Pure nematic transition inside the superconducting dome of iron chalcogenide superconductor FeSe$_{1-x}$Te$_x$
Nematicity and magnetism are prevalent orders in high transition temperature (Tc) superconductors, coexisting in the parent compound of most material families. Quantum fluctuations of nematicity or spin orders are both plausible candidates for mediating unconventional Cooper pairing. Identifying the sole effect of a nematic quantum critical point (QCP) on the emergence of superconducting dome without interference of spin fluctuations is therefore highly desirable. The iron chalcogenide superconductor FeSe exhibits pure nematicity without any magnetic ordering. A nematic quantum phase transition can be induced by Te substitution but experimental study of such transition is so far limited to its normal state. By performing local susceptometry on composition-spread FeSe$_{1-x}$Te$_x$ films ($0 < x < 1$) using scanning Superconducting Quantum Interference Device (sSQUID) microscopy, we investigate the superfluid density ($\rho_s$) across the pure nematic transition in extremely fine steps of ${\Delta}x$ = 0.0008. The temperature dependence of $\rho_s$ changes from the form of anisotropic pairing on the nematic side to an isotropic one across the critical doping $x_c$. The power-law dependence of gap anisotropy on $|x - x_c|$ provides evidence for nematic quantum criticality under the superconducting dome. The low-temperature $\rho_s$ scales linearly with Tc in the nematic phase $x < x_c$, whereas the gap amplitude, maximized at $x_c$, determines the Tc for $x>x_c$. Our results establish a pure nematic QCP in FeSe$_{1-x}$Te$_x$, separating two superconducting orders with distinct pairing boosted by nematic quantum fluctuations.