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Grain boundaries have extensive influence on the performance of crystal materials. However, the atomic-scale structure and its relation with local and crystallographic symmetries remain elusive in low-symmetry crystals. Herein, we find that the local pseudo-mirror-symmetric atomic layer is the common physical origin of a series of highly coherent grain boundaries in the low-symmetry $\beta$-Ga2O3 crystal. These include the (100) twin boundary and an emerging series of $(h-1'0'2)/(h+1'0'\bar{2})$ coherent asymmetric grain boundaries (CAGBs). Owing to the local pseudo-mirror symmetry and the special geometric relation of the $\beta$-Ga2O3 conventional cell, these CAGBs place 80% of the boundary atoms in pseudo-coincident sites, exhibiting high coherence under the coincident-site lattice model. With a combination of density functional theory calculations, Czochralski growth experiment, and atomic-scale characterizations, the structure and stability of the $(002)/(20\bar{2})$-A CAGB are confirmed, with a boundary energy density as low as 0.36 J/m2. This CAGB is responsible for the spontaneous formation of a twinned defect facet at the surface steps during the epitaxy growth of $\beta$-Ga2O3, warranting a substrate orientation selection rule for $\beta$-Ga2O3. Through this study, we provide insights into the grain boundary physics in the low-symmetry $\beta$-Ga2O3 crystal while emphasizing the importance of the local pseudo-symmetries in the low-symmetry crystals.

Inspired by recent experimental findings, we investigate various scenarios of the doped Hubbard model with impurity potentials. We calculate the lattice Green's function in a finite-size cluster and then map it to the continuum real space, which allows for a direct comparison with scanning-tunneling-microscopy measurements on the local density of states. Our simulations successfully reproduce experimental data, including the characteristic stripe- and ladder-shaped structures observed in cuprate systems. Moreover, our results establish a connection between previous numerical findings on stripe-ordered ground states and experimental observations, thereby providing new insights into doped Mott insulators., Comment: 11 pages, 7 figures

Chemical reaction practicality is the core task among all symbol intelligence based chemical information processing, for example, it provides indispensable clue for further automatic synthesis route inference. Considering that chemical reactions have been represented in a language form, we propose a new solution to generally judge the practicality of organic reaction without considering complex quantum physical modeling or chemistry knowledge. While tackling the practicality judgment as a machine learning task from positive and negative (chemical reaction) samples, all existing studies have to carefully handle the serious insufficiency issue on the negative samples. We propose an auto-construction method to well solve the extensively existed long-term difficulty. Experimental results show our model can effectively predict the practicality of chemical reactions, which achieves a high accuracy of 99.76\% on real large-scale chemical lab reaction practicality judgment.