The perfect transmission of charge carriers through potential barriers in graphene (Klein tunneling) is a direct consequence of the Dirac equation that governs the low-energy carrier dynamics. As a result, localized states do not exist in unpatterned graphene, but quasibound states can occur for potentials with closed integrable dynamics. Here, we report the observation of resonance states in photoswitchable self-assembled molecular(SAM)-graphene hybrid. Conductive AFM measurements performed at room temperature reveal strong current resonances, the strength of which can be reversibly gated on- and off- by optically switching the molecular conformation of the mSAM. Comparisons of the voltage separation between current resonances (∼ 70-120 mV) with solutions of the Dirac equation indicate that the radius of the gating potential is ∼ 7 ± 2 nm with a strength ≥ 0.5 eV. Our results and methods might provide a route toward optically programmable carrier dynamics and transport in graphene nanomaterials.
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http://dx.doi.org/10.1021/nl503681z | DOI Listing |
Ultramicroscopy
December 2024
Department of Materials, University of Oxford, 16 Parks Road, Oxford OX1 3PH, United Kingdom. Electronic address:
The rich information of electron energy-loss spectroscopy (EELS) comes from the complex inelastic scattering process whereby fast electrons transfer energy and momentum to atoms, exciting bound electrons from their ground states to higher unoccupied states. To quantify EELS, the common practice is to compare the cross-sections integrated within an energy window or fit the observed spectrum with theoretical differential cross-sections calculated from a generalized oscillator strength (GOS) database with experimental parameters. The previous Hartree-Fock-based and DFT-based GOS are calculated from Schrödinger's solution of atomic orbitals, which does not include the full relativistic effects.
View Article and Find Full Text PDFNanophotonics
July 2024
Inha University, Incheon, Republic of Korea.
Two-dimensional (2D) Dirac materials, e.g., graphene and transition metal dichalcogenides (TMDs), are one-atom-thick monolayers whose electronic behaviors are described by the Dirac equation.
View Article and Find Full Text PDFJ Chem Phys
December 2024
Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
The widely used thermal Hartree-Fock (HF) theory is generalized to include the effect of electron correlation while maintaining its quasi-independent-particle framework. An electron-correlated internal energy (or grand potential) is postulated in consultation with the second-order finite-temperature many-body perturbation theory (MBPT), which then dictates the corresponding thermal orbital (quasiparticle) energies in such a way that all fundamental thermodynamic relations are obeyed. The associated density matrix is of a one-electron type, whose diagonal elements take the form of the Fermi-Dirac distribution functions, when the grand potential is minimized.
View Article and Find Full Text PDFJ Chem Theory Comput
December 2024
Departamento de Química, Universidad Autónoma de Madrid, 28049 Madrid, Spain.
In this work, the two-center Dirac equation is solved numerically using an extension of an adapted B-spline basis set method previously implemented in relativistic atomic calculations (Fischer, C. F.; Zatsarinny, O.
View Article and Find Full Text PDFEntropy (Basel)
November 2024
Department of Electrical & Electronic Engineering, Faculty of Engineering, Ariel University, Ariel 40700, Israel.
Previously, it was shown that Schrödinger's theory can be derived from a potential flow Lagrangian provided a Fisher information term is added. This approach was later expanded to Pauli's theory of an electron with spin, which required a Clebsch flow Lagrangian with non-zero vorticity. Here, we use the recent relativistic flow Lagrangian to represent Dirac's theory with the addition of a Lorentz invariant Fisher information term as is required by quantum mechanics.
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