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The recent discoveries of strikingly large zero-field Hall and Nernst effects in antiferromagnets Mn$_3$$X$, ($X$ = Sn, Ge) have brought the study of magnetic topological states to the forefront of condensed matter research and technological innovation. These effects are considered fingerprints of Weyl nodes residing near the Fermi energy, promoting Mn$_3$$X$, ($X$ = Sn, Ge) as a fascinating platform to explore the elusive magnetic Weyl fermions. In this review, we provide recent updates on the insights drawn from experimental and theoretical studies of Mn$_3$$X$, ($X$ = Sn, Ge) by combining previous reports with our new, comprehensive set of transport measurements of high-quality Mn$_3$Sn and Mn$_3$Ge single crystals. In particular, we report magnetotransport signatures specific to chiral anomalies in Mn$_3$Ge and planar Hall effect in Mn$_3$Sn, which have not yet been found in earlier studies. The results summarized here indicate the essential role of magnetic Weyl fermions in producing the large transverse responses in the absence of magnetization., Comment: 40 pages, 6 figures

The off-diagonal (electric, thermal, and thermoelectric) transport coefficients of a solid can acquire an anomalous component due to the nontrivial topology of the Bloch waves. We present a study of the anomalous Hall effect (AHE), anomalous Nernst effect (ANE), and thermal Hall effect in the Heusler-Weyl ferromagnet ${\mathrm{Co}}_{2}\mathrm{MnGa}$. The anomalous Wiedemann-Franz law, linking electric and thermal responses, was found to be valid over the whole temperature window. This indicates that the AHE has an intrinsic origin and the Berry spectrum is smooth in the immediate vicinity of the Fermi level. We extract ${\ensuremath{\alpha}}_{ij}^{A}$ from our ANE data and find that the ${\ensuremath{\alpha}}_{ij}^{A}/{\ensuremath{\sigma}}_{ij}^{A}$ ratio approaches ${k}_{B}/e$ at room temperature. Scrutinizing all topological magnets previously explored, we observe that this ratio is a sizable fraction of ${k}_{B}/e$ at room temperature. We provide a rough explanation for this feature by arguing that the two anomalous transverse coefficients depend on universal constants, the Berry curvature averaged over a window set by either the Fermi wavelength (for Hall) or the de Broglie thermal length (for Nernst). The universal scaling indicates that the widths of the two windows approaches each other at room temperature.

Quantum materials with strong transport responses to disparate physical quantities are of great fundamental significance and may hold technological potentials. The interplay between interactions and topology drive such responses through the effects of spontaneous symmetry breaking and the associated domain configurations on quantum transport. Here we provide a comprehensive description of the magnetism of Mn3Ge, an antiferromagnetic kagomebased semimetal with room temperature transport anomalies associated with topologically protected Weyl nodes. Using polarized neutron diffraction, we show the all-important magnetic structure is anti-chiral and coplanar carrying the symmetry of a ferromagnet without appreciable magnetization. We probe and classify the long wavelength excitations that determine its macroscopic responses including a set of collective magneto-elastic modes. We develop a phenomenological spin Hamiltonian with exchange, Dzyaloshinskii-Moriya, and crystal field interactions to describe its collective magnetism. The itinerant character of the magnetism that drives quantum transport is apparent in spin wave damping and extended magnetic interactions. Our work provides the scientific basis for manipulation of the chiral antiferromagnetic texture of Mn3Ge to control its topological quantum transport., Comment: Main text has 40 pages, 6 figures. Supplemental Information has 14 pages, 2 figures

We observe quantized Hall plateaus and Shubnikov de Haas oscillations in 10 at% Fe-doped Bi2Se3 flakes. All the features of the quantum transport coincide while normalizing the field-angle variable magnetoresistance to the perpendicular direction. The Hall step gives a specific contribution of ~1 e2/h per quintuple layer. This reveals a two-dimensional (2D) transport of the bulk electrons in the topological insulators. The crystal is demonstrated with an obvious ferromagnetism. Further evidences including a Berry phase of zero, a weak localization and a large effective mass rule out the contribution of the topological surface states (SS), suggesting that a great care should be taken to pindown the transport of the topological SS in topological insulators.

Topological insulators (TIs) are renowned for their exotic topological surface states (TSSs) that reside in the top atomic layers, and hence, detailed knowledge of the surface top atomic layers is of utmost importance. Here we present the remarkable morphology changes of Bi2Te3 surfaces, which have been freshly cleaved in air, upon subsequent systematic annealing in ultrahigh vacuum and the resulting effects on the local and area-averaging electronic properties of the surface states, which are investigated by combining scanning tunneling microscopy (STM), scanning tunneling spectroscopy (STS), and Auger electron spectroscopy (AES) experiments with density functional theory (DFT) calculations. Our findings demonstrate that the annealing induces the formation of a Bi bilayer atop the Bi2Te3 surface. The adlayer results in n-type doping, and the atomic defects act as scattering centers of the TSS electrons. We also investigated the annealing-induced Bi bilayer surface on Bi2Te3 via voltage-dependent quasi-particle-interference (QPI) mapping of the surface local density of states and via comparison with the calculated constant-energy contours and QPI patterns. We observed closed hexagonal patterns in the Fourier transform of real-space QPI maps with secondary outer spikes. DFT calculations attribute these complex QPI patterns to the appearance of a second cone due to the surface charge transfer between the Bi bilayer and the Bi2Te3. Annealing in ultrahigh vacuum offers a facile route for tuning of the topological properties and may yield similar results for other topological materials.

Metallic Bi2Te3 crystalline sheets with the room-temperature resistivity of above 10 m{\Omega} cm were prepared and their magnetoresistive transport was measured in a field of up to 9 Tesla. The Shubnikov de Haas oscillations were identified from the secondly-derived magnetoresistance curves. While changing the angle between the field and normal axis of the sheets, we find that the oscillation periods present a cosine dependence on the angle. This indicates a two-dimensional transport due to the surface state. The work reveals a resolvable surface contribution to the overall conduction even in a metallic topological insulator., Comment: accepted by EPJD, 2013

The universal conductance fluctuations (UCFs), one of the most important manifestations of mesoscopic electronic interference, have not yet been demonstrated for the two-dimensional surface state of topological insulators (TIs). Even if one delicately suppresses the bulk conductance by improving the quality of TI crystals, the fluctuation of the bulk conductance still keeps competitive and difficult to be separated from the desired UCFs of surface carriers. Here we report on the experimental evidence of the UCFs of the two-dimensional surface state in the bulk insulating Bi2Te2Se nanoribbons. The solely-B\perp-dependent UCF is achieved and its temperature dependence is investigated. The surface transport is further revealed by weak antilocalizations. Such survived UCFs of the topological surface states result from the limited dephasing length of the bulk carriers in ternary crystals. The electron-phonon interaction is addressed as a secondary source of the surface state dephasing based on the temperature-dependent scaling behavior.

Universal conductance fluctuations (UCFs) are extracted in the magnetoresistance responses in bulk-insulating Bi2Te2Se microflakes. Their two-dimensional character is demonstrated by field-tilting magnetoresistance measurements. Their origin from the surface electrons is determined by the fact that the UCF amplitudes remain unchanged while applying an in-plane field to suppress the coherence of bulk electrons. After considering the ensemble average in a batch of micrometer-sized samples, the intrinsic UCF magnitude of over 0.37 e2/h is obtained. This agrees with the theoretical prediction on topological surface states. All the lines of evidence point to the successful observation of the UCF of topological surface states.