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Energy Bands in Solids

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Isolated atoms have discrete energy levels that are well described by the Bohr model. And, it quantifies the energy of an electron in a hydrogen atom as En. Higher quantum numbers 'n' yield less negative, closer electron energy levels.
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Fabrication of Gate-tunable Graphene Devices for Scanning Tunneling Microscopy Studies with Coulomb Impurities

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Published on: July 24, 2015

How electrons Coulomb repulsion changes graphene band structure.

Rostam Moradian^1,2, Poorya Rabibeigi^3,4

¹Physics Department, Faculty of Science Razi University, Kermanshah, Iran. rmoradian@razi.ac.ir.

Scientific Reports

|April 1, 2022

Summary

We developed a multi-site method to accurately calculate energy bands in strongly correlated systems. This method reveals graphene

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Area of Science:

Condensed Matter Physics
Materials Science

Background:

Accurate calculation of energy bands is crucial for understanding strongly correlated systems.
Previous methods using local Green functions showed limitations in reflecting true energy bands.
Electron-electron repulsion significantly influences the electronic properties of materials like graphene.

Purpose of the Study:

To introduce a multi-site method based on effective medium theory for realistic energy band calculations.
To investigate the renormalization of graphene's energy bands due to electron-electron repulsion.
To determine the critical electron repulsion values for phase transitions in graphene.

Main Methods:

Development of a multi-site method incorporating effective medium theory.
Calculation of realistic energy bands for strongly correlated systems.
Application of dynamical mean-field theory (DMFT) and a four-site supercell approximation.

Main Results:

The multi-site method provides a more accurate representation of energy bands compared to direct local Green function methods.
Electron repulsion was found to significantly renormalize graphene's energy bands.
A semi-metal to Mott insulator anti-ferromagnetic phase transition was observed at lower repulsion values than predicted by other methods.

Conclusions:

The proposed multi-site method offers improved accuracy for energy band calculations in strongly correlated systems.
Graphene exhibits high sensitivity to electron repulsion, leading to phase transitions at relatively low interaction strengths.
The findings challenge existing predictions for phase transition thresholds in graphene.