Temperature and Angular Dependence of the Upper Critical Field in K$_{2}$Cr$_{3}$As$_{3}$

Abstract

We report measurements of the upper critical field $H_{\mathrm{c2}}$ as functions of temperature $T$, polar angle $θ$ (of the field direction with respect to the crystallographic $c$ axis), and azimuthal angle $ϕ$ (of the field direction relative to the $a$ axis within the $ab$ plane) for the Cr-based superconductor K$_{2}$Cr$_{3}$As$_{3}$ with a quasi-one-dimensional and non-centrosymmetric crystal structure. We confirm that the anisotropy in $H_{\mathrm{c2}}(T)$ becomes inverse with decreasing temperature. At low temperatures, $H_{\mathrm{c2}}(θ)$ data are featured by two maxima at $θ$ = 0 ($\mathbf{H}\parallel c$) and $π/2$ ($\mathbf{H}\bot c$), which can be quantitatively understood only if uniaxial effective-mass anisotropy and absence of Pauli paramagnetic effect for $\mathbf{H}\bot c$ are taken simultaneously into consideration. The in-plane $H_{\mathrm{c2}}(ϕ)$ profile shows a unique threefold modulation especially at low temperatures. Overall, the characteristic of the $H_{\mathrm{c2}}(θ, ϕ, T)$ data mostly resemble those of the heavy-fermion superconductor UPt$_3$, and we argue in favor of a dominant spin-triplet superconductivity with odd parity in K$_{2}$Cr$_{3}$As$_{3}$.