In this work, we introduce a new calculation method for disordered interacting electron systems. Since both the Coulomb repulsion and impurity potential modify the system band structure and hence its electronic properties, we investigate the competition between the electrons’ Coulomb repulsion potential and the impurity potential in changing the system band structure and its phase diagram. This method is applied to a disordered interacting electron square lattice system. The advantages of our method include eliminating the influence of random numbers in the Monte Carlo process and avoiding computational errors caused by repeated evaluations of Green’s function. For comparison of the advantages of our multi-site versus single-site methods, the renormalized band structure in the dynamical mean field theory (DMFT) plus coherent potential approximation (CPA) and the multi-site beyond effective medium supercell approximation (BEMSCA) are calculated. By using realistic calculated band structures, we investigate the competition between the Coulomb interaction and impurity potential parameters in the system phase diagram. Our calculated renormalized band structures show that the (<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10825_2025_2404_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="61" /> </InlineMediaObject> <EquationSource Format="TEX">$\delta = 4.0t$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>δ</mi> <mo>=</mo> <mn>4.0</mn> <mi>t</mi> </mrow> </math></EquationSource> </InlineEquation>, u = 0) point is a point at which band splitting is observed. By increasing the Coulomb repulsion, u, the energy gap between split bands reduces and completely disappears at uc1 = 3.11t and uc1 = 2.7t for the DMFT+CPA and four-site BEMSCA, respectively. For Coulomb repulsion strengths greater than uc1, u > uc1, the two bands merge into a single energy band, hence creating a paramagnetic metallic state. The metallic state occurs in a region where the strength of the Coulomb interaction is large enough to overcome the disorder potential effects. This metallic state extends until uc2 = 13.99t and uc2 = 8.15t for the DMFT+CPA and four sites for BEMSCA, respectively. These metallic states are sandwiched between two insulator states, band insulation u < uc1 and Mott insulation u > uc2. Another important result is the creation of a flat valence band at the Fermi energy for special Coulomb repulsion strengths. The flattening of the valence band can be considered as a mechanism contributing to the high-temperature superconductivity in ceramic superconductors.

Electron Coulomb repulsion versus impurity potential in disordered interacting systems

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发表日期：

2025年9月12日

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Poorya Rabi-beigi,
Rostam Moradian,
Chinedu E. Ekuma

摘要

In this work, we introduce a new calculation method for disordered interacting electron systems. Since both the Coulomb repulsion and impurity potential modify the system band structure and hence its electronic properties, we investigate the competition between the electrons’ Coulomb repulsion potential and the impurity potential in changing the system band structure and its phase diagram. This method is applied to a disordered interacting electron square lattice system. The advantages of our method include eliminating the influence of random numbers in the Monte Carlo process and avoiding computational errors caused by repeated evaluations of Green’s function. For comparison of the advantages of our multi-site versus single-site methods, the renormalized band structure in the dynamical mean field theory (DMFT) plus coherent potential approximation (CPA) and the multi-site beyond effective medium supercell approximation (BEMSCA) are calculated. By using realistic calculated band structures, we investigate the competition between the Coulomb interaction and impurity potential parameters in the system phase diagram. Our calculated renormalized band structures show that the ( $\delta = 4.0t$ $δ = 4.0 t$ , u = 0) point is a point at which band splitting is observed. By increasing the Coulomb repulsion, u, the energy gap between split bands reduces and completely disappears at u_c1 = 3.11t and u_c1 = 2.7t for the DMFT+CPA and four-site BEMSCA, respectively. For Coulomb repulsion strengths greater than u_c1, u > u_c1, the two bands merge into a single energy band, hence creating a paramagnetic metallic state. The metallic state occurs in a region where the strength of the Coulomb interaction is large enough to overcome the disorder potential effects. This metallic state extends until u_c2 = 13.99t and u_c2 = 8.15t for the DMFT+CPA and four sites for BEMSCA, respectively. These metallic states are sandwiched between two insulator states, band insulation u < u_c1 and Mott insulation u > u_c2. Another important result is the creation of a flat valence band at the Fermi energy for special Coulomb repulsion strengths. The flattening of the valence band can be considered as a mechanism contributing to the high-temperature superconductivity in ceramic superconductors.