Two-gap to single-gap superconducting transition on a honeycomb lattice in ${\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x\mathrm{Al}\mathrm{Si}$

We report on the structural and microscopic superconducting properties of the ${\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x\mathrm{AlSi}$ solid solution. Specifically, we have realized the continuous solid solution, which for all members, other than $x=0$ (CaAlSi), crystallizes in the ${\mathrm{AlB}}_2$-type structure. For CaAlSi, we present an improved structural model where all Al/Si layers are buckled, leading to a 6-folded structure along the crystallographic $c$ direction. We, furthermore, find indications for the structural instability in the parent compound CaAlSi to enhance the superconductivity across the solid solution. Our investigation of the magnetic penetration depths by means of muon-spin rotation experiments reveals that CaAlSi is a two-gap superconductor, that SrAlSi is a single-gap superconductor, and that there is a continuous transition from one electronic state to the other across the solid solution. Hence, we show that the ${\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x\mathrm{AlSi}$ solid solution is a highly tunable two-gap to single-gap superconducting system on a honeycomb lattice, where the superconductivity is strongly connected to a structural instability, i.e., the buckling of the Al/Si layers.

Figure 1

Structure and bonding of the ${\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x\mathrm{AlSi}$ solid solution. Crystal structure of CaAlSi with space group $P{6}_3/mmc$ (a) along the $a$ direction with an emphasis on the 6-layered super-cell, (b) along the $c$ direction, showing the honeycomb Al/Si layers, and (c) a single layer of CaAlSi showing the buckling of the Al/Si layers. Crystal structure of SrAlSi with space group $P6/mmm$ in the ${\mathrm{AlB}}_2$ structure type (d) along $a$ direction and (e) along $c$ direction. (f) Powder x-ray diffraction patterns of the ${\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x\mathrm{AlSi}$ solid solution with $x=0$, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1 (g) Zoom-in of $2\mathrm{\Theta }=30.0$ to 33.0 region showing the pronounced shifting as a function of Ca/Sr content and the slight splitting for the samples $x=0.3$ to 0.7 of the (101) Bragg reflection.

Figure 2

Superconducting properties of the ${\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x\mathrm{AlSi}$ solid-solution. (a) ZFC magnetization in an external magnetic field of ${\mu }_{0}H=2\mathrm{mT}$ for $x=0$, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1, plotted between 2 and 10 K. Data were normalized by being plotted as $-M\left(T\right)/M\left(2\mathrm{K}\right)$. (b) Summary of the crystallographic and superconducting parameters of the samples of the solid solution for $x=0$, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1. The cell parameter $c$ for CaAlSi was divided by 6 for comparability.

Figure 3

(a) Specific heat capacity jump for the samples with $x=0$, 0.1, 0.3, 0.5, and 1 in a temperature range of between 2 K to 10 K. The entropy conserving construction is depicted for CaAlSi ($x=0$). (b) Values of $\mathrm{\Delta }C/\gamma T_{\mathrm{c}}$ and the electron-phonon coupling constant ${\lambda }_{e-p}$.

Figure 4

Transverse-field $\mu \mathrm{SR}$ time spectra of the ${\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x\mathrm{AlSi}$ solid solution. (a) CaAlSi, (b) ${\mathrm{Ca}}_{0.7}{\mathrm{Sr}}_{0.3}\mathrm{AlSi}$, and (c) SrAlSi spectra in the normal state at $T=10\mathrm{K}$ (gray points) and in the superconducting state at $T=1.5\mathrm{K}$ (blue, green, and orange points, respectively). The solid lines represent fits to the data points by means of Eq. (5).

Figure 5

Temperature evolution of the London magnetic penetration depth ${\lambda }^{-2}(T$) for ${\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x\mathrm{AlSi}$. The temperature dependence of the inverse squared magnetic penetration depth ${\lambda }^{-2}$ for CaAlSi (blue), ${\mathrm{Ca}}_{0.7}{\mathrm{Sr}}_{0.3}\mathrm{AlSi}$ (green), and SrAlSi (orange), measured at ambient and under pressure in a temperature range between $T=300\mathrm{mK}$ and 10 K. Dashed line represents a fit with the single gap $s$-wave model, while the solid line corresponds to the two-gap $s+s$-wave model.

Figure 6

Superconducting gap evolution as a function of the critical temperature. Details of the analysis of ${\lambda }^{-2}$ and ${\mathrm{\Delta }}_0$ for $x=0$, 0.3, and 1 with (a) the fraction of the large gap vs $T_{\mathrm{c}}$, (b) the size of the superconducting gaps vs $T_{\mathrm{c}}$, and (c) the critical temperature $T_{\mathrm{c}}$ against the ${\lambda }_{\mathrm{eff}}^{-2}\left(0\right)$ obtained from the $\mu \mathrm{SR}$ experiments. In (a) and (b) the dotted line is a guide for the eye, while in (c) it represents the expected behavior according to the BCS weak-coupling limit.