Charge-Density-Wave-Induced Bands Renormalization and Energy Gaps in a Kagome Superconductor ${\mathrm{RbV}}_3{\mathrm{Sb}}_5$

Recently discovered $Z_2$ topological kagome metals $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, and Cs) exhibit charge-density-wave (CDW) phases and novel superconducting paring states providing a versatile platform for studying the interplay between electron correlation and quantum orders. Here we directly visualize CDW-induced bands renormalization and energy gaps in ${\mathrm{RbV}}_3{\mathrm{Sb}}_5$ using angle-resolved photoemission spectroscopy pointing to the key role of tuning van Hove singularities to the Fermi energy in mechanisms of ordering phases. Near the CDW transition temperature, the bands around the Brillouin zone (BZ) boundary are shifted to high-binding energy, forming an $\mathsf{M}$-shaped band with singularities near the Fermi energy. The Fermi surfaces are partially gapped, and the electronic states on the residual ones should be possibly dedicated to the superconductivity. Our findings are significant in understanding CDW formation and its associated superconductivity.

Popular Summary

In a kagome metal, atoms are arranged in a lattice of interlacing triangles that resembles the traditional Japanese weaving pattern of the same name. Recently, in one family of kagome metals, researchers discovered evidence of superconductivity and charge-density waves (CDWs), which in turn seem to be associated with many exotic quantum behaviors. But fully understanding these behaviors requires information on how the low-energy electronic structure of these kagome metals evolves with temperature. Here, we present that information for one type of kagome metal.

Using angle-resolved photoemission spectroscopy, we directly visualize the temperature evolution of the electronic structure of the kagome metal ${\mathrm{RbV}}_3{\mathrm{Sb}}_5$. As a result of the CDW formation at a certain temperature, we find that the bands are strongly renormalized, and the energy gaps are partially opened at the Fermi surfaces. We conclude that tuning singularities with a high density of states to the Fermi energy plays a key role in mechanisms of ordering phases, and the electronic states on the residual Fermi surfaces could possibly be dedicated to the superconducting pairing.

Our findings are significant in understanding CDW formation and its associated superconductivity in these kagome materials, and they also shed light on the study of electronic correlations in other condensed-matter systems.

Figure 1

(a) Crystal structure of ${\mathrm{RbV}}_3{\mathrm{Sb}}_5$ with space group $P6/mmm$ (no. 191). (b) The original (red lines) and $2\times 2$ reconstructed (blue lines) BZs projected on the (001) surface with the high-symmetry points. (c),(d) Integrated intensity plot ($\pm 10\mathrm{meV}$) at $E_F$ and $E_F-0.28\mathrm{eV}$ taken at 140 K. The red lines indicate the high-symmetry directions and the original BZs. (e),(f) Integrated intensity plots ($\pm 10\mathrm{meV}$) on the $k_z-k_{\parallel }$ plane at $E_F$ and $E_F-0.28\mathrm{eV}$ with $k_{\parallel }$ oriented along the $\overline{\mathrm{\Gamma }}\text{−}\overline{K}$ direction. The high-symmetry points are plotted. (g),(h) Intensity plot and corresponding second derivative plot along the $\overline{\mathrm{\Gamma }}\text{−}\overline{K}$ direction. The MDCs taken at $E_F$ and $E_F-0.28\mathrm{eV}$ are shown by the red curves. The bands are indicated by the greek letters and the red dashed lines.

Figure 2

(a),(b) Intensity plots along the $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ direction taken at 120 and 10 K. The sample ($\#S1$) is cleaved at 120 K and measured along with the decreasing temperature. The bands are indicated by the greek letters. (c) MDCs around the $\overline{\mathrm{\Gamma }}$ point taken at 120 K, as indicated by the dashed rectangles in (a). (d),(e) Energy distribution curves (EDCs) around the $\overline{M}$ point at 120 and 10 K, as indicated by the dashed rectangles in (a) and (b). The ${\kappa }^{\prime }$ and $\gamma$ bands are indicated by different color makers. (f) EDCs at the $\overline{M}$ center taken at different temperatures. (g),(h) EDCs and their symmetrizations at the $k_F$ of the $\gamma$ band along $\overline{\mathrm{\Gamma }}\text{−}\overline{M}$ taken at different temperatures. Different colors represent different temperatures.

Figure 3

(a)–(d) Intensity plots and corresponding EDCs along the $\overline{K}\text{−}\overline{M}$ direction taken at 140 and 30 K, respectively. The sample ($\#S2$) is cleaved at 140 K and measured along with the decreasing temperature. The ${\kappa }^{\prime }$ and $\gamma$ bands are indicated by different color makers. (e) EDCs at the $\overline{M}$ center as indicated by the line in (a), taken at different temperatures. The energy positions are indicated by the black arrows. (f) EDCs at the fixed momentum [indicated by $◂$ in (d)] taken at different temperatures and divided by the EDC taken at 140 K. (g) EDCs at the $\overline{K}$ center as indicated by the line in (a), taken at different temperatures. The energy positions are indicated by the black arrows. (h) The symmetrized EDCs at the $k_F$ of the $\gamma$ band along $\overline{K}\text{−}\overline{M}$ taken at different temperatures. The values of the gaps are marked. $\#S3$ represents the EDCs taken on the third sample. (i) Intensity plot along the $\overline{K}\text{−}\overline{M}$ direction taken on the freshly cleaved sample at 10 K ($\#S3$). $k_F$ is indicated by the black arrows. (j) EDCs and their symmetrizations at the $k_F$ of the $\gamma$ band along $\overline{K}\text{−}\overline{M}$, as indicated in (i).

Figure 4

(a) Orbital-projection band-structure calculation of ${\mathrm{RbV}}_3{\mathrm{Sb}}_5$ with spin-orbit coupling for the normal state. Here the main contribution orbitals near $E_F$ are shown, and the orbitals’ weights are represented by both the colors and the size of the bands. The orbitals’ weights of V atoms are the average values of the adjacent three V atoms. The saddle points (SPs) are indicated by the arrows, and the Dirac points (DPs) are marked with the dashed circles. The features at $\overline{M}$ ($M$ and $L$) are indicated by the red squares. (b) The unfolded band structure of the inverse Star of David phase. The bands with a strong renormalization at the $M$ and $L$ points are marked with the dashed ellipses. The marked band at $L$ sinks below $E_F$ in the CDW state.