Untangling charge-order dependent bulk states from surface effects in a topological kagome metal ${\mathrm{ScV}}_6{\mathrm{Sn}}_6$

Kagome metals with charge density wave (CDW) order exhibit a broad spectrum of intriguing quantum phenomena. The recent discovery of the novel kagome CDW compound ${\mathrm{ScV}}_6{\mathrm{Sn}}_6$ has spurred significant interest. However, understanding the interplay between CDW and the bulk electronic structure has been obscured by a profusion of surface states and terminations in this quantum material. Here, we employ photoemission spectroscopy and potassium dosing to elucidate the complete bulk band structure of ${\mathrm{ScV}}_6{\mathrm{Sn}}_6$, revealing multiple van Hove singularities near the Fermi level. We surprisingly discover a robust spin-polarized topological Dirac surface resonance state at the $M$ point within the twofold van Hove singularities. Assisted by first-principles calculations, the temperature dependence of the $k_z$-resolved angle-resolved photoemission spectroscopy spectrum provides unequivocal evidence for the proposed $\sqrt{3}\times \sqrt{3}\times 3$ charge order over other candidates. Our work not only enhances the understanding of the CDW-dependent bulk and surface states in ${\mathrm{ScV}}_6{\mathrm{Sn}}_6$, but also establishes an essential foundation for potential manipulation of the CDW order in kagome materials.

Figure 1

Termination-dependent band structure in ${\mathrm{ScV}}_6{\mathrm{Sn}}_6$. (a) Side view of the crystal structure of ${\mathrm{ScV}}_6{\mathrm{Sn}}_6$ in the normal phase. (b) Brillouin zone (BZ) and high-symmetry points. (c) Theoretical band structure of the normal phase of ${\mathrm{ScV}}_6{\mathrm{Sn}}_6$. The two types of van Hove singularities (V1 and V2) and Dirac cone (D1) are marked with arrows, respectively. (d) Core-level spectrum of Sn $4d$ orbitals on the ${\mathrm{Sc}}_2\mathrm{Sn}$ layer. (e) The corresponding Fermi surface map, measured with 80 eV photon energy and at 10 K. (f) Energy-momentum cuts along high-symmetry lines. For visual clarity, a dashed line has been plotted at the V2 state. (g)–(i) Same as (d)–(f), but at ${\mathrm{V}}_3\mathrm{Sn}$ termination. A notable difference between (e), (f) and (h), (i) emphasizes the presence of surface states.

Figure 2

Unravel the bulk band structure with K dosing. (a) Core-level spectrum of Sn $4d$ state and K $3p$ state before and after the K dosing. Throughout the dosing process, the number of Sn $4d$ peaks remains unchanged, confirming measurements taken at the V termination. (b) A schematic representation of the K dosing at the ${\mathrm{V}}_3\mathrm{Sn}$ termination. (c), (e) The Fermi surface map acquired on (c) the pristine surface and (e) the surface after dosing. 129 eV light with linear horizontal polarization was used for collecting the data. (d), (f) Energy-momentum cuts along high-symmetry directions, derived, respectively, from the maps in (c) and (e). The V $d$-orbital-resolved DFT calculation is overlaid and shows remarkable consistency with the ARPES features near the Fermi level.

Figure 3

Spin polarization of the Dirac surface resonance state at the $M$ point. (a) Left: Energy-momentum cut along the $\mathrm{\Gamma }-M$ direction, acquired with 50 eV photons. A green rectangle accentuates the detected range of spin EDCs. Right: Extracted and symmetrized dispersion of the S1 state, revealing the full linear crossing around the $M$ point. (b) The geometry of the spin-resolved ARPES measurement. (c), (d) Spin-resolved energy-dispersion curves (EDCs) for (c) the $S_y$ direction and (d) the $S_x$ directions. The inset in (c) depicts the relative orientation of the spin polarization in relation to the BZ. (e), (f) The binding energy dependence of net spin polarization along $S_y$ and $S_x$. Data measured at the opposite $M$ point ($-M$) were plotted and revealed the opposite spin polarization. (g) Surface-projected bulk band structure along the $\mathrm{\Gamma }-M-K$ path of the surface BZ. (h) Calculated surface spectrum at ${\mathrm{V}}_3\mathrm{Sn}$ termination, in which a singularly degenerated Dirac state emerges between the two VHS. (i), (j) Computed spin polarization of the bands near the $M$ point. The green dashed rectangles in (i) and (j) represent the effective detection regions of spin EDCs in (c) and (d), respectively. (k), (l) In-plane spin-polarization distribution at binding energy $-18$ meV [green dashed line in (h)].

Figure 4

Direct observation of the band-folding effect of $\sqrt{3}\times \sqrt{3}\times 3$ charge order. (a) Core-level spectroscopy of the Sn $4d$ core level measured at both 10 and 110 K. (b) Cut along the $\mathrm{\Gamma }-M-\mathrm{\Gamma }$ direction, obtained with 80 eV photons. (c) Its second derivative. (d),(e) Similar cut to (b),(c), but measured below the CDW transition temperature, showing a distinct gap feature below the Fermi level. (f) EDCs cross the gap feature, which are extracted from the dashed line in (d) and the same momentum location in (b). (g)–(j) Unfolded band structure in various configurations: (g) the normal phase, (h) $\sqrt{3}\times \sqrt{3}\times 3$ order, (i) $\sqrt{3}\times \sqrt{3}\times 2$ order, and (j) $2\times 2\times 2$ charge order. The corresponding BZs (red for the normal phase and blue for the CDW phases) are also presented above the calculations. The consistency between (h) and (d) confirms the type of order.