Optical study of magnetic topological insulator MnBi_(4)Te_7

We present an infrared spectroscopy study of the magnetic topological insulator MnBi_(4)Te_7 with antiferromagnetic(AFM) order below the Neel temperature TN= 13 K. Our investigation reveals that the low-frequency optical conductivity consists of two Drude peaks, indicating a response of free carriers involving multiple bands. Interestingly, the narrow Drude peak grows strongly as the temperature decreases, while the broad Drude peak remains relatively unchanged. The onset of interband transitions starts around 2000 cm^(-1), followed by two prominent absorption peaks around 10000 cm^(-1) and 20000 cm^(-1). Upon cooling, there is a notable transfer of spectral weight from the interband transitions to the Drude response. Below TN, the AFM transition gives rise to small anomalies of the charge response due to a band reconstruction.These findings provide valuable insights into the interplay between magnetism and the electronic properties in MnBi_(4)Te_7.

Magnetic and electrical transport study of the intrinsic magnetic topological insulator MnBi_(2)Te_(4)with Ge doping

As an intrinsic magnetic topological insulator with magnetic order and non-trivial topological structure,MnBi_(2)Te_(4)is an ideal material for studying exotic topological states such as quantum anomalous Hall effect and topological axion insulating states.Here,we carry out magnetic and electrical transport measurements on(Mn1–xGex)Bi_(2)Te_(4)(x=0,0.15,0.30,0.45,0.60,and 0.75)single crystals.It is found that with increasing x,the dilution of magnetic moments gradually weakens the antiferromagnetic exchange interaction.Moreover,Ge doping reduces the critical field of ferromagnetic ordering,which may provide a possible way to implement the quantum anomalous Hall effect at lower magnetic field.Electrical transport measurements suggest that electrons are the dominant charge carriers,and the carrier density increases with the Ge doping ratio.Additionally,the Kondo effect is observed in the samples with x=0.45,0.60,and 0.75.Our results suggest that doping germanium is a viable way to tune the magnetic and electrical transport properties of MnBi_(2)Te_(4),opening up the possibility of future applications in magnetic topological insulators.

On the half-quantized Hall conductance of massive surface electrons in magnetic topological insulator films

In topological insulators,massive surface states resulting from local symmetry breaking were thought to exhibit a half-quantized Hall conductance,obtained from the low-energy effective model in an infinite Brillouin zone.In a lattice model,the surface band is composed of a combination of surface states and bulk states.The massive surface states alone may not be enough to support an exact one-half quantized surface Hall conductance in a finite Brillouin zone and the whole surface band always gives an integer quantized Hall conductance as enforced by the TKNN theorem.To explore this,we investigate the band structures of a lattice model describing the magnetic topological insulator film that supports the axion insulator,Chern insulator,and semi-magnetic topological insulator phases.We reveal that the gapped and gapless surface bands in the three phases are characterized by an integer-quantized Hall conductance and a half-quantized Hall conductance,respectively.We propose an effective model to describe the three phases and show that the low-energy dispersion of the surface bands inherits from the surface Dirac fermions.The gapped surface band manifests a nearly half-quantized Hall conductance at low energy near the center of Brillouin zone,but is compensated by another nearly half-quantized Hall conductance at high energy near the boundary of Brillouin zone because a single band can only have an integer-quantized Hall conductance.The gapless band hosts a zero Hall conductance at low energy but is compensated by another half-quantized Hall conductance at high energy,and thus the half-quantized Hall conductance can only originate from the gapless band.Moreover,we calculate the layer-resolved Hall conductance of the system.The conclusion suggests that the individual gapped surface band alone does not support the half-quantized surface Hall effect in a lattice model.

Three-Dirac-fermion approach to unexpected universal gapless surface states in van der Waals magnetic topological insulators

Layered van der Waals(vdW) topological materials, especially the recently discovered MnBi_(2)Te_(4)-family magnetic topological insulators(TIs), have aroused great attention. However, there has been a serious debate about whether the surface states are gapped or gapless for antiferromagnetic(AFM) TI MnBi_(2)Te_(4), which is crucial to the prospect of various magnetic topological phenomena. Here, a minimal three-Dirac-fermion approach is developed to generally describe topological surface states of nonmagnetic/magnetic vdW TIs under the modulation of the interlayer vdW gap. In particular, this approach is applied to address the controversial issues concerning the surface states of vdW AFM TIs. Remarkably, topologically protected gapless Dirac-cone surface states are found to arise due to a small expansion of the interlayer vdW gap on the surface, when the Chern number equals zero for the surface ferromagnetic layer;while the surface states remain gapped in all other cases. These results are further confirmed by our first-principles calculations on AFM TI MnBi_(2)Te_(4). The theorectically discovered gapless Dirac-cone states provide a unique mechanism for understanding the puzzle of the experimentally observed gapless surface states in MnBi_(2)Te_(4).This work also provides a promising way for experiments to realize the intrinsic magnetic quantum anomalous Hall efect in MnBi_(2)Te_(4) films with a large energy gap.

Persistent surface states with diminishing gap in MnBi_(2)Te_(4)/Bi_(2)Te_(3) superlattice antiferromagnetic topological insulator

Magnetic topological quantum materials(TQMs) provide a fertile ground for the emergence of fascinating topological magneto-electric effects. Recently, the discovery of intrinsic antiferromagnetic(AFM) topological insulator MnBi_(2)Te_(4) that could realize quantized anomalous Hall effect and axion insulator phase ignited intensive study on this family of TQM compounds. Here, we investigated the AFM compound Mn Bi4 Te7 where Bi_(2)Te_(3) and MnBi_(2)Te_(4) layers alternate to form a superlattice. Using spatial-and angleresolved photoemission spectroscopy, we identified ubiquitous(albeit termination dependent) topological electronic structures from both Bi_(2)Te_(3) and MnBi_(2)Te_(4) terminations. Unexpectedly, while the bulk bands show strong temperature dependence correlated with the AFM transition, the topological surface states with a diminishing gap show negligible temperature dependence across the AFM transition.Together with the results of its sister compound MnBi_(2)Te_(4), we illustrate important aspects of electronic structures and the effect of magnetic ordering in this family of magnetic TQMs.

Magnetic Proximity Effect in an Antiferromagnetic Insulator/Topological Insulator Heterostructure with Sharp Interface

We report an experimental study of electron transport properties of MnSe/(Bi,Sb)_2Te_3 heterostructures,in which MnSe is an antiferromagnetic insulator,and(Bi,Sb)_2Te_3 is a three-dimensional topological insulator(TI).Strong magnetic proximity effect is manifested in the measurements of the Hall effect and longitudinal resistances.Our analysis shows that the gate voltage can substantially modify the anomalous Hall conductance,which exceeds 0.1 e^(2)/h at temperature T=1.6 K and magnetic field μ_0H=5 T,even though only the top TI surface is in proximity to MnSe.This work suggests that heterostructures based on antiferromagnetic insulators provide a promising platform for investigating a wide range of topological spintronic phenomena.

Optical spectrum of ferrovalley materials:A case study of Janus H-VSSe

As opposed to the prototypical MoS2 with centroasymmetry,Janus ferrovalley materials such as H-VSSe are less symmetric with the mirror symmetry and time reversal symmetry broken,and hence possess spontaneous valley polarization and strong ferroelasticity.The optical transition is an important means to excite the valley carriers.We investigate the optical spectrum of H-VSSe by using the many-body perturbation-based GW approach and solving the Bethe–Salpeter equation(BSE)to include the electron–hole interactions.It is found that after the GW correction,the band gaps of the quasiparticle bands are much larger than those obtained by the normal density functional theory.The system is ferromagnetic and the valley gaps become non-degenerate due to spin–orbit coupling(SOC).The position of the lowest BSE peak is much lower than the quasiparticle band gap,indicating that the excitonic effect is large.The peak is split into two peaks by the SOC.The binding energy difference between these two BSE peaks is about the same as the difference between the inequivalent valley gaps.Our results show that in Janus H-VSSe the two lowest exciton peaks are from the two inequivalent valleys with different gaps,in contrast to the A and B exciton peaks of MoS2 which are from the same valley.

Relationship between disorder,magnetism and band topology in Mn(Sb_(1-x)Bi_(x))_(2)Te_(4) single crystals

We investigate the evolution of magnetic properties as well as the content and distribution of Mn for Mn(Sb_(1-x)Bi_(x))_(2)Te_(4) single crystals grown by large-temperature-gradient chemical vapor transport method.It is found that the ferromagnetic MnSb_(2)Te_(4) changes to antiferromagnetism with Bi doping when x≥0.25.Further analysis implies that the occupations of Mn ions at Sb/Bi site Mn_(Sb/Bi) and Mn site Mn_(Mn) have a strong influence on the magnetic ground states of these systems.With the decrease of Mn_(Mn) increase of Mn_(Sb/Bi),the system will favor the ferromagnetic ground state.In addition,the rapid decrease of T_(C/N) with increasing Bi content when x ≤0.25 and the insensitivity of T_(N) to x when x> 0.25 suggest that the main magnetic interaction may change from the Ruderman-Kittel-Kasuya-Yosida type at low Bi doping region to the van-Vleck type in high Bi doped samples.

Intrinsic magnetic topological materials

Topological states of matter possess bulk electronic structures categorized by topological invariants and edge/surface states due to the bulk-boundary correspondence. Topological materials hold great potential in the development of dissipationless spintronics, information storage and quantum computation, particularly if combined with magnetic order intrinsically or extrinsically. Here, we review the recent progress in the exploration of intrinsic magnetic topological materials, including but not limited to magnetic topological insulators, magnetic topological metals, and magnetic Weyl semimetals. We pay special attention to their characteristic band features such as the gap of topological surface state, gapped Dirac cone induced by magnetization (either bulk or surface), Weyl nodal point/line and Fermi arc, as well as the exotic transport responses resulting from such band features. We conclude with a brief envision for experimental explorations of new physics or effects by incorporating other orders in intrinsic magnetic topological materials.