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Register a new userM{o}bius Insulator and Higher-Order Topology in MnBi$_{2n}$Te$_{3n+1}$
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We propose MnBi$_{2n}$Te$_{3n+1}$ as a magnetically tunable platform for realizing various symmetry-protected higher-order topology. Its canted antiferromagnetic phase can host exotic topological surface states with a Mobius twist that are protected by nonsymmorphic symmetry. Moreover, opposite surfaces hosting Mobius fermions are connected by one-dimensional chiral hinge modes, which offers the first material candidate of a higher-order topological Mobius insulator. We uncover a general mechanism to feasibly induce this exotic physics by applying a small in-plane magnetic field to the antiferromagnetic topological insulating phase of MnBi$_{2n}$Te$_{3n+1}$, as well as other proposed axion insulators. For other magnetic configurations, two classes of inversion-protected higher-order topological phases are ubiquitous in this system, which both manifest gapped surfaces and gapless chiral hinge modes. We systematically discuss their classification, microscopic mechanisms, and experimental signatures. Remarkably, the magnetic-field-induced transition between distinct chiral hinge mode configurations provides an effective topological magnetic switch.
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Two-dimensional van der Waals MnBi$_{2n}$Te$_{3n+1}$ (n = 1, 2, 3, 4) compounds have been recently found to be intrinsic magnetic topological insulators rendering quantum anomalous Hall effect and diverse topological states. Here, we summarize and compare the crystal and magnetic structures of this family, and discuss the effects of chemical composition on their magnetism. We found that a considerable fraction of Bi occupies at the Mn sites in MnBi$_{2n}$Te$_{3n+1}$ (n = 1, 2, 3, 4) while Mn is no detectable at the non-magnetic atomic sites within the resolution of neutron diffraction experiments. The occupancy of Mn monotonically decreases with the increase of n. The polarized neutron diffraction on the representative MnBi$_{4}$Te$_{7}$ reveals that its magnetization density is exclusively accumulated at the Mn site, in good agreement with the results from the unpolarized neutron diffraction. The defects of Bi at the Mn site naturally explain the continuously reduced saturated magnetic moments from n = 1 to n = 4. The experimentally estimated critical exponents of all the compounds generally suggest a three-dimensional character of magnetism. Our work provides material-specified structural parameters that may be useful for band structure calculations to understand the observed topological surface states and for designing quantum magnetic materials through chemical doping.
We report intertwined Weyl phases, which come from superposing topological phases by crystalline symmetry. In the intertwined Weyl phases, an unconventional Weyl phase where Weyl points possess a higher charge (monopole charge>1) due to rotation symmetry, and a higher-order topological phase enforced by rotation symmetry, are superposed. The two phases are no longer separable, but intertwine with each other, resulting in the novel phase. Remarkably, the intertwining leads to a prominent characteristic feature of the intertwined Weyl phases: $textit{the change of Fermi-arc topology}$ in a periodic pattern, i.e., the way how Fermi arcs connect to Weyl points changes drastically with respect to surface orientation, which exhibits a periodic pattern. Such a phenomenon is absent in any individual phase alone. Moreover, we elaborate on how to emulate the intertwined double-Weyl phase in cold atoms. Our theory is quite promising for generating new topological phases based on existing ones.
We identify topological aspects of the subextensive magnetic moment contributed by the surfaces of a three-dimensional crystallite -- assumed to be insulating in the bulk as well as on all surface facets, with trivial Chern invariants in the bulk. The geometric component of this subextensive moment is given by its derivative with respect to the chemical potential, at zero temperature and zero field, per unit surface area, and hence corresponds to the surface magnetic compressibility. The sum of the surface compressibilities contributed by two opposite facets of a cube-shaped crystallite is quantized to an integer multiple of the fundamental constant $e/h c$; this integer is in one-to-one correspondence with the net chirality of hinge modes on the surface of the crystallite, manifesting a link with higher-order topology. The contribution by a single facet to the magnetic compressibility need not be quantized to integers; however, symmetry and/or Hilbert-space constraints can fix the single-facet compressibility to half-integer multiples of $e/hc$, as will be exemplified by the Hopf insulator.
Three-dimensional topological (crystalline) insulators are materials with an insulating bulk, but conducting surface states which are topologically protected by time-reversal (or spatial) symmetries. Here, we extend the notion of three-dimensional topological insulators to systems that host no gapless surface states, but exhibit topologically protected gapless hinge states. Their topological character is protected by spatio-temporal symmetries, of which we present two cases: (1) Chiral higher-order topological insulators protected by the combination of time-reversal and a four-fold rotation symmetry. Their hinge states are chiral modes and the bulk topology is $mathbb{Z}_2$-classified. (2) Helical higher-order topological insulators protected by time-reversal and mirror symmetries. Their hinge states come in Kramers pairs and the bulk topology is $mathbb{Z}$-classified. We provide the topological invariants for both cases. Furthermore we show that SnTe as well as surface-modified Bi$_2$TeI, BiSe, and BiTe are helical higher-order topological insulators and propose a realistic experimental setup to detect the hinge states.
We investigate higher-order Weyl semimetals (HOWSMs) having bulk Weyl nodes attached to both surface and hinge Fermi arcs. We identify a new type of Weyl node, that we dub a $2nd$ order Weyl node, that can be identified as a transition in momentum space in which both the Chern number and a higher order topological invariant change. As a proof of concept we use a model of stacked higher order quadrupole insulators to identify three types of WSM phases: $1st$-order, $2nd$-order, and hybrid-order. The model can also realize type-II and hybrid-tilt WSMs with various surface and hinge arcs. Moreover, we show that a measurement of charge density in the presence of magnetic flux can help identify some classes of $2nd$ order WSMs. Remarkably, we find that coupling a $2nd$-order Weyl phase with a conventional $1st$-order one can lead to a hybrid-order topological insulator having coexisting surface cones and flat hinge arcs that are independent and not attached to each other. Finally, we show that periodic driving can be utilized as a way for generating HOWSMs. Our results are relevant to metamaterials as well as various phases of Cd$_3$As$_2$, KMgBi, and rutile-structure PtO$_2$ that have been predicted to realize higher order Dirac semimetals.
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