Here we discover spontaneous toroidal polar topology in an emerging ferroelectric liquid state with polarization helices, dubbed ‘helielectric nematic’. The interplay between liquid-crystal elasticity and polar interactions results in a continuous in-plane rotation of the polarization, producing a ...
Such toroidal polar topology gives rise to periodic absorption of polarized far-infrared (FIR) waves, enabling the manipulation of the terahertz wave on a mesoscopic scale. Our observations should inform design principles for flexible ferroic materials toward complex topologies and provide opportunities ...
Polar and toroidal electromechanical properties designed by ferroelectric nano-metamaterials - ScienceDirectFerroelectric nano-metamaterialsPiezoelectric responsePiezotoroidic responsePhase-field modelThe recent advance in metamaterials provides a promising route to efficiently tailor and design a variety of material...
www.nature.com/scientificreports OPEN Large and Tunable Polar- Toroidal Coupling in Ferroelectric Composite Nanowires toward received: 10 November 2014 accepted: 18 May 2015 Published: 23 June 2015 Superior Electromechanical Responses W. J. Chen1,3, Yue Zheng1,2,3 & Biao Wang1 The ...
Transformation properties of electric (P), magnetic (M), polar toroidal (T), and axial toroidal (G) moments under space inversion and time reversal operations. MultipoleParity SpaceTime P – + M + – T – – G + + Although parity considerations in space-time is believed to provide a comp...
1. According to conformal mapping theory, the complex exponential function corresponds to a log-polar-to-Cartesian coordinate transformation. This conformal mapping transforms a line to a circle in two dimensions and performs a tube-to-toroidal mapping in 3D space. Here we adopt an afocal system ...