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Abstract Model Hamiltonians are regularly derived from first principles to describe correlated matter. However, the standard methods for this contain a number of largely unexplored approximations. For a strongly correlated impurity model system, here we carefully compare a standard downfolding technique with the best possible ground-truth estimates for charge-neutral excited-state energies and wave functions using state-of-the-art first-principles many-body wave function approaches. To this end, we use the vanadocene molecule and analyze all downfolding aspects, including the Hamiltonian form, target basis, double-counting correction, and Coulomb interaction screening models. We find that the choice of target-space basis functions emerges as a key factor for the quality of the downfolded results, while orbital-dependent double-counting corrections diminish the quality. Background screening of the Coulomb interaction matrix elements primarily affects crystal-field excitations. Our benchmark uncovers the relative importance of each downfolding step and offers insights into the potential accuracy of minimal downfolded model Hamiltonians. 

Abstract Optically active point defects in wide‐bandgap semiconductors have been demonstrated to be attractive for a variety of quantum and nanoscale applications. In particular, color centers in hexagonal boron nitride (hBN) have recently gained substantial attention owing to their spectral tunability, brightness, stability, and room‐temperature operation. Despite all of the recent studies, precise detection of the defect‐induced mid‐gap electronic states (MESs) and their simultaneous correlations with the observed emission in hBN remain elusive. Directly probing these MESs provides a powerful approach toward atomic identification and optical control of the defect centers underlying the sub‐bandgap emission in hBN. Combining optical and electron spectroscopy, the existence of mid‐gap absorptive features is revealed at the emissive sites in hBN, along with an atom‐by‐atom identification of the underlying defect configuration. The atomically resolved defect structure, primarily constituted by vacancies and carbon/oxygen substitutions, is further studied via first‐principles calculations, which support the correlation with the observed MESs through the electronic density of states. This work provides a direct relationship between the observed visible emission in hBN, the underlying defect structure, and its absorptive MESs, opening venues for atomic‐scale and optical control in hBN for quantum technology. 

First-principles calculations of defects and electron–phonon interactions play a critical role in the design and optimization of materials for electronic and optoelectronic devices. The late Audrius Alkauskas made seminal contributions to developing rigorous first-principles methodologies for the computation of defects and electron–phonon interactions, especially in the context of understanding the fundamental mechanisms of carrier recombination in semiconductors. Alkauskas was also a pioneer in the field of quantum defects, helping to build a first-principles understanding of the prototype nitrogen-vacancy center in diamond, as well as identifying novel defects. Here, we describe the important contributions made by Alkauskas and his collaborators and outline fruitful research directions that Alkauskas would have been keen to pursue. Audrius Alkauskas’ scientific achievements and insights highlighted in this article will inspire and guide future developments and advances in the field.