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Novel Quantum Phenomena in Fractal Band Structures.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Novel Quantum Phenomena in Fractal Band Structures./
Author:	Wang, Jian.
Description:	1 online resource (199 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 84-04, Section: B.
Contained By:	Dissertations Abstracts International84-04B.
Subject:	Condensed matter physics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=30058403click for full text (PQDT)
ISBN:	9798351449586

Novel Quantum Phenomena in Fractal Band Structures.
Wang, Jian.

Novel Quantum Phenomena in Fractal Band Structures. - 1 online resource (199 pages)

Source: Dissertations Abstracts International, Volume: 84-04, Section: B.

Thesis (Ph.D.)--Emory University, 2022.

Includes bibliographical references

This dissertation investigates novel quantum phenomena in fractal electronic energy bands also known as Hofstadter bands. In two-dimensional lattices subject to an external perpendicular magnetic field, Hofstadter bands arise when the semi-classical cyclotron radius of the electron becomes comparable to the lattice constant. Hofstadter lattices exhibit a strong interplay between topological electronic states and lattice effects, suggesting rich quantum critical phenomena and novel phases of electronic matter beyond conventional quantum Hall physics. However, this regime had remained inaccessible due to limitations in accessing large magnetic flux per unit cell in conventional 2D materials at laboratory-scale fields, causing Hofstadter bands to collapse into degenerate Landau levels which have been much explored in the quantum Hall effect. In recent years, the emergence of new 2D quantum platforms with nanometer scale unit cells, such as moire materials and nano patterned superlattices, has led to experimental realization of Hofstadter bands. Consequently, Hofstadter physics has experienced a renaissance, emerging as an active frontier to investigate new fundamental questions in quantum matter. Exploiting these opportunities, this thesis develops a theoretical investigation of novel quantum phenomena in Hofstadter quantum materials, concerned with three central themes: (1) a study of the nature of topological quantum phase transitions, (2) a new framework to classify the poorly understood regime of superconductivity in fractal electronic systems and (3) an investigation of the nature of competing electronic orders, uncovering mechanisms to realize unconventional symmetry-broken and topological electronic orders driven entirely by repulsive interactions. The theoretical framework established in this thesis opens a new path toward the realization of novel quantum states, unleashing new paradigms in Hofstadter quantum materials.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798351449586Subjects--Topical Terms:

3173567
Condensed matter physics.
Subjects--Index Terms:

Quantum phase transitionIndex Terms--Genre/Form:

542853
Electronic books.

Novel Quantum Phenomena in Fractal Band Structures.
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502 $a Thesis (Ph.D.)--Emory University, 2022.
504 $a Includes bibliographical references
520 $a This dissertation investigates novel quantum phenomena in fractal electronic energy bands also known as Hofstadter bands. In two-dimensional lattices subject to an external perpendicular magnetic field, Hofstadter bands arise when the semi-classical cyclotron radius of the electron becomes comparable to the lattice constant. Hofstadter lattices exhibit a strong interplay between topological electronic states and lattice effects, suggesting rich quantum critical phenomena and novel phases of electronic matter beyond conventional quantum Hall physics. However, this regime had remained inaccessible due to limitations in accessing large magnetic flux per unit cell in conventional 2D materials at laboratory-scale fields, causing Hofstadter bands to collapse into degenerate Landau levels which have been much explored in the quantum Hall effect. In recent years, the emergence of new 2D quantum platforms with nanometer scale unit cells, such as moire materials and nano patterned superlattices, has led to experimental realization of Hofstadter bands. Consequently, Hofstadter physics has experienced a renaissance, emerging as an active frontier to investigate new fundamental questions in quantum matter. Exploiting these opportunities, this thesis develops a theoretical investigation of novel quantum phenomena in Hofstadter quantum materials, concerned with three central themes: (1) a study of the nature of topological quantum phase transitions, (2) a new framework to classify the poorly understood regime of superconductivity in fractal electronic systems and (3) an investigation of the nature of competing electronic orders, uncovering mechanisms to realize unconventional symmetry-broken and topological electronic orders driven entirely by repulsive interactions. The theoretical framework established in this thesis opens a new path toward the realization of novel quantum states, unleashing new paradigms in Hofstadter quantum materials.
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653 $a Hubbard-Hofstadter model
653 $a Ginzburg-Landau theory
653 $a Chern insulator
653 $a Hofstadter system
653 $a Reentrant superconductivity
653 $a Magnetic translation group
653 $a Topological superconductor
653 $a Quantum Hall effect
653 $a Renormalization group
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