Emergence of quantum confinement in topological kagome superconductor CsV₃Sb₅

The AV3Sb5 (A = K, Rb, Cs) kagome metals host superconductivity (Tc ≈ 0.9–2.5 K) and a chiral charge-density-wave (CDW) order (T ≈ 80–103 K), sparking extensive interest in their intertwined orders and topological electronic structure. Prior ARPES and theory studies focused on CDW gaps and van Hove singularities (VHSs), but inconsistencies emerged: DFT predicts two VHSs near M with strong kz dispersion along M–L, whereas many ARPES spectra near M resemble bulk L, showing little kz dependence. Simultaneously, reports on time-reversal symmetry breaking (TRSB) associated with chiral flux phases are controversial across different probes. This work addresses the discrepancy between ARPES and bulk DFT by testing whether quantum confinement at the surface alters the measured electronic structure, hypothesizing that surface relaxation creates a potential well that confines bulk states into quasi-2D quantum well subbands dominating ARPES.

- Superconductivity and chiral CDW in AV3Sb5 are established, with unconventional features reported. - TRSB signatures have been observed in some experiments (μSR, Kerr, magnetochiral transport), but other studies report sample-dependent or null results, raising controversy about the existence and surface/bulk character of TRSB. - ARPES studies documented momentum-dependent CDW gaps and multiple VHSs around M, partially consistent with DFT; however, DFT predicts kz dispersion between M–L with two VHSs near M only, and none at L in the same energy window. Many ARPES spectra near M more closely resemble DFT bands at L, implying suppressed kz dispersion experimentally. - Prior explanations invoked kz-projection effects or superlattice bands from CDW; these do not fully account for the multiplicity and dispersion character of the observed bands at Γ and M. These works motivate reassessing the surface sensitivity of ARPES and the role of surface-induced quantum confinement in shaping observed spectra.

- Crystal growth: High-quality single crystals of KV3Sb5 and CsV3Sb5 were synthesized via self-flux. High-purity K/Cs, V, and Sb (2:1:6) were loaded in an alumina crucible, double-sealed in a quartz tube (≈10 Torr), heated to 500 °C (10 h), then to 1050 °C (12 h), and slowly cooled to 650 °C before centrifuging to remove flux. Samples exhibited TCDW ≈ 94 K and Tc ≈ 2.5 K (CsV3Sb5) by transport, heat capacity, and magnetization. - Transport, heat capacity, magnetization: PPMS for resistivity (four-probe, I = 0.5 mA in ab-plane) and heat capacity (Apezion N-grease for thermal contact on ≈1.5 mm crystals). MPMS3 used for magnetization with field ⟂ c-axis. - ARPES: Measurements performed at SSRF BL03U and NSRL 13U. Energy resolution: 15 meV (Fermi surface) and 7.5 meV (bands); angular resolution 0.1°. Samples cleaved in situ under UHV (<5×10−10 mbar), mostly below 20 K; some above 120 K. Photon-energy dependent scans mapped kz between ≈6.5×(2π/c) and 7.0×(2π/c). High-symmetry kz planes identified via periodic EDC intensity at Γ: Γ-plane at hν ≈ 83 eV (kz = 7π/c), A-plane at hν ≈ 70 eV (kz = 6.5×2π/c). - First-principles calculations: VASP with PAW and PBE-GGA; plane-wave cutoff 400 eV. k-meshes: bulk 12×12×6; slab 12×12×1. Experimental lattice constants a=b=5.495 Å; c=9.308 Å (bulk). Slab model: symmetric, six Cs–Sb2–V/Sb1–Sb2 unit-cell layers with Cs terminations and 16 Å vacuum. van der Waals corrections included. Structures relaxed until forces <0.005 eV/Å. Surface relaxation, interlayer spacing, and layer-resolved local potential were analyzed. Band projections onto topmost and top-two unit-cell layers were computed and unfolded where applicable.

- ARPES vs bulk DFT: Despite DFT predicting strong kz dispersion along M–L (e.g., gap at M and Dirac crossing at L near EF), ARPES Fermi surfaces and dispersions measured at Γ–M–K and A–L–H are nearly identical and closely match DFT at A–L–H, indicating suppressed kz dispersion near M experimentally. - Γ electron pocket subbands: ARPES reveals two concentric Fermi circles at Γ and multiple electron-like bands along Γ–K, inconsistent with a single bulk pocket. The band duplications persist above TCDW and are symmetric about Γ, disfavoring surface inhomogeneity and CDW replicas. kz-projection scenario is also unlikely because the subbands are nearly rigidly shifted (similar curvature/effective mass), exceed two in number, and lack the expected photon-energy intensity swapping. - Quasi-2D outer subband: Photon-energy-dependent ARPES shows the outmost electron-like subband at Γ is kz-independent in both band bottom and kF, identifying it as a surface quantum well state. The inner subband has weak kz dispersion (~100 meV bandwidth) versus bulk DFT (~400 meV), implying partial confinement. - Slab DFT with surface relaxation: Structural relaxation strongly affects only the outermost unit-cell layer, increasing the spacing to subsurface layers and rendering the top UC relatively free-standing. A ~1 eV surface potential drop forms a quantum well near the surface. Calculated bands projected onto the topmost layer reproduce the pure surface quantum well state (outer subband), while the top-two-layer projection reproduces the overall ARPES spectra, consistent with ARPES probe depth (~1–2 nm). - Nearly kz-independent Fermi surface: The slab-projected (top-two layers) Fermi surface agrees with ARPES and is nearly kz-independent due to the (quasi-)2D character of confined states. - Resolution of prior discrepancies: Quantum confinement explains why ARPES near M resembles bulk L from DFT and why kz dispersion is weak or absent for key features, reconciling experiment-theory differences.

The study demonstrates that surface quantum confinement, induced by relaxation of the polar (0001) surface, dominates the ARPES-observed electronic structure of CsV3Sb5. Confinement transforms bulk Γ-centered electron and Dirac-like states into quasi-2D quantum well subbands localized on the top one to two kagome layers, eliminating the strong kz dispersion predicted for the bulk along M–L and making spectra at Γ–M–K and A–L–H appear similar. This resolves longstanding discrepancies between ARPES and bulk DFT around VHSs and Dirac features near M/L. Beyond band mapping, the layer-selective confinement and weakened interlayer coupling bear on ongoing debates about TRSB and CDW chirality. DFT phonon and reconstruction analyses indicate reduced CDW instability and minimal tri-hexagonal reconstruction in the relaxed surface layers compared to inner layers, leaving surface Dirac nodes intact while inner-layer Dirac nodes gap. Such layer dependence can reconcile why bulk-sensitive probes (μSR, Kerr, magnetochiral anisotropy) often detect TRSB signatures, whereas surface-sensitive spin-polarized STM may not, as the surface may be less prone to chiral flux phases due to confinement and reduced interlayer coupling.

This work identifies quantum confinement at the polar surface of CsV3Sb5 as a key factor shaping its ARPES-visible electronic structure. Photon-energy-dependent ARPES reveals kz-independent quantum well subbands at Γ, including a purely 2D outer subband, while slab DFT with surface relaxation reproduces the spectra using contributions from only the top one to two layers and shows a ~1 eV surface potential well. Quantum confinement thus reconciles ARPES-bulk DFT discrepancies and provides a framework to interpret surface-versus-bulk differences in CDW and TRSB behaviors. Future directions include: direct structural characterization of surface relaxation and termination dependence; extending confinement studies across AV3Sb5 (A = K, Rb) and under controlled surface dosing or gating; quantitative modeling of how confinement modifies CDW, superconductivity, and potential chiral flux phases; and depth-resolved spectroscopies to map the evolution from surface-confined to bulk-like states.

- ARPES is surface-sensitive, so conclusions primarily pertain to the top few layers and rely on slab modeling to infer bulk–surface relationships. - The observed confinement and subband structure may depend on surface termination and relaxation, which can vary between cleaves/samples; termination control was not exhaustively explored. - The slab model uses six layers and specific vacuum/relaxation parameters; while capturing key features, finite-size and functional approximations (PBE, vdW corrections) may limit quantitative accuracy (e.g., exact potential drop magnitude and subband energies). - The study focuses on CsV3Sb5; generalization to K/Rb analogs and to different temperatures/pressures remains to be validated. - While phonon softening and reconstruction trends suggest weaker surface CDW, direct surface structural probes (e.g., surface XRD, LEED I–V) were not reported.