Large Landau level splitting with tunable one-dimensional graphene superlattice probed by magneto capacitance measurements

The unique zero energy Landau Level of graphene has a particle-hole symmetry in the bulk, which is lifted at the boundary leading to a splitting into two chiral edge modes. It has long been theoretically predicted that the splitting of the zero-energy Landau level inside the {\it bulk} can lead to many interesting physics, such as quantum spin Hall effect, Dirac like singular points of the chiral edge modes, and others. However, so far the obtained splitting with high-magnetic field even on a hBN substrate are not amenable to experimental detection, and functionality. Guided by theoretical calculations, here we produce a large gap zero-energy Landau level splitting ($\sim$ 150 meV) with the usage of a one-dimensional (1D) superlattice potential. We have created tunable 1D superlattice in a hBN encapsulated graphene device using an array of metal gates with a period of $\sim$ 100 nm. The Landau level spectrum is visualized by measuring magneto capacitance spectroscopy. We monitor the splitting of the zeroth Landau level as a function of superlattice potential. The observed splitting energy is an order higher in magnitude compared to the previous studies of splitting due to the symmetry breaking in pristine graphene. The origin of such large Landau level spitting in 1D potential is explained with a degenerate perturbation theory. We find that owing to the periodic potential, the Landau level becomes dispersive, and acquires sharp peaks at the tunable band edges. Our study will pave the way to create the tunable 1D periodic structure for multi-functionalization and device application like graphene electronic circuits from appropriately engineered periodic patterns in near future

Synthesizing a Fractional v=2/3 State from Particle and Hole States

Topological edge-reconstruction occurs in hole-conjugate states of the fractional quantum Hall effect. The frequently studied polarized state of filling factor v=2/3 was originally proposed to harbor two counter-propagating edge modes: a downstream v=1 and an upstream v=1/3. However, charge equilibration between these two modes always led to an observed downstream v=2/3 charge mode accompanied by an upstream neutral mode (preventing an observation of the original proposal). Here, we present a new approach to synthetize the v=2/3 edge mode from its basic counter-propagating charged constituents, allowing a controlled equilibration between the two counter-propagating charge modes. This novel platform is based on a carefully designed double-quantum-well, which hosts two populated electronic sub-bands (lower and upper), with corresponding filling factors, vl & vu. By separating the 2D plane to two gated intersecting halves, each with different fillings, counter-propagating chiral modes can be formed along the intersection line. Equilibration between these modes can be controlled with the top gates' voltage and the magnetic field. Our measurements of the two-terminal conductance G2T and the presence of a neutral mode allowed following the transition from the non-equilibrated charged modes, manifested by G2T=(4/3)e2/h, to the fully equilibrated modes, with a downstream charge mode with G2T=(2/3)e2/h accompanied by an upstream neutral mode.Comment: 16 pages,4 figure

Equal Opportunity through Higher Education: Theory and Evidence on Privilege and Ability

We model a higher education system that admits students according to their admission signal (e.g., matriculation GPA, SAT), which is, in turn, affected by their cognitive ability and socioeconomic background. We show that subsidizing education loans increases neither human capital stock nor aggregate consumption, but only yields income redistribution mainly among the upper class. We show that the policies aimed at compensating for poor socioeconomic background result in a higher aggregate consumption, as well as income redistribution from top to bottom. We test the model using a unique dataset that includes proxies of socioeconomic background and cognitive ability. Results show that the high school matriculation GPA is a weak predictor of academic achievements. We demonstrate that, while the high school matriculation GPA is explained by proxies of cognitive ability and socioeconomic background, academic GPA is solely explained by cognitive ability proxies. Finally, the lack of a matriculation certificate is associated with a poor socioeconomic background

GRelPose: Generalizable End-to-End Relative Camera Pose Regression

This paper proposes a generalizable, end-to-end deep learning-based method for relative pose regression between two images. Given two images of the same scene captured from different viewpoints, our algorithm predicts the relative rotation and translation between the two respective cameras. Despite recent progress in the field, current deep-based methods exhibit only limited generalization to scenes not seen in training. Our approach introduces a network architecture that extracts a grid of coarse features for each input image using the pre-trained LoFTR network. It subsequently relates corresponding features in the two images, and finally uses a convolutional network to recover the relative rotation and translation between the respective cameras. Our experiments indicate that the proposed architecture can generalize to novel scenes, obtaining higher accuracy than existing deep-learning-based methods in various settings and datasets, in particular with limited training data