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Register a new userCondensed matter realization of fermion quasiparticles in Minkowski space
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What is the difference between space and time? is an ancient question that remains a matter of intense debate. In Newtonian mechanics time is absolute, while in Einsteins theory of relativity time and space combine into Minkowski spacetime. Here, we firstly propose Minkowski fermions in 2+1 dimensional Minkowski spacetime which have two space-like and one time-like momentum axes. These quasiparticles can be further classified as Klein-Gordon fermions and Dirac-Minkowski fermions according to the linearly and quadratically dispersing excitations. Realization of Dirac-Minkowski quasiparticles requires systems with particular topological nodal-line band degeneracies, such as hyperbolic nodal lines or coplanar band crossings. With the help of first-principles calculations we find that novel massless Dirac-Minkowski fermions are realized in a metastable bulk boron allotrope, Pnnm-B16.
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The electronic density of states (DOS) quantifies the distribution of the energy levels that can be occupied by electrons in a quasiparticle picture, and is central to modern electronic structure theory. It also underpins the computation and interpretation of experimentally observable material properties such as optical absorption and electrical conductivity. We discuss the challenges inherent in the construction of a machine-learning (ML) framework aimed at predicting the DOS as a combination of local contributions that depend in turn on the geometric configuration of neighbours around each atom, using quasiparticle energy levels from density functional theory as training data. We present a challenging case study that includes configurations of silicon spanning a broad set of thermodynamic conditions, ranging from bulk structures to clusters, and from semiconducting to metallic behavior. We compare different approaches to represent the DOS, and the accuracy of predicting quantities such as the Fermi level, the DOS at the Fermi level, or the band energy, either directly or as a side-product of the evaluation of the DOS. The performance of the model depends crucially on the smoothening of the DOS, and there is a tradeoff to be made between the systematic error associated with the smoothening and the error in the ML model for a specific structure. We demonstrate the usefulness of this approach by computing the density of states of a large amorphous silicon sample, for which it would be prohibitively expensive to compute the DOS by direct electronic structure calculations, and show how the atom-centred decomposition of the DOS that is obtained through our model can be used to extract physical insights into the connections between structural and electronic features.
The spin-3/2 elementary particle, known as Rarita-Schwinger (RS) fermion, is described by a vector-spinor field {psi}_{{mu}{alpha}}, whose number of components is larger than its independent degrees of freedom (DOF). Thus the RS equations contain nontrivial constraints to eliminate the redundant DOF. Consequently the standard procedure adopted in realizing relativistic spin-1/2 quasi-particle is not capable of creating the RS fermion in condensed matter systems. In this work, we propose a generic method to construct a Hamiltonian which implicitly contains the RS constraints, thus includes the eigenstates and energy dispersions being exactly the same as those of RS equations. By implementing our 16X16 or 6X6 Hamiltonian, one can realize the 3 dimensional or 2 dimensional (2D) massive RS quasiparticles, respectively. In the non-relativistic limit, the 2D 6X6 Hamiltonian can be reduced to two 3X3 Hamiltonians which describe the positive and negative energy parts respectively. Due to the nontrivial constraints, this simplified 2D massive RS quasiparticle has an exotic property: it has vanishing orbital magnetic moment while its orbital magnetization is finite. Finally, we discuss the material realization of RS quasiparticle. Our study provides an opportunity to realize higher spin elementary fermions with constraints in condensed matter systems.
The quantum many-body problem in condensed phases is often simplified using a quasiparticle description, such as effective mass theory for electron motion in a periodic solid. These approaches are often the basis for understanding many fundamental condensed phase processes, including the molecular mechanisms underlying solar energy harvesting and photocatalysis. Despite the importance of these effective particles, there is still a need for computational methods that can explore their behavior on chemically relevant length and time scales. This is especially true when the interactions between the particles and their environment are important. We introduce an approach for studying quasiparticles in condensed phases by combining effective mass theory with the path integral treatment of quantum particles. This framework incorporates the generally anisotropic electronic band structure of materials into path integral simulation schemes to enable modeling of quasiparticles in quantum confinement, for example. We demonstrate the utility of effective mass path integral simulations by modeling an exciton in solid potassium chloride and electron trapping by a sulfur vacancy in monolayer molybdenum disulfide.
Materials characterization remains a significant, time-consuming undertaking. Generally speaking, spectroscopic techniques are used in conjunction with empirical and ab-initio calculations in order to elucidate structure. These experimental and computational methods typically require significant human input and interpretation, particularly with regards to novel materials. Recently, the application of data mining and machine learning to problems in material science have shown great promise in reducing this overhead. In the work presented here, several aspects of machine learning are explored with regards to characterizing a model material, titania, using solid-state Nuclear Magnetic Resonance (NMR). Specifically, a large dataset is generated, corresponding to NMR $^{47}$Ti spectra, using ab-initio calculations for generated TiO$_2$ structures. Principal Components Analysis (PCA) reveals that input spectra may be compressed by more than 90%, before being used for subsequent machine learning. Two key methods are used to learn the complex mapping between structural details and input NMR spectra, demonstrating excellent accuracy when presented with test sample spectra. This work compares Support Vector Regression (SVR) and Artificial Neural Networks (ANNs), as one step towards the construction of an expert system for solid state materials characterization.
Semilocal density functionals for the exchange-correlation energy are needed for large electronic systems. The Tao-Perdew-Staroverov-Scuseria (TPSS) meta-generalized gradient approximation (meta-GGA) is semilocal and usefully accurate, but predicts too-long lattice constants. Recent GGAs for solids yield good lattice constants but poor atomization energies of molecules. We show that the construction principle for one of them (restoring the density gradient expansion for exchange over a wide range of densities) can be used to construct a revised TPSS meta-GGA with accurate lattice constants, surface energies, and atomization energies for ordinary matter.
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