Observation of the nonlinear Hall effect under time-reversal-symmetric conditions.

The electrical Hall effect is the production, upon the application of an electric field, of a transverse voltage under an out-of-plane magnetic field. Studies of the Hall effect have led to important breakthroughs, including the discoveries of Berry curvature and topological Chern invariants1,2. The internal magnetization of magnets means that the electrical Hall effect can occur in the absence of an external magnetic field2; this 'anomalous' Hall effect is important for the study of quantum magnets2-7. The electrical Hall effect has rarely been studied in non-magnetic materials without external magnetic fields, owing to the constraint of time-reversal symmetry. However, only in the linear response regime-when the Hall voltage is linearly proportional to the external electric field-does the Hall effect identically vanish as a result of time-reversal symmetry; the Hall effect in the nonlinear response regime is not subject to such symmetry constraints8-10. Here we report observations of the nonlinear Hall effect10 in electrical transport in bilayers of the non-magnetic quantum material WTe2 under time-reversal-symmetric conditions. We show that an electric current in bilayer WTe2 leads to a nonlinear Hall voltage in the absence of a magnetic field. The properties of this nonlinear Hall effect are distinct from those of the anomalous Hall effect in metals: the nonlinear Hall effect results in a quadratic, rather than linear, current-voltage characteristic and, in contrast to the anomalous Hall effect, the nonlinear Hall effect results in a much larger transverse than longitudinal voltage response, leading to a nonlinear Hall angle (the angle between the total voltage response and the applied electric field) of nearly 90 degrees. We further show that the nonlinear Hall effect provides a direct measure of the dipole moment10 of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe2. Our results demonstrate a new type of Hall effect and provide a way of detecting Berry curvature in non-magnetic quantum materials.

Information Scrambling in Quantum Neural Networks.

The quantum neural network is one of the promising applications for near-term noisy intermediate-scale quantum computers. A quantum neural network distills the information from the input wave function into the output qubits. In this Letter, we show that this process can also be viewed from the opposite direction: the quantum information in the output qubits is scrambled into the input. This observation motivates us to use the tripartite information-a quantity recently developed to characterize information scrambling-to diagnose the training dynamics of quantum neural networks. We empirically find strong correlation between the dynamical behavior of the tripartite information and the loss function in the training process, from which we identify that the training process has two stages for randomly initialized networks. In the early stage, the network performance improves rapidly and the tripartite information increases linearly with a universal slope, meaning that the neural network becomes less scrambled than the random unitary. In the latter stage, the network performance improves slowly while the tripartite information decreases. We present evidences that the network constructs local correlations in the early stage and learns large-scale structures in the latter stage. We believe this two-stage training dynamics is universal and is applicable to a wide range of problems. Our work builds bridges between two research subjects of quantum neural networks and information scrambling, which opens up a new perspective to understand quantum neural networks.

Quantum Oscillation from In-Gap States and a Non-Hermitian Landau Level Problem.

Motivated by recent experiments on Kondo insulators, we theoretically study quantum oscillations from disorder-induced in-gap states in small-gap insulators. By solving a non-Hermitian Landau level problem that incorporates the imaginary part of electron's self-energy, we show that the oscillation period is determined by the Fermi surface area in the absence of the hybridization gap, and we derive an analytical formula for the oscillation amplitude as a function of the indirect band gap, scattering rates, and temperature. Over a wide parameter range, we find that the effective mass is controlled by scattering rates, while the Dingle factor is controlled by the indirect band gap. We also show the important effect of scattering rates in reshaping the quasiparticle dispersion in connection with angle-resolved photoemission measurements on heavy fermion materials.

Machine Learning Topological Invariants with Neural Networks.

In this Letter we supervisedly train neural networks to distinguish different topological phases in the context of topological band insulators. After training with Hamiltonians of one-dimensional insulators with chiral symmetry, the neural network can predict their topological winding numbers with nearly 100% accuracy, even for Hamiltonians with larger winding numbers that are not included in the training data. These results show a remarkable success that the neural network can capture the global and nonlinear topological features of quantum phases from local inputs. By opening up the neural network, we confirm that the network does learn the discrete version of the winding number formula. We also make a couple of remarks regarding the role of the symmetry and the opposite effect of regularization techniques when applying machine learning to physical systems.

Topological Band Theory for Non-Hermitian Hamiltonians.

We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped" bands in one and two dimensions by explicitly finding their topological invariants. We find nontrivial generalizations of the Chern number in two dimensions, and a new classification in one dimension, whose topology is determined by the energy dispersion rather than the energy eigenstates. We then study the bulk-edge correspondence and the topological phase transition in two dimensions. Different from the Hermitian case, the transition generically involves an extended intermediate phase with complex-energy band degeneracies at isolated "exceptional points" in momentum space. We also systematically classify all types of band degeneracies.

Effects of three different mannans on obesity and gut microbiota in high-fat diet-fed C57BL/6J mice.

To compare the effects of three mannans, Konjac glucomannan (KGM), guar gum (GG) and locust bean gum (LBG), on obesity and obesity-related metabolic disorders in mice fed with high-fat diet (HFD), and to investigate the potential modulation of gut microbiota, we performed a 14 week study on C57BL/6J mice fed a HFD with/without mannan supplementation. The results showed that supplementing 8% KGM, GG, and LBG to a HFD dramatically reduced the body weight gain and adipose accumulation, attenuated liver injury, and antagonized glycolipid metabolism and inflammation-related parameters of HFD-fed mice in different degrees. However, only LBG had such roles when the supplement dose was reduced to 2%. In addition, it was found that LBG required more time to exert its impacts on weight control and lipid metabolism. Furthermore, 16S rRNA gene sequencing of gut microbiota indicated that mannans with different structures and supplement doses affected the overall structure of the gut microbiota to a varying extent and specifically changed the abundance of some OTUs. Moreover, several OTUs belonging to the genera Muribaculum, Staphylococcus, [Eubacterium] fissicatena group, and Christensenella had a high correlation with obesity and obesity-related metabolic disorders of the host. In summary, all the three mannans had the potential to be used as alternative dietary supplements or functional foods to prevent obesity and obesity-related metabolic disorders induced by a HFD, but the effects of the dose and time varied, and the functions of the mannans were associated with their ability to regulate the gut microbiota.

Out-of-time-order correlation for many-body localization.

In this paper we first compute the out-of-time-order correlators (OTOC) for both a phenomenological model and a random-field XXZ model in the many-body localized phase. We show that the OTOC decreases in power law in a many-body localized system at the scrambling time. We also find that the OTOC can also be used to distinguish a many-body localized phase from an Anderson localized phase, while a normal correlator cannot. Furthermore, we prove an exact theorem that relates the growth of the second Rényi entropy in the quench dynamics to the decay of the OTOC in equilibrium. This theorem works for a generic quantum system. We discuss various implications of this theorem.

Winter soil CO2 flux from different mid-latitude sites from Middle Taihang Mountain in north China.

Winter soil respiration is a very important component of the annual soil carbon flux in some ecosystems. We hypothesized that, with all other factors being equal, shorter winter SR result in reduced contribution to annual soil C flux. In this study, the contribution of winter soil respiration to annual soil respiration was measured for three sites (grassland: dominated by Artemisia sacrorum, Bothriochloa ischaemum and Themeda japonica; shrubland: dominated by Vitex negundo var. heterophylla; plantation: dominated by Populus tomatosa) in a mountainous area of north China. Diurnal and intra-annual soil CO2 flux patterns were consistent among different sites, with the maximum soil respiration rates at 12∶00 or 14∶00, and in July or August. The lowest respiration rates were seen in February. Mean soil respiration rates ranged from 0.26 to 0.45 µmol m(-2) s(-1) in the winter (December to February), and between 2.38 to 3.16 µmol m(-2) s(-1) during the growing season (May-September). The winter soil carbon flux was 24.6 to 42.8 g C m(-2), which contributed 4.8 to 7.1% of the annual soil carbon flux. Based on exponential functions, soil temperature explained 73.8 to 91.8% of the within year variability in soil respiration rates. The Q10 values of SR against ST at 10 cm ranged from 3.60 to 4.90 among different sites. In addition, the equation between soil respiration and soil temperature for the growing season was used to calculate the "modeled" annual soil carbon flux based on the actual measured soil temperature. The "measured" annual value was significantly higher than the "modeled" annual value. Our results suggest that winter soil respiration plays a significant role in annual soil carbon balance, and should not be neglected when soil ecosystems are assessed as either sinks or sources of atmospheric CO2.

Carbon storages in plantation ecosystems in sand source areas of north Beijing, China.

Afforestation is a mitigation option to reduce the increased atmospheric carbon dioxide levels as well as the predicted high possibility of climate change. In this paper, vegetation survey data, statistical database, National Forest Resource Inventory database, and allometric equations were used to estimate carbon density (carbon mass per hectare) and carbon storage, and identify the size and spatial distribution of forest carbon sinks in plantation ecosystems in sand source areas of north Beijing, China. From 2001 to the end of 2010, the forest areas increased more than 2.3 million ha, and total carbon storage in forest ecosystems was 173.02 Tg C, of which 82.80 percent was contained in soil in the top 0-100 cm layer. Younger forests have a large potential for enhancing carbon sequestration in terrestrial ecosystems than older ones. Regarding future afforestation efforts, it will be more effective to increase forest area and vegetation carbon density through selection of appropriate tree species and stand structure according to local climate and soil conditions, and application of proper forest management including land-shaping, artificial tending and fencing plantations. It would be also important to protect the organic carbon in surface soils during forest management.