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Yi, Jinjing,

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Two Dimensional Dirac Semimetals Near the Magic-Angle: Excitations, Interactions, Impurities, and Methods /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Two Dimensional Dirac Semimetals Near the Magic-Angle: Excitations, Interactions, Impurities, and Methods // Jinjing Yi.
Author:	Yi, Jinjing,
Description:	1 electronic resource (114 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 86-08, Section: B.
Contained By:	Dissertations Abstracts International86-08B.
Subject:	Physics. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31766911
ISBN:	9798304910712

Two Dimensional Dirac Semimetals Near the Magic-Angle: Excitations, Interactions, Impurities, and Methods /
Yi, Jinjing,

Two Dimensional Dirac Semimetals Near the Magic-Angle: Excitations, Interactions, Impurities, and Methods /Jinjing Yi. - 1 electronic resource (114 pages)

Source: Dissertations Abstracts International, Volume: 86-08, Section: B.

We theoretically study the excitation spectrum of a two-dimensional Dirac semi-metal in the presence of an incommensurate potential. Such models have been shown to possess magic-angle critical points in the single particle wavefunctions, signaled by a momentum space delocalization of plane wave eigenstates and flat bands due to a vanishing Dirac cone velocity. Using the kernel polynomial method, we compute the single particle Green's function to extract the nature of the single particle excitation energy, damping rate, and quasi-particle residue. As a result, we are able to clearly demonstrate the redistribution of spectral weight due to quasi-periodicity-induced downfolding of the Brillouin zone creating minibands with effective mini Brillouin zones that correspond to emergent superlattices. By computing the damping rate we show that the vanishing of the velocity and generation of finite density of states at the magic-angle transition coincides with the development of an imaginary part in the self energy and a suppression of the quasiparticle residue that vanishes in a power law like fashion. Observing these effects with ultracold atoms using momentum resolved radiofrequency spectroscopy is discussed.We then extended the discussion of two dimensional Dirac semimetal to the case of with Hubbard interaction and later with coulomb interaction.We also explore a new method to accelerate the computation of physical properties similar to Kernel Polynomial method, which is currently widely used in computational condensed matter, to compute density of states, Green's function and conductivity. We used a new method that can approximate the delta function in term of lorentzian functions in a higher order fashion in the applied math community to introduce this new method. Finally, we explore vacancy-induced impurity states in twisted bilayer graphene (TBG) near the magic angle, where ab-initio calculations and atomic-scale modeling demonstrate that these vacancies act as quantum impurities. By constructing an Anderson impurity model and solving it using the numerical renormalization group and kernel polynomial method, we uncover a dichotomy between vacancies in AA/BB and AB/BA regions, with the latter exhibiting multifractal wavefunctions and a broad distribution of Kondo temperatures. These findings highlight the potential of scanning tunneling microscopy to probe both critical single-particle states and many-body ground states in magic-angle TBG.

English

ISBN: 9798304910712Subjects--Topical Terms:

516296
Physics.
Subjects--Index Terms:

Wavefunctions

Two Dimensional Dirac Semimetals Near the Magic-Angle: Excitations, Interactions, Impurities, and Methods /
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500 $a Advisors: Pixley, Jedediah H. Committee members: Kaye, Jason; Yuzbashyan, Emil; Goldstein, Sheldon; Chakram, Srivatsan.
502 $b Ph.D. $c Rutgers The State University of New Jersey, School of Graduate Studies $d 2025.
520 $a We theoretically study the excitation spectrum of a two-dimensional Dirac semi-metal in the presence of an incommensurate potential. Such models have been shown to possess magic-angle critical points in the single particle wavefunctions, signaled by a momentum space delocalization of plane wave eigenstates and flat bands due to a vanishing Dirac cone velocity. Using the kernel polynomial method, we compute the single particle Green's function to extract the nature of the single particle excitation energy, damping rate, and quasi-particle residue. As a result, we are able to clearly demonstrate the redistribution of spectral weight due to quasi-periodicity-induced downfolding of the Brillouin zone creating minibands with effective mini Brillouin zones that correspond to emergent superlattices. By computing the damping rate we show that the vanishing of the velocity and generation of finite density of states at the magic-angle transition coincides with the development of an imaginary part in the self energy and a suppression of the quasiparticle residue that vanishes in a power law like fashion. Observing these effects with ultracold atoms using momentum resolved radiofrequency spectroscopy is discussed.We then extended the discussion of two dimensional Dirac semimetal to the case of with Hubbard interaction and later with coulomb interaction.We also explore a new method to accelerate the computation of physical properties similar to Kernel Polynomial method, which is currently widely used in computational condensed matter, to compute density of states, Green's function and conductivity. We used a new method that can approximate the delta function in term of lorentzian functions in a higher order fashion in the applied math community to introduce this new method. Finally, we explore vacancy-induced impurity states in twisted bilayer graphene (TBG) near the magic angle, where ab-initio calculations and atomic-scale modeling demonstrate that these vacancies act as quantum impurities. By constructing an Anderson impurity model and solving it using the numerical renormalization group and kernel polynomial method, we uncover a dichotomy between vacancies in AA/BB and AB/BA regions, with the latter exhibiting multifractal wavefunctions and a broad distribution of Kondo temperatures. These findings highlight the potential of scanning tunneling microscopy to probe both critical single-particle states and many-body ground states in magic-angle TBG.
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590 $a School code: 0190
650 4 $a Physics. $3 516296
650 4 $a Applied mathematics. $3 2122814
650 4 $a Astronomy. $3 517668
650 4 $a Theoretical physics. $3 2144760
653 $a Wavefunctions
653 $a Brillouin zones
653 $a Twisted bilayer graphene
653 $a Magic angle
653 $a Kondo temperatures
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690 $a 0753
690 $a 0606
690 $a 0364
710 2 $a Rutgers The State University of New Jersey, School of Graduate Studies. $b Physics and Astronomy. $e degree granting institution. $3 3824510
720 1 $a Pixley, Jedediah H. $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-08B.
790 $a 0190
791 $a Ph.D.
792 $a 2025
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31766911