Spin Excitations and Flat Electronic Bands in a Cr-based Kagome Superconductor

TL;DR

This work establishes direct evidence that kagome flat bands in CsCr$_3$Sb$_5$ lie near $E_F$ and interact with magnetic excitations, as shown by ARPES, RIXS, and DFT together with correlation effects. The FBs are observed within $60$ meV of $E_F$ and shift by about $20$ meV across the CDW transition at $T_{ m CDW}=54$ K, with a non-dispersive $∼70$ meV spin excitation revealed by RIXS that tracks the FB behavior. The data indicate a magnetic component to the low-temperature order and suggest the kagome FBs play a role in the emergent order and the pressure-tuned superconductivity observed in this system. Overall, the results highlight flat-band physics in a bulk kagome metal as a promising avenue for realizing correlated and potentially topological electronic states.

Abstract

In the quest for topology- and correlation-driven quantum states, kagome lattice materials have garnered significant interest for their band structures, featuring flat bands (FBs) from the quantum destructive interference of the electronic wavefunction. Tuning an FB to the chemical potential could induce electronic instabilities and emergent orders. Despite extensive studies, direct evidence of FBs tuned to the chemical potential and their role in emergent orders in bulk materials remains lacking. Using angle-resolved photoemission spectroscopy, resonant inelastic X-ray scattering, and density functional theory, we show that the low-energy structure of the Cr-based kagome metal superconductor {\Cr} is dominated by FBs at the Fermi level. We also observe low-energy magnetic excitations evolving across the low-temperature transition, largely consistent with the FB shift. Our results suggest that the low-temperature order contains a magnetic origin and that the kagome FBs may play a role in the emergence of this order.

Figures (7)

• Figure 1: Crystal structure, X-ray diffraction, Schematic of ARPES and RIXS results. (A) Unit cell of CsCr$_3$Sb$_5$. The Cr forms a kagome lattice. (B) and (C) Reciprocal space of CsCr$_3$Sb$_5$. CDW observed by XRD are shown as red arrows or red points. The green arrow marks the $q$ of temperature-dependent RIXS, where $q_\parallel$ is the projection of $q$ onto the sample surface. (D) and (F) XRD in the $(H,K,0)$ plane at 110 K and 35 K. (E) and (G) Corresponding cuts of (F) and (G), respectively. (H) Cartoon illustration of the ARPES observed shift of the kagome flat band away from $E_F$ below $T_{\rm CDW}$. (I) Cartoon illustration of the observed shift of the magnetic excitations observed by RIXS across $T_{\rm CDW}$. The light orange and light blue shaded areas indicate the spectral weight that is coupled to particle-hole excitations across $E_F$ illustrated in (H).
• Figure 2: Electronic structure of CsCr$_3$Sb$_5$. (A) DFT-calculated band structure of CsCr$_3$Sb$_5$. (B) DFT-calculated band structure of CsV$_3$Sb$_5$. In (A) and (B), red arrows mark the energy position of the flat bands (FB) while red circles mark the positions of the VHSs in both CsCr$_3$Sb$_5$ and CsV$_3$Sb$_5$. (C) Comparison of the DOS of CsCr$_3$Sb$_5$ (cyan) and CsV$_3$Sb$_5$ (orange) whose FB
• Figure 2: (continued) energy positions are indicated by the red arrows, respectively. (D) Fermi surface of CsCr$_3$Sb$_5$ measured with 102eV photons on the left and DFT calculation on the right. Red solid lines mark the 2D projected BZ. Blue arrows denote the light polarization. (E) Same as (D) but at E$_B$ = 0.5eV. The black dashed circles mark the position of the VHS at the M point. (F) The definition and illustration of the orbitals in CsCr$_3$Sb$_5$. (G)-(J) band dispersion taken with 114 eV (G)(H) LV and (I)(J) LH polarization along the $\bar{\Gamma}$-$\bar{K}$-$\bar{M}$-$\bar{K}$ and $\bar{\Gamma}$-$\bar{M}$-$\bar{\Gamma}$ directions. The DFT calculations projected onto the orbitals observable in each measurement geometry according to the selection rules are overlapped on the band dispersions for comparison. Blue arrows denote the polarization direction. The white solid arrow denotes the ${d_{yz}}$ character band position while the white dashed arrow denotes its position in the observation, suggesting a possible orbital-selective band renormalization for ${d_{yz}}$ orbitals. (K) Band dispersions measured with 100 eV photons ($k_z$ = 0) along $\bar{\Gamma}$-$\bar{M}$. The measurement geometry and polarization are as marked. (L) EDCs stacking in band dispersions taken with LH polarization at in (K). (M) Same as (L) but taken with LV polarization. Lines of the same colors in (K)-(M) denote high symmetry point positions.
• Figure 3: RIXS measurements. (A) Illustration of RIXS scattering geometry. The scattering plane was perpendicular to the $ab$ plane of CsCr$_3$Sb$_5$. The incident and scattered wave vectors of X-rays, i.e., $\bf{k}_{\rm in}$ and $\bf{k}_{\rm out}$, are orthogonal. The polarization of incident X-rays was in the scattering plane, i.e., $\pi$-polarized, resulting in RIXS with a cross-polarization geometry. The polarization of scattered X-rays was unresolved. The projection of wavevector change $\bf q$ onto the $ab$ plane is denoted as ${\bf q}_{\|}$. (B) Cr $L_3$-edge X-ray absorption spectrum (XAS) of CsCr$_3$Sb$_5$ recorded at 300 K. Colored vertical bars indicate the X-ray energies used in RIXS measurements. (C) Incident-energy-dependent RIXS with ${\bf q}_{\|}$ along the ${\Gamma}M$ direction at $25$ K. Spectra in color were recorded with
• Figure 3: (continued) $\pi$-polarized X-rays at selected energies. The RIXS spectrum with $\sigma$ polarization, i.e., X-ray polarization perpendicular to the scattering plane, shows the instrumental energy resolution of RIXS. (D) Demonstration of curve fitting for RIXS data analysis. In addition to a linear background, a measured RIXS spectrum was fitted to a spectral profile consisting of three components: one elastic and two electronic excitations. See SM for fitting details. (E) First Brillouin zone in the $a^{*}b^{*}$ plane of reciprocal space. The red arrow indicates ${\bf q}_{\|}$ of momentum-dependent RIXS measurements. (F) Momentum-dependent RIXS with ${\bf q}_{\|}$ along ${\Gamma}K$ at $25$ K. The energy of incident photons was set to 575.2 eV to optimize the shoulder feature. The black lines plot the elastic components; the colored shades indicate spectral profiles arising from spin excitations. (G) Dispersion of fitted $E_0$ of two spin excitations as a function of in-plane momentum ${\bf q}_{\|}$.