On the matter of topological insulators as magnetoelectrics

Abstract

It has been proposed that topological insulators can be best characterized not as surface conductors, but as bulk magnetoelectrics that -- under the right conditions-- have a universal quantized magnetoelectric response coefficient $e^2/2h$. However, it is not clear to what extent these conditions are achievable in real materials that can have disorder, finite chemical potential, residual dissipation, and even inversion symmetry. This has led to some confusion and misconceptions. The primary goal of this work is to illustrate exactly under what real life scenarios and in what context topological insulators can be described as magnetoelectrics. We explore analogies of the 3D magnetoelectric response to electric polarization in 1D in detail, the formal vs. effective polarization and magnetoelectric susceptibility, the 1/2 quantized surface quantum Hall effect, the multivalued nature of the magnetoelectric susceptibility, the role of inversion symmetry, the effects of dissipation, and the necessity for finite frequency measurements. We present these issues from the perspective of experimentalists who have struggled to take the beautiful theoretical ideas and to try to measure their (sometimes subtle) physical consequences in messy real material systems.

arXiv comment34 pages, 14 figures; very informal exposition on aspects of topological insulators as magnetoelectrics. Comments welcome. This version some references and a table added

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• Layer Hall effect in a 2D topological Axion antiferromagnet
• Gapless Dirac surface states in the antiferromagnetic topological insulator MnBi2Te4
• Light control with Weyl semimetals
• Royal Society Inaugural Article Perspective: Multiferroics Beyond Electric-Field Control of Magnetism
• Topological electronic structure and intrinsic magnetization in MnBi${}_4$Te${}_7$: a Bi${}_2$Te${}_3$-derivative with a periodic Mn sublattice
• Axion Quasiparticles for Axion Dark Matter Detection
• Half-Magnetic Topological Insulator
• Spectral signatures of the surface anomalous Hall effect in magnetic axion insulators
• Hybridization-Induced Gapped and Gapless States on the Surfaces of Magnetic Topological Insulators
• Spectroscopic realization of large surface gap in a doped magnetic topological insulator
• Axionic Band Topology in Inversion-Symmetric Weyl-Charge-Density Waves
• Time-Domain Terahertz Spectroscopy in High Magnetic Fields
• Magnetic field tuning of the spin dynamics in the magnetic topological insulators (MnBi${}_2$Te${}_4$)(Bi${}_2$Te${}_3$)${}_n$
• Probing charge pumping and relaxation of the chiral anomaly in a Dirac semimetal
• Axion-matter coupling in multiferroics
• Topological polarization, dual invariants, and surface flat band in crystalline insulators
• Realization of the Chern insulator and Axion insulator phases in antiferromagnetic $MnTe$-$B{i}_2(Se,Te{)}_3$-$MnTe$ heterostructures
• Terahertz Faraday and Kerr rotation spectroscopy of Bi${}_{1-x}$Sb${}_x$ films in high magnetic fields up to 30 Tesla
• Observation of magnetism induced topological edge state in antiferromagnetic topological insulator MnBi4Te7
• Quantized surface magnetism and higher-order topology: Application to the Hopf insulator
• Non-local sidewall response and deviation from exact quantization of the topological magnetoelectric effect in axion-insulator thin films
• High spin axion insulator
• Axionic surface wave in dynamical axion insulators
• Kerr, Faraday, and Magnetoelectric Effects in MnBi${}_2$Te${}_4$ Thin Films
• Magnetoelectricity in two-dimensional materials
• Topological Magnetoelectric Response in Ferromagnetic Axion Insulators
• Hybrid-order topology in unconventional magnets of Eu-based Zintl compounds with surface-dependent quantum geometry
• Topological Magnetoelectric Effect: Nonlinear Time-Reversal-Symmetric Response, Witten Effect, and Half-Integer Quantum Hall Effect
• Engineering axion insulator phase in superlattices with inversion symmetry breaking
• Ambipolar magneto-optical response of ultra-low carrier density topological insulators
• Capacitive scheme to detect the topological magnetoelectric effect
• Symmetry, topology, and geometry: The many faces of the topological magnetoelectric effect
• From classical to quantum regime of topological surface states via defect engineering
• Nonreciprocal Weyl semimetal waveguide
• Mirror Chern numbers in the hybrid Wannier representation
• Phononic dynamical axion in magnetic Dirac insulators
• Topological insulators and geometry of vector bundles
• Universal Role of Combined Symmetry for the Protection of the Dirac Cone in Antiferromagnetic Topological Insulators
• Topological magnetoelectric response in passive magnetic devices
• Hedgehog-like spin texture in Sb-doped MnBi${}_2$Te${}_4$
• Emerging axion detection in artificial magnetoelectric materials