Three-dimensional Fermi surfaces from charge order in layered ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$

The cascade of electronic phases in ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ raises the prospect to disentangle their mutual interactions in a clean, strongly interacting kagome lattice. When the kagome planes are stacked into a crystal, its electronic dimensionality encodes how much of the kagome physics and its topological aspects survive. The layered structure of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ reflects in Brillouin-zone-sized quasi-two-dimensional Fermi surfaces and significant transport anisotropy. Yet here we demonstrate that ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ is a three-dimensional (3D) metal within the charge density wave (CDW) state. Small 3D pockets play a crucial role in its low-temperature magneto- and quantum transport. Their emergence at $T_{\mathrm{CDW}}\approx 93\text{K}$ results in an anomalous sudden increase of the in-plane magnetoresistance by four orders of magnitude. The presence of these 3D pockets is further confirmed by quantum oscillations under in-plane magnetic fields, demonstrating their closed nature. These results emphasize the impact of interlayer coupling on the kagome physics in 3D materials.

Figure 1

(a) Side and (b) top view of crystal structure of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$, which consists of layers of Cs, V, and Sb atoms that form the kagome lattice plane. (c) Electronic structure of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ calculated by density-functional theory. There exist multiple electronic bands across the Fermi level. (d) Fermi surfaces in the Brillouin zone, including several types of Fermi surfaces and their symmetric copies. (e) Illustration of membrane-mount ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ device. The sample is suspended with soft ${\mathrm{SiN}}_x$ springs, which ensures minimum strain effect. (f) Scanning electron microscope (SEM) image of the membrane device. The $250\times 250\mu \mathrm{m}$ membrane window was patterned into several branches of springs with FIB.

Figure 2

(a) Temperature dependence of the out-of-plane (${\rho }_c$) and in-plane resistivity (${\rho }_{ab}$). (b) An abrupt jump occurs in the temperature dependence of ${\rho }_c$, which corresponds to the charge-density-wave transition temperature $T_{\mathrm{CDW}}$. Consistently, ${\rho }_{ab}$ also displays a weak discontinuity. (c) Enlarged view of (a) within the low-temperature range which demonstrates a clear superconducting transition at $T_c$ = 2.8 K. (d) Temperature dependence of resistivity anisotropy (${\rho }_c/{\rho }_{ab}$). The dashed lines stand for the averaged Fermi velocity anisotropy for all Fermi surfaces. (e) First-order derivative of temperature dependence of resistivity anisotropy [$d({\rho }_c/{\rho }_{ab}$)/$dT$]. At the charge-density-wave transition temperature ($T_{\mathrm{CDW}}$) a sharp peak can be observed, as well as a broad hump at $T$” $\approx$ 14 K.

Figure 3

Field dependence of (a) out-of-plane and (b) in-plane magnetoresistance ratio [$\mathrm{MR}=\left(\rho \right(18\mathrm{T})-\rho (0\mathrm{T}\left)\right)/\rho \left(0\mathrm{T}\right)$] with field applied along the $a$ and $c$($ab$) axis. (c) Temperature dependence of magnetoresistance ratio at $B$ = 18 T with current along the $ab$ axis and field along the $a$ axis, which are defined in the inset. (d) Illustration of Fermi surface reconstruction due to charge ordering. The abrupt appearance of magnetoresistance below $T_{\mathrm{CDW}}$ is a direct consequence of the 3D pockets that appear only after the CDW reconstruction.

Figure 4

(a) Fast-Fourier-transformation (FFT) spectrum with different field directions for Shubnikov-de-Hass (SdH) oscillations measured with current applied along the $c$ axis. Here $\theta$ stands for the angle between the $a$ axis and field direction. (b) SdH oscillations (${\rho }_{\mathrm{osc}}$) at $\theta =6^{\circ }, 0^{\circ },$ and $-{10}^{\circ }$. Here ${\rho }_{\mathrm{osc}}=\mathrm{\Delta }\rho /{\rho }_{BG}$, with $\mathrm{\Delta }\rho$ as the oscillatory part of the magnetoresistivity and ${\rho }_{BG}$ as a polynomial fit to the magnetoresistivity background. (c) Corresponding FFT spectrum with star symbols indicating the identified peaks. (d) Angular dependence of SdH oscillation frequencies. The error bar is defined as full width at half maximum of the peaks in the FFT spectrum.