Browsing by Subject "Tight-binding model"
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Item Open Access Geometric band properties in strained monolayer transition metal dichalcogenides using simple band structures(American Institute of Physics, 2019) Aas, Shahnaz; Bulutay, CeyhunMonolayer transition metal dichalcogenides (TMDs) bare large Berry curvature hotspots readily exploitable for geometric band effects. Tailoring and enhancement of these features via strain is an active research direction. Here, we consider spinless two- and three-band and spinful four-band models capable to quantify the Berry curvature and the orbital magnetic moment of strained TMDs. First, we provide a k⋅p parameter set for MoS2, MoSe2, WS2, and WSe2 in the light of the recently released ab initio and experimental band properties. Its validity range extends from the K valley edge to about one hundred millielectron volts into valence and conduction bands for these TMDs. To expand this over a larger part of the Brillouin zone, we incorporate strain to an available three-band tight-binding Hamiltonian. With these techniques, we demonstrate that both the Berry curvature and the orbital magnetic moment can be doubled compared to their intrinsic values by applying typically a 2.5% biaxial tensile strain. These simple band structure tools can find application in the quantitative device modeling of the geometric band effects in strained monolayer TMDs.Item Open Access Perpendicular space accounting of localized states in a quasicrystal(American Physical Society, 2020) Mirzhalilov, Murod; Oktel, Mehmet ÖzgürQuasicrystals can be described as projections of sections of higher dimensional periodic lattices into real space. The image of the lattice points in the projected-out dimensions, called the perpendicular space, carries valuable information about the local structure of the real space lattice. In this paper, we use perpendicular space projections to analyze the elementary excitations of a quasicrystal. In particular, we consider the vertex tight-binding model on the two-dimensional Penrose lattice and investigate the properties of strictly localized states using their perpendicular space images. Our method reproduces the previously reported frequencies for the six types of localized states in this model. We also calculate the overlaps between different localized states and show that the number of type-five and type-six localized states which are independent from the four other types is a factor of golden ratio τ=(1+√5)/2 higher than previously reported values. Two orientations of the same type-five or type-six which are supported around the same site are shown to be linearly dependent with the addition of other types. We also show through exhaustion of all lattice sites in perpendicular space that any point in the Penrose lattice is either in the support of at least one localized state or is forbidden by local geometry to host a strictly localized state.Item Open Access Strictly localized states in the octagonal Ammann-Beenker quasicrystal(American Physical Society, 2021-07-06) Oktel, Mehmet ÖzgürAmmann-Beenker lattice is a two-dimensional quasicrystal with eightfold symmetry, which can be described as a projection of a cut from a four-dimensional simple cubic lattice. We consider the vertex tight-binding model on this lattice and investigate the strictly localized states at the center of the spectrum. We use a numerical method based on the generation of finite lattices around a given perpendicular space point and QR decomposition of the Hamiltonian to count the strictly localized states. We apply this method to count the frequency of localized states in lattices of up to 100 000 sites. We obtain an orthogonal set of compact localized states by diagonalizing the position operator projected onto the manifold spanned by the zero-energy states. We identify 20 localized state types and calculate their exact frequencies through their perpendicular space images. Unlike the Penrose lattice, all the localized state types are eightfold symmetric around an eight edge vertex, and all vertex types can support localized states. The total frequency of these 20 types gives a lower bound of fLS=30796−21776√2≃0.08547 for the fraction of strictly localized states in the spectrum. This value is in agreement with the numerical calculation and very close to the recently conjectured exact fraction of localized states fEx=3/2−√2≃0.08579.