† People involved in the organization of the challenge. ‡ People contributing data from their institutions.§ Equal senior authors.

We investigate the possibility of band structure engineering in the recently predicted 2D layered form of blue phosphorus via an electric field (Ez) applied perpendicular to the layer(s). Using density functional theory, we study the effect of a transverse electric field in monolayer, as well as three differently stacked bilayer structures of blue phosphorus. We find that, for Ez > 0.2 V/Å the direct energy gap at the Γ point, which is much larger than the default indirect band gap of mono-and bilayer blue phosphorus, decreases linearly with the increasing electric field; becomes comparable to the default indirect band gap at Ez ≈ 0.45 (0.35) V/Å for monolayer (bilayers) and decreases further until the semiconductor to metal transition of 2D blue phosphorus takes place at Ez ≈ 0.7 (0.5) V/Å for monolayer (bilayers). Calculated values of the electron and hole effective masses along various high symmetry directions in the reciprocal lattice suggests that the mobility of charge carriers is also influenced by the applied electric field.

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Novel magnetic topological materials pave the way for studying the interplay between band topology and magnetism. However, an intrinsically ferromagnetic topological material with only topological bands at the charge neutrality energy has so far remained elusive. Using rational design, we synthesized MnBi8Te13, a natural heterostructure with [MnBi2Te4] and [Bi2Te3] layers. Thermodynamic, transport, and neutron diffraction measurements show that despite the adjacent [MnBi2Te4] being 44.1 Å apart, MnBi8Te13 manifests long-range ferromagnetism below 10.5 K with strong coupling between magnetism and charge carriers. First-principles calculations and angle-resolved photoemission spectroscopy measurements reveal it is an axion insulator with sizable surface hybridization gaps. Our calculations further demonstrate the hybridization gap persists in the two-dimensional limit with a nontrivial Chern number. Therefore, as an intrinsic ferromagnetic axion insulator with clean low-energy band structures, MnBi8Te13 serves as an ideal system to investigate rich emergent phenomena, including the quantized anomalous Hall effect and quantized magnetoelectric effect.

Berry curvature in Weyl semimetals leads to intriguing magnetoconductivity and magneto-thermal transport properties. Here, we explore the impact of the tilting of the Weyl nodes, on the magnetoconductivity of type-I and type-II Weyl semimetals using the Berry curvature connected Boltzmann transport formalism. We find that in addition to the quadratic magnetic field (B) corrections induced by the tilt, there are also anisotropic and B-linear corrections in several elements of the conductivity matrix. For the case of magnetic field applied perpendicular to the tilt direction, we show the existence of previously unexplored B-linear transverse conductivity components. For the other case of magnetic field applied parallel to the tilt axis, the B-linear corrections appear in the longitudinal conductivity giving rise to anisotropic magnetoresistance measurements. Our systematic analysis of the full magnetoconductivity matrix, predicts several specific experimental signatures related to the tilting of the Weyl nodes in both type-I and type-II Weyl semimetals. * kamaldas@iitk.ac.in †