The Berry curvature and quantum metric are the imaginary part and real part, respectively, of the quantum geometric tensor, which characterizes the topology of quantum states1. The Berry curvature is known to generate a number of important transport phenomena, such as the quantum Hall effect and the anomalous Hall effect2,3; however, the consequences of the quantum metric have rarely been probed by transport measurements. Here we report the observation of quantum-metric-induced nonlinear transport, including both a nonlinear anomalous Hall effect and a diode-like non-reciprocal longitudinal response, in thin films of a topological antiferromagnet, MnBi2Te4. Our observations reveal that the transverse and longitudinal nonlinear conductivities reverse signs when reversing the antiferromagnetic order, diminish above the Néel temperature and are insensitive to disorder scattering, thus verifying their origin in the band-structure topology. They also flip signs between electron- and hole-doped regions, in agreement with theoretical calculations. Our work provides a means to probe the quantum metric through nonlinear transport and to design magnetic nonlinear devices.

Mitochondria import nearly all of their approximately 1,000-2,000 constituent proteins from the cytosol across their double-membrane envelope1-5. Genetic and biochemical studies have shown that the conserved protein translocase, termed the TIM23 complex, mediates import of presequence-containing proteins (preproteins) into the mitochondrial matrix and inner membrane. Among about ten different subunits of the TIM23 complex, the essential multipass membrane protein Tim23, together with the evolutionarily related protein Tim17, has long been postulated to form a protein-conducting channel6-11. However, the mechanism by which these subunits form a translocation path in the membrane and enable the import process remains unclear due to a lack of structural information. Here we determined the cryo-electron microscopy structure of the core TIM23 complex (heterotrimeric Tim17-Tim23-Tim44) from Saccharomyces cerevisiae. Contrary to the prevailing model, Tim23 and Tim17 themselves do not form a water-filled channel, but instead have separate, lipid-exposed concave cavities that face in opposite directions. Our structural and biochemical analyses show that the cavity of Tim17, but not Tim23, forms the protein translocation path, whereas Tim23 probably has a structural role. The results further suggest that, during translocation of substrate polypeptides, the nonessential subunit Mgr2 seals the lateral opening of the Tim17 cavity to facilitate the translocation process. We propose a new model for the TIM23-mediated protein import and sorting mechanism, a central pathway in mitochondrial biogenesis.

The interplay between spontaneous symmetry breaking and topology can result in exotic quantum states of matter. A celebrated example is the quantum anomalous Hall (QAH) state, which exhibits an integer quantum Hall effect at zero magnetic field due to intrinsic ferromagnetism1-3. In the presence of strong electron-electron interactions, fractional-QAH (FQAH) states at zero magnetic field can emerge4-8. These states could host fractional excitations, including non-Abelian anyons - crucial building blocks for topological quantum computation9. Here, we report experimental signatures of FQAH states in twisted MoTe2 bilayer. Magnetic circular dichroism measurements reveal robust ferromagnetic states at fractionally hole filled moiré minibands. Using trion photoluminescence as a sensor10, we obtain a Landau fan diagram showing linear shifts in carrier densities corresponding to the v = -2/3 and -3/5 ferromagnetic states with applied magnetic field. These shifts match the Streda formula dispersion of FQAH states with fractionally quantized Hall conductance of [Formula: see text] and [Formula: see text], respectively. Moreover, the v = -1 state exhibits a dispersion corresponding to Chern number -1, consistent with the predicted QAH state11-14. In comparison, several non-ferromagnetic states on the electron doping side do not disperse, i.e., are trivial correlated insulators. The observed topological states can be electrically driven into topologically trivial states. Our findings provide evidence of the long-sought FQAH states, demonstrating MoTe2 moiré superlattices as a fascinating platform for exploring fractional excitations.