Three-dimensional (3D) topological insulators (TIs) are unusual quantum materials that host conducting helical Dirac states on their surfaces, which are protected by time reversal symmetry (TRS), but are electrically insulating in the bulk [1,2]. TI is distinct from a trivial insulator by its unique electromagnetic response, described by the so-called  term shown below in addition to the ordinary Maxwell terms [3][4][5][6]. Here E and B are the conventional electric and magnetic fields inside an insulator, e is electron charge, and θ is the dimensionless pseudo-scalar parameter describing the insulator. For a trivial insulator, θ=0, while for a TI, θ=. When TRS is preserved, θ is either 0 or , reflecting its topological nature. This  term is related to the axion electrodynamics in particle physics [7]. Since the EB  term can be rewritten as a total derivative, its effect manifests on the surface states. A half-integer quantum Hall effect on the TI surface occurs once the surface Dirac Fermions acquire a mass, i.e. the surface state is gapped by magnetism. Such half-integer quantum Hall effect on TI surface can lead to a variety of exotic phenomena such as the quantum anomalous Hall (QAH) effect [3,[8][9][10][11][12][13][14][15], the quantized magneto-optical effect [3,16,17], the topological magnetoelectric (TME) effect [3][4][5][6]18], and the image magnetic monopole [19]. The QAH and quantized magneto-optical effects have been experimentally demonstrated in pure or magnetic TI films [10][11][12][13][20][21][22]. The TME effect refers to the quantized response of electric 3 polarization to applied magnetic fields and vice versa. The realization of the TME effect requires the following three conditions: (i) the TI film should be in the 3D regime; (ii) all the surfaces are gapped with the chemical potential lying within the gaps; (iii) the interior of the TI maintains TRS or inversion symmetry to maintain  in the bulk. A material system allowing for the realization of TME effect is known as an axion insulator [3][4][5].Recently, two papers reported the possible realization of the axion insulator. (Figs. 3k and 3m). We note that the zero  yx plateau is absent in either uniformly doped or the Cr modulation doped QAH samples [23,26,31,32]. The 3-5-3 SH2 was magnetically trained first by an upward sweep up to  0 H=1.5T before being swept downward. When  0 H=-0.01T, the MFM contrast is uniform (red), indicating that both top V-and bottom Cr-doped TI layers have upward magnetization (Fig. 3c). At  0 H=-0.05T, some reversed magnetic domains (green regions in Fig. 3d) appear, presumably in the 'softer' Cr-doped TI layer. As  0 H is swept further, the green regions expand and fill up the whole scan area at  0 H=-0.09T, indicating the uniform antiparallel magnetization alignment over the entire 3-5-3 SH2. When  0 H is further swept toward H c1 , new reversed magnetic domains (blue regions in Fig. 3g) nucleate at different locations, presumably in the 'harder' V-doped TI layer. Downward parallel magnetiza...

The quantum anomalous Hall (QAH) state is a two-dimensional topological insulating state that has quantized Hall resistance of h/Ce 2 and vanishing longitudinal resistance under zero magnetic field, where C is called the Chern number 1,2 . The QAH effect has been realized in magnetic topological insulators (TIs) 3-9 and magic-angle twisted bilayer graphene 10,11 . Despite considerable experimental efforts, the zero magnetic field QAH effect has so far been realized only for C = 1. Here we used molecular beam epitaxy to fabricate magnetic TI multilayers and realized the QAH effect with tunable Chern number C up to 5. The Chern number of these QAH insulators is tuned by varying the magnetic doping concentration or the thickness of the interior magnetic TI layers in the multilayer samples. A theoretical model is developed to understand our experimental observations and establish phase diagrams for QAH insulators with tunable Chern numbers. The realization of QAH insulators with high tunable Chern numbers facilitates the potential applications of dissipationless chiral edge currents in energy-

A quantum anomalous Hall (QAH) insulator coupled to an s-wave superconductor is predicted to harbor chiral Majorana modes. A recent experiment interprets the half-quantized two-terminal conductance plateau as evidence for these modes in a millimeter-size QAH-niobium hybrid device. However, non-Majorana mechanisms can also generate similar signatures, especially in disordered samples. Here, we studied similar hybrid devices with a well-controlled and transparent interface between the superconductor and the QAH insulator. When the devices are in the QAH state with well-aligned magnetization, the two-terminal conductance is always half-quantized. Our experiment provides a comprehensive understanding of the superconducting proximity effect observed in QAH-superconductor hybrid devices and shows that the half-quantized conductance plateau is unlikely to be induced by chiral Majorana fermions in samples with a highly transparent interface.

Recently, MnBi 2 Te 4 has been demonstrated to be an intrinsic magnetic topological insulator and the quantum anomalous Hall (QAH) effect was observed in exfoliated MnBi 2 Te 4 flakes. Here, we used molecular beam epitaxy (MBE) to grow MnBi 2 Te 4 films with thickness down to 1 septuple layer (SL) and performed thickness-dependent transport measurements. We observed a nonsquare hysteresis loop in the antiferromagnetic state for films with thickness greater than 2 SL. The hysteresis loop can be separated into two AH components. We demonstrated that one AH component with the larger coercive field is from the dominant MnBi 2 Te 4 phase, whereas the other AH component with the smaller coercive field is from the minor Mn-doped Bi 2 Te 3 phase. The extracted AH component of the MnBi 2 Te 4 phase shows a clear even− odd layer-dependent behavior. Our studies reveal insights on how to optimize the MBE growth conditions to improve the quality of MnBi 2 Te 4 films.

Superconductivity in topological kagome metals has recently received great research interests. Here, charge density wave (CDW) orders and the evolution of superconductivity under various pressures in CsV3Sb5 single crystal with V kagome lattice are investigated. By using high‐resolution scanning tunneling microscopy/spectroscopy (STM/STS), two CDW orders in CsV3Sb5 are observed which correspond to 4a × 1a and 2a × 2a superlattices. By applying pressure, the superconducting transition temperature Tc is significantly enhanced and reaches a maximum value of 8.2 K at around 1 GPa. Accordingly, CDW state is gradually declined as increasing the pressure, which indicates the competing interplay between CDW and superconducting state in this material. The broad superconducting transitions around 0.4–0.8 GPa can be related to the strong competition relation among two CDW states and superconductivity. These results demonstrate that CsV3Sb5 is a new platform for exploring the interplay between superconductivity and CDW in topological kagome metals.