title: Effective Topological Charge Cancelation Mechanism.
abstract: Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems' microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs {defect, antidefect} on curved surfaces and/or presence of relevant "impurities" (e.g. nanoparticles). For this purpose, we define an effective topological charge Δmeff consisting of real, virtual and smeared curvature topological charges within a surface patch Δς identified by the typical spatially averaged local Gaussian curvature K. We demonstrate a strong tendency enforcing Δmeff → 0 on surfaces composed of Δς exhibiting significantly different values of spatially averaged K. For Δmeff ≠ 0 we estimate a critical depinning threshold to form pairs {defect, antidefect} using the electrostatic analogy.
authors.affiliation: Laboratory of Biophysics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000 Ljubljana, Slovenia.
authors.forename: Luka
authors.initials: L
authors.lastname: Mesarec
authors.affiliation: Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland.
authors.forename: Wojciech
authors.initials: W
authors.lastname: Góźdź
authors.affiliation: Laboratory of Biophysics, Faculty of Electrical Engineering, University of Ljubljana, Tržaška 25, 1000 Ljubljana, Slovenia.
authors.forename: Aleš
authors.initials: A
authors.lastname: Iglič
authors.affiliation: Condensed Matter Physics Department, Jožef Stefan Institute, Jamova 39, 1000 Ljubljana, Slovenia.|Jožef Stefan International Postgraduate School, Jamova 39, 1000 Ljubljana, Slovenia.|Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška 160, 2000 Maribor, Slovenia.
authors.forename: Samo
authors.initials: S
authors.lastname: Kralj