Correlated quantum criticality and topological magnetoelectric response in Bi2Se3

Abstract

A defining feature of quantum materials is that multiple orders govern low-energy physics and are not independent. We study Bi$_2$Se$_3$ by combining DFT with a renormalized correlated honeycomb model in which frustrated magnetic order and helical topological surface states are coupled via one control parameter. The surface states map to a honeycomb Hubbard model with frustrated $J_1$--$J_2$ exchange. Exact diagonalization up to 20 sites shows the Néel structure factor and valence-bond-solid order parameter cross at $J_2/J_1 \approx 0.22$, agreeing with QMC/DMRG, and a dynamical spin structure factor broadens near the crossover, as expected for a spinon continuum. Band inversion of the renormalized tight-binding model occurs on the same critical locus, producing jumps in the Chern number and $\mathbb{Z}_2$ invariant mirrored by the skyrmion charge $Q$. This gives a microscopic link: $Q$ selects the axion angle and thus the topological magnetoelectric coupling. We distinguish axion coupling, independent of skyrmion helicity, from the helicity-dependent magnetoelectric multipole coupling, whose toroidal component scales as $\sinγ$ and vanishes for Néel-type textures. We derive the $Q$-topological magnetoelectric energy and estimate $\sim 10^{-20}\,\mathrm{J}$ per skyrmion per cycle for few-tesla fields. The cycle is thermodynamically bounded: constant-$θ$ cycles extract no net work, and efficiency is limited by axionic entropy change.