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A three-dimensional topological insulator features a two-dimensional surface state consisting of a single linearly-dispersive Dirac cone. Under broken time-reversal symmetry, the single Dirac cone is predicted to cause half-integer quantization of Hall conductance, which is a manifestation of the parity anomaly in quantum field theory. However, despite various observations of quantization phenomena, the half-integer quantization has been elusive because a pair of equivalent Dirac cones on two opposing surfaces are simultaneously measured in ordinary experiments. Here we demonstrate the half-integer quantization of Hall conductance in a synthetic heterostructure termed a 'semi-magnetic' topological insulator, where only one surface state is gapped by magnetic doping and the opposite one is non-magnetic and gapless. We observe half quantized Faraday/Kerr rotations with terahertz magneto-optical spectroscopy and half quantized Hall conductance in transport at zero magnetic field. Our results suggest a condensed-matter realization of the parity anomaly and open a way for studying unconventional physics enabled by a single Dirac fermion., Comment: 25 pages, 7 figures

Magnetic Weyl semimetals attract considerable interest not only for their topological quantum phenomena but also as an emerging materials class for realizing quantum anomalous Hall effect in the two-dimensional limit. A shandite compound Co3Sn2S2 with layered Kagome-lattices is one such material, where vigorous efforts have been devoted to synthesize the two-dimensional crystal. Here we report a synthesis of Co3Sn2S2 thin flakes with a thickness of 250 nm by chemical vapor transport method. We find that this facile bottom-up approach allows the formation of large-sized Co3Sn2S2 thin flakes of high-quality, where we identify the largest electron mobility (~2,600 cm2V-1s-1) among magnetic topological semimetals, as well as the large anomalous Hall conductivity (~1,400 {\Omega}-1cm-1) and anomalous Hall angle (~32 %) arising from the Berry curvature. Our study provides a viable platform for studying high-quality thin flakes of magnetic Weyl semimetal and stimulate further research on unexplored topological phenomena in the two-dimensional limit.

Simultaneous transport and scanning nanoSQUID-on-tip magnetic imaging studies in Cr-(Bi,Sb)$_2$Te$_3$ modulation-doped films reveal the presence of superparamagnetic order within the quantum anomalous Hall regime. In contrast to the expectation that a long-range ferromagnetic order is required for establishing the quantum anomalous Hall state, superparamagnetic dynamics of weakly interacting nanoscale magnetic islands is observed both in the plateau transition regions as well as within the fully quantized C=$\pm$1 Chern plateaus. Modulation doping of the topological insulator films is found to give rise to significantly larger superparamagnetic islands as compared to uniform magnetic doping, evidently leading to enhanced robustness of the quantum anomalous Hall effect. Nonetheless, even in this more robust quantum state, attaining full quantization of transport coefficients requires magnetic alignment of at least 95% of the superparamagnetic islands. The superparamagnetic order is also found within the incipient C=0 zero Hall plateau, which may host an axion state if the top and bottom magnetic layers are magnetized in opposite directions. In this regime, however, a significantly lower level of island alignment is found in our samples, hindering the formation of the axion state. Comprehension and control of superparamagnetic dynamics is thus a key factor in apprehending the fragility of the quantum anomalous Hall state and in enhancing the endurance of the different quantized states to higher temperatures for utilization of robust topological protection in novel devices., Comment: 17 pages, 3 figures

Exploration of novel electromagnetic phenomena is a subject of great interest in topological quantum materials. One of the unprecedented effects to be experimentally verified is topological magnetoelectric (TME) effect originating from an unusual coupling of electric and magnetic fields in materials. A magnetic heterostructure of topological insulator (TI) hosts such an exotic magnetoelectric coupling and can be expected to realize the TME effect as an axion insulator. Here we designed a magnetic TI with tricolor structure where a non-magnetic layer of (Bi, Sb)2Te3 is sandwiched by a soft ferromagnetic Cr-doped (Bi, Sb)2Te3 and a hard ferromagnetic V-doped (Bi, Sb)2Te3. Accompanied by the quantum anomalous Hall (QAH) effect, we observe zero Hall conductivity plateaus, which are a hallmark of the axion insulator state, in a wide range of magnetic field between the coercive fields of Cr- and V-doped layers. The resistance of the axion insulator state reaches as high as 10^9 ohm, leading to a gigantic magnetoresistance ratio exceeding 10,000,000% upon the transition from the QAH state. The tricolor structure of TI may not only be an ideal arena for the topologically distinct phenomena, but also provide magnetoresistive applications for advancing dissipationless topological electronics., Comment: 16 pages, 4 figures

The electronic orders in magnetic and dielectric materials form the domains with different signs of order parameters. The control of configuration and motion of the domain walls (DWs) enables gigantic, nonvolatile responses against minute external fields, forming the bases of contemporary electronics. As an extension of the DW function concept, we realize the one-dimensional quantized conduction on the magnetic DWs of a topological insulator (TI). The DW of a magnetic TI is predicted to host the chiral edge state (CES) of dissipation-less nature when each magnetic domain is in the quantum anomalous Hall state. We design and fabricate the magnetic domains in a magnetic TI film with the tip of the magnetic force microscope, and clearly prove the existence of the chiral one-dimensional edge conduction along the prescribed DWs. The proof-of-concept devices based on the reconfigurable CES and Landauer-Buttiker formalism are exemplified for multiple-domain configurations with the well-defined DW channels., Comment: 11 pages, 4 figures

Electrodynamic responses from three-dimensional (3D) topological insulators (TIs) are characterized by the universal magnetoelectric $E\cdot B$ term constituent of the Lagrangian formalism. The quantized magnetoelectric coupling, which is generally referred to as topological magnetoelectric (TME) effect, has been predicted to induce exotic phenomena including the universal low-energy magneto-optical effects. Here we report the experimental demonstration of the long-sought TME effect, which is exemplified by magneto-optical Faraday and Kerr rotations in the quantum anomalous Hall (QAH) states of magnetic TI surfaces by terahertz magneto-optics. The universal relation composed of the observed Faraday and Kerr rotation angles but not of any material parameters (e.g. dielectric constant and magnetic susceptibility) well exhibits the trajectory toward the fine structure constant $\alpha$ $(= 2\pi e^2/hc \sim 1/137)$ in the quantized limit. Our result will pave a way for versatile TME effects with emergent topological functions.

Quantum anomalous Hall effect (QAHE), which generates dissipation-less edge current without external magnetic field, is observed in magnetic-ion doped topological insulators (TIs), such as Cr- and V-doped (Bi,Sb)2Te3. The QAHE emerges when the Fermi level is inside the magnetically induced gap around the original Dirac point of the TI surface state. Although the size of gap is reported to be about 50 meV, the observable temperature of QAHE has been limited below 300 mK. We attempt magnetic-Cr modulation doping into topological insulator (Bi,Sb)2Te3 films to increase the observable temperature of QAHE. By introducing the rich-Cr-doped thin (1 nm) layers at the vicinity of the both surfaces based on non-Cr-doped (Bi,Sb)2Te3 films, we have succeeded in observing the QAHE up to 2 K. The improvement in the observable temperature achieved by this modulation-doping appears to be originating from the suppression of the disorder in the surface state interacting with the rich magnetic moments. Such a superlattice designing of the stabilized QAHE may pave a way to dissipation-less electronics based on the highertemperature and zero magnetic-field quantum conduction., Comment: 14 pages, 4 figures