Realization of a two-dimensional Weyl semimetal and topological Fermi strings

Weyl semimetals, hosting spin-split massless quasiparticles, represent a significant advancement in condensed matter physics, mirroring concepts from particle physics. Three-dimensional (3D) Weyl semimetals exhibit chiral nodal points and 2D Fermi arc surface states, leading to exotic properties such as the chiral anomaly, unusual optical conductivity, and nonlocal transport. While the Weyl equation is defined for odd spatial dimensions, its 2D generalization yields a distinct topological state – the 2D Weyl semimetal – exhibiting a spin-polarized analogue of graphene. These 2D systems possess unique properties, including the parity anomaly in (2+1)-D quantum field theory, charge fractionalization, spin-valley Hall effects, giant Berry curvature dipole (BCD), and topological quantum criticality. However, the experimental realization of an intrinsic 2D Weyl semimetal has remained elusive. This research aims to address this gap by creating and characterizing such a material.

Extensive theoretical work has predicted the unique properties of 2D Weyl semimetals, including their topological edge states known as Fermi strings. These Fermi strings, 1D counterparts to the Fermi arc surface states in 3D Weyl semimetals, connect the projections of bulk Weyl nodes at the Fermi level. However, experimental verification of these properties has been lacking. Several theoretical studies have explored the potential for realizing 2D Weyl semimetals in various material systems, but a definitive experimental demonstration has been absent until this work. The theoretical studies highlighted the importance of breaking inversion symmetry to induce the necessary spin splitting and the formation of Weyl nodes. Previous experimental efforts focusing on other 2D materials haven't successfully demonstrated the full suite of properties characteristic of a 2D Weyl semimetal.

This study employed epitaxial bismuthene, a single atomic layer of bismuth in a phosphorene-like structure, grown on SnS(Se) substrates via molecular beam epitaxy (MBE). SnS(Se) was chosen due to its van der Waals semiconductor properties and lattice structure similarity to bismuthene. Scanning tunneling microscopy (STM) was used to characterize the surface topography and lattice parameters of the bismuthene, revealing high structural quality. First-principles calculations based on density functional theory (DFT) using the Vienna ab initio Simulation Package (VASP) were performed to predict the band structure of both free-standing and substrate-supported bismuthene. Angle-resolved photoemission spectroscopy (ARPES), including spin-resolved ARPES, was used to experimentally determine the band structure and spin texture of the bismuthene monolayer. The ARPES measurements used a Scienta DA30L hemispherical analyzer with a high-resolution laser system. Scanning tunneling spectroscopy (STS) measurements, conducted using an Omicron LT-Nanoprobe system, probed the local density of states (LDOS) at the bismuthene edges to identify Fermi strings. A tight-binding model was developed to simulate the edge electronic structure and quasiparticle interference patterns, which were compared with experimental STM results. The photoemission matrix element effects were simulated using a unitary transformation applied to the tight-binding Hamiltonian. Quasiparticle interference (QPI) patterns were calculated using a Green's function method incorporating spin-dependent scattering probability.

The research successfully demonstrated the experimental realization of a 2D Weyl semimetal in epitaxial bismuthene grown on SnS(Se) substrates. ARPES measurements directly observed spin-polarized Weyl cones and Weyl nodes near the Fermi level, confirming the presence of Weyl fermion states. The observed spin polarization aligns with theoretical predictions, showcasing the characteristic canted spin texture of the Weyl cones. STS measurements revealed a significantly enhanced LDOS at the bismuthene edges, corresponding to the predicted Fermi string edge states. The energy range of the enhanced LDOS closely matches the calculated energy of the bulk Weyl nodes. Quasiparticle interference (QPI) patterns obtained from STM measurements showed a wavevector consistent with the separation between the two Weyl nodes observed in ARPES, supporting the theoretical model. The calculations showed that the inclusion of the SnSe substrate breaks the space inversion symmetry and induces spin splitting in the bismuthene bands, creating the Weyl nodes. Importantly, states from the SnSe substrate are outside of the energy range where the 2D Weyl fermion states are observed, confirming the 2D nature of the Weyl states. The variation in Fermi level position between the bismuthene/SnSe and bismuthene/SnS samples highlight the robustness of the Weyl fermion states to external perturbations.

The findings directly address the long-standing challenge of experimentally realizing a 2D Weyl semimetal. The combined experimental (ARPES, STS, STM) and theoretical (DFT, tight-binding) results provide strong evidence for the existence of spin-polarized Weyl fermions and topologically protected Fermi string edge states. The observation of these features validates theoretical predictions and establishes bismuthene on SnS(Se) as a model system for studying the unique properties of 2D Weyl semimetals. This opens a new chapter in the exploration of topological materials and their potential applications in various technological fields such as spintronics and quantum computing.

This work successfully demonstrated the experimental realization of a 2D Weyl semimetal in epitaxial bismuthene on SnS(Se). The observation of spin-polarized Weyl cones, Weyl nodes, and Fermi strings provides definitive evidence of the predicted topological characteristics. This achievement opens exciting possibilities for investigating the exotic properties of Weyl fermions in low dimensions and exploring potential applications in novel quantum devices. Future research could explore the effects of different substrates, doping levels, and external fields on the Weyl fermion states and Fermi strings.

While the study provides compelling evidence for the existence of 2D Weyl semimetal states, the presence of rotated Bi domains in the MBE samples may have influenced the precise measurement of the out-of-plane spin polarization. Further studies could focus on improving the sample growth techniques to minimize the presence of such domains. The theoretical models used in this study are based on certain approximations, which could introduce some degree of uncertainty. More sophisticated theoretical methods could be used in future work to address this limitation.