Studies on Fractionalization and Topology in Strongly Correlated Systems from Zero to Two Dimensions / Yichen Hu.

Format:

Book

Thesis/Dissertation

Author/Creator:

Hu, Yichen, author.

Contributor:

Kane, C. L. (Charles L.), degree supervisor.

University of Pennsylvania. Department of Physics and Astronomy, degree granting institution.

Language:

English

Subjects (All):

Condensed matter physics.

Physics.

Physics and astronomy--Penn dissertations.

Penn dissertations--Physics and astronomy.

Local Subjects:

Condensed matter physics.

Physics.

Physics and astronomy--Penn dissertations.

Penn dissertations--Physics and astronomy.

Genre:

Academic theses.

Physical Description:

1 online resource (195 pages)

Contained In:

Dissertations Abstracts International 81-02B.

Place of Publication:

[Philadelphia, Pennsylvania] : University of Pennsylvania ; Ann Arbor : ProQuest Dissertations & Theses, 2019.

Language Note:

English

System Details:

Mode of access: World Wide Web.

text file

Summary:

The interplay among symmetry, topology and condensed matter systems has deepened our understandings of matter and lead to tremendous recent progresses in finding new topological phases of matter such as topological insulators, superconductors and semi-metals. Most examples of the aforementioned topological materials are free fermion systems, in this thesis, however, we focus on their strongly correlated counterparts where electron-electron interactions play a major role. With interactions, exotic topological phases and quantum critical points with fractionalized quantum degrees of freedom emerge. In the first part of this thesis, we study the problem of resonant tunneling through a quantum dot in a spinful Luttinger liquid. It provides the simplest example of a (0+1)d system with symmetry-protected phase transitions. We show that the problem is equivalent to a two channel SU(3) Kondo problem and can be mapped to a quantum Brownian motion model on a Kagome lattice. Utilizing boundary conformal field theory, we find the universal peak conductance and compute the scaling behavior of the resonance line-shape. For the second part, we present a model of interacting Majorana fermions that describes a superconducting phase with a topological order characterized by the Fibonacci topological field theory. Our theory is based on a SO(7)1 = SO(7)1/(G2)1 x (G2)1 coset construction and implemented by a solvable two-dimensional network model. In addition, we predict a closely related ''anti-Fibonacci'' phase, whose topological order is characterized by the tricritical Ising model. Finally, we propose an interferometer that generalizes the Z2 Majorana interferometer and directly probes the Fibonacci non-Abelian statistics. For the third part, we argue that a correlated fluid of electrons and holes can exhibit fractional quantum Hall effects at zero magnetic field. We first show that a Chern insulator can be realized as a free fermion model with p-wave(m = 1) excitonic pairing. Its ground state wavefunction is then worked out and generalized to m > 1. We give several pieces of evidence that this conjectured wavefunction correctly describes a topological phase, dubbed ''fractional excitonic insulator'', within the same universality class as the corresponding Laughlin state at filling 1/m. We present physical arguments that gapless states with higher angular momentum pairing between energy bands are conducive to forming the fractional excitonic insulator in the presence of repulsive interactions. Without interactions, these gapless states appear at topological phase transitions which separate the trivial insulator from a Chern insulator with higher Chern number. Since the nonvanishing density of states at these higher angular momentum band inversion transitions can give rise to interesting many-body effects, we introduce a series of minimal lattice models realizations in two dimensions. We also study the effect of rotational symmetry broken electron-hole exciton condensation in our lattice models using mean field theory.

Notes:

Source: Dissertations Abstracts International, Volume: 81-02, Section: B.

Advisors: Kane, Charles L.; Committee members: Randall Kamien; Eugene Mele; Jonathan Heckman; Bo Zhen.

Department: Physics and Astronomy.

Ph.D. University of Pennsylvania 2019.

Local Notes:

School code: 0175

ISBN:

9781085586467

Access Restriction:

Restricted for use by site license.

This item must not be sold to any third party vendors.