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Exploitation of Symmetries of Quantu...

Sharma, Shivam,

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Exploitation of Symmetries of Quantum Mechanics in Nanostructures /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Exploitation of Symmetries of Quantum Mechanics in Nanostructures // Shivam Sharma.
作者:	Sharma, Shivam,
面頁冊數:	1 electronic resource (197 pages)
附註:	Source: Dissertations Abstracts International, Volume: 86-07, Section: B.
Contained By:	Dissertations Abstracts International86-07B.
標題:	Aerospace engineering. -
電子資源:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31640092
ISBN:	9798302184641

Exploitation of Symmetries of Quantum Mechanics in Nanostructures /
Sharma, Shivam,

Exploitation of Symmetries of Quantum Mechanics in Nanostructures /Shivam Sharma. - 1 electronic resource (197 pages)

Source: Dissertations Abstracts International, Volume: 86-07, Section: B.

The design, discovery, synthesis and characterization of novel nanomaterials and nanostructures with intriguing electronic and functional properties are central to contemporary scientific research. Symmetries of quantum mechanics such as time-reversal, spatial, and particle-hole symmetry govern the range of remarkable phenomena including superconductivity, ferromagnetism, electron transport, spin dynamics and emergence of topological states. The exploitation of these symmetries plays a pivotal role in understanding and controlling the behavior of quantum systems at nanoscale.Following this line of thought, this thesis first deals with quasi-one-dimensional (1D) materials with helical and cyclic symmetries such as nanotubes, nanowires and nanoribbons. The emergent forms of such matter can exhibit strongly correlated phases and collective electronic phases such as superconductivity, ferromagnetism, Wigner crystallization and Mott insulating states. Due to the unique morphology of these materials, they are expected to exhibit these properties significantly different from bulk phase materials. Moreover, its 1D geometry offers excellent opportunities for incorporating them in novel quantum, electromagnetic and photonic device applications. In this work, we use specialized symmetry-adapted first principles calculations to investigate the electromechanical properties of a set of 1D materials featuring flat bands. Specifically, two prototypical nanotubes based on Kagome and hexagonal lattice geometries of carbon and phosphorus are studied. All types of nanotubes explored here display flat bands degenerate with either parabolic or Dirac bands, which makes them multifunctional. Our findings unveil a range of noteworthy phase transitions, electronic, structural, and magnetic characteristics unique to these nanotubes.The thesis further leverages a graph theoretic framework to systematically generate a variety of 2D lattices which feature fascinating electronic states including flat bands and Dirac cone. Specifically, the split and line graphs of a bipartite lattices exhibit a degenerate combination of flat and dispersive bands in their band diagram. These bands are usually topologically trivial but by introducing spin-orbit coupling, the flat band transforms into a quasi-flat, become gapped and show topologically non-trivial state. Remarkably, tuning system parameters and applying external strain trigger quantum and topological phase transition transitions between trivial insulator, semimetallic, and topological phases across different lattices. These findings highlight the potential of strain engineering as a powerful tool for manipulating quantum phases.Finally, we have extended the objective molecular dynamics (OMD) framework to nonadiabatic quantum dynamics. In the nonadiabatic regime, the system's characteristics are influenced by the coupled electron-nuclei dynamics. The nuclei follow the classical description of OMD, and the electronic motion is described by the time-dependent Schrödinger equation. Using the time-dependent symmetry groups, we derived the exact simplification of time-dependent Schrödinger equation. Such phenomena break Born-Oppenheimer approximation and offer opportunity to investigate non-equilibrium electron transport, photoexcitation and superfluidity.

English

ISBN: 9798302184641Subjects--Topical Terms:

1002622
Aerospace engineering.
Subjects--Index Terms:

Flat band physics

Exploitation of Symmetries of Quantum Mechanics in Nanostructures /
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245 1 0 $a Exploitation of Symmetries of Quantum Mechanics in Nanostructures / $c Shivam Sharma.
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300 $a 1 electronic resource (197 pages)
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500 $a Source: Dissertations Abstracts International, Volume: 86-07, Section: B.
500 $a Advisors: James, Richard D. Committee members: Tadmor, Ellad; Luskin, Mitchell; Banerjee, Amartya; Leo, Perry.
502 $b Ph.D. $c University of Minnesota $d 2024.
520 $a The design, discovery, synthesis and characterization of novel nanomaterials and nanostructures with intriguing electronic and functional properties are central to contemporary scientific research. Symmetries of quantum mechanics such as time-reversal, spatial, and particle-hole symmetry govern the range of remarkable phenomena including superconductivity, ferromagnetism, electron transport, spin dynamics and emergence of topological states. The exploitation of these symmetries plays a pivotal role in understanding and controlling the behavior of quantum systems at nanoscale.Following this line of thought, this thesis first deals with quasi-one-dimensional (1D) materials with helical and cyclic symmetries such as nanotubes, nanowires and nanoribbons. The emergent forms of such matter can exhibit strongly correlated phases and collective electronic phases such as superconductivity, ferromagnetism, Wigner crystallization and Mott insulating states. Due to the unique morphology of these materials, they are expected to exhibit these properties significantly different from bulk phase materials. Moreover, its 1D geometry offers excellent opportunities for incorporating them in novel quantum, electromagnetic and photonic device applications. In this work, we use specialized symmetry-adapted first principles calculations to investigate the electromechanical properties of a set of 1D materials featuring flat bands. Specifically, two prototypical nanotubes based on Kagome and hexagonal lattice geometries of carbon and phosphorus are studied. All types of nanotubes explored here display flat bands degenerate with either parabolic or Dirac bands, which makes them multifunctional. Our findings unveil a range of noteworthy phase transitions, electronic, structural, and magnetic characteristics unique to these nanotubes.The thesis further leverages a graph theoretic framework to systematically generate a variety of 2D lattices which feature fascinating electronic states including flat bands and Dirac cone. Specifically, the split and line graphs of a bipartite lattices exhibit a degenerate combination of flat and dispersive bands in their band diagram. These bands are usually topologically trivial but by introducing spin-orbit coupling, the flat band transforms into a quasi-flat, become gapped and show topologically non-trivial state. Remarkably, tuning system parameters and applying external strain trigger quantum and topological phase transition transitions between trivial insulator, semimetallic, and topological phases across different lattices. These findings highlight the potential of strain engineering as a powerful tool for manipulating quantum phases.Finally, we have extended the objective molecular dynamics (OMD) framework to nonadiabatic quantum dynamics. In the nonadiabatic regime, the system's characteristics are influenced by the coupled electron-nuclei dynamics. The nuclei follow the classical description of OMD, and the electronic motion is described by the time-dependent Schrödinger equation. Using the time-dependent symmetry groups, we derived the exact simplification of time-dependent Schrödinger equation. Such phenomena break Born-Oppenheimer approximation and offer opportunity to investigate non-equilibrium electron transport, photoexcitation and superfluidity.
546 $a English
590 $a School code: 0130
650 4 $a Aerospace engineering. $3 1002622
650 4 $a Applied physics. $3 3343996
650 4 $a Quantum physics. $3 726746
650 4 $a Electromagnetics. $3 3173223
653 $a Flat band physics
653 $a Objective quantum dynamics
653 $a Quantum mechanics
653 $a Topological insulators
653 $a Ferromagnetism
690 $a 0538
690 $a 0215
690 $a 0599
690 $a 0607
710 2 $a University of Minnesota. $b Aerospace Engineering and Mechanics. $e degree granting institution. $3 3830106
720 1 $a James, Richard D. $e degree supervisor.
773 0 $t Dissertations Abstracts International $g 86-07B.
790 $a 0130
791 $a Ph.D.
792 $a 2024
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=31640092