Fermi level tuning and double-dome superconductivity in the kagome metal ${\mathrm{CsV}}_3{\mathrm{Sb}}_{5-x}{\mathrm{Sn}}_x$

The recently reported $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\text{K}$, Rb, Cs) family of kagome metals are candidates for unconventional superconductivity and chiral charge density wave (CDW) order; both potentially arise from nested saddle points in their band structures close to the Fermi energy. Here, we use chemical substitution to introduce holes into ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ and unveil an unconventional coupling of the CDW and superconducting states. Specifically, we generate a phase diagram for ${\mathrm{CsV}}_3{\mathrm{Sb}}_{5-x}{\mathrm{Sn}}_x$ that illustrates the impact of hole doping the system and lifting the nearest van Hove singularity toward and above $E_F$. Superconductivity exhibits a nonmonotonic evolution with the introduction of holes, resulting in two “domes” peaked at 3.6 and 4.1 K and the rapid suppression of three-dimensional CDW order. The evolution of CDW and superconducting order is compared with the evolution of the electronic band structure of ${\mathrm{CsV}}_3{\mathrm{Sb}}_{5-x}{\mathrm{Sn}}_x$, where the complete suppression of superconductivity seemingly coincides with an electronlike band comprised of Sb $p_z$ orbitals pushed above $E_F$.

Figure 1

(a) ${\mathrm{CsV}}_3{\mathrm{Sb}}_{5-x}{\mathrm{Sn}}_x$ crystallizes in the parent ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ ($P6/mmm$) structure. Sn can substitute on either the Sb1 or Sb2 sublattices, and at low doping we establish a preference for the Sb site in the V kagome plane. (b), (c) Sn integration into ${\mathrm{CsV}}_3{\mathrm{Sb}}_{5-x}{\mathrm{Sn}}_x$ causes the $c/a$ ratio to steadily decrease until the termination of solid solubility at $x=1$. (d) For samples with concentrations above EDS sensitivity threshold, nominal Sn tracks measured Sn. Error bars are shown unless they are smaller than the associated point size. The different colors correspond to sample composition and are consistent throughout the figures.

Figure 2

(a) The superconducting $T_C$ measured under a field of $H$ = 5 Oe shows a systematic shift to higher temperature in the compositions leading to the two $T_C$ maximums. The superconducting fraction is normalized to account for errors in mass and packing fraction so all data have a minimum of $-1$, the theoretical minimum. (b) $dM/dT$ for compositions $x\le 0.06$ show a decrease in CDW $T^{*}$, and this transition disappears for greater Sn compositions. (c) Resistivity data also show this enhancement in $T_C$, and the low-$T$, normal-state resistivity for $x=0.35$ is about four times higher than $x=0.03$.

Figure 3

Hole-doping phase diagram for ${\mathrm{CsV}}_3{\mathrm{Sb}}_{5-x}{\mathrm{Sn}}_x$. The double-dome structure is clearly evident, as is the depression of the CDW ordering temperature. $T_C$ shows two maxima at $x=0.03$ and at $x=0.35$ and the CDW state disappears by $x=0.06$. We note that the first $T_C$ maximum occurs while the CDW is still present, and the CDW vanishes once $T_C$ is already declining again $x>0.03$. For $x\ge 0.65$, the volume fraction of superconductivity decreases and the onset $T_C$'s are represented with open circles.

Figure 4

(a) DFT calculations for ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ highlighting the allowable range of Fermi levels under the rigid-band approximation for substitution of one Sn atom per formula unit. (b) Calculation of the band structure of ${\mathrm{CsV}}_3{\mathrm{Sb}}_4\mathrm{Sn}$ where one Sn has been substituted within the kagome plane. Here, the majority of the electronic structure is preserved with the exception of the $\mathrm{\Gamma }$ pocket, where the occupied Sb band is replaced with an unoccupied Sn band above $E_F$. (c) Calculation of the band structure of ${\mathrm{CsV}}_3{\mathrm{Sb}}_4\mathrm{Sn}$ where one Sn has been substituted at a Sb site outside of the kagome plane (OKP). A strong reconstruction of many bands can be observed, in particular near $K, H$, and $K-\mathrm{\Gamma }$.