Keywords

Quantum Hall effect, Quantum dots, Tunneling (Physics)

Abstract

This work represents a first-principles calculation of the electron tunneling current into quantum dots in the fractional quantum Hall effect regime. The system under consideration consists of an idealized Scanning Tunneling Microscope (STM) tip and a quantum dot with disk geometry and interacting electrons in a transverse magnetic field. Within the context of this model the tunneling current between the STM tip and the dot is examined for spin-polarized electrons at and around a filling factor of 1/3. The current expression is based on a second-quantized Hamiltonian in which electrons in the dot are interacting, confined, and restricted to the lowest Landau level, necessary to capture the physics of the fractional quantum Hall effect. The Hamiltonian includes simple approximations for the STM tip and the tip-dot tunneling. An exact analytic expression for the first-order tunneling current is derived using a Green's function approach. To calculate the tunneling current numerically the infinite Hilbert space of the dot is truncated to have a finite dimension within the lowest Landau level. This simplification is appropriate for a low temperature system in the fractional quantum Hall regime because of the finite size of the quantum dot and the large energy gap between Landau levels. The tunneling current is then solved in two steps. First, many-electron energy eigenstates are calculated from the truncated Hamiltonian by numerical diagonalization. This is carried out for varying numbers of electrons N. The energy eigenstates form a set of complete basis states of the system and are used in the expression for the tunneling current. In the second step, the chemical potential in the dot is chosen to select a desired number of electrons and the tunneling current evaluated. We have carried out this program for filling factors near 1=3 while modulating the system parameters of interest to determine functional dependencies.

Notes

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Graduation Date

2011

Semester

Summer

Advisor

Johnson, Michael D.

Degree

Doctor of Philosophy (Ph.D.)

College

College of Sciences

Department

Physics

Format

application/pdf

Identifier

CFE0003990

URL

http://purl.fcla.edu/fcla/etd/CFE0003990

Language

English

Release Date

August 2011

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

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Physics Commons

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