Artificial relativistic molecules

Park, Jae Whan; Kim, Hyo Sung; Brumme, Thomas; Heine, Thomas; Yeom, Han Woong

doi:10.1038/s41467-020-14635-z

Cited by 6 publications

(4 citation statements)

References 47 publications

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“…With respect to studying electronic properties of extended systems, two complementary approaches have been used. The first approach is based on coupling localized states of either adatoms, vacancies or dangling bonds, [16][17][18][19][20][21][22][23]. By positioning such species with atomic scale precision, artificial electronic molecules or lattices can be created and their electronic structure studied.…”

Section: Introductionmentioning

confidence: 99%

Coupling quantum corrals to form artificial molecules

et al. 2020

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Quantum corrals can be considered artificial atoms. By coupling many quantum corrals together, artificial matter can be created at will. The atomic scale precision with which the quantum corrals can be made grants the ability to tune parameters that are difficult to control in real materials, such as the symmetry of the states that couple, the on-site energy of these states, the hopping strength and the magnitude of the orbital overlap. Here, we systematically investigate the accessible parameter space for the CO on Cu(111) platform by constructing (coupled) quantum corrals of different sizes and shapes. By changing the configuration of the CO molecules that constitute the barrier between two quantum corrals, the hopping integral can be tuned between 0 and -0.3 eV for s- and p-like states, respectively. Incorporation of orbital overlap is essential to account for the experimental observations. Our results aid the design of future artificial lattices.

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Section: Introductionmentioning

confidence: 99%

Coupling quantum corrals to form artificial molecules

et al. 2020

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“…In recent years, there have been efforts to represent the observation of movements inside materials using Dirac electric states [50] as well as to use relativistic methods to understand atomic and molecular structure [51]. There have also been efforts to provide covariant formulation of the electrodynamics of nonlinear media [52].…”

Section: Historical Notementioning

confidence: 99%

Integration of Dirac’s Efforts to Construct a Quantum Mechanics Which is Lorentz-Covariant

Kim

Noz

2020

Symmetry

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The lifelong efforts of Paul A. M. Dirac were to construct localized quantum systems in the Lorentz covariant world. In 1927, he noted that the time-energy uncertainty should be included in the Lorentz-covariant picture. In 1945, he attempted to construct a representation of the Lorentz group using a normalizable Gaussian function localized both in the space and time variables. In 1949, he introduced his instant form to exclude time-like oscillations. He also introduced the light-cone coordinate system for Lorentz boosts. Also in 1949, he stated the Lie algebra of the inhomogeneous Lorentz group can serve as the uncertainty relations in the Lorentz-covariant world. It is possible to integrate these three papers to produce the harmonic oscillator wave function which can be Lorentz-transformed. In addition, Dirac, in 1963, considered two coupled oscillators to derive the Lie algebra for the generators of the O(3,2) de Sitter group, which has ten generators. It is proven possible to contract this group to the inhomogeneous Lorentz group with ten generators, which constitute the fundamental symmetry of quantum mechanics in Einstein’s Lorentz-covariant world.

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“…In recent years, there have been efforts to represent the observation of movements inside materials using Dirac electric states [49] as well as to use relativistic methods to understand atomic and molecular structure [50]. There have also been efforts to provide covariant formulation of the electrodynamics of nonlinear media [51].…”

Section: Historical Notementioning

confidence: 99%

Integration of Dirac's Efforts to construct Lorentz-covariant Quantum Mechanics

Kim,

Noz

2020

Preprint

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The lifelong efforts of Paul A. M. Dirac were to construct localized quantum systems in the Lorentz covariant world. In 1927, he noted that the time-energy uncertainty should be included in the Lorentz-covariant picture. In 1945, he attempted to construct a representation of the Lorentz group using a normalizable Gaussian function localized both in the space and time variables. In 1949, he introduced his instant form to exclude time-like oscillations. He also introduced the light-cone coordinate system for Lorentz boosts. Also in 1949, he stated the Lie algebra of the inhomogeneous Lorentz group can serve as the uncertainty relations in the Lorentz-covariant world. It is possible to integrate these three papers to produce the harmonic oscillator wave function which can be Lorentz-transformed. In addition, Dirac, in 1963, considered two coupled oscillators to derive the Lie algebra for the generators of the O(3, 2) de Sitter group, which has ten generators. It is proven possible to contract this group to the inhomogeneous Lorentz group with ten generators, which constitute the fundamental symmetry of quantum mechanics in Einstein's Lorentz-covariant world.

show abstract

Artificial relativistic molecules

Cited by 6 publications

References 47 publications

Coupling quantum corrals to form artificial molecules

Coupling quantum corrals to form artificial molecules

Integration of Dirac’s Efforts to Construct a Quantum Mechanics Which is Lorentz-Covariant

Integration of Dirac's Efforts to construct Lorentz-covariant Quantum Mechanics

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