Related papers: Closed Shell States in Periodic Compounds
The angular momentum formalism provides a powerful way to classify atomic states. Yet, requiring a spherical symmetry from the very first line, this formalism cannot be used for periodic systems, even though cubic semiconductor states are…
The quantum states of a system of particles in a finite spatial domain in general consist of a set of discrete energy eigenvalues; these are usually grouped into bunches of degenerate or close-lying levels, called shells. In fermionic…
In this article, we provide a pedagogical review of the theory of topological quantum chemistry and topological crystalline insulators. We begin with an overview of the properties of crystal symmetry groups in position and momentum space.…
Exact conservation of the angular momentum is worked out for an elastic medium with spins. The intrinsic anharmonicity of the elastic theory is shown to be crucial for conserving the total momentum. As a result, any spin-lattice dynamics…
Topological materials are quantum materials with nontrivial ground-state entanglement that are irremovable so long as certain rules, like invariance under symmetries and the existence of an energy gap, are respected. They showcase…
Elementary band representations are the fundamental building blocks of atomic limit band structures. They have the defining property that at partial filling they cannot be both gapped and trivial. Here, we give two examples -- one each in a…
Rotational bands are commonplace in the spectra of atomic nuclei. Inspired by early descriptions of these bands by quadrupole deformations of a liquid drop, Elliott constructed a discrete nucleon representations of $\mathrm{SU}(3)$ from…
A reflection-asymmetric deformed oscillator potential is analysed from the classical and quantum mechanical point of view. The connection between occurrence of shell structures and classical periodic orbits is studied using the ''removal of…
We formulate a quantum coherent state picture for topological and non-topological solitons. We recognize that the topological charge arises from the infinite occupation number of zero momentum quanta flowing in one direction. Thus, the…
The quest to realize topological band structures in artificial matter is strongly focused on lattice systems, and only quantum Hall physics is known to appear naturally also in the continuum. In this letter, we present a proposal based on a…
It was recently discovered that plasma waves possess topologically protected edge modes, indicating the existence of topologically nontrivial structures in the governing equations. Here we give a rigorous study of the underlying topological…
We show how arbitrary unit cells of periodic materials can be represented as graphs whose nodes represent atoms and whose weighted edges represent tunneling connections between atoms. Further, we present methods to calculate the band…
Isolated electrons resting above a helium surface are predicted to have a bound spectrum corresponding to a one-dimensional hydrogen atom. But in fact, the observed spectrum is closer to that of a quantum-defect atom. Such a model is…
A band gap for electronic states in crystals governs various properties of solids, such as transport, optical and magnetic properties. Its estimation and control have been an important issue in solid state physics. The band gap can be…
In this paper we study static spherically symmetric Einstein-Vlasov shells, made up of equal mass particles, where the angular momentum L of particles takes values only on a discrete finite set. We consider first the case where there is…
The effect of an octupole term in a quadrupole deformed single particle potential is studied from the classical and quantum mechanical view point. Whereas the problem is nonintegrable, the quantum mechanical spectrum nevertheless shows some…
We discuss annular confinement for electrons on liquid helium surface induced by a tubular electrode submerged beneath the surface. For shallow liquid layer above the tube the resulting potential has a minimum off the axis of the tube. The…
We explain the dynamics of cold atoms, initially trapped and cooled in a magneto-optic trap, in a monochromatic stationary standing electromagnetic wave field. In the large detuning limit the system is modeled as a nonlinear quantum…
We derive general results for the mass shift of bound states with angular momentum l >= 1 in a periodic cubic box in two and three spatial dimensions. Our results have applications to lattice simulations of hadronic molecules, halo nuclei,…
We show that the spectrum of orbital angular momentum in quantum mechanics consists of two parts when the underlying space has periodic boundaries. While the first part consists of the usual textbook integer quantized values, the second is…