The discovery of superconductivity and chiral charge density wave (CDW) orders in the AV₃Sb₅ (A = K, Rb, Cs) family of materials has spurred significant research. These materials exhibit superconductivity with critical temperatures (T_c) varying across the family: 0.93 K for KV₃Sb₅, 0.92 K for RbV₃Sb₅, and 2.5 K for CsV₃Sb₅. A chiral CDW order is observed at approximately 80-103 K, and its relationship with superconductivity remains a key question. The unconventional nature of both orders has been suggested by experimental and theoretical studies. The nontrivial band topology plays a fundamental role. While some studies report time-reversal symmetry breaking (TRSB), others show sample-dependent results or lack of evidence. Prior research on the electronic structures has primarily focused on CDW gaps and van Hove singularities (VHSs), with some discrepancies between ARPES experiments and DFT calculations. Specifically, DFT predicts two VHSs near the Fermi level at the M point of the bulk but none at the L point, while ARPES observes features closer to the L point bulk bands. These disagreements highlight the need for a comprehensive understanding, potentially incorporating a previously unconsidered element: quantum confinement.

Numerous studies have investigated the superconductivity and charge density wave (CDW) behavior in the AV3Sb5 (A = K, Rb, Cs) family. The unconventional nature of both phenomena has been suggested. Experimental and theoretical works have explored the band topology and its influence. Some studies have shown evidence of time-reversal symmetry breaking (TRSB) through various techniques, while others have reported conflicting or negative findings. Research into the electronic structure has focused on CDW gaps and van Hove singularities (VHSs), using ARPES and DFT calculations, but inconsistencies remain between experimental observations and theoretical predictions, particularly regarding the location and number of VHSs at the M and L points of the Brillouin zone. These discrepancies motivated the current work, suggesting the possibility of a missing factor in explaining the experimental observations.

High-quality CsV₃Sb₅ single crystals were grown using the self-flux method. CDW transition (at ~94 K) and superconductivity (at ~2.5 K) were confirmed through resistivity, heat capacity, and magnetization measurements. Angle-resolved photoemission spectroscopy (ARPES) measurements were performed at the BL03U beamline of the SSRF and beamline 13U of the NSRL, with energy and angular resolutions of 15 meV/7.5 meV and 0.1°, respectively. Samples were cleaved in situ under ultra-high vacuum. Density functional theory (DFT) calculations were performed using the Vienna ab initio simulation package (VASP) with the projector augmented wave method (PAW) and the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. A slab model with six Cs–Sb₂–V/Sb₁–Sb₂ layers was used to simulate the surface effects, incorporating van der Waals corrections. The experimental lattice constants were used, and the structures were relaxed until forces were less than 0.005 eV/Å. The DFT calculations included band structure calculations, Fermi surface mapping, and analysis of surface relaxation effects on the electronic structure. Comparisons between the ARPES measurements and the DFT calculations were used to understand the origin of the observed spectral features and resolve inconsistencies between previous experimental and theoretical studies. The photon energy dependence of the ARPES spectra was particularly crucial in identifying the surface quantum well states.

The study reveals a dominant role of quantum confinement in determining the surface electronic structure of CsV₃Sb₅. ARPES measurements, combined with DFT calculations on a six-layer slab model, reveal two-dimensional quantum well states arising from the confinement of bulk electron pockets and Dirac cones to the surface layer. The ARPES spectra are almost entirely attributed to the top two layers. A clear band splitting is observed for the electron pocket at Γ, consistent with the formation of quantized subbands, indicative of quantum well states. The outer electron-like band shows negligible k_z dispersion, confirming its two-dimensional (2D) nature and quantum well state origin. The inner electron subband exhibits weaker k_z dependence, suggesting a similar origin but weaker confinement. Several possibilities (surface inhomogeneity, CDW-induced superlattice bands, and k_z projection) are ruled out as explanations for the observed band splitting. DFT calculations on the slab model, considering surface relaxation, successfully reproduce the observed ARPES spectral features, including the lack of k_z dispersion at K and M points. The surface relaxation creates a potential drop of ~1 eV, forming a quantum well at the surface. The discrepancy between the bulk-sensitive probes showing TRSB and surface-sensitive probes is explained by the layer-dependent CDW instability due to surface relaxation.

The findings resolve inconsistencies between previous ARPES experiments and DFT calculations by incorporating the significant effect of quantum confinement. The observed quantum well states provide a compelling explanation for the previously unexplained similarities between ARPES spectra at different k_z values and DFT calculations at the L point rather than the M point of the bulk Brillouin zone. The work highlights the critical role of quantum confinement in addition to strong correlation and band topology in shaping the electronic properties of CsV₃Sb₅. The layer-dependent CDW instability, attributed to quantum confinement and surface relaxation, offers a possible explanation for the conflicting experimental results on TRSB. This suggests that surface-sensitive techniques may not always provide a complete picture of bulk properties in layered materials.

This study demonstrates the significant influence of quantum confinement on the surface electronic structure of the kagome superconductor CsV₃Sb₅. The identification of two-dimensional quantum well states, supported by both ARPES and DFT calculations, resolves previous inconsistencies between experimental and theoretical band structures. The layer-dependent CDW instability, arising from surface relaxation, provides an explanation for conflicting results regarding time-reversal symmetry breaking. Future work could explore other kagome superconductors to determine the universality of quantum confinement effects and investigate the interplay between quantum confinement and other factors governing the unique properties of these materials.

The study focuses primarily on the surface electronic structure of CsV₃Sb₅. While the slab model provides insights into surface effects, it is an approximation of the real material. The influence of potential defects or impurities on the quantum well states is not fully explored. Further investigations are needed to fully understand the bulk properties and the interplay between surface and bulk phenomena in this material.