for studying a range of topological phenomena relevant to both condensed matter and particle physics.

Within the Landau paradigm of continuous phase transitions, ordered states of matter are characterized by a broken symmetry. Although the broken symmetry is usually evident, determining the driving force behind the phase transition is often a more subtle matter due to coupling between otherwise distinct order parameters. In this paper we show how measurement of the divergent nematic susceptibility of an iron pnictide superconductor unambiguously distinguishes an electronic nematic phase transition from a simple ferroelastic distortion. These measurements also reveal an electronic nematic quantum phase transition at the composition with optimal superconducting transition temperature. [6][7][8][9] and iron pnictides [10][11][12] have been proposed as candidate platforms that might harbour an electronic nematic phase, which opens up exciting new possibilities related to the interplay of nematic order with high temperature superconductivity. However, one of the key doubts accompanied by the experimental discoveries is that the crystal lattice of these two systems does not retain a fourfold symmetry. In particular, in iron pnictides there is an orthorhombic structural distortion accompanying the rapid increase of resistivity anisotropy, which puts the legitimacy of the term "electronic nematic" into question. Here we report measurements of the resistivity anisotropy of Ba(Fe 1−x Co x ) 2 As 2 induced by a tunable uni-axial strain, which exhibits a divergent behaviour as the system approaches the phase transition from the high temperature side. Our result explicitly shows that the structural phase transition in Ba(Fe 1−x Co x ) 2 As 2 is purely driven by the instability in the electronic part of the free energy, and furthermore reveals an electronic nematic quantum phase transition at the composition with optimal superconducting transition temperature.We apply a tuneable in-plane uniaxial strain to single crystal samples of Ba(Fe 1−x Co x ) 2 As 2 to probe the nematic response. As shown in Fig. 1(A), by gluing the sample on the side wall of a piezostack, strains can be applied by the deformation of the piezo, which is controlled by an applied voltage(V P ) [13]. The strain (i.e. the fractional change of length along the current direction, ǫ P = ∆L/L) was monitored via a strain gauge glued on the back side of the piezo stack. Both ǫ P and the fractional change of resistivity (η = ∆ρ/ρ 0 , where ρ 0 is the resistivity of the free standing sample before gluing on the piezo stack) were measured at constant temperature while the applied voltage was swept, as shown in Fig.

A key actor in the conventional theory of superconductivity is the induced interaction between electrons mediated by the exchange of virtual collective fluctuations (phonons in the case of conventional s-wave superconductors). Other collective modes that can play the same role, especially spin fluctuations, have been widely discussed in the context of high-temperature and heavy Fermion superconductors. The strength of such collective fluctuations is measured by the associated susceptibility. Here we use differential elastoresistance measurements from five optimally doped iron-based superconductors to show that divergent nematic susceptibility appears to be a generic feature in the optimal doping regime of these materials. This observation motivates consideration of the effects of nematic fluctuations on the superconducting pairing interaction in this family of compounds and possibly beyond.