Revealing Rotational Symmetry Breaking Charge-density Wave Order in Kagome Superconductor (Rb, K)V$_3$Sb$_5$ by Ultrafast Pump-probe Experiments

Abstract

The recently discovered Kagome superconductor AV$_3$Sb$_5$ (where A refers to K, Rb, Cs) has stimulated widespread research interest due to its interplay of non-trivial topology and unconventional correlated physics including charge-density waves (CDW) and superconductivity. The essential prerequisite to understanding the microscopic mechanisms of this complex electronic landscape is to unveil the configuration and symmetry of the charge-density wave order. As to now, little consensus has been made on what symmetry is broken. Herein, we clarify the microscopic structure and symmetry breaking of the CDW phase in RbV$_3$Sb$_5$ and KV$_3$Sb$_5$ by ultrafast time-resolved reflectivity. Our approach is based on extracting coherent phonon spectra induced by three-dimensional CDW and comparing them to calculated phonon frequencies via density-functional theory. The combination of these experimental results and calculations provides compelling evidence that the CDW structure of both compounds prevailing up to T$_{\text{CDW}}$ is the 2 $\times$ 2 $\times$ 2 staggered inverse Star-of-David pattern with interlayer $π$ phase shift, in which the six-fold rotational symmetry is broken. These observations thus corroborate six-fold rotational symmetry breaking throughout the CDW phase of RbV$_3$Sb$_5$ and KV$_3$Sb$_5$.

Figures (7)

• Figure 1: Unstable phonon modes and CDW distortions in RbV$_3$Sb$_5$ and KV$_3$Sb$_5$. (a) 2 $\times$ 2 $\times$ 1 SD. (b) 2 $\times$ 2 $\times$ 1 ISD. (c) Distortion corresponding to the unstable M phonon. (d) Distortion corresponding to the unstable L phonon. (e) ISD + ISD with interlayer $\pi$-phase shift via combination of one M and two L unstable phonons (MLL). (f) SD + ISD without interlayer phase shift via combination of three L unstable phonons (LLL). From (a) to (f) The V atoms are shown in gray. In (a) and (b) the alkali metal atoms (Rb or K) are shown in orange, and from (c) to (f) only the vanadium atoms are shown for simplicity. The lines connecting V atoms indicate shorter bonds. Note that the structure in (a), (b) and (f) keeps the $D_{6h}$ symmetry while the structure in (e) breaks the six-fold rotational symmetry down to two-fold (point group $D_{2h}$).
• Figure 1: The zoomed-in plots highlighting the oscillation patterns of time-resolved reflectivity curves at 5 K for (a) RbV$_3$Sb$_5$ and (b) KV$_3$Sb$_5$. (c) The oscillatory part of the measured time-resolved reflectivity curve on RbV$_3$Sb$_5$ at 5 K in the first 12 ps. (d) The oscillatory part of the measured time-resolved reflectivity curve on KV$_3$Sb$_5$ at 5 K in the first 12 ps.
• Figure 2: Evolution of the coherent phonon spectrum in RbV$_3$Sb$_5$ vs. temperature. (a) Time-resolved reflectivity curves $\Delta$R/R in the temperature range of 5 K – 110 K across the CDW transition temperature. (b) Amplitudes of Fourier transforms of coherent phonon oscillations in $\Delta$R/R time traces after subtracting the decay background. Inset (c) shows the weak 1.75 THz mode. Curves in (a) and (b) are offset for clarity.
• Figure 3: Temperature-dependent coherent phonon spectroscopy in KV$_3$Sb$_5$. (a) Time-resolved reflectivity curves $\Delta$R/R at different temperatures across the CDW transition temperature. Each curve is normalized to its peak value. (b) Amplitudes of Fourier transforms of coherent phonon oscillations in (a) after subtracting the decaying background. Inset (c) shows the weak 1.68 THz mode. Curves in (a) and (b) are offset for clarity.
• Figure 4: Comparison of the phonon spectrum of RbV$_3$Sb$_5$ calculated by DFT and measured by time-resolved reflectivity at T = 5 K. (a) DFT-calculated $A_{1g}$ phonon frequencies in the SD and ISD CDW phases in RbV$_3$Sb$_5$. (b) The calculated $A_{1g}$ ($A_g$) Raman mode frequencies in the SD+ISD without interlayer $\pi$ phase shift (ISD+ISD with interlayer $\pi$ phase shift) state and comparison with the time-resolved reflectivity results. The vertical lines in both figures denote the frequency of the measured phonon peak or the fully-symmetric $A_{1g}$ ($A_g$) modes in DFT calculation. (c) The DFT-calculated oscillation pattern of the fully-symmetric Raman active modes in ISD + ISD with interlayer $\pi$ phase shift (MLL) in RbV$_3$Sb$_5$ that are near our detected 1.53 and 1.75 THz modes via time-resolved reflectivity, respectively. The 1.42 and 1.60 THz $A_g$ modes are the lowest and second-lowest frequency mode in the $A_g$ phonon spectrum of MLL phase in (b). (d) The DFT-calculated oscillation pattern of the fully-symmetric Raman active modes in SD + ISD without interlayer $\pi$ phase shift (LLL) CDW state in RbV$_3$Sb$_5$ that are near our detected 1.53 and 1.75 THz modes via time-resolved reflectivity, respectively. The 1.27 and 1.78 THz $A_{1g}$ modes are the lowest and second-lowest frequency mode in the $A_{1g}$ phonon spectrum of LLL phase in (b). In (c) and (d), the Rb atoms are shown in cyan, the V atoms are shown in blue, and the Sb atoms are shown in yellow.