Study of Anderson localization in disordered system with bond breaking disorder
Malik, Mohammed Zahid
North Carolina State University, US
Abstract
The dynamics and transport of a particle in condensed-matter systems can be described using a tight-binding Hamiltonian. In this work, we present a simple approach to investigate Anderson localization in a three-dimensional system with an off-diagonal disorder. We construct the tight-binding Hamiltonian for the system in which a single random energy is assigned to each lattice site, and the hopping integrals are restricted to nearest-neighbour sites only. We introduce bond-breaking disorder, where some hopping terms between sites are randomly weakened. We compute disorder-impacted density of states (DOS), the inverse participation ratio (IPR), and level statistics to identify the Anderson transition. Emergence of mobility edge has been seen while analysing inverse participation ratio with disorder. We address our problem in the thermodynamic limit by applying appropriate periodic boundary conditions and numerically demonstrate the existence of an Anderson localization transition.
Keywords: Disordered, localization, numerically, inverse participation ratio, dynamic
Impact Statement
Our research investigates Anderson localization in disordered systems, focusing on the effects of bond-breaking disorder. Anderson localization, where the electronic wavefunctions localize due to disorder, plays a key role in understanding electronic transport properties in various materials. In this study, we explore the specific case of bond-breaking disorder, where random changes in bond strengths can disrupt the structure of the system, leading to alterations in the electronic states and transport behavior.
We have demonstrated the Anderson transition — the shift from extended to localized electronic states — using two powerful techniques: the Inverse Participation Ratio (IPR) and level statistics. By analyzing the IPR, we identified the critical disorder strength that marks the localization transition. Furthermore, level statistics provided additional confirmation by revealing how the distribution of energy levels changes as the disorder increases. This method is sensitive to the subtle effects of bond-breaking disorder, offering deeper insights into the role of local perturbations in driving localization.
Our findings contribute to a more nuanced understanding of Anderson localization in disordered systems, particularly in the context of bond-breaking disorder. This work not only advances theoretical models of electronic transport in disordered systems but also has significant implications for the design of materials in nanoelectronics, quantum computing, and material science, where control over disorder plays a critical role in determining device properties.
About The Author
Dr. Mohammed Zahid Malik is a theoretical physicist specializing in Condensed Matter Physics. He is currently working as a Postdoctoral Fellow at the Department of Chemistry, North Carolina State University. His recent research work focuses on disordered systems in condensed matter theory. He has authored a paper titled “Study of Anderson Localization in Disordered System with Bond Breaking Disorder,” which explores the phenomenon of electron localization due to the presence of disorder and how bond-breaking impacts this behavior in various systems. His research contributes to the deeper understanding of electronic transport in complex and disordered materials.
References
Abrahams, E., & PWA. (1979). D.C.L. and T.V.R. scaling theory of localization: Absence of quantum diffusion in two dimensions. Physical Review Letters, 42, 4. S. Aubry and G. Andr´e. Analyticity breaking and Anderson localization in incommensurate lattices. Ann. Isr. Phys. Soc.3 18, (1980).
Anderson, P. W. (1958). Absence of diffusion in certain random lattices. Phys. Rev. Reviews of Modern Physics 50, (1978), 109, 2. N. F. Mott. Electrons in glass.
Ogwazu, J. E., & Ayannuga, O. M. (2024). Teachers’ Integration Strategies and Challenges on inclusion in selected public primary schools in Lagos, Nigeria. Edumania-An International Multidisciplinary Journal, 02(02), 175–192. https://doi.org/10.59231/edumania/9046
Chalker, J. T., Pickles, T. S., & Shukla, P. (2010). Anderson localization in tight-binding models with flat bands. Physical Review. Part B, 82(10). https://doi.org/10.1103/PhysRevB.82.104209
Guan, C., & Guan, X. (2019). A brief introduction to Anderson Localization. Department of Phy, Massachusetts Institute of Technology.
Gupta, T. (2025c). Redefining Employment Relations: Understanding Recent Advances and Innovative ideas Guiding the New Era of human resource development. Shodh Sari-An International Multidisciplinary Journal, 04(01), 95–110. https://doi.org/10.59231/sari7781
E. N. Economu. Economou Green’s Functions in Quantum Physics. (1990).
Markos, P. (2006). Numerical analysis of the Anderson localization. Acta Physica Slovaca, 56.
Rodríguez, A. MA MD J. R. L. G. S. V. A. M. F. D. A. J. P. L. (2001). Absence of weak localization in two-dimensional disordered Frenkel lattices. Journal of Luminescence, 94.