3,115 research outputs found
Efficient Learning of a One-dimensional Density Functional Theory
Density functional theory underlies the most successful and widely used
numerical methods for electronic structure prediction of solids. However, it
has the fundamental shortcoming that the universal density functional is
unknown. In addition, the computational result---energy and charge density
distribution of the ground state---is useful for electronic properties of
solids mostly when reduced to a band structure interpretation based on the
Kohn-Sham approach. Here, we demonstrate how machine learning algorithms can
help to free density functional theory from these limitations. We study a
theory of spinless fermions on a one-dimensional lattice. The density
functional is implicitly represented by a neural network, which predicts,
besides the ground-state energy and density distribution, density-density
correlation functions. At no point do we require a band structure
interpretation. The training data, obtained via exact diagonalization, feeds
into a learning scheme inspired by active learning, which minimizes the
computational costs for data generation. We show that the network results are
of high quantitative accuracy and, despite learning on random potentials,
capture both symmetry-breaking and topological phase transitions correctly.Comment: 5 pages, 3 figures; 4+ pages appendi
Creating better superconductors by periodic nanopatterning
The quest to create superconductors with higher transition temperatures is as
old as superconductivity itself. One strategy, popular after the realization
that (conventional) superconductivity is mediated by phonons, is to chemically
combine different elements within the crystalline unit cell to maximize the
electron-phonon coupling. This led to the discovery of NbTi and Nb3Sn, to name
just the most technologically relevant examples. Here, we propose a radically
different approach to transform a `pristine' material into a better (meta-)
superconductor by making use of modern fabrication techniques: designing and
engineering the electronic properties of thin films via periodic patterning on
the nanoscale. We present a model calculation to explore the key effects of
different supercells that could be fabricated using nanofabrication or
deliberate lattice mismatch, and demonstrate that specific pattern will enhance
the coupling and the transition temperature. We also discuss how numerical
methods could predict the correct design parameters to improve
superconductivity in materials including Al, NbTi, and MgB
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