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 . A number of different predictions of quantum dragon materials and devices  will be presented. Furthermore, conjectures and testing of scaling for materials that are ‘close to quantum dragons’ are given . 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 ), while others may make a unique FET (Field Effect Transistor) or quantum sensor or spintronics nanodevice.
 M.A. Novotny, Energy-independent total quantum transmission of electrons through nanodevices with correlated disorder, Phys. Rev. B 90, 165103 (2014).
 G. Inkoom and M. Novotny, Quantum dragon solutions for electron transport through nanostructures based on rectangular graphs, J. Physics Commun. 11, 115019 (2018).
 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).