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

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).

*Order amidst Disorder in 2D+3D Quantum Dragon Composite Nanodevices with varying Breadth*, J. Phys: Conf. Ser.

**1740**, 012002 (2021).