Flexoelectrically Driven Electroclinic Effect in the Twist-Bend Nematic Phase of Achiral Molecules with Bent Shapes C. Meyer, 1 G. R. Luckhurst, 2 and I. Dozov 1 1 Physique des Syste `mes Complexes, Universite ´ de Picardie Jules Verne, 80039 Amiens, France 2 School of Chemistry, University of Southampton, Highfield, Southampton SO171BJ, United Kingdom (Received 5 February 2013; published 6 August 2013) We extend the twist-bend nematic (N TB ) model to describe the electro-optics of this novel phase. We predict an electroclinic effect (ECE) subject to a dc electric field E applied perpendicular to the helix axis or wave vector q, with rotation of the N TB optic axis around E. This linear effect, with its flexoelectric origin, is a close analog to the electro-optic effects observed for chiral liquid crystals. However, in nematics composed of achiral molecules having a bent shape, it is the electro-optic signature of the N TB phase. We test our model experimentally in the low-temperature nematic phase of the odd liquid crystal dimer, CB7CB, with its molecules having, on average, a bent shape. The ECE measurements confirm the previously proposed twist-bend nematic structure of this phase, with its broken chiral symmetry, extremely short (<10 nm) doubly degenerate pitch and ultrafast, submicrosecond response times. DOI: 10.1103/PhysRevLett.111.067801 PACS numbers: 61.30.Gd, 61.30.Eb, 64.70.M Chirality plays an important role in physics, chemistry, and biology, and especially for soft matter systems such as biological tissues, polymers, and liquid crystals (LC). This lack of mirror symmetry often leads to qualitative new effects, impossible in achiral systems. For example, chiral nematics (N  ) and chiral smectics (SmA  , SmC  ) exhibit strong polar electro-optic effects [1–3], which are symmetry forbidden in their achiral analogs (N, SmA, and SmC). Normally, the chirality of LC phases results from their chiral building blocks, typically molecules. Calamitic molecules tend to orient along an average direction, the nematic direc- tor, n. For achiral molecules, the equilibrium state corre- sponds to uniform n, rn ¼ 0. Chiral molecules distort the director field, inducing a twist distortion, n ðr  nÞ Þ 0. The phase then has a chiral superstructure, with n arranged on a helix (N  ), or on a conical helix (SmC  ), enhancing some of the chirality-dependent properties, e.g., resulting in a huge optical activity in both N  and SmC  . Macroscopic chirality can also be created with achiral molecules, by surface alignment [4], or due to symmetry breaking at an interface [5]. Bulk chiral-symmetry break- ing is also possible with achiral molecules of low symme- try, as has been discovered by the Takezoe Group [6,7] for bent-core smectics. In these phases, the coupling between the orientational, translational, and polar order results in a spontaneous twist, with doubly degenerate handedness, and spectacular electric properties [8]. Twelve years ago, Dozov [9] proposed that chiral symmetry breaking might also take place in the nematic phase of achiral, bent-shaped molecules. Independently, Memmer [10] arrived at the same conclusion by Monte Carlo simulations of idealized bent-core molecules. Indeed, such molecules induce a bend distortion of the nematic director. Formally, this is equivalent to a decrease of the bend elastic constant, K 3 . If K 3 becomes negative, as expected for highly bent molecules [11], the usual uniform nematic is destabilized with respect to periodically dis- torted states. In one of the predicted states [9], the twist- bend nematic phase N TB , the directors form a conical helix with a doubly degenerate handedness. Indeed, the chiral symmetry is spontaneously broken in the N TB phase, even though there is no positional order as in bent-core smectics. Recently, several optical experiments on achiral bent- shaped mesogens [12–17] reported nematic phases with doubly degenerate chirality, predicted for N TB . However, the unambiguous identification of this phase remains diffi- cult, the observed textures being much more complex than those predicted. Here we extend the original macroscopic model to describe the electro-optic behavior of the N TB phase. In addition to the trivial helical reorientation, we predict an electroclinic effect (ECE): a dc field E applied perpen- dicular to the helix axis, induces a rotation of the N TB optic axis N around E. This linear electro-optic effect of flexo- electric origin is a close analog to both the ECE in SmA  [2] and the flexoelectric effect [3] in N  . However, if observed in nematics composed of achiral molecules, the ECE is the signature of the N TB phase. To test our model, we study the electric-field behavior of the low-temperature nematic phase of the odd LC dimer, CB7CB. We observe the predicted ECE, consistent with the N TB nature of the phase, with an extremely short (<10 nm) and doubly degenerate pitch. We consider the elastic energy density of a uniaxial nematic, composed of achiral bent-shaped molecules, whose shape leads to a negative value of the bend elastic constant. For simplicity, we assume a constant nematic order parameter and a 1D distortion of the director, n ¼ nðzÞ. The expansion of f dist in a series of spatial derivatives of the director gives [9] PRL 111, 067801 (2013) PHYSICAL REVIEW LETTERS week ending 9 AUGUST 2013 0031-9007= 13=111(6)=067801(5) 067801-1 Ó 2013 American Physical Society