Any axion insulator must be a bulk three-dimensional topological insulator

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Any axion insulator must be a bulk three-dimensional topological insulator

K. M. Fijalkowski, N. Liu, M. Hartl, M. Winnerlein, P. Mandal, A. Coschizza, A. Fothergill, S. Grauer, S. Schreyeck, K. Brunner, M. Greiter, R. Thomale, C. Gould, and L. W. Molenkamp

Phys. Rev. B 103, 235111 – Published 3 June 2021

Abstract

In recent attempts to observe axion electrodynamics, much effort has focused on trilayer heterostructures of magnetic topological insulators, and in particular on the examination of a so-called zero Hall plateau, which has misguidedly been overstated as direct evidence of an axion insulator state. We investigate the general notion of axion insulators, which by definition must contain a nontrivial volume to host the axion term. We conduct a detailed magneto-transport analysis of Chern insulators comprising a single magnetic topological insulator layer of varying thickness as well as trilayer structures, for samples optimized to yield a perfectly quantized anomalous Hall effect. Our analysis gives evidence for a topological magneto-electric effect quantized in units of $e^{2} / 2 h$ , allowing us to identify signatures of axion electrodynamics. Our observations may provide direct experimental access to electrodynamic properties of the universe beyond the traditional Maxwell equations, and challenge the hitherto proclaimed exclusive link between the observation of a zero Hall plateau and an axion insulator.

Received 31 August 2020
Accepted 18 May 2021

DOI:https://doi.org/10.1103/PhysRevB.103.235111

Physics Subject Headings (PhySH)

Magnetoelectric effect Quantum anomalous Hall effect Topological insulators

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

K. M. Fijalkowski ^1,2, N. Liu^1,2, M. Hartl ^1,2, M. Winnerlein^1,2, P. Mandal^1,2, A. Coschizza^1,2, A. Fothergill ^1,2, S. Grauer^1,2, S. Schreyeck^1,2, K. Brunner^1,2, M. Greiter ³, R. Thomale ³, C. Gould^1,2, and L. W. Molenkamp ^1,2

¹Faculty for Physics and Astronomy (EP3), Universität Würzburg, Am Hubland, D-97074, Würzburg, Germany
²Institute for Topological Insulators, Am Hubland, D-97074, Würzburg, Germany
³Faculty for Physics and Astronomy (TP1), Universität Würzburg, Am Hubland, D-97074, Würzburg, Germany

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Vol. 103, Iss. 23 — 15 June 2021

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Images

Figure 1
(a) External magnetic field dependence of the conductivity tensor elements for a device patterned from a 6.4 nm thick $V_{0.1} {({Bi}_{0.18} {Sb}_{0.82})}_{1.9} Te_{3}$ film at temperature 30 mK. (b) The same, for a 9.3 nm thick $V_{0.1} {({Bi}_{0.27} {Sb}_{0.73})}_{1.9} Te_{3}$ film at temperature 55 mK. (c) Base temperature thickness dependence of the sheet resistance during the magnetization reversal at $σ_{x y} = 0$ for all samples. VBST stands for (V,Bi, ${Sb)}_{2} Te_{3}$ , and the solid line is a guide to the eye. The sheet resistance for the 5.3 nm thick film is an estimated lower boundary (see the Supplemental Material [22] for more details). (d) Thickness evolution of the scaling behavior for samples ranging in thickness from the 2D integer quantum Hall to the 3D limit. (e) Photograph of a patterned sample glued and bonded to a chip carrier (top), and optical microscope image of one of the devices (bottom) with labeled contacts.
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Figure 2
(a) (top) Schematic of a global conductivity tensor flow diagram for the integer quantum Hall effect with dots marking the points used in the temperature dependence analysis. The scale on the axes matches the data panel below. (bottom) Experimental magnetic field-driven scaling diagram for a 6.4 nm thick film. The red corresponds to a temperature of 30 mK and blue to 650 mK, with the intermediate values being 205 mK, 300 mK, 410 mK, and 540 mK. (b) (top) Schematic of a global conductivity tensor flow diagram for Dirac fermions on two parallel topological interfaces; (bottom) experimental magnetic field-driven scaling diagram for a 9.3 nm thick film. The red corresponds to temperature 55 mK and blue to 800 mK, with intermediate values being 140 mK and 410 mK. (c) Temperature dependence of film resistivity at $σ_{x y} = 0$ and $σ_{x y} = e^{2} / 2 h$ for the layers in the 2D limit. The data for the 5.3 nm thick film are extracted from a two-terminal resistance measurement (see the Supplemental Material [22] for details). (d) Temperature dependence of film resistivity when $σ_{x y} = 0$ for the layers in the 3D axion limit. Solid lines in (c) and (d) are guides to the eye. The schematics inset to (c) and (d) indicate with a dot the point in the scaling diagram that is being plotted in the main figure.
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Figure 3
(a) Hall and longitudinal magneto-conductivity data collected at a temperature of 30 mK for a sample patterned from a magnetic trilayer. A schematic of the heterostructure is given on the right. VBST stands for $V_{0.1} {({Bi}_{0.31} {Sb}_{0.69})}_{1.9} Te_{3}$ , and BST stands for ( ${Bi}_{0.31} {Sb}_{0.69})_{2} Te_{3}$ . The plateau region where the sample resistance exceeds $10 M Ω$ cannot be resolved in this measurement configuration (see the Supplemental Material [22] for the collected resistivity values). (b) The conductivity tensor scaling behavior of the data in (a).
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