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Generalization of Bloch’s Theorem for Tight-binding Models: Quantum Dragon Nanomaterials and Nanodevices

Blazer 335
Speaker(s) / Presenter(s):
Prof. Mark Novotny

Professor Mark Novotny

Mississippi State University

Department of Physics and Astronomy

Title: Generalization of Bloch’s Theorem for Tight-binding Models:Quantum Dragon Nanomaterials and Nanodevices

Abstract: Bloch’s Theorem arguably has the largest economic impact of any condensed matter theorem.  Bloch’s Theorem can only be used for translationally invariant systems, and together with the tight-binding model gives band structures and hence devices such as transistors and optoelectronics.  For tight-binding models, a generalization of Bloch’s Theorem for some strongly disordered (non-translationally invariant) systems is stated and proved.  The theorem generalization leads to predictions of novel electrical properties for some nanomaterials and nanodevices with strong disorder, whimsically called quantum dragons [1].  A number of different predictions of quantum dragon materials and devices [2] will be presented.  Furthermore, conjectures and testing of scaling for materials that are ‘close to quantum dragons’ are given [3].  For example, a perfect quantum wire is one in which impinging electrons from an appropriate incoming lead have probability unity of propagating through the device to the end of an outgoing lead, T(E)=1, for all electron energies E that propagate through the leads. Some quantum dragons are predicted to be perfect quantum wires (see the device in the figure below [3]), while others may make a unique FET (Field Effect Transistor) or quantum sensor or spintronics nanodevice. 

[1] M.A. Novotny, Energy-independent total quantum transmission of electrons through nanodevices with correlated disorder, Phys. Rev. B 90, 165103 (2014).

[2] G. Inkoom and M. Novotny, Quantum dragon solutions for electron transport through nanostructures based on rectangular graphs, J. Physics Commun. 11, 115019 (2018). 

[3] M.A. Novotny and T. Novotný, Order amidst Disorder in 2D+3D Quantum Dragon Composite Nanodevices with varying Breadth, J. Phys: Conf. Ser. 1740, 012002 (2021).