Origins of electrostriction of MoS ₂ and HfS ₂ in 2 and 3 dimensional 1T and 2H structures

Understanding and controlling electromechanical responses of bulk and low-dimensional materials are of fundamental and technological importance. Electrostriction and piezoelectricity are two key phenomena in which mechanical strain is generated in response to electric fields, forming the basis for a wide range of electromechanical devices. The piezoelectric response is linear and symmetry-restricted, while electrostriction is a universal, second order response that occurs in all dielectrics, including centrosymmetric systems. In this work, we present a theoretical analysis of electrostrictive responses of two- and three-dimensional 1T and 2H polymorphs of TMS₂ (TM = Mo and Hf), with first-principles calculations of the changes in dielectric susceptibility, <i>χ</i>, arising in response to applied stress. We uncover the effects of chemical composition, polymorph (structure) and dimensionality (number of layers (<i>N</i>) in their two-dimensional forms) on the electronic (<i>M</i>^elec) and phononic (<i>M</i>^phononic) contributions to the electrostrictive response of TMS₂. We find that (a) composition has a remarkable impact on the electronic part of electrostriction: <i>M</i>^elec is positive for MoS₂ and negative for HfS₂; (b) the electrostrictive response depends strongly on the structure: while it is dominated by the electronic contribution in the 2H form, it is largely phononic in the 1T form; and (c) the number of layers (<i>N</i>) further influences the response: the phononic contribution (<i>M</i>^phononic) is nearly unaffected by the reduction in <i>N</i>, whereas the electronic contribution (<i>M</i>^elec) decreases notably, consistent with the widening of the band gap responsible for the weakening of the electronic response. Analyzing the contributions of IR-active modes in terms of their mode effective charges and oscillator strengths (<i>ε</i>_<i>λ</i>), we show that strong coupling of the soft modes in the 1T structure with the IR field plays a pivotal role in enhancing the phonon contribution to the dielectric and electrostrictive responses. Our finding that the in-plane electric field induces tensile and compressive electrostrictive strains, respectively, in monolayer MoS₂ and HfS₂ has important consequences for their electronic devices and heterostructures, possibly with a twist.