자료유형  

 학위논문

Control Number  

0017165180

International Standard Book Number  

9798346853626

Dewey Decimal Classification Number  

530

Main Entry-Personal Name  

Joy, Sandeep.

Publication, Distribution, etc. (Imprint  

[S.l.] : The Ohio State University., 2024

Publication, Distribution, etc. (Imprint  

Ann Arbor : ProQuest Dissertations & Theses, 2024

Physical Description  

134 p.

General Note  

Source: Dissertations Abstracts International, Volume: 86-06, Section: B.

General Note  

Advisor: Skinner, Brian.

Dissertation Note  

Thesis (Ph.D.)--The Ohio State University, 2024.

Summary, Etc.  

요약The Wigner crystal (WC) phase represents one of the earliest proposed strongly correlated states of electrons. In this phase, when the density of a two-dimensional electron system is sufficiently low, the system becomes unstable (at low temperatures) and undergoes a phase transition into a solid phase with spontaneously broken translational symmetry. This occurs because, at such low densities, the Coulomb interaction, which localizes electrons, dominates the kinetic energy. Motivated by recent experimental progress on realizing and controlling low density two-dimensional electron systems, this thesis considers various fundamental properties of the WC phase and modifications and extensions of the traditional WC phase.In the first project, we consider the fate of the WC state in a two-dimensional system of massive Dirac electrons as the effective fine structure constantα is increased. In a Dirac system, larger α naively corresponds to stronger electron-electron interactions, but it also implies a stronger interband dielectric response that effectively renormalizes the electron charge. We calculate the critical density and critical temperature associated with the quantum and thermal melting of the WC state using two independent approaches. We show that at α ≫ 1, the WC state is best understood in terms of logarithmically-interacting electrons and that both the critical density and the melting temperature approach a universal, α-independent value. We discuss our results in the context of recent experiments in twisted bilayer graphene near the magic angle.In the second project we focus on WC state formed in Bernal bilayer graphene (BBG) under the application of a perpendicular displacement field. Here, the applied perpendicular electric field flattens the bottom of the conduction band, thereby facilitating the formation of strongly correlated states. Initially, we consider a model of BBG without trigonal warping and theoretically demonstrate that the Berry curvature introduces a novel type of WC state. In this state, electrons develop a spontaneous orbital magnetization once the displacement field surpasses a critical threshold. Next, we consider the impact of trigonal warping in BBG and reveal that it results in an unusual "doubly re-entrant" behavior of the WC phase as a function of density. The rotational symmetry breaking associated with trigonal warping leads to a complex "minivalley order" in the WC state, which shifts abruptly at a critical displacement field value. In both scenarios, we estimate the phase boundary of the WC state concerning density, displacement field, and temperature.In two-dimensional electronic systems, a direct first-order phase transitions (for example the melting of WC to Fermi liquid state) are prohibited as a consequence of the long-range Coulomb interaction, which implies a stiff energetic penalty for macroscopic phase separation. A prominent proposal is that any direct first-order transition is instead replaced by a sequence of "microemulsion" phases, in which the two phases are mixed in patterns of mesoscopic domains. In the third project, we comment on the range Δn of average electron density that such microemulsion phases may occupy. We point out that, even without knowing the value of a phenomenological parameter associated with surface tension between the two phases, one can place a fairly strong upper bound on the value of Δn. We make numerical estimates for Δn in the case of the Fermi liquid to Wigner crystal transition and find Δn to be on the order of 107 cm-2. This value is much smaller than the width of the phase transition observed in experiments, suggesting that disorder is a more likely explanation for the apparent broadening of the transition. Our results also contributed to a collaborative effort with Andrea Young's experimental group at the University of California, Santa Barbara, which explored the transition between stripe and bubble phases of graphene electrons in higher Landau levels.

Subject Added Entry-Topical Term  

Physics.

Subject Added Entry-Topical Term  

Applied physics.

Subject Added Entry-Topical Term  

Quantum physics.

Index Term-Uncontrolled  

Wigner crystal

Index Term-Uncontrolled  

Two-dimensional electron system

Index Term-Uncontrolled  

Coulomb interaction

Index Term-Uncontrolled  

Phase transition

Added Entry-Corporate Name  

The Ohio State University Physics

Host Item Entry  

Dissertations Abstracts International. 86-06B.

Electronic Location and Access  

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Control Number  

joongbu:657538