Electronic properties of a defected ring-shaped quantum dot array

Shakouri, Kh.; Esmaeilzadeh, Mahdi; Szafran, B.; Salehani, Hojjatollah K.

doi:10.1088/0953-8984/23/22/225801

Cited by 2 publications

(3 citation statements)

References 43 publications

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“…Although the proof presented here is up to second order, we conjecture that this could be carried to all orders in degenerate perturbation theory. Of course, this conjecture is in agreement with our numerical simulations and previous works [28,30,107,109,113,117,118].…”

Section: The Effects Of Cyclic Symmetries In Perturbation Theorysupporting

confidence: 93%

“…This simple rule explains all the observed spectra considered here and is consistent with previous results in 1D [28,30,107,118] and 2D [109,113,117] QRs with cyclic symmetries.…”

Section: Asymmetric Deformationssupporting

confidence: 93%

“…More importantly, we find that for rings with a cyclic symmetry C n , the Aharonov-Bohm oscillations are split into sets of n-states. This property is compatible with previous simulations where the system had a cyclic symmetry [28,30,107,118], even if the system is a 2DQR [109,113,117].…”

Section: Example 3: Aharonov-bohm Oscillationssupporting

confidence: 91%

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Teoria quântica em uma subvariedade: Efeitos clássicos, quânticos e térmicos

Monroy¹

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The problem of how to describe the effective dynamics of particles or fields confined to a lower dimensional curved space-time is of interest in many areas of physics. In the literature, several methods have been proposed to attack this problem. Recently it has been reported some experimental evidences that are consistent with the so-called confining potential approach. In light of these results, the purpose of this thesis is to construct a quantum theory for particles confined in a submanifold of a flat space-time employing the theoretical framework of the confining potential approach. The thesis is divided into two parts. The first one is dedicated exclusively to the study of quantum mechanics on a submanifold. For this purpose, we derive the effective Schrödinger, Dirac and Klein-Gordon equations on a curved submanifold, in the presence of an external electromagnetic field. We examine the singular features of these equations and present some applications to condensed matter. In the second part of this thesis, we start from the quantum mechanics on the submanifold and then we formulate the quantum field theory (QFT) on the submanifold. We will show that the "free" QFT on a submanifold can be schematically represented as a quantum theory of free fields on a curved background plus a scalar potential and an external SO(n − m) Yang-Mills field. For this theory, we compute the one-loop effective action for scalars and fermions at finite temperature and chemical potential to all orders using the Seely-DeWitt expansion. For interacting theories, we will prove that the theory known as reduced quantum electrodynamics (RQED dγ ,de) can be recovered from the confining potential approach. For a two-dimensional theory, we propose a large class of extensions of the Schwinger model, in which the interaction between fermions goes beyond the linear potential. We demonstrate that, remarkably, these extensions are exactly solvable for massless fermions and that there is no dynamical mass generation for the fermions. Furthermore, we construct a new family of exactly bosonized theories. We also show that RQED 4,2 has the necessary features to be identified as an effective field theory for graphene wires. Finally, we study the effect of an interplay of real and pseudomagnetic fields in graphene. We compute the fermion condensate, the induced vacuum charge density, the one-loop effective action and the magnetization, for this system. We will show that the presence of a non-zero pseudomagnetic field makes it possible, experimentally, to observe an induced vacuum charge density. Moreover, we will show that it is possible to have control over the magnetization as well as the dynamical mass for each valley in graphene, by straining or varying the applied magnetic field.

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Section: The Effects Of Cyclic Symmetries In Perturbation Theorysupporting

confidence: 93%

“…This simple rule explains all the observed spectra considered here and is consistent with previous results in 1D [28,30,107,118] and 2D [109,113,117] QRs with cyclic symmetries.…”

Section: Asymmetric Deformationssupporting

confidence: 93%

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Teoria quântica em uma subvariedade: Efeitos clássicos, quânticos e térmicos

Monroy¹

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Theoretical study of persistent current in a nanoring made of a band insulator

Mošková

Moško

Tóbik

2012

Physica Status Solidi (b)

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We study theoretically persistent currents in rings made of band insulators with a fully occupied valence band and empty conduction band. We derive an expression for the persistent current in a one‐dimensional (1D) insulating ring with an arbitrary valence band ε(k). Setting for ε(k) the realistic (numerically calculated) valence bands, we estimate persistent currents in the nanorings made of real band insulators like GaAs, Ge, and InAs. Further, we express the persistent current in the insulating 1D ring through the Wannier functions of the constituting infinite 1D crystal. We find these Wannier functions analytically in the LCAO approximation. We obtain fully analytically the persistent current in the insulating ring and we apply the result to a 1D GaAs ring with conduction electrons subjected to a periodic potential emulating the insulating lattice. In general, persistent currents in rings made of band insulators decay with the ring length exponentially due to the exponential decay of the Wannier function tails. In spite of that, the currents of measurable size are found for a suitably chosen nanorings similar to those fabricated recently for coherent nanoelectronics. Finally, to provide insight, our major results are rederived from the so‐called ring Wannier functions.

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Electronic properties of a defected ring-shaped quantum dot array

Cited by 2 publications

References 43 publications

Teoria quântica em uma subvariedade: Efeitos clássicos, quânticos e térmicos

Teoria quântica em uma subvariedade: Efeitos clássicos, quânticos e térmicos

Theoretical study of persistent current in a nanoring made of a band insulator

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