addition, a link with nonlinear second-order differential equations, and the possibility of generating some solutions, can be explored. Recent applications concern the study of Dirac electrons in graphene placed either in electric or magnetic fields, and the analysis of optical systems whose relevant equations are the same as those of SUSY QM. These issues will be reviewed briefly in this paper, trying to identify the most important subjects explored currently in the literature. KeywordsSupersymmetric quantum mechanics • Coherent states • Painlevé equations • Painlevé transcendents • Polynomial Heisenberg algebras • Factorization method • Exact solutions • Spectral design • Graphene Dedicated to my dear friend and colleague Véronique Hussin. D. J. Fernández C ( )

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Magnetic dispersion of Dirac fermions in graphene under inhomogeneous field profiles

Cited by 6 publications

References 27 publications

Dirac electron in graphene with magnetic fields arising from first-order intertwining operators

Dirac electron in graphene with magnetic fields arising from first-order intertwining operators

Ritus functions for graphene-like systems with magnetic fields generated by first-order intertwining operators

Trends in Supersymmetric Quantum Mechanics

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