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Localizing Transitions via Interaction-Induced Flat Bands
Alireza Parhizkar1, Victor Galitski1
1University of Maryland, College Park, Joint Quantum Institute, Department of Physics, Maryland 20742, USA.
Physical Review Letters
|November 1, 2024
Summary
This study introduces a new theory for interaction-induced band flattening in correlated electron systems. It reveals a generic mechanism for creating flat bands, crucial for understanding spontaneous symmetry breaking in materials.
Area of Science:
- Condensed Matter Physics
- Theoretical Physics
- Quantum Mechanics
Background:
- Strongly correlated electron systems exhibit complex phenomena.
- Flat bands in electronic systems are linked to unique quantum properties.
- Topological concepts offer novel ways to engineer material properties.
Purpose of the Study:
- To develop a theoretical framework for interaction-induced band flattening.
- To establish a generic method for constructing flat bands using topological zero modes.
- To explore the role of such mechanisms in spontaneous symmetry breaking.
Main Methods:
- Developing a theory connecting flat bands with index theorems.
- Constructing flat bands via periodic repetition of local Hamiltonians with topological zero modes.
- Analyzing interacting models of Dirac fermions in inhomogeneous fields using Hubbard-Stratonovich transformations.
Main Results:
- Demonstrated a method to create perfectly flat bands for Dirac particles in periodic magnetic fields.
- Derived exact analytical solutions for flat band wave functions.
- Showed that specific field configurations induce band flattening in interacting Dirac fermions, energetically favoring localization in systems with nearly flat bands.
Conclusions:
- Interaction-induced band flattening is a generic nonperturbative mechanism for spontaneous symmetry breaking.
- This mechanism is relevant to various strongly correlated electron systems.
- Superconductivity and other symmetry-breaking channels are potential avenues for realizing these effects.
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