Temperature-driven reorganization of electronic order in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$

We report x-ray diffraction studies of the electronic ordering instabilities in the kagome material ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ as a function of temperature and applied magnetic field. Our zero-field measurements between 10 and 120 K reveal an unexpected reorganization of the three-dimensional electronic order in the bulk of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$: At low temperatures, a $2\times 2\times 2$ superstructure modulation due to electronic order is observed, which upon warming changes to a $2\times 2\times 4$ superstructure at 60 K. The electronic order-order transition discovered here involves a change in the stacking of electronically ordered ${\mathrm{V}}_3{\mathrm{Sb}}_5$ layers, which coincides with anomalies previously observed in magnetotransport measurements. This implies that the temperature-dependent three-dimensional electronic order plays a decisive role for transport properties, which are related to the Berry curvature of the V bands. We also show that the bulk electronic order in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ breaks the sixfold rotational symmetry of the underlying $P6/mmm$ lattice and perform a crystallographic analysis of the $2\times 2\times 2$ phase. The latter yields two possible superlattices, namely a staggered star-of-David and a staggered inverse star-of-David structure. Applied magnetic fields up to 10 T have no effect on the x-ray diffraction signal. This, however, does not rule out time-reversal symmetry breaking in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$.

Figure 1

Temperature-dependent XRD measurements and illustration of the three-dimensional room-temperature $P6/mmm$ structure of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$. The latter is shown in (a) together with the kagome V sublattice of a ${\mathrm{V}}_3{\mathrm{Sb}}_5$ layer in (b). The XRD data in (c)–(f) reveal the appearance of two distinct 3D superlattice modulations with different out-of-plane correlations along $c_h$. Data were taken with increasing temperature. (c) Temperature-dependent integrated intensity of the $(0.5,2.5,-0.5)$ and $(0.5,2.5,-0.25)$ superstructure reflections, which signal the presence of a $2\times 2\times 2$ and a $2\times 2\times 4$ superlattice, respectively. The red and blue lines serve as guides to the eye. Inset: Reciprocal space map parallel to the $\left(hk\overline{\frac{1}{2}}\right)$ plane for the $2\times 2\times 2$ phase at 10 K. The chirality of the XRD intensity is similar to that observed by STM [14]. $\left(h3l\right)$ planes for the undistorted $1\times 1\times 1$ host phase (d) at 300 K, the $2\times 2\times 4$ phase (e) at 75 K, and the $2\times 2\times 2$ phase (f) at 10 K.

Figure 2

Breaking of the sixfold rotational symmetry due to electronic order in the $2\times 2\times 2$ and $2\times 2\times 4$ phase. (a), (d) $l$ cuts $(-0.5,3.0,l)$ and $(2.5,0.5,l)$, which are related by sixfold symmetry, differ in both phases (integration thickness $\delta h=\delta k=0.06$ r.l.u.). Also the intensity distributions in reciprocal lattice planes related by sixfold symmetry are distinct as demonstrated in (b), (c) for the $2\times 2\times 2$ phase and in (e), (f) for the $2\times 2\times 4$. In the $2\times 2\times 4$ phase the peak intensities for $l=0.25$ still possess the sixfold rotation symmetry, while the ones with $l=0.5$ do not (d). In the $2\times 2\times 2$ phase sixfold rotation symmetry of the XRD pattern is completely lost (a). Inset: Schematic, indicating the $hk$ positions of the measurements in (a), (d).

Figure 3

Magnetic field-dependent XRD measurements. Blue curve: $(5.0,1.5,-0.5)$ peak of the $2\times 2\times 2$ phase in the zero-field cooled state at 10 K and 0 T. The structure of the intensity profile is due to the mosaic of the sample. As the magnetic field along the $c_h$ direction is increased from 0 to 10 T, the intensity of the $(5.0,1.5,-0.5)$ superstructure peak remains unchanged (red curve). Inset: A two-dimensional detector image showing twin-induced peak splitting at the (5.0,2.0,0.0) position. Increasing $q_x$ corresponds to an increasing scattering angle $2\mathrm{\Theta }$.

Figure 4

Illustration of the refined structural models for the $2\times 2\times 2$ phase at low temperatures. Model 1 (staggered inverse SOD) in (a), (b) and model 2 (staggered SOD) in (c), (d). The two planes at $z=0$ and $z=0.5$ alternate along the $c$ direction (out of plane), which results in a staggered ordering. The different nearest-neighbor V-V distances are encoded by different colors, as indicated below the corresponding panels.