Axion insulators are magnetic topological insulators in which the non-trivial Z2 index is protected by inversion symmetry instead of time-reversal symmetry. The naturally gapped surfaces of axion insulators give rise to a half-quantized surface anomalous Hall conductivity (AHC), but the sign of the surface AHC cannot be determined from topological arguments. In this paper, we consider topological phenomena at the surface of an axion insulator. To be explicit, we construct a minimal tight-binding model on the pyrochlore lattice and investigate the all-in-all-out (AIAO) and ferromagnetic (FM) spin configurations. We also implement a recently proposed approach for calculating the surface AHC directly, which allows us to explore how the interplay between surface termination and magnetic ordering determines the sign of the half-quantized surface AHC. In the case of AIAO ordering, we show that it is possible to construct a topological state with no protected metallic states on boundaries of any dimension (surfaces, hinges, or corners), although chiral hinge modes do occur for many surface configurations. In the FM case, rotation of the magnetization by an external field offers promising means of control of chiral hinge modes, which can also appear on surface steps or where bulk domain walls emerge at the surface. arXiv:1809.02853v2 [cond-mat.mtrl-sci]
Many magnetic point-group symmetries induce a topological classification on crystalline insulators, dividing them into those that have a nonzero quantized Chern-Simons magnetoelectric coupling ("axion-odd" or "topological"), and those that do not ("axion-even" or "trivial"). For time-reversal or inversion symmetries, the resulting topological state is usually denoted as a "strong topological insulator" or an "axion insulator" respectively, but many other symmetries can also protect this "axion Z2" index. Topological states are often insightfully characterized by choosing one crystallographic direction of interest, and inspecting the hybrid Wannier (or equivalently, the non-Abelian Wilson-loop) band structure, considered as a function of the two-dimensional Brillouin zone in the orthogonal directions. Here, we systematically classify the axion-quantizing symmetries, and explore the implications of such symmetries on the Wannier band structure. Conversely, we clarify the conditions under which the axion Z2 index can be deduced from the Wannier band structure. In particular, we identify cases in which a counting of Dirac touchings between Wannier bands, or a calculation of the Chern number of certain Wannier bands, or both, allows for a direct determination of the axion Z2 index. We also discuss when such symmetries impose a "flow" on the Wannier bands, such that they are always glued to higher and lower bands by degeneracies somewhere in the projected Brillouin zone, and the related question of when the corresponding surfaces can remain gapped, thus exhibiting a half-quantized surface anomalous Hall conductivity. Our formal arguments are confirmed and illustrated in the context of tight-binding models for several paradigmatic axion-odd symmetries including time reversal, inversion, simple mirror, and glide mirror symmetries.
This is the accepted manuscript made available via CHORUS. The article has been published as: math xmlns="http://www.w3.org/1998/Math/MathML">mi>A/mi> /math>-type antiferromagnetic order in the Zintl-phase insulator math xmlns="http://www.w3.org/1998/Math/MathML">mrow>ms ub>mi>EuZn/mi>mn>2/mn>/msub>msub>mi mathvariant="normal">P/mi>mn>2/mn>/msub>/mrow>/ math>
Engineering and manipulation of unidirectional channels has been achieved in quantum Hall systems, leading to the construction of electron interferometers and proposals for low-power electronics and quantum information science applications. However, to fully control the mixing and interference of edge-state wave functions, one needs stable and tunable junctions. Encouraged by recent material candidates, here we propose to achieve this using an antiferromagnetic topological insulator that supports two distinct types of gapless unidirectional channels, one from antiferromagnetic domain walls and the other from single-height steps. Their distinct geometric nature allows them to intersect robustly to form quantum point junctions, which then enables their control by magnetic and electrostatic local probes. We show how the existence of stable and tunable junctions, the intrinsic magnetism and the potential for higher-temperature performance make antiferromagnetic topological insulators a promising platform for electron quantum optics and microelectronic applications.
Electrons in solids often adopt complex patterns of chemical bonding driven by the competition between energy gains from covalency and delocalization, and energy costs of double occupation to satisfy Pauli exclusion, with multiple intermediate states in the transition between highly localized, and magnetic, and delocalized, and nonmagnetic limits. Herein, we report a chemical pressure-driven transition from a proper Mn magnetic ordering phase transition to a Mn magnetic phase crossover in EuMn 2 P 2 the limiting end member of the EuMn 2 X 2 (X = Sb, As, P) family of layered materials. This loss of a magnetic ordering occurs despite EuMn 2 P 2 remaining an insulator at all temperatures, and with a phase transition to long-range Eu antiferromagnetic order at T N ≈ 17 K. The absence of a Mn magnetic phase transition contrasts with the formation of long-range Mn order at T ≈ 130 K in isoelectronic EuMn 2 Sb 2 and EuMn 2 As 2 . Temperature-dependent specific heat and 31 P NMR measurements provide evidence for the development of short-range Mn magnetic correlations from T ≈ 250− 100 K, interpreted as a precursor to covalent bond formation. Density functional theory calculations demonstrate an unusual sensitivity of the band structure to the details of the imposed Mn and Eu magnetic order, with an antiferromagnetic Mn arrangement required to recapitulate an insulating state. Our results imply a picture in which long-range Mn magnetic order is suppressed by chemical pressure, but that antiferromagnetic correlations persist, narrowing bands and producing an insulating state.
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