Abstract

MgB2, a phonon-mediated superconductor with record-high critical temperature Tc ≃39 K, is revisited to obtain a comprehensive theory of electrons, phonons, and their coupling with minimal ab initio input. Compact analytic models are constructed for the electronic structure, phonons, and electron-phonon coupling (EPC) of MgB2. The work argues that strong in-plane B sp2 bonding realizes an obstructed band structure whose natural description is a bond-centered kagome lattice, yielding small quasi-2D σ-band Fermi-surface cylinders and pronounced quantum-geometric effects. The phonon spectrum is shown to closely track that of a graphene-like boron layer, with heavy intercalated Mg atoms dominating the acoustic branches and lifting boron modes into the optical sector, while the bond-stretching mode softens along Γ–A. By symmetry, this Γ-point bond-stretching mode is the only Γ phonon that can couple to the σ Fermi surface, explaining its dominant contribution to the EPC. Under light electron doping toward the doubly degenerate σ-band edge, ab initio calculations indicate that EPC enhancement dominates over the reduced density of states, yielding an increase in Tc in the clean doping limit. Using a Gaussian approximation for the EPC tensor, the enhancement is attributed predominantly to a quantum-geometric contribution from the small σ Fermi surface peaked at Γ.

Abstract

MgB2, a phonon-mediated superconductor with record-high critical temperature Tc ≃39 K, is revisited to obtain a comprehensive theory of electrons, phonons, and their coupling with minimal ab initio input. Compact analytic models are constructed for the electronic structure, phonons, and electron-phonon coupling (EPC) of MgB2. The work argues that strong in-plane B sp2 bonding realizes an obstructed band structure whose natural description is a bond-centered kagome lattice, yielding small quasi-2D σ-band Fermi-surface cylinders and pronounced quantum-geometric effects. The phonon spectrum is shown to closely track that of a graphene-like boron layer, with heavy intercalated Mg atoms dominating the acoustic branches and lifting boron modes into the optical sector, while the bond-stretching mode softens along Γ–A. By symmetry, this Γ-point bond-stretching mode is the only Γ phonon that can couple to the σ Fermi surface, explaining its dominant contribution to the EPC. Under light electron doping toward the doubly degenerate σ-band edge, ab initio calculations indicate that EPC enhancement dominates over the reduced density of states, yielding an increase in Tc in the clean doping limit. Using a Gaussian approximation for the EPC tensor, the enhancement is attributed predominantly to a quantum-geometric contribution from the small σ Fermi surface peaked at Γ.

Abstract

MgB2, a phonon-mediated superconductor with record-high critical temperature Tc ≃39 K, is revisited to obtain a comprehensive theory of electrons, phonons, and their coupling with minimal ab initio input. Compact analytic models are constructed for the electronic structure, phonons, and electron-phonon coupling (EPC) of MgB2. The work argues that strong in-plane B sp2 bonding realizes an obstructed band structure whose natural description is a bond-centered kagome lattice, yielding small quasi-2D σ-band Fermi-surface cylinders and pronounced quantum-geometric effects. The phonon spectrum is shown to closely track that of a graphene-like boron layer, with heavy intercalated Mg atoms dominating the acoustic branches and lifting boron modes into the optical sector, while the bond-stretching mode softens along Γ–A. By symmetry, this Γ-point bond-stretching mode is the only Γ phonon that can couple to the σ Fermi surface, explaining its dominant contribution to the EPC. Under light electron doping toward the doubly degenerate σ-band edge, ab initio calculations indicate that EPC enhancement dominates over the reduced density of states, yielding an increase in Tc in the clean doping limit. Using a Gaussian approximation for the EPC tensor, the enhancement is attributed predominantly to a quantum-geometric contribution from the small σ Fermi surface peaked at Γ.

Abstract

MgB2, a phonon-mediated superconductor with record-high critical temperature Tc ≃39 K, is revisited to obtain a comprehensive theory of electrons, phonons, and their coupling with minimal ab initio input. Compact analytic models are constructed for the electronic structure, phonons, and electron-phonon coupling (EPC) of MgB2. The work argues that strong in-plane B sp2 bonding realizes an obstructed band structure whose natural description is a bond-centered kagome lattice, yielding small quasi-2D σ-band Fermi-surface cylinders and pronounced quantum-geometric effects. The phonon spectrum is shown to closely track that of a graphene-like boron layer, with heavy intercalated Mg atoms dominating the acoustic branches and lifting boron modes into the optical sector, while the bond-stretching mode softens along Γ–A. By symmetry, this Γ-point bond-stretching mode is the only Γ phonon that can couple to the σ Fermi surface, explaining its dominant contribution to the EPC. Under light electron doping toward the doubly degenerate σ-band edge, ab initio calculations indicate that EPC enhancement dominates over the reduced density of states, yielding an increase in Tc in the clean doping limit. Using a Gaussian approximation for the EPC tensor, the enhancement is attributed predominantly to a quantum-geometric contribution from the small σ Fermi surface peaked at Γ.