Superconductivity and topological aspects of two-dimensional transition-metal monohalides

Two-dimensional (2D) superconductivity, a field of significant fundamental and practical interest, has gained considerable attention due to its potential applications and the intriguing phenomena observed in ultrathin superconducting materials. Recent advancements in nanofabrication techniques have enabled the exploration of these materials, revealing phenomena such as quantum Griffiths singularity, anomalous/bosonic metallic states, and enhanced upper critical fields. Some 2D superconductors exhibit significantly higher superconducting transition temperatures (Tc) compared to their bulk counterparts, highlighting the potential for Tc enhancement in reduced dimensions. However, practical applications must account for substrate effects, which can suppress superconductivity. Van der Waals (vdW) layered materials offer an advantage in this regard due to their weak interaction with substrates. Transition metal dichalcogenides (TMDs) have emerged as a rich source of 2D superconductors, exhibiting diverse behaviors including the coexistence of superconductivity and charge density waves. The interplay between superconductivity and nontrivial band topology is particularly fascinating, as it can lead to exotic topological superconducting (TSC) states and the emergence of Majorana fermions, which are promising for fault-tolerant quantum computing. Realizing Majorana fermions necessitates the coexistence of superconducting and topological states, either intrinsically within a single material or through heterostructure interfaces. This research explores the possibility of both, aiming to find 2D superconductors with both electronic and phononic topology to enhance electron-phonon coupling and superconductivity. This paper focuses on the investigation of superconductivity and topological aspects of vdW monolayered MX (M=Zr, Mo; X=F, Cl) using first-principles calculations, aiming to explore the interplay between superconductivity and nontrivial electronic and phononic topology in these materials.

The introduction provides a comprehensive review of the existing literature on 2D superconductivity, highlighting key discoveries and advancements in the field. It discusses the challenges associated with substrate effects and the advantages of vdW layered materials. The review covers various 2D superconductors, including TMDs, and emphasizes the exciting prospect of combining superconductivity with nontrivial band topology to create TSC states and Majorana fermions. Existing research on achieving TSC states through heterostructures or intrinsic material properties is also summarized, providing a context for the current study's investigation of vdW monolayered transition-metal monohalides.

The study employed first-principles calculations using the QUANTUM ESPRESSO package with relativistic norm-conserving ONCV pseudopotentials and the Perdew-Burke-Ernzerhof exchange-correlation functional. Plane-wave cutoff energy, force tolerance, k-mesh, and smearing parameters were carefully chosen to ensure accuracy. Phonon dispersions, electron-phonon coupling (EPC), and Eliashberg functions were calculated using density functional perturbation theory with spin-orbit coupling. Maximally localized Wannier functions were generated using Wannier90, and phononic tight-binding Hamiltonians were created using phonopyTB. Electronic and phononic edge spectra were calculated using the iterative Green's function technique implemented in WannierTools. Superconducting properties were determined by employing EPC matrix interpolation to denser k- and q-meshes using the EPW code. The Eliashberg spectral function was calculated, and the EPC constant λ was obtained through integration. The critical superconducting temperature Tc was estimated using both the McMillan-Allen-Dynes formula and by solving anisotropic (and isotropic) Migdal-Eliashberg equations. Electronic nesting functions were calculated to understand EPC mechanisms. Band topology was investigated using symmetry-indicator theory to determine the Z2 invariant, and electronic edge states were analyzed. Phononic topology was explored by calculating Berry phases of phonon crossing points.

The calculations predicted that the vdW monolayered transition-metal monohalides MX (M=Zr, Mo; X=F, Cl) are 2D superconductors with significant transition temperatures (Tc) ranging from 5.9 K to 12.4 K. ZrCl exhibits a single superconducting gap, while MoCl displays a distinct two-gap superconductivity. The analysis revealed that low-frequency phonons significantly contribute to the EPC. For ZrCl, a soft mode at the K point, originating from circular vibrations of Zr atoms with opposite chirality, is crucial for the enhanced EPC. The Janus structure Zr2FCl showed a further Tc enhancement. For MoCl, the phonon softening is attributed to Fermi surface nesting. The study uncovered the Z2 band topology of 2D MX, indicating MoF and MoCl as TSC candidates. Dirac phonons were identified in ZrCl and MoCl, exhibiting quantized Berry phases at Brillouin zone boundaries, with corresponding zigzag edge states displaying w-shape dispersions, suggesting potential edge-enhanced EPC. The two-gap superconductivity in MoCl is attributed to the distinct Fermi surface sheets and disparate pairing strengths. The analysis of the electronic EPC strength revealed hot spots, further explaining the observed superconductivity. The investigation of electronic edge states along zigzag edges showed topological edge states (TESs) for MoCl and MoF, supporting their classification as TSC candidates. The phononic edge spectra revealed w-shape TESs connecting to nontrivial projected Dirac points, suggesting potential for edge-enhanced EPC.

The findings address the research question by identifying a new class of 2D superconductors with promising Tc values. The observed two-gap superconductivity in MoCl is a noteworthy discovery, and the exploration of the Janus structure provides further insights into the relationship between chirality and superconductivity. The demonstration of electronic and phononic topology enhances the potential for achieving TSC states and edge-enhanced superconductivity. The results are significant as they offer a new material platform for exploring the interplay between superconductivity and topology. The findings enrich the understanding of 2D superconducting and topological states and provide a foundation for future experimental verification and exploration of related phenomena.

This study successfully predicted phonon-mediated superconductivity and topological aspects in vdW monolayered MX (M = Zr, Mo; X = F, Cl). The high Tc values, particularly the striking two-gap superconductivity in MoCl, highlight the potential of this material family. The investigation of the Janus structure Zr2FCl suggests a pathway for further enhancing Tc through chiral phonon effects. The confirmation of electronic and phononic topology, including the identification of TSC candidates and Dirac phonons, expands the understanding of 2D materials. Future research could focus on experimental verification of these predictions and exploring the potential of these materials for applications in quantum computing and other technological areas.

While the study provides strong theoretical evidence, experimental verification is crucial to confirm the predicted superconducting properties and topological characteristics. The study focused on specific MX compounds; exploring a wider range of transition metals and halides could reveal further interesting behaviors. The computational methods used have inherent limitations, and approximations made in the calculations might slightly affect the accuracy of the results.