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1.
Li, Feifei.
Transport in Low Dimensional Strongly Correlated Electronic
System.
Degree: PhD, Physics, 2009, Brown University
URL: https://repository.library.brown.edu/studio/item/bdr:203/ 
This thesis presents two theoretical investigations on
transport in low dimensional strongly correlated electronic
systems. In the study of one dimensional system, we demonstrate
that spin current can be generated by an ac voltage in a
one-channel quantum wire with strong repulsive electron
interactions in the presence of a non-magnetic impurity and uniform
static magnetic field. We show that in a certain range of voltages,
the spin current can exhibit a power dependence on the ac voltage
bias with a negative exponent. The spin current expressed in units
of \hbar/2 per second can become much larger than the charge
current in units of the electron charge per second. The spin
current generation requires neither spin-polarized particle
injection nor time-dependent magnetic fields. In the study of
on-Abelian statistics in two dimensional quantum Hall system, we
suggest an experiment which can determine the physical state for
the ν=5/2 quantum Hall plateau. The proposal involves transport
measurements in the geometry with three quantum Hall edges
connected by two quantum point contacts. In contrast to
interference experiments, this approach can distinguish the
Pfaffian and anti-Pfaffian states as well as different states with
identical Pfaffian or anti-Pfaffian statistics. In addition, the
transport is not sensitive to the fluctuations of the number of the
quasiparticles trapped in the system.
Advisors/Committee Members: Feldman, Dima (director), Marston, Brad (reader), Valles, James (reader).Subjects/Keywords: Luttinger Liquid
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APA (6th Edition):
Li, F. (2009). Transport in Low Dimensional Strongly Correlated Electronic
System. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:203/
Chicago Manual of Style (16th Edition):
Li, Feifei. “Transport in Low Dimensional Strongly Correlated Electronic
System.” 2009. Doctoral Dissertation, Brown University. Accessed January 22, 2021.
https://repository.library.brown.edu/studio/item/bdr:203/.
MLA Handbook (7th Edition):
Li, Feifei. “Transport in Low Dimensional Strongly Correlated Electronic
System.” 2009. Web. 22 Jan 2021.
Vancouver:
Li F. Transport in Low Dimensional Strongly Correlated Electronic
System. [Internet] [Doctoral dissertation]. Brown University; 2009. [cited 2021 Jan 22].
Available from: https://repository.library.brown.edu/studio/item/bdr:203/.
Council of Science Editors:
Li F. Transport in Low Dimensional Strongly Correlated Electronic
System. [Doctoral Dissertation]. Brown University; 2009. Available from: https://repository.library.brown.edu/studio/item/bdr:203/
2.
Law, Kam Tuen.
Probing Abelian and Non-Abelian Statistics in Fractional
Quantum Hall States.
Degree: PhD, Physics, 2008, Brown University
URL: https://repository.library.brown.edu/studio/item/bdr:17/
Particles other than bosons and fermions can exist in
two dimensions. One possibility is that when one particle makes a
circle around another particle the total many-particle wave
function acquires a non-trivial phase factor. Such particles are
called Abelian anyons. In a more exotic situation, the action of
moving one particle around other particles or in other words,
particle braiding, is represented by a unitary matrix acting on the
quantum-state vector. If the braiding matrices do not commute with
each other, the particles are called non-Abelian anyons.\ The
existence of both Abelian and non-Abelian anyons has been predicted
in Fractional Quantum Hall systems. Quasiparticles in the Laughlin
states with filling factor ν=1/(2m+1) are Abelian anyons. On
the other hand, quasiparticles in the Moore-Read and Read-Rezayi
states with filling factors ν=5/2 and ν=12/5 ,
respectively, are proposed to be non-Abelian anyons. However, no
experimental observation of the exchange statistics of identical
anyons has been reported so far. \ In this thesis we demonstrate
that the current and shot noise in the topologically nontrivially
set-up of the electronic Mach-Zehnder interferometer can be used to
detect anyonic statistics. The transport is not sensitive to the
fluctuations of the topological charge inside the interferometer
and hence the interference picture is not destroyed by the
tunneling of low-energy neutral excitations between the edges and
localized states in the interferometer. The current and noise
exhibit non-Analytic dependences on small tunneling amplitudes. The
low-temperature Fano factor is always below 1 for Abelian anyons
and can greatly exceed 1 for non-Abelian statistics.
Advisors/Committee Members: Feldman, Dima (director), Mitrovic, Vesna (reader), Ying, See-Chen (reader).Subjects/Keywords: Anyonic Statistics
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APA (6th Edition):
Law, K. T. (2008). Probing Abelian and Non-Abelian Statistics in Fractional
Quantum Hall States. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:17/
Chicago Manual of Style (16th Edition):
Law, Kam Tuen. “Probing Abelian and Non-Abelian Statistics in Fractional
Quantum Hall States.” 2008. Doctoral Dissertation, Brown University. Accessed January 22, 2021.
https://repository.library.brown.edu/studio/item/bdr:17/.
MLA Handbook (7th Edition):
Law, Kam Tuen. “Probing Abelian and Non-Abelian Statistics in Fractional
Quantum Hall States.” 2008. Web. 22 Jan 2021.
Vancouver:
Law KT. Probing Abelian and Non-Abelian Statistics in Fractional
Quantum Hall States. [Internet] [Doctoral dissertation]. Brown University; 2008. [cited 2021 Jan 22].
Available from: https://repository.library.brown.edu/studio/item/bdr:17/.
Council of Science Editors:
Law KT. Probing Abelian and Non-Abelian Statistics in Fractional
Quantum Hall States. [Doctoral Dissertation]. Brown University; 2008. Available from: https://repository.library.brown.edu/studio/item/bdr:17/
3.
Stewart, Michael D.
Superconductor to Insulator Transitions in Amorphous
Nanohoneycomb Films.
Degree: PhD, Physics, 2008, Brown University
URL: https://repository.library.brown.edu/studio/item/bdr:48/
Two dimensional electronic systems exhibit a wide
variety of phenomena including the quantum Hall effect, weak and
strong localization, and metal-insulator transitions, including the
superconductor to insulator transition (SIT). In each case the
possibility of a universal explanation, independent of the
microscopic details of the system, has tantalized researchers. In
some cases, such as the temperature dependence of the conductance
of metal films, or the spacing of resistance plateaus in the Hall
effect, universal behavior is without doubt. Universal explanations
of the amorphous film SIT revolve around the dirty Boson model, in
which the sharp rise in the resistance of a film at low temperature
is due to the localization of Cooper pairs. The existence of
long-lived Cooper pairs in an electrically insulating system, the
central assumption of the model, has remained in doubt because some
measurements support the assertion and others refute it. This
thesis addresses this experimental dissonance by investigating the
SITs of amorphous Bismuth films perforated with a regular
nanohoneycomb (NHC) array of holes. The nanoscale perforations
allow a direct measurement of phase coherent Cooper pairs with an
applied magnetic field. On the insulating side of the disorder
driven SIT the resistance as a function of magnetic field
oscillates with a period, h/2eS, where S is the area of a unit cell
of holes. The 2e period betrays the presence of localized Cooper
pairs in an electrically insulating state. The magnetoresistance of
weak superconducting films reveals several SITs which qualitatively
resemble the disorder driven SIT. The behavior of these transitions
borrows heavily from both sides of a dichotomy exhibited by
different materials through their field driven SITs. NHC films show
activated resistances and a large peak in the magnetoresistance,
analogous to the more spectacular behavior of some materials.
However, they also show a weak, almost metallic, temperature
dependence for a range of fields near the SIT, not unlike the
metallic phase of unpatterned Bismuth and other materials. These
results suggest that an underlying multiply connected geometry in
ostensibly amorphous, unpatterned films may account for some of the
range of material dependent behavior.
Advisors/Committee Members: Valles, James (director), Feldman, Dima (reader), Ling, Xinsheng (reader).Subjects/Keywords: superconductor insulator transition
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Manager
APA (6th Edition):
Stewart, M. D. (2008). Superconductor to Insulator Transitions in Amorphous
Nanohoneycomb Films. (Doctoral Dissertation). Brown University. Retrieved from https://repository.library.brown.edu/studio/item/bdr:48/
Chicago Manual of Style (16th Edition):
Stewart, Michael D. “Superconductor to Insulator Transitions in Amorphous
Nanohoneycomb Films.” 2008. Doctoral Dissertation, Brown University. Accessed January 22, 2021.
https://repository.library.brown.edu/studio/item/bdr:48/.
MLA Handbook (7th Edition):
Stewart, Michael D. “Superconductor to Insulator Transitions in Amorphous
Nanohoneycomb Films.” 2008. Web. 22 Jan 2021.
Vancouver:
Stewart MD. Superconductor to Insulator Transitions in Amorphous
Nanohoneycomb Films. [Internet] [Doctoral dissertation]. Brown University; 2008. [cited 2021 Jan 22].
Available from: https://repository.library.brown.edu/studio/item/bdr:48/.
Council of Science Editors:
Stewart MD. Superconductor to Insulator Transitions in Amorphous
Nanohoneycomb Films. [Doctoral Dissertation]. Brown University; 2008. Available from: https://repository.library.brown.edu/studio/item/bdr:48/
. 
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