Tunable electronic anisotropy in single-crystal $A_2{\mathrm{Cr}}_3{\mathrm{As}}_3(A=\mathrm{K}, \mathrm{Rb})$ quasi-one-dimensional superconductors

Single crystals of $A_2{\mathrm{Cr}}_3{\mathrm{As}}_3(A=\text{K}, \mathrm{Rb})$ were successfully grown using a self-flux method and studied via structural, transport, and thermodynamic measurement techniques. The superconducting state properties between the two species are similar, with critical temperatures of 6.1 and 4.8 K in ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ and ${\mathrm{Rb}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$, respectively. However, the emergence of a strong normal state electronic anisotropy in ${\mathrm{Rb}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ suggests a unique electronic tuning parameter is coupled to the interchain spacing in the $A_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ structure, which increases with alkali-metal ionic size while the one-dimensional ${\left[{\left({\mathrm{Cr}}_3{\mathrm{As}}_3\right)}^{2-}\right]}_{\infty }$ chain structure itself remains essentially unchanged. Together with dramatic enhancements in both conductivity and magnetoresistance (MR), the appearance of a strong anisotropy in the MR of ${\mathrm{Rb}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ is consistent with the proposed quasi-one-dimensional character of band structure and its evolution with alkali-metal species in this new family of superconductors.

Figure 1

Schematic view of the structure of ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ and ${\mathrm{Rb}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$. A detailed comparison of the lattice parameters is listed in Table 2. Data for ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ is from Ref. [1].

Figure 2

Resistivity of ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ and ${\mathrm{Rb}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ single crystals measured along the [001] crystallographic (needle) direction, shown in panels (a) and (b), respectively. Insets present low-temperature zoom, highlighting the superconducting transition in each compound.

Figure 3

Normalized magnetoresistance of ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ and ${\mathrm{Rb}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ single-crystal samples measured at 7 K under different field orientation configurations, with current applied along the needle ([001]) direction. The inset presents the field-angle-dependent resistivity of ${\mathrm{Rb}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ at 7 K and 14 T.

Figure 4

Magnetic susceptibility of ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ and ${\mathrm{Rb}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ single-crystal collections under zero-field cooled and field-cooled conditions. Panel (a) presents measurements of ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ single crystals with 1 mT field applied along the [001] needle direction. The inset shows field-dependent magnetization of ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ single crystals with field applied both parallel and perpendicular to [001]. Panel (b) presents measurements of ${\mathrm{Rb}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ single crystals with 2 mT field applied along the [001] needle direction. The inset shows the field-dependent magnetization for parallel ($H_{\parallel }$) fields.

Figure 5

Heat capacity of ${\mathrm{Rb}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ single crystals with $H\perp \left[001\right]$. The inset shows the normalized electronic specific heat ${\mathrm{C}}_e$/(${\gamma }_{n}T$) as a function of temperature; the blue line is the theoretical BCS expectation for a single-band $s$-wave superconductor (see text).

Figure 6

Upper critical field of ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ single crystal under different field configurations. Panels (a), (b), (c) and (d) present the field evolution of temperature-dependent resistivity under different field orientations with $\theta =0^{\circ }, {45}^{\circ }, {60}^{\circ }$ and ${90}^{\circ }$, respectively. Panel (e) shows the upper critical field temperature dependence in different field orientations as extracted from resistivity transitions in panels (a)–(d), with $T_c\left(H\right)$ defined by the midpoint between zero and full resistance.

Figure 7

Upper critical field of ${\mathrm{Rb}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ single crystal under perpendicular [panel (a)] and parallel [panel (b)] field orientations. Temperature dependence of $H_{c2}$ from resistance data is shown in panel (c), with $T_c\left(H\right)$ defined by the midpoint between zero and full resistance. This is compared with $T_c$ ($H$) data obtained from heat capacity with $H\perp \left[001\right]$ orientation (solid purple circles), with $T_c$ values defined by the midpoint of the jump in specific heat and error bars corresponding to the transition width.

Figure 8

Anisotropy of the upper critical field $\mathrm{\Gamma }\equiv H_{c2}^{\parallel }$ ($\mathrm{H}\parallel 001$ for 233, $H\parallel a$ for TMTSF salts)/$H_{c2}^{\perp }$ ($\mathrm{H}\perp 001$ for 233, $\mathrm{H}\parallel b$ for TMTSF salts). $T_c$ of ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ and ${\mathrm{Rb}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ are defined using the midpoint between zero and full resistance. The data for TMTSF salt is taken from Refs. [15] and [5], and high-field data for ${\mathrm{K}}_2{\mathrm{Cr}}_3{\mathrm{As}}_3$ is from Ref. [17].