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Kinetic energy (KE) functional is crucial to speed up density functional theory calculation. However, deriving it accurately through traditional physics reasoning is challenging. We develop a generally applicable KE functional estimator for a one-dimensional (1D) extended system using a machine learning method. Our end-to-end solution combines the dimensionality reduction method with the Gaussian process regression, and simple scaling method to adapt to various 1D lattices. In addition to reaching chemical accuracy in KE calculation, our estimator also performs well on KE functional derivative prediction. Integrating this machine learning KE functional into the current orbital free density functional theory scheme is able to provide us with expected ground state electron density.

There is a long-standing confusion concerning the physical origin of the anomalous resistivity peak in transition metal pentatelluride HfTe5. Several mechanisms, such as the formation of charge density wave or polaron, have been proposed, but so far no conclusive evidence has been presented. In this work, we investigate the unusual temperature dependence of magneto-transport properties in HfTe5. It is found that a three-dimensional topological Dirac semimetal state emerges only at around Tp (at which the resistivity shows a pronounced peak), as manifested by a large negative magnetoresistance. This accidental Dirac semimetal state mediates the topological quantum phase transition between the two distinct weak and strong topological insulator phases in HfTe5. Our work not only provides the first evidence of a temperature-induced critical topological phase transition in HfTe5 but also gives a reasonable explanation on the long-lasting question.

Angle-resolved photoemission spectroscopy is performed to study the bulk and surface electronic structures of nonsuperconducting IrTe2 and superconducting Pt0.05Ir0.95Te2. In addition to the bulk electronic bands predicted by the local density approximation calculations, we observe two Dirac cone-like bands at the Brillouin zone center, which are non-dispersive along kz, suggesting that the extra bands are surface state bands. As the experimental results are well consistent with the ab initio calculations of surface states, the parity analysis proves that these surface state bands are topologically trivial and thus exclude (PtxIr1−x)Te2 as a possible topological superconductor candidate.

Stochastic analytic continuation is an excellent numerical method for analytically continuing Green's functions from imaginary frequencies to real frequencies, although it requires significantly more computational time than the traditional MaxEnt method. We develop an alternate implementation of stochastic analytic continuation which expands the dimensionless field n(x) introduced by Beach using orthogonal polynomials. We use the kernel polynomial method (KPM) to control the Gibbs oscillations associated with truncation of the expansion in orthogonal polynomials. Our KPM variant of stochastic analytic continuation delivers improved precision at a significantly reduced computational cost.