Nanocalorimetric evidence for nematic superconductivity in the doped topological insulator ${\mathrm{Sr}}_{0.1}{\mathrm{Bi}}_2{\mathrm{Se}}_3$

Spontaneous rotational-symmetry breaking in the superconducting state of doped ${\mathrm{Bi}}_2{\mathrm{Se}}_3$ has attracted significant attention as an indicator for topological superconductivity. In this paper, high-resolution calorimetry of the single-crystal ${\mathrm{Sr}}_{0.1}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ provides unequivocal evidence of a twofold rotational symmetry in the superconducting gap by a bulk thermodynamic probe, a fingerprint of nematic superconductivity. The extremely small specific heat anomaly resolved with our high-sensitivity technique is consistent with the material's low carrier concentration proving bulk superconductivity. The large basal-plane anisotropy of $H_{c2}$ (${\mathrm{\Gamma }}_{\exp }=3.5$) is attributed to a nematic phase of a two-component topological gap structure $\mathbf{\eta }=({\eta }_1,{\eta }_2)$ and caused by a symmetry-breaking energy term $\delta \left(\right|{\eta }_1{|}^2-|{\eta }_2{|}^2)T_c$. A quantitative analysis of our data excludes more conventional sources of this twofold anisotropy and provides an estimate for the symmetry-breaking strength $\delta \approx 0.1$, a value that points to an onset transition of the second order parameter component below 2 K.

Figure 1

Zero-field heat capacity measurement of ${\mathrm{Sr}}_{0.1}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ from room temperature down to 1.8 K (green, inset) and a closeup near the superconducting transition (main figure). The latter becomes visible only after subtraction of a normal-state background (orange). The subtracted curve (black, and normalized by $T$) reveals a small relative specific heat jump $\mathrm{\Delta }C/C\sim {10}^{-2}$; yet compatible with bulk superconductivity.

Figure 2

(a) Calorimetric scans—taken at fixed magnetic field strength ${\mu }_{0}H=0.4$ T—for different field orientations in the basal plane. (b) Angular dependence of the upper critical temperature $T_{c2}\left(\theta \right)$, where each point results from a full specific heat scan [see colored squares in (a)]. $T_{c2}\left(\theta \right)$ assumes a maximal (minimal) value 2.9 K (2.6 K) along the $a$ ($a^{★}$) direction. Weak and strong pinning fits are discussed in the main text. (c) Appearance of anisotropy in the specific heat when the sample is cooled through the superconducting transition. Each curve corresponds to a cut at constant temperature [indicated by vertical arrows in (a)]. The absence of an anisotropy above $T_c$ is consistent with earlier works on magnetization and magnetotransport. (d) Microscope image of ${\mathrm{Sr}}_{0.1}{\mathrm{Bi}}_2{\mathrm{Se}}_3$ single crystal on the nanocalorimetric platform, and platform architecture.

Figure 3

(a) Calorimetric scans along the basal principal axes for various field strengths (curves are arbitrarily offset for better visibility), see blue and red arrows in Fig. 2 (b), reveal a robust superconducting order along $a$ and a less robust one along $a^{★}$. (b) The $H_{c2}$ phase boundary—shown for all three principal axes—features a temperature-independent anisotropy ${\mathrm{\Gamma }}_{\exp }=3.5$ between the two basal-plane upper critical fields. A comparison between the 0.4 T calorimetric scans along the three crystallographic directions (blue, red, green) and the zero field specific heat (black) is given in the inset.