English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

In the last few years a lot of exotic and anomalous topological phases wereconstructed by proliferating the vortex like topological defects on the surfaceof the $3d$ topological insulator (TI). In this work, rather than consideringtopological phases at the boundary, we will study quantum critical pointsdriven by vortex like topological defects. In general we will discuss a$(2+1)d$ quantum phase transition described by the following field theory:$\mathcal{L} = \bar{\psi}\gamma_\mu (\partial_\mu - i a_\mu) \psi +|(\partial_\mu - i k a_\mu)\phi|^2 + r |\phi|^2 + g |\phi|^4$, with tuningparameter $r$, arbitrary integer $k$, Dirac fermion $\psi$ and complex scalarbosonic field $\phi$ which both couple to the same $(2+1)d$ dynamicalnoncompact U(1) gauge field $a_\mu$. The physical meaning of thesequantities/fields will be explained in the text. We demonstrate that thisquantum critical point has a quasi self-dual nature. And at this quantumcritical point, various universal quantities such as the electricalconductivity, and scaling dimension of gauge invariant operators can becalculated systematically through a $1/k^2$ expansion, based on the observationthat the limit $k \rightarrow + \infty$ corresponds to an ordinary $3d$ XYtransition.

"Self-Dual" Quantum Critical Point on the surface of $3d$ Topological Insulator