Elastocaloric evidence for a multicomponent superconductor stabilized within the nematic state in Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$

The iron-based high-$T_c$ superconductors exhibit rich phase diagrams with intertwined phases, including magnetism, nematicity and superconductivity. The superconducting $T_c$ in many of these materials is maximized in the regime of strong nematic fluctuations, making the role of nematicity in influencing the superconductivity a topic of intense research. Here, we use the AC elastocaloric effect (ECE) to map out the phase diagram of Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$ near optimal doping. The ECE signature at $T_c$ on the overdoped side, where superconductivity condenses without any nematic order, is quantitatively consistent with other thermodynamic probes that indicate a single-component superconducting state. In contrast, on the slightly underdoped side, where superconductivity condenses within the nematic phase, ECE reveals a second thermodynamic transition proximate to and below $T_c$. We rule out magnetism and re-entrant tetragonality as the origin of this transition, and find that our observations strongly suggest a phase transition into a multicomponent superconducting state. This implies the existence of a sub-dominant pairing instability that competes strongly with the dominant $s^\pm$ instability. Our results thus motivate a re-examination of the pairing state and its interplay with nematicity in this extensively studied iron-based superconductor, while also demonstrating the power of ECE in uncovering strain-tuned phase diagrams of quantum materials.