Related Experiment Video
Updated: Jun 3, 2026
11:24
Optimized Fabrication Procedure for High-Quality Graphene-based Moiré Superlattice Devices
Published on: July 11, 2025
Anderson transition in disordered bilayer graphene
M H Zare1, Mohsen Amini, Farhad Shahbazi
1Department of Physics, Isfahan University of Technology, Isfahan, Iran.
Summary
This study on graphene bilayers with disorder reveals an Anderson metal-insulator transition. The kernel polynomial method (KPM) was used to analyze electronic properties and distinguish localized from extended states.
Area of Science:
- Condensed Matter Physics
- Materials Science
- Quantum Mechanics
Background:
- Graphene bilayers with Bernal stacking exhibit unique electronic properties.
- Disorder in materials can significantly alter their electronic behavior, potentially leading to metal-insulator transitions.
- Understanding these transitions is crucial for designing novel electronic devices.
Purpose of the Study:
- To investigate the electronic properties of Bernal-stacked graphene bilayers under diagonal disorder.
- To determine the critical disorder strength at which a metal-insulator transition occurs.
- To employ the kernel polynomial method (KPM) for efficient calculation of electronic states.
Main Methods:
- Utilizing the kernel polynomial method (KPM) for calculating the local density of states (LDOS).
- Applying the tight-binding approximation with nearest-neighbor interactions.
- Geometrically averaging LDOS across different lattice sites to identify localized and extended states.
Main Results:
- The study successfully calculated the LDOS without full Hamiltonian diagonalization.
- A clear criterion for distinguishing localized from extended states based on LDOS averaging was established.
- The graphene bilayer model demonstrated an Anderson metal-insulator transition at a specific disorder strength.
Conclusions:
- The kernel polynomial method is an efficient tool for studying disordered electronic systems.
- Bernal-stacked graphene bilayers exhibit a disorder-driven Anderson metal-insulator transition.
- The findings contribute to the understanding of electron localization in low-dimensional materials.
Related Concept Videos
01:35Asymmetric Lipid Bilayer
Biological membranes show uneven distribution of different types of lipids in the inner and outer layers, resulting in transverse asymmetric membranes. The treatment of the erythrocyte membrane with the enzyme phospholipase confirmed the asymmetric nature of the lipid bilayer. The enzyme hydrolyzes lipids into fatty acids and hydrophilic groups. The phospholipase acts only on the outer layer of the membrane, while the inner layer remains intact. The phospholipase treatment resulted in 80%...
01:25Transition State Theory
Transition-state theory, also known as activated-complex theory, provides a molecular-level explanation of reaction rates in both gas-phase and solution-phase reactions. It extends earlier kinetic models by considering the formation of a short-lived, high-energy configuration during a reaction.The progress of a chemical reaction can be represented using a reaction profile, which plots potential energy against the reaction coordinate. As two reactant molecules approach one another, their...
01:28Debye–Huckel–Onsager Conductance Equation
The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
02:31Phase Transitions
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to occupy...
01:21Phase Transitions
A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
01:58Cooperative Allosteric Transitions
Cooperative allosteric transitions can occur in multimeric proteins, where each subunit of the protein has its own ligand-binding site. When a ligand binds to any of these subunits, it triggers a conformational change that affects the binding sites in the other subunits; this can change the affinity of the other sites for their respective ligands. The ability of the protein to change the shape of its binding site is attributed to the presence of a mix of flexible and stable segments in the...