Superconductivity in unconventional metals

Topological materials have garnered significant attention due to their unique properties. Recently, a new class of unconventional materials, characterized by topologically trivial Wannierizable valence Bloch states but possessing bands from an elementary band representation (EBR) on an empty site, has emerged. These unconventional insulators are also known as obstructed atomic insulators. Unconventional metals, encompassing electrides, catalysts, and superconductors, represent another facet of this class. Transition metal dichalcogenides (TMDs), such as 2H-MX₂, exhibit charge density waves (CDWs) and superconductivity, with varying transition temperatures (Tc) and CDW temperatures depending on the specific material. While these properties have been extensively studied, the underlying mechanism for superconductivity remains elusive. This work utilizes first-principles calculations and band representation analysis to investigate the electronic structure and superconductivity of 1H-MX₂ monolayers, which are identified as unconventional metals with a half-filled EBR at an empty site. The impact of electron doping on CDW formation and the correlation between the partially filled empty-site band, electron-phonon coupling (EPC), and superconductivity are explored, leading to predictions of superconductivity in novel materials.

The literature extensively explores the CDW and superconducting properties of 2H-MX₂ materials. The CDW transition temperature varies significantly, ranging from around 120 K in 2H-TaSe₂ to a complete absence in 2H-NbS₂. Similarly, the superconducting critical temperature (Tc) shows a marked dependence on the specific TMD, increasing from approximately 0.2 K in 2H-TaSe₂ to 7.2 K and 6 K in 2H-NbSe₂ and 2H-NbS₂, respectively. Despite extensive research, the origin of superconductivity in these systems remains unclear. This study builds upon previous theoretical investigations of phonon dispersions in these materials, addressing the unanswered questions regarding the link between the electronic structure and the observed superconductivity.

First-principles calculations were performed using the QUANTUM ESPRESSO (QE) package, employing density functional theory (DFT) with projector-augmented wave (PAW) pseudopotentials and the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. Dynamical matrices and electron-phonon coupling calculations were carried out within the framework of density functional perturbation theory (DFPT), as implemented in QE. The superconducting transition temperature (Tc) was estimated using the Allen-Dynes modified McMillan equation. Band representations were calculated using IR2PW and POS2ABR. The analysis focuses on the electronic band structure, phonon dispersions, and electron-phonon coupling, using these computational techniques to investigate the relationship between the unconventional metallic state, characterized by the empty-site EBR, and the observed or predicted superconducting behavior. The impact of electron doping was also investigated by simulating Na intercalation (NaNbX₂) and Mo substitution (1H-MoX₂) to analyze the dependence of the soft phonon mode on the filling of the empty-site EBR. The Eliashberg spectral function and frequency-dependent coupling were calculated to analyze the contributions of different phonon modes to the EPC.

The study reveals that monolayer 1H-MX₂ are unconventional metals featuring a half-filled empty-site EBR (A’@1e) at the Fermi level. Phonon dispersion calculations indicate stability at high temperatures and the presence of a soft phonon mode associated with charge density wave instability at low temperatures. Analysis of electron-phonon coupling (EPC) in NbSe₂ indicates that superconductivity is primarily attributed to this soft phonon mode, with strong EPC (λ > 1) driven by the half-filling of the empty-site band. This strong EPC is linked to the spatial coincidence of Fermi-level states and the phonon mode, resulting in a significant coupling strength. Electron doping through Na intercalation or Mo substitution leads to a fully occupied empty-site EBR and suppresses the soft phonon mode, stabilizing the crystal structure and preventing the CDW transition. Based on these findings, the researchers predicted superconductivity in two new materials: TaNS monolayer (Tc ≈ 10 K) and 2H-TaN₂ bulk (Tc ≈ 26 K). Both materials exhibit a half-filled empty-site EBR and strong EPC, supporting the hypothesis that the partial filling of this band is critical for superconductivity. The calculated Tc values were obtained using the Allen-Dynes modified McMillan equation, considering the electron-phonon coupling constant (λ) and the logarithmic average phonon frequency (ωlog). The high Tc in 2H-TaN₂ is attributed to its high ωlog, contributed by the light nitrogen atoms.

This work establishes a clear link between the partially filled empty-site EBR in unconventional metals and the emergence of superconductivity. The strong electron-phonon coupling arising from the spatial overlap of Fermi-level states and specific phonon modes, particularly the soft phonon mode, is identified as the driving force behind the superconducting behavior. The findings support the notion that unconventional metals represent a potentially rich source of novel superconductors. The successful prediction of superconductivity in TaNS and 2H-TaN₂ validates the proposed mechanism. The results highlight the importance of considering the interplay between electronic structure, particularly the presence and filling of empty-site EBRs, and lattice dynamics in the search for new superconducting materials.

This study demonstrates that unconventional metals with partially filled empty-site EBRs offer a promising platform for discovering new superconductors. The strong electron-phonon coupling associated with these bands, particularly the contribution from soft phonon modes, is identified as a key factor driving superconductivity. The successful prediction of superconductivity in TaNS monolayer and 2H-TaN₂ bulk validates this hypothesis. Further experimental investigation to confirm these predictions and explore other unconventional metals with similar electronic structures is strongly encouraged.

The accuracy of the predicted Tc values relies on the accuracy of the calculated electron-phonon coupling constants and the applicability of the Allen-Dynes modified McMillan equation. The study focuses on theoretical calculations; experimental verification is necessary to fully validate the predictions. The consideration of other possible interactions beyond electron-phonon coupling could potentially refine the accuracy of the predictions. The study focuses on specific material systems; further investigation is needed to generalize the findings to a broader range of unconventional metals.