Extreme orbital $ab$-plane upper critical fields far beyond the Pauli limit in $4H_b\text{−}\mathrm{Ta}{(\mathrm{S},\mathrm{Se})}_2$ bulk crystals

Transition metal disulfides $4H_b$-Ta(S, ${\mathrm{Se})}_2$ with natural heterostructure of $1T$- and $1H$-Ta(S, ${\mathrm{Se})}_2$ layers have became the focus of correlated materials their unique combinations of Mott physics and possible topological superconductivity. In this work, we study the upper critical fields ${\mu }_0{H}_{c2}$ of $4H_b\text{−}{\mathrm{TaS}}_2$ and $4H_b\text{−}{\mathrm{TaS}}_{1.99}{\mathrm{Se}}_{0.01}$ single crystals systematically. Transport measurements up to 35 T show that both of $ab$-plane and $c$-axis upper critical fields (${\mu }_0{H}_{c2,ab}$ and ${\mu }_0{H}_{c2,c}$) for $4H_b\text{−}{\mathrm{TaS}}_2$ and $4H_b\text{−}{\mathrm{TaS}}_{1.99}{\mathrm{Se}}_{0.01}$ exhibit a linear temperature dependent behavior down to 0.3 K, suggesting the three-dimensional superconductivity with dominant orbital depairing mechanism in bulk $4H_b$-Ta(S, ${\mathrm{Se})}_2$. However, the zero-temperature ${\mu }_0{H}_{c2,ab}$(0) for both crystals are far beyond the Pauli paramagnetic limit ${\mu }_{0}H{}_{\mathrm{P}}$. It could be explained by the effects of spin-momentum locking in $1H$-Ta(S, ${\mathrm{Se})}_2$ layers with local inversion symmetry broken and the relatively weak intersublattice interaction between $1H$ layers due to the existence of $1T$ layers.

Figure 1

(a) Crystal structure of $4H_b$-Ta(S, ${\mathrm{Se})}_2$. (b) Powder XRD pattern of crushed $4H_b\text{−}{\mathrm{TaS}}_2$ single crystals. Inset shows the XRD pattern of a $4H_b\text{−}{\mathrm{TaS}}_2$ single crystal. (c) Temperature dependence of zero-field ${\rho }_{ab}\left(T\right)$ for $4H_b\text{−}{\mathrm{TaS}}_2$ and $4H_b\text{−}{\mathrm{TaS}}_{1.99}{\mathrm{Se}}_{0.01}$ single crystals. Inset shows the enlarged view of ${\rho }_{ab}\left(T\right)$ curves at low-temperature region. (d) Temperature dependence of $4\pi \chi \left(T\right)$ at ${\mu }_{0}H$ = 1 mT along the $ab$ plane with ZFC and FC modes.

Figure 2

Field dependence of ${\rho }_{ab}\left({\mu }_{0}H\right)$ of $4H_b\text{−}{\mathrm{TaS}}_2$ single crystal for (a) $H\parallel c$ and (b) $H\parallel ab$, and of the $4H_b\text{−}{\mathrm{TaS}}_{1.99}{\mathrm{Se}}_{0.01}$ single crystal for (c) $H\parallel c$ and ($\mathrm{d})H\parallel ab$ measured at various temperatures in field up to 35 T. (e), (f) Temperature dependence of ${\mu }_0{H}_{c2}\left(T\right)$ for $H\parallel c$ (red circles) and $H\parallel ab$ (blue square) for $4H_b\text{−}{\mathrm{TaS}}_2$ and $4H_b\text{−}{\mathrm{TaS}}_{1.99}{\mathrm{Se}}_{0.01}$ single crystal, respectively. Red and blue dashed lines are the fits using 3D GL model for ${\mu }_0{H}_{c2,ab}\left(T\right)$ and ${\mu }_0{H}_{c2,c}\left(T\right)$. Green dashed lines denote the ${\mu }_0{H}_{\mathrm{P}}$.

Figure 3

Field dependence of ${\rho }_{ab}\left({\mu }_{0}H\right)$ at 2 K and various field directions for (a) $4H_b\text{−}{\mathrm{TaS}}_2$ and (b) $4H_b\text{−}{\mathrm{TaS}}_{1.99}{\mathrm{Se}}_{0.01}$ single crystals. Angular dependence of ${\mu }_0{H}_{c2}\left(\theta \right)$ of (c) $4H_b\text{−}{\mathrm{TaS}}_2$ and (d) $4H_b\text{−}{\mathrm{TaS}}_{1.99}{\mathrm{Se}}_{0.01}$ single crystals at 2.0 K. The ${\mu }_0{H}_{c2}\left(\theta \right)$ at each $\theta$ are determined using the criterion of 50% normal-state resistivity ${\rho }_{n,ab}({\mu }_{0}H,\theta )$. The green and blue curves in panels (c) and (d) represent the fits using 3D anisotropic GL and 2D Tinkham models. Insets: enlarged views of ${\mu }_0{H}_{c2}\left(\theta \right)$ near $\theta ={90}^{\circ }$ ($H\left|\right|ab$).