Pressure-Induced Enhancement of Superfluid Density in Transition Metal Dichalcogenides with and without Charge Density Wave

Abstract: Gaining a deeper understanding of the interplay between charge density wave (CDW) order and superconductivity in transition metal dichalcogenides (TMDs), particularly within the (4H/2H)-NbX${2}$ (X=Se,S) family, remains an open and intriguing challenge. A systematic microscopic study across various compounds in this family is therefore required to unravel this complex interplay. Here, we report on muon spin rotation and magnetotransport experiments investigating the effects of hydrostatic pressure on the superconducting transition temperature ($T{\rm c}$), the temperature-dependent magnetic penetration depth ($\lambda_\mathrm{eff}$), and the charge density wave order (CDW) in two layered chalcogenide superconductors: 4H-NbSe${2}$, which exhibits CDW order, and 2H-NbS${2}$, which lacks such order. Our observations reveal a substantial 75$\%$ enhancement of the superfluid density ($n_{s}/m^{*}$) in 4H-NbSe${2}$ upon maximum applied pressure of 2 GPa, surpassing that of 2H-NbSe${2}$. Despite the absence of CDW order, a sizeable 20$\%$ growth in superfluid density is also observed for 2H-NbS${2}$ under an applied pressure of 1.8 GPa. Notably, the evaluated superconducting gaps in all these TMDs remain largely unaffected by changes in applied pressure, irrespective of pressure-induced partial suppression of CDW order in (4H/2H)-NbSe${2}$ or its general absence in 2H-NbS${2}$. These results underscore the complex nature of pressure-induced behaviors in these TMDs, challenging a simplistic view of competition solely between CDW order and superconductivity. Remarkably, the relationship between $n{s}/m^{*}$ and $T_{\rm c}$ exhibits an unconventional correlation, indicating a noteworthy similarity with the behavior observed in cuprate, kagome, and iron-based superconductors.