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arXiv · 1605.09423

Superconducting quantum criticality of topological surface states at three loops

Nikolai Zerf·Chien-Hung Lin·Joseph Maciejko
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Abstract

The semimetal-superconductor quantum phase transition on the two-dimensional (2D) surface of a 3D topological insulator is conjectured to exhibit an emergent $\mathcal{N}=2$ supersymmetry, based on a renormalization group (RG) analysis at one-loop order in the $\epsilon$ expansion. We provide additional support for this conjecture by performing a three-loop RG analysis and showing that the supersymmetric fixed point found at this order survives the extrapolation to 2D. We compute critical exponents to order $\epsilon^3$, obtaining the more accurate value $\nu\approx 0.985$ for the correlation length exponent and confirming that the fermion and boson anomalous dimensions remain unchanged beyond one loop, as expected from non-renormalization theorems in supersymmetric theories. We further couple the system to a dynamical $U(1)$ gauge field, and argue that the transition becomes fluctuation-induced first order. We discuss implications of this result for quantum phase transitions between certain symmetry-preserving correlated surface states of 3D topological insulators.

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Nikolai Zerf, Chien-Hung Lin, Joseph Maciejko. 2016-05-30. Superconducting quantum criticality of topological surface states at three loops. https://doi.org/10.1103/physrevb.94.205106

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