Doping evolution of superconductivity, charge order, and band topology in hole-doped topological kagome superconductors $\mathrm{Cs}{\left({\mathrm{V}}_{1-x}{\mathrm{Ti}}_x\right)}_3{\mathrm{Sb}}_5$

The newly discovered kagome superconductors $A{\mathrm{V}}_3{\mathrm{Sb}}_5$ ($A=\mathrm{K}$, Rb, Cs) exhibit superconductivity, charge order, and band topology simultaneously. To explore the intricate interplay between the superconducting and charge-density-wave (CDW) orders, we investigate the doping evolution of underlying electronic structures in doped topological kagome superconductors $\mathrm{Cs}{\left({\mathrm{V}}_{1-x}{\mathrm{Ti}}_x\right)}_3{\mathrm{Sb}}_5$ where the Ti dopant introduces hole-like charge carriers. Despite the absence of the CDW phase transition in doped compounds even for the lowest doping level of $x=0.047$, the superconductivity survives in all doped samples with enhanced critical temperatures. The high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements reveal that the Ti dopant in the kagome plane lowers the chemical potential, pushing the van Hove singularity (VHS) at $M$ point above the Fermi level. First-principle simulations corroborate the doping evolution of the band structure observed in ARPES, and affirm that the CDW instability does not occur once the VHS moves above the Fermi level, explaining the absence of the CDW ordering in our doped samples $\mathrm{Cs}{\left({\mathrm{V}}_{1-x}{\mathrm{Ti}}_x\right)}_3{\mathrm{Sb}}_5$. Our results also demonstrate a competition between the CDW and superconducting orders in the kagome-metal superconductor ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$, although the superconductivity is likely inconsequential of the CDW order.

Figure 1

Thermodynamic and transport properties of $\mathrm{Cs}{\left({\mathrm{V}}_{1-x}{\mathrm{Ti}}_x\right)}_3{\mathrm{Sb}}_5$. (a) Temperature-dependent uniform magnetic susceptibilities $\chi =M/H$ with $H={10}^5\mathrm{Oe}$ perpendicular to the $c$ axis. (b) The zero-field-cool (ZFC) and field-cool (FC) magnetic susceptibility data under $H=20\mathrm{Oe}$. (c) Temperature-dependent specific heat coefficient $C_p/T$ at zero field. The inset is the zoom-in low-temperature data. (d) Temperature-dependent resistivity $\rho$ with respect to the 300 K result. (e) The zoom-in low-temperature data of (d). (f) The doping-dependent CDW and superconducting transition temperatures. We take the temperature that heat capacity curves begin to upturn, ZFC and FC curves first deviate and the temperature whose resistance is 90% of normal metallic state value as $T_{c-HC}, T_{c-MT}$, and $T_{c-RT}$.

Figure 2

The doping evolution of the electronic structures of $\mathrm{Cs}{\left({\mathrm{V}}_{1-x}{\mathrm{Ti}}_x\right)}_3{\mathrm{Sb}}_5$. (a) Band structures measured along the A-H-L directions with 31 eV photons at 17 K with different doping levels. (b) The corresponding schematic band dispersions extracted from (a).

Figure 3

Doping evolution of VHSs at the $M/L$ points in $\mathrm{Cs}{\left({\mathrm{V}}_{1-x}{\mathrm{Ti}}_x\right)}_3{\mathrm{Sb}}_5$. [(a)–(d)] ARPES measurements along the H-L-H direction with selected doping levels. In (a) the DFT calculated band structure (green dashed lines) is also overplotted with shifting the Fermi level of 38 meV to match the experimental result. The DFT calculated projected bulk band structure along $\mathrm{\Gamma }$-M-K-$\mathrm{\Gamma }$ and A-L-H-A directions in (e) and along the M-L direction in (f). (g) The comparison between the calculated and experimental results on the energy shift of VHSs with doping. (h) The calculated phonon dispersion relations with doping level $x=0.046$.

Figure 4

Doping evolution of the CDW order $T_{\mathrm{cdw}}$, superconducting transition temperatures $T_c$, and effective mass $m^{*}$ of the Sb-derived electron pockets at $\mathrm{\Gamma }$ of $\mathrm{Cs}{\left({\mathrm{V}}_{1-x}{\mathrm{Ti}}_x\right)}_3{\mathrm{Sb}}_5$.

Figure 5

EDX results of ${\mathrm{Cs}}_3{\left({\mathrm{V}}_{1-x}{\mathrm{Ti}}_x\right)}_3{\mathrm{Sb}}_5$ ($x=0.047$ and $x=0.117$).

Figure 6

The differentiation of resistivity curve $dR/dT$ and heat capacity curve $d{C}_p/dT$ for the x = 0.02 sample, depicted in (a) and (b) respectively.

Figure 7

Doping effect of Ti substitution with the supercell structures. (a) Crystal structure (top view) of (221) supercell of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$, where one V atom is substituted by Ti, resulting in the doping concentration of $x=0.083$. (b) Band structures of (221) ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ ($x=0$) and $\mathrm{Cs}{\left({\mathrm{V}}_{0.917}{\mathrm{Ti}}_{0.083}\right)}_3{\mathrm{Sb}}_5$ ($x=0.083$), where the VHS1 is marked. (c) Crystal structure (side view) of (112) supercell of ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$, where one V atom is substituted by Ti, resulting in the doping concentration of $x=0.167$. (d) Band structures of (112) ${\mathrm{CsV}}_3{\mathrm{Sb}}_5$ ($x=0$) and $\mathrm{Cs}{\left({\mathrm{V}}_{0.833}{\mathrm{Ti}}_{0.167}\right)}_3{\mathrm{Sb}}_5$ ($x=0.167$), where the VHS1 is marked.

Figure 8

Doping evolution of phonon spectrum for $\mathrm{Cs}{\left({\mathrm{V}}_{1-x}{\mathrm{Ti}}_x\right)}_3{\mathrm{Sb}}_5$ (x = 0–0.07). Imaginary phonon frequency at M and L points is related to the CDW instability.