Topological defects as relics of emergent continuous symmetry and Higgs condensation of disorder in ferroelectrics

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.

Enhancement and termination of the superconducting proximity effect due to atomic-scale defects visualized by scanning tunneling microscopy

Using low-temperature scanning tunneling microscopy and spectroscopy, we have studied the proximity effect at the interfaces between superconducting Pb island structures and metallic Pb-induced striped-incommensurate phase formed on a Si(111) substrate. Our real-space observation revealed that the step structures on the two-dimensional metallic layer exhibit significant roles on the propagation of the superconducting pair correlation; the proximity effect is terminated by the steps, and in the confined area by the interface and the steps the effect is enhanced. The observed results are explained quantitatively with an elastic reflection of electrons at the step edges based on calculations with the quasi-classical Greens function formulation using Usadel equation.