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Lars Onsager and Richard Feynman envisioned that the three-dimensional (3D) superfluid-to-normal $lambda$ transition in $^{4}$He occurs through the proliferation of vortices. This process should hold for every phase transition in the same universality class. The role of topological defects in symmetry-breaking phase transitions has become a prime topic in cosmology and high-temperature superconductivity, even though direct imaging of these defects is challenging. Here we show that the U(1) continuous symmetry that emerges at the ferroelectric critical point of multiferroic hexagonal manganites leads to a similar proliferation of vortices. Moreover, the disorder field (vortices) is coupled to an emergent U(1) gauge field, which becomes massive by means of the Higgs mechanism when vortices condense (span the whole system) upon heating above the ferroelectric transition temperature. Direct imaging of the vortex network in hexagonal manganites offers unique experimental access to this dual description of the ferroelectric transition, while enabling tests of the Kibble-Zurek mechanism.
Formation and evolution of topological defects in course of non-equilibrium symmetry breaking phase transitions is of wide interest in many areas of physics, from cosmology through condensed matter to low temperature physics. Its study in strongly co
We use first-principles methods to study doped strong ferroelectrics (taking BaTiO$_3$ as a prototype). Here we find a strong coupling between itinerant electrons and soft polar phonons in doped BaTiO$_3$, contrary to Anderson/Blounts weakly coupled
The surface orientation dependence on the hydrogen evolution reaction (HER) performance of topological crystalline insulator (TCI) SnTe thin films is studied. Their intrinsic activities are determined by linear sweep voltammetry and cyclic voltammetr
We discuss the origin of topological defects in phase transitions and analyze their role as a diagnostic tool in the study of the non-equilibrium dynamics of symmetry breaking. Homogeneous second order phase transitions are the focus of our attention
Layered narrow band gap semiconductor Bi2Se3 is composed of heavy elements with strong spin-orbital coupling (SOC), which has been identified both as a good candidate of thermoelectric material of high thermoelectric figure-of-merit (ZT) and a topolo