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Emergent phenomena arising from nontrivial band structures based on topology and symmetry have been attracting keen interest in contemporary condensed-matter physics. Materials such as SnTe and PbTe are one such example, which demonstrate a topological phase transition while showing ferroelectric instability derived from their rock-salt structure. The ferroelectricity can lift the valley degeneracy, enabling the emergence of the Z2 topological insulator phase, although its observation in transport phenomena remains elusive. Here, we report magnetotransport properties of ferroelectric (Sn,Pb)Te thin films with finely-controlled Fermi levels via In doping. We identified the ferroelectric topological insulator phase from the observations of the quantum Hall states with filling factors of $\nu$ = 1, 2 and 3 with both spin- and valley-degeneracy lifting. The electronic states are two-dimensional, indicating the ferroelectricity-induced topological surface states with a single Dirac cone. The finding of the new topological state with ferroelectricity will further expand the field of topological physics and advance the development of functional properties, such as topological nonlinear photonics and nonreciprocal transport with memory effect., Comment: 21 pages, 4 figures

Quantum materials governed by emergent topological fermions have become a cornerstone of physics. Dirac fermions in graphene form the basis for moir\'e quantum matter, and Dirac fermions in magnetic topological insulators enabled the discovery of the quantum anomalous Hall effect. In contrast, there are few materials whose electromagnetic response is dominated by emergent Weyl fermions. Nearly all known Weyl materials are overwhelmingly metallic, and are largely governed by irrelevant, conventional electrons. Here we theoretically predict and experimentally observe a semimetallic Weyl ferromagnet in van der Waals (Cr,Bi)$_2$Te$_3$. In transport, we find a record bulk anomalous Hall angle $> 0.5$ along with non-metallic conductivity, a regime sharply distinct from conventional ferromagnets. Together with symmetry analysis, our data suggest a semimetallic Fermi surface composed of two Weyl points, with a giant separation $> 75\%$ of the linear dimension of the bulk Brillouin zone, and no other electronic states. Using state-of-the-art crystal synthesis techniques, we widely tune the electronic structure, allowing us to annihilate the Weyl state and visualize a unique topological phase diagram exhibiting broad Chern insulating, Weyl semimetallic and magnetic semiconducting regions. Our observation of a semimetallic Weyl ferromagnet offers an avenue toward novel correlated states and non-linear phenomena, as well as zero-magnetic-field Weyl spintronic and optical devices., Comment: Nature, in press

Photodetection is an indispensable function of optoelectronic devices in modern communication and sensing systems. Contrary to the near-infrared/visible regions, the fast and sensitive photodetectors operated at room temperature for the far-infrared/terahertz regions are not well developed despite a possibly vast range of applications. The bulk photovoltaic effect (BPVE) in single-phase noncentrosymmetric materials based on the shift current mechanism enables less-dissipative energy conversion endowed with instantaneous responsivity owing to the quantum-mechanical geometric phase of electronic states. Nevertheless, the small-band-gap material for the low-energy BPVE inevitably suffers from the thermal noise due to the intrinsically high conductivity. Here, we demonstrate the shift current induced by soft-phonon excitations without creation of electron-hole pairs in the archetypal ferroelectric BaTiO3 by using the terahertz light, whose energy scale is three orders of magnitude smaller than the electronic band gap. At and above room temperature, we observe appreciable photocurrents caused by the soft-phonon excitation as large as that for electronic excitation and their strong phonon-mode dependence. The observed phonon-driven BPVE can be well accounted for by the shift current model considering the electron-phonon coupling in the displacement-type ferroelectrics as supported by the first-principles calculation. Our findings establish the efficient quantum BPVE arising from low-energy elementary excitations, suggesting the novel principle for the high-performance terahertz photodetectors., Comment: 25 pages, 8 figures