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Three-dimensional topological insulators are a phase of matter that hosts unique spin-polarized gapless surface states that are protected by time-reversal symmetry. They exhibit unconventional charge and spin transport properties1,2. Intense laser fields can drive ballistic charge dynamics in Dirac bands3,4 or they can coherently steer spin5 and valley pseudospin6. Similarly, high-harmonic generation (HHG) in solids provides insights into the dynamics of the electrons in topological insulators7–13. Despite several theoretical attempts to identify a topological signature in the high-harmonic spectrum14–16, a unique fingerprint has yet to be found experimentally. Here, we observe HHG that arises from topological surface states in the intrinsic topological insulator BiSbTeSe2. The components of the even-order harmonics that are polarized along the pump polarization stem from the spin current in helical surface states, whereas the perpendicular components originate from the out-of-plane spin polarization related to the hexagonal wrapping effect17. The dependence of HHG on surface doping in ambient air also suggests the presence of a Rashba-split two-dimensional electron gas, whose strength can be enhanced by an increase in the intensity of the mid-infrared pump. High-harmonic generation up to the seventh harmonic is observed from the intrinsic three-dimensional topological insulator BiSbTeSe2. The parallel components of the even-order harmonics arise directly from the topological surface states.

Magnetic topological insulator, a platform for realizing quantum anomalous Hall effect, axion state, and other novel quantum transport phenomena, has attracted a lot of interest. Recently, it is proposed that MnBi2Te4 is an intrinsic magnetic topological insulator, which may overcome the disadvantages in the magnetic doped topological insulator, such as disorder. Here we report on the gate-reserved anomalous Hall effect (AHE) in the MnBi2Te4 thin film. By tuning the Fermi level using the top/bottom gate, the AHE loop gradually decreases to zero and the sign is reversed. The positive AHE exhibits distinct coercive fields compared with the negative AHE. It reaches a maximum inside the gap of the Dirac cone, and its amplitude exhibits a linear scaling with the longitudinal conductance. The positive AHE is attributed to the competition of the intrinsic Berry curvature and the extrinsic skew scattering. Its gate-controlled switching contributes a scheme for the topological spin field-effect transistors.

Intrinsic magnetic topological insulators (MTIs) $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}$ and $\mathrm{Mn}{\mathrm{Bi}}_{2}{\mathrm{Te}}_{4}/{({\mathrm{Bi}}_{2}{\mathrm{Te}}_{3})}_{n}$ are expected to realize the high-temperature quantum anomalous Hall effect and dissipationless electrical transport. However, there is still a lack of ideal MTI candidates with magnetic ordering of the ferromagnetic (FM) ground state. Here, we show a MTI sample of $\mathrm{Mn}{({\mathrm{Bi}}_{0.7}{\mathrm{Sb}}_{0.3})}_{4}{\mathrm{Te}}_{7}$ which holds the coexistence of a FM behavior state and topological nontriviality. The dramatic modulation of the magnetism is induced by a charge carrier engineering process via the Sb substitution in the $\mathrm{Mn}{\mathrm{Bi}}_{4}{\mathrm{Te}}_{7}$ matrix with antiferromagnetic ordering. The evolution of magnetism in $\mathrm{Mn}{({\mathrm{Bi}}_{1\ensuremath{-}x}{\mathrm{Sb}}_{x})}_{4}{\mathrm{Te}}_{7}$ is systematically investigated by our magnetic measurements and theoretical calculations. The clear topological surface states of the FM sample of $\mathrm{Mn}{({\mathrm{Bi}}_{0.7}{\mathrm{Sb}}_{0.3})}_{4}{\mathrm{Te}}_{7}$ are further verified by angle-resolved photoemission spectroscopy. The demonstration of the intrinsic FM-MTI of $\mathrm{Mn}{({\mathrm{Bi}}_{0.7}{\mathrm{Sb}}_{0.3})}_{4}{\mathrm{Te}}_{7}$ in this paper sheds light on further material optimization of intrinsic MTIs and paves the way for further studies to clarify the relationships between topology, magnetism, and charge carriers in topological materials.

Performing angle-resolved photoemission spectroscopy (ARPES) and theoretical calculations for ZrSnTe, we find a nodal line in the k x - k y plane with a tiny gap and two nodal lines without gaps along the k z direction. The constant energy contours are plotted in the k x - k y plane at a photon energy of 30 eV to examine the gapping feature of the nodal line. In addition, we depict the band dispersions along the Γ-M and Γ-X directions from the ARPES images at photon energies ranging from 24 to 40 eV. The k z mapping confirms the presence of stable Dirac points with obvious k z dependences along the M-A and X-R directions. In this paper, we report the two types of nodal lines associated with the theoretical local-density approximation calculations, broadening the horizons of nodal-line semimetal research.

The scaling physics of quantum Hall transport in optimized topological insulators with a plateau precision of $\ensuremath{\sim}1/1000\phantom{\rule{0.16em}{0ex}}{e}^{2}/h$ is considered. Two exponential scaling regimes are observed in temperature-dependent transport dissipation, one of which accords with thermal-activation behavior with a gap of 2.8 meV (g20 K), the other being attributed to variable-range hopping (1--20 K). Magnetic-field-driven plateau-to-plateau transition gives scaling relations of ${(d{R}_{xy}/dB)}^{max}\ensuremath{\propto}{T}^{\ensuremath{-}\ensuremath{\kappa}}$ and $\mathrm{\ensuremath{\Delta}}{B}^{\ensuremath{-}1}\ensuremath{\propto}{T}^{\ensuremath{-}\ensuremath{\kappa}}$ with a consistent exponent of \ensuremath{\kappa} \ensuremath{\sim} 0.2, which is half the universal value for a conventional two-dimensional electron gas. This is evidence of percolation assisted by quantum tunneling and reveals the dominance of electron-electron interaction of the topological surface states.

The natural intrinsic magnetic topological insulator MnBi2Te4(Bi2Te3)n is a platform for studying intriguing transport phenomena and provides an essential chance for the fundamental understanding of the combination of magnetism and topology. Here, we fabricated MnBi4Te7 thin film devices and carried out the transport measurement. It shows the unconventional anomalous Hall effect in the devices with the hysteresis anomaly and hump-like behavior. The gate-controlled sign reversal is also an interesting feature. With the modulation of gate voltage and temperature, we suggest that the unconventional anomalous Hall effect is due to the coexistence of the antiferromagnetic component and ferromagnetic component, which may result from the inhomogeneous spatial variation. Our work provides a resourceful insight into the study of the material family.

Large unsaturated magnetoresistance (XMR) with magnitude about 1000% is observed in topological insulator candidate TaSe3 from our high field (up to 38 T) measurements. Two oscillation modes, associated with one hole pocket and two electron pockets in the bulk, respectively, are detected from our Shubnikov-de Hass (SdH) measurements, consistent with our first-principles calculations. With the detailed Hall measurements performed, our two-band model analysis exhibits an imperfect density ratio n_h/n_e closing 0.9 at T< 20 K , which suggests that the carrier compensations account for the XMR in TaSe3.

Topological semimetals characterize a unique class of quantum materials hosting Dirac/Weyl fermions. The important features of topological fermions can be exhibited by quantum oscillations. Here, we report the magnetoresistance and Shubnikov-de Haas (SdH) quantum oscillation of longitudinal resistance in the single crystal of topological semimetal candidate Ta3SiTe6 with a magnetic field up to 38 T. The periodic amplitude of the oscillations shows related information about the Fermi surface. The fast Fourier transformation spectra represent a single oscillatory frequency. The analysis of the oscillations shows the Fermi pocket with a cross sectional area of 0.13 A−2. Combining magneto-transport measurements and the first-principles calculation, we find that these oscillations come from the hole pocket. Hall resistivity and the SdH oscillations recommend that Ta3SiTe6 is a hole dominated system.

Dirac Fermions with different helicities exist on the top and bottom surfaces of topological insulators, offering a rare opportunity to break the degeneracy protected by the no-go theorem. Through the application of Co clusters, quantum Hall plateaus were modulated for the topological insulator BiSbTeSe2, allowing an optimized surface transport. Here, using renormalization group flow diagrams, we show the extraction of two sets of converging points in the conductivity tensor space, revealing that the top surface exhibits an anomalous quantization trajectory, while the bottom surface retains the 1/2 quantization. Co clusters are believed to induce a sizeable Zeeman gap ( > 4.8 meV) through antiferromagnetic exchange coupling, which delays the Landau level hybridization on the top surface for a moderate magnetic field. A quasi-half-integer plateau also appears at −7.2 Tesla. This allows us to study the interesting physics of parity anomaly, and paves the way for further studies simulating exotic particles in condensed matter physics., The topological surface states usually appear in pairs in a topological insulator, with one on the top surface and the other on the bottom surface. Here, Zhang et al. utilize Co cluster to induce a Zeeman gap on one surface through antiferromagnetic exchange coupling, and observe a quasi-half-integer plateau, suggesting the parity anomaly of Dirac fermions.

Recently, the picture of type-II energy dispersion with broken Lorentz invariance has been adapted from Weyl to Dirac fermions. It is demonstrated in PdTe${}_{2}$ in this paper by extensive evidence from electrical transport, de Haas--van Alphen oscillations, first-principles calculations, and angle-resolved photoemission spectroscopy. The type-II Dirac cone looks like a pinnacle in momentum space. It may be cut by the Fermi level with the result of a pair of Dirac pockets (of $p$/$n$ type), whose sizes change dramatically with the Fermi level. The nontrivial Berry phase of the hole pocket is also displayed. This also means a nonvanishing density of states in the whole Dirac cones, which makes PdTe${}_{2}$ an improved platform for possible topological superconductors and Majorana fermions

We report the low-temperature magneto-transport in the bulk-insulating single crystal of topological insulator Sn doped Bi1.1Sb0.9Te2S. Shubnikov-de Haas oscillations appear with their reciprocal frequency proportional to cos θ, demonstrating the dominant transport of topological surface states. While the magnetic field rotates on the sample surface, the planar Hall effect arises with sizeable oscillations following a relation of cos θ sin θ. Its amplitude reaches the maximum at the lowest temperature and drops to nearly zero at temperature higher than 100 K. All these evidences consolidate such planar Hall oscillations as another golden criterion on the topological surface transport.