[Paper Review] Electronic structure and transport in graphene: quasi-relativistic Dirac--Hartry--Fock self-consistent field approximation

H. V. Grushevskaya, George Krylov|arXiv (Cornell University)|Sep 7, 2013

Graphene research and applications24 references3 citations

TL;DR

This paper proposes a quasi-relativistic Dirac–Hartree–Fock self-consistent field approach to model electronic structure and transport in monolayer graphene, incorporating electron correlation and exchange effects beyond the standard tight-binding model. It explains charge carrier asymmetry, mini-gaps in ARPES spectra, and cyclotron mass behavior through symmetry-breaking corrections and replica Dirac cone formation, yielding quantitative agreement with experimental data on band structure and transport properties.

ABSTRACT

Application of secondary quantized self-consistent Dirac -- Hartree -- Fock approach to consider electronic properties of monolayer graphene with accounting of spin-polarized states allows to coherently explain experimental results on energy band minigaps and charge carrier asymmetry in graphene, propose a description of valent and conduction zones shifts and gives a nice theoretical estimation of electron and holes cyclotron masses which is in very good agreement with known experimental data.

Motivation & Objective

• To address limitations in existing pseudo-relativistic models that oversimplify electron correlation and exchange in graphene.
• To explain experimental observations of electron-hole asymmetry and mini-gaps in ARPES spectra that contradict the symmetric Dirac cone model.
• To provide a self-consistent theoretical framework incorporating spin-polarized states and correlation effects for accurate band structure and transport predictions.
• To quantitatively estimate cyclotron masses of electrons and holes in graphene, aligning with experimental measurements.

Proposed method

• Formulates a quasi-relativistic Dirac–Hartree–Fock approach using a secondary quantized Hamiltonian to include electron correlation and exchange interactions.
• Applies a generalized LMTO method to perform ab initio band structure simulations of loosely-packed 2D graphite, accounting for interlayer correlations.
• Derives effective Hamiltonians with momentum-dependent self-energies ΣAB and ΣBA to model higher-order corrections beyond linear Dirac dispersion.
• Uses symmetry-breaking terms to describe the displacement and rotation of Dirac cone replicas relative to the primary cone, forming a hexagonal mini-Brillouin zone.
• Analyzes ARPES experimental planes to model quasi-crossings between the main Dirac cone and its replicas, predicting intensity differences and mini-gaps.
• Solves the eigenvalue problem for the effective Hamiltonian to compute dispersion relations E(q), revealing deviations from conic form at higher q-values.

Experimental results

Research questions

• RQ1 How do electron correlation and exchange interactions modify the electronic band structure of graphene beyond the massless Dirac fermion approximation?
• RQ2 What causes the observed electron-hole asymmetry in graphene’s transport and ARPES spectra, despite the expected symmetry of the Dirac cone?
• RQ3 How do replica Dirac cones form in epitaxial graphene on Ir(111), and what is their role in generating observed mini-gaps and intensity asymmetries in ARPES spectra?
• RQ4 To what extent do higher-order corrections in momentum space break the sixfold rotational symmetry near the Dirac point and lead to a mini-Brillouin zone?
• RQ5 Can the cyclotron masses of electrons and holes in graphene be quantitatively predicted from a self-consistent field approach that includes correlation effects?

Key findings

• The self-consistent Dirac–Hartree–Fock approach reproduces the linear Dirac cone dispersion near the Dirac point but reveals higher-order corrections that break conic symmetry at larger momentum values.
• The model predicts a sixfold-rotated, displaced mini-Brillouin zone formed by Dirac cone replicas, with corners aligned along the same line as the primary cone, explaining observed mini-gaps.
• The displacement of replicas leads to electron-hole asymmetry, with different Fermi velocities for conduction and valence bands, consistent with experimental ARPES observations.
• The intensity asymmetry in ARPES spectra—where the main Dirac cone is more intense than its replicas—is explained by ΔBA < ΔAB, indicating lower transition probability for replica photoelectrons.
• The calculated cyclotron masses for electrons and holes (≈0.02 of the free electron mass) are in excellent quantitative agreement with experimental measurements.
• The model successfully explains the origin of mini-gaps in ARPES spectra (≈0.02 kFvF) as a result of quasi-crossings between the main Dirac cone and its replicas in momentum space.