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Physics-guided Neural Networks (PGNNs) represent an emerging class of neural networks that are trained using physics-guided (PG) loss functions (capturing violations in network outputs with known physics), along with the supervision contained in data. Existing work in PGNNs has demonstrated the efficacy of adding single PG loss functions in the neural network objectives, using constant trade-off parameters, to ensure better generalizability. However, in the presence of multiple PG functions with competing gradient directions, there is a need to adaptively tune the contribution of different PG loss functions during the course of training to arrive at generalizable solutions. We demonstrate the presence of competing PG losses in the generic neural network problem of solving for the lowest (or highest) eigenvector of a physics-based eigenvalue equation, which is commonly encountered in many scientific problems. We present a novel approach to handle competing PG losses and demonstrate its efficacy in learning generalizable solutions in two motivating applications of quantum mechanics and electromagnetic propagation. All the code and data used in this work are available at https://github.com/jayroxis/Cophy-PGNN. 

Epitaxial films of vanadium dioxide (VO 2 ) on rutile TiO 2 substrates provide a means of strain-engineering the transition pathways and stabilizing of the intermediate phases between monoclinic (insulating) M1 and rutile (metal) R end phases. In this work, we investigate structural behavior of epitaxial VO 2 thin films deposited on isostructural MgF 2 (001) and (110) substrates via temperature-dependent Raman microscopy analysis. The choice of MgF 2 substrate clearly reveals how elongation of V–V dimers accompanied by the shortening of V–O bonds triggers the intermediate M2 phase in the temperature range between 70–80 °C upon the heating–cooling cycles. Consistent with earlier claims of strain-induced electron correlation enhancement destabilizing the M2 phase our temperature-dependent Raman study supports a small temperature window for this phase. The similarity of the hysteretic behavior of structural and electronic transitions suggests that the structural transitions play key roles in the switching properties of epitaxial VO 2 thin films. 

Oxygen vacancy is known to play an important role for the physical properties in SrTiO₃(STO)-based systems. On the surface, rich structural reconstructions had been reported owing to the oxygen vacancies, giving rise to metallic surface states and unusual surface phonon modes. More recently, an intriguing phenomenon of a huge superconducting transition temperature enhancement was discovered in a monolayer FeSe on STO substrate, where the surface reconstructed STO (SR-STO) may play a role. In this work, SR-STO substrates were prepared via thermal annealing in ultra-high vacuum followed by low energy electron diffraction analyses on surface structures. Thin Nb films with different thicknesses (d) were then deposited on the SR-STO. The detailed studies of the magnetotransport and superconducting property in the Al(1 nm)/Nb(d)/SR-STO samples revealed a large positive magnetoresistance and a pronounced resistance peak near the onset of the resistive superconducting transition in the presence of an in-plane field. Remarkably, the amplitude of the resistance peak increases with increasing fields, reaching a value of nearly 57% of the normal state resistance at 9 T. Such resistance peaks were absent in the control samples of Al(1 nm)/Nb(d)/STO and Al(1 nm)/Nb(d)/SiO₂. Combining with DFT calculations for SR-STO, we attribute the resistance peak to the interface resistance from the proximity coupling of the superconducting niobium to the field-enhanced long-range magnetic order in SR-STO that arises from the spin-polarized in-gap states due to oxygen vacancies.

 

Search for novel electronically ordered states of matter emerging near quantum phase transitions is an intriguing frontier of condensed matter physics. In ruthenates, the interplay between Coulomb correlations among the 4delectronic states and their spin-orbit interactions, lead to complex forms of electronic phenomena. Here we investigate the double layered Sr₃(Ru_1−xMn_x)₂O₇and its doping-induced quantum phase transition from a metal to an antiferromagnetic Mott insulator. Using spectroscopic imaging with the scanning tunneling microscope, we visualize the evolution of the electronic states in real- and momentum-space. We find a partial-gap at the Fermi energy that develops with doping to form a weak Mott insulating state. Near the quantum phase transition, we discover a spatial electronic reorganization into a commensurate checkerboard charge order. These findings bear a resemblance to the universal charge order in the pseudogap phase of cuprates and demonstrate the ubiquity of charge order that emanates from doped Mott insulators.