AV3Sb5 ARPES
\(AV_3Sb_5\) ARPES¶
ARPES study for KV3Sb5¶
Abstract
Kagome lattices offer a fertile ground to explore exotic quantum phenomena associated with electron correlation and band topology. The recent discovery of superconductivity coexisting with charge-density wave (CDW) in the kagome metals \(KV_3Sb_5\), \(RbV_3Sb_5\), and \(CsV_3Sb_5\) suggests an intriguing entanglement of electronic order and superconductivity. However, the microscopic origin of CDW, a key to understanding the superconducting mechanism and its possible topological nature, remains elusive. Here, we report angle-resolved photoemission spectroscopy of \(KV_3Sb_5\) and demonstrate a substantial reconstruction of Fermi surface in the CDW state that accompanies the formation of small three-dimensional pockets. The CDW gap exhibits a periodicity of undistorted Brillouin zone along the out-of-plane wave vector, signifying a dominant role of the in-plane inter-saddle-point scattering to the mechanism of CDW. The characteristics of experimental band dispersion can be captured by first-principles calculations with the inverse star-of-David structural distortion. The present result indicates a direct link between the low-energy excitations and CDW, and puts constraints on the microscopic theory of superconductivity in alkali-metal kagome lattices.
Fermi surface¶
Figure 1
- Fig. 1c shows the ARPES-intensity mapping at \(E_F\) as a function of \(k_x\) and \(k_y\) at T = 120 K (above \(T_{CDW}\)) measured with 114 eV photons which probe the \(k_z\) ~ 0 plane of the bulk Brillouin zone
- A circular pocket centered at the Γ point and two (small and large) triangular shaped intensity patterns centered at each K point are resolved, as also visualized in Fig. 1d.
Figure 2
- According to the band structure calculations (Fig. 2), they are attributed to the \(5p_z\) band of Sb atoms embedded in the kagome lattice plane (Sb1) and the kagome lattice band with mainly the 3d character of V atoms respectively (note that the small and large triangular features have the dominant \(d_{x^2-y^2}\) and \(d_{xz/yz}\) character, respectively).
- The large triangular feature with the V-\(3d_{xz/yz}\) character connects to each other around the M point and forms a large hexagonal FS centered at the Γ point.
- The bright spots around the M point originate from the large Density of states associated with the saddle-point van Hove singularity in the band dispersion.
Influence of CDW on FS¶
Normal ARPES¶
- ARPES intensity mappings at T = 20 K and 120 K (Fig. 1c, e) share several common features such as the Γ-centered electron pocket and the triangular pattern around the K point, a closer look reveals some intrinsic differences between them. For example, the intensity around the M point associated with the saddle point is substantially suppressed at T = 20 K due to the CDW-gap opening.
- The intensity of triangular pockets is strongly distorted at T = 20 K to show a discontinuous behavior at particular k points (black arrows), in contrast to that at T = 120 K which shows a smooth intensity distribution.
- This indicates the reconstruction of FS due to the strong modulation of band dispersion by the periodic lattice distortion associated with the CDW.
| T = 120K > (\(T_{CDW}\)) | T = 20K (<\(T_{CDW}\)) |
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Band dispersion across \(T_{CDW}\)¶
| T =20K(<\(T_{CDW}\)) | Band dispersion |
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Figure (h, i) shows a comparison of the ARPES intensity along a k cut indicated by a red dashed line in Fig. (e) which traverses the reconstructed Fermi surface at T = 20 K. One can recognize an obvious difference in the intensity distribution between T = 120 K and 20 K in Fig. (h, i). A new holelike band which crosses \(E_F\) (indicated by blue circles and lines) appears at T = 20 K in the k region where FS is absent at T = 120 K.
Second derivative ARPES¶
- Plot of second-derivative ARPES intensity at T = 20 K in Fig. 1f signifies that the discontinuous intensity distribution (Fig. below) is accompanied by the emergence of a small pocket-like feature near the K point (white dotted ellipse). This pocket is associated with the CDW because it is absent at T = 120 K (Fig. 1d).
| T = 120K > (\(T_{CDW}\)) | T = 20K (<\(T_{CDW}\)) |
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Abstract
The Kagome superconductors \(AV_3Sb_5\) (A = K, Rb, Cs) have received enormous attention due to their nontrivial topological electronic structure, anomalous physical properties and superconductivity. Unconventional charge density wave (CDW) has been detected in AV3Sb5. High-precision electronic structure determination is essential to understand its origin. Here we unveil electronic nature of the CDW phase in our high-resolution angle-resolved photoemission measurements on \(KV_3Sb_5\). We have observed CDW-induced Fermi surface reconstruction and the associated band folding. The CDW-induced band splitting and the associated gap opening have been revealed at the boundary of the pristine and reconstructed Brillouin zones. The Fermi surface- and momentum-dependent CDW gap is measured and the strongly anisotropic CDW gap is observed for all the V-derived Fermi surface. In particular, we have observed signatures of the electron-phonon coupling in \(KV_3Sb_5\). These results provide key insights in understanding the nature of the CDW state and its interplay with superconductivity in AV3Sb5 superconductors.
Fermi Surface¶
The CDW-related 2 × 2 lattice reconstruction generates electronic structure reconstruction.
| ARPES : FS | Reconstructed FS |
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Four Fermi surface(FS) sheets can be seen in the figure (left). FS topology is mainly composed of circular electron like pocket around \(\bar{\Gamma}(\alpha)\). A large hexagon-shaped hole-like sheet centered around \(\bar{\Gamma}(\beta)\), a triangular hole-like pocket around \(\bar{K}(\gamma)\) and a triangular electron-like pocket around \(\bar{K}(\delta)\).
Figure (right) shows the effect of the 2 × 2 lattice reconstruction on the Fermi surface as induced by one of the three wavevectors, \(Q_1\). The reconstructed FS is produced by shifting the original lines by the wave vector \(\pm Q_1\). Under the measurement geometry used, the observed folded bands are mainly from \(\pm Q_1\), while those from \(\pm Q_2\) and \(\pm Q_3\) are rather weak. The electronic reconstruction is also directly evidenced in the measured band structure(see original paper fig. 2c), in which the band measured along
the \(\Gamma - M\) direction coincides with the direction of Q1 wave vector.
Signatures of Electron-Phonon coupling¶
The CDW state was first proposed for a one-dimensional chain of atoms with an equal spacing a which is argued to be inherently unstable against the dimerized ground state. It usually involves one band with a half electron filling. This would open a CDW gap at the Fermi point \(k_F\) = ±π/2a and produce a lattice reconstruction with a wavevector of π/a. Such a Fermi surface nesting picture is extended to real materials with higher dimensions, where the CDW state is realized because segments of the Fermi surface are nearly parallel, connected by a wavevector \(Q_{CDW}\).
The CDW transition typically involves electronic structure reconstruction and lattice distortion, in which the electron–phonon coupling plays an important role. The evidence of this Strong coupling approach to CDW has been observed in \(KV_3Sb_5\).
| Bandstructure(BS) | Zoomed BS & Self-Energy |
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A kink in the dispersion can be observed in the above figure. The quantitative dispersion is obtained by fitting momentum distribution curves at different binding energies. Taking a linear line as an empirical bare band, the effective real part of the electron self-energy is shown in Fig. (h). It shows a peak at ~36 meV. The observed kink in the energy dispersion and the peak-dip-hump structure in EDCs (see paper) are reminiscent of those from the electron–boson coupling in simple metal and high-temperature superconductors. The phonon frequency of the vanadium vibrations in AV3Sb5 can reach up to ~36meV, that is consistent with the mode energy observed. Therefore, significant self energy effects in \(KV_3Sb_5\) is observed. It can be interpreted in terms of electron–phonon coupling, which is present for all bands.
ARPES study for CsV3Sb5¶
- Data collected with differing photon energies did not reveal any appreciable dispersion along \(k_z\), consistent with a quasi-2D band structure.
- ARPES data, collected at 50, 80, 100, and 120 K, showed no resolvable change in the band structure when transitioning through the \(T^*\) transition.
Fig.2 a–d, Fermi surface (a) and constant energy contours at E = −0.15 eV (b), −0.30 eV (c) and −0.45 eV (d) as measured with 95 eV photons. The hexagonal surface Brillouin zones are marked with dashed hexagons.
- The Fermi surface of \(CsV_3Sb_5\) display the characteristic hexagonal symmetry and Brillouin zone expected from the underlying kagome lattice.
- A circular electron pocket is at the Brillouin zone center \(\bar{\Gamma}\), labelled as the G band. The orbital projection from DFT reveals that the G band has dominant Sb character (see AV3Sb5 band structure#Orbital-projected electronic structure of CsV_3Sb_5).
Tomographic sections of the vHS of K2 (a), K1 (b) and K2′ (c) bands. Panels 1–6 correspond to the energy– momentum slices of Fig. 2a at \(k_y\) = −0.76, −0.86, −0.96, −1.06, −1.16 and −1.26 Å−1, respectively.