Related papers: Electrons in deterministic quasicrystalline potent…
We investigate the physics of quasicrystalline models in the presence of a uniform magnetic field, focusing on the presence and construction of topological states. This is done by using the Hofstadter model but with the sites and couplings…
Quasicrystals lack translational symmetry, but can still exhibit long-ranged order, promoting them to candidates for unconventional physics beyond the paradigm of crystals. Here, we apply a real-space functional renormalization group…
New trial wave functions corresponding to half filling quantum Hall states are proposed. These wave functions are constructed by first pairing up the quasielectrons of the 1/3 Laughlin quantum Hall state, with the same relative angular…
Quasicrystals possess long-range order but lack the translational symmetry of crystalline solids. In solid state physics, periodicity is one of the fundamental properties that prescribes the electronic band structure in crystals. In the…
Analytic and numerical results for quasiperiodic tight-binding models are reviewed, with emphasis on two and three-dimensional models which so far are beyond a mathematically rigorous treatment. In particular, we consider energy spectra of…
We demonstrate that in semiconductor quantum dots wave functions probed by imaging techniques based on local tunneling spectroscopies like STM show characteristic signatures of electron-electron Coulomb correlation. We predict that such…
Relations between particle and wave properties for charge carriers in periodic potentials of crystalline metals and semiconductors are derived. The particle aspects of electrons and holes in periodic potentials are considered using…
We study electronic eigenstates on quasiperiodic lattices using a tight-binding Hamiltonian in the vertex model. In particular, the two-dimensional Penrose tiling and the three-dimensional icosahedral Ammann-Kramer tiling are considered.…
Electrons in quasicrystals generically possess critical wave functions that are neither exponentially-localized nor extended, but rather decay algebraically in space. Nevertheless, motivated by recent calculations on the square and cubic…
Our understanding of physical properties of quasicrystals owes a great deal to studies of tight-binding models constructed on quasiperiodic tilings. Among the large number of possible quasiperiodic structures, two dimensional tilings are of…
We show that in quantum dots the physical quantities probed by local tunneling spectroscopies, namely the quasi-particle wavefunctions of interacting electrons, can considerably deviate from their single-particle counterparts as an effect…
By introducing concepts of beam shaping into quantum mechanics, we show how interference effects of the quantum wavefunction describing multiple electrons can exactly balance the repulsion among the electrons. With proper shaping of the…
We study the percolation of a quantum particle on quasicrystal lattices and compare it with the square lattice. For our study, we have considered quasicrystal lattices modelled on the pentagonally symmetric Penrose tiling and the…
The interplay between interactions and topology in quantum materials is of extensive current interest. Strong correlations are known to be important for insulating topological states, as exemplified by the fractional quantum Hall effect.…
We develop a method to design tunable quasiperiodic structures of particles suspended in a fluid by controlling standing acoustic waves. One application of our results is to ultrasound directed self-assembly, which allows fabricating…
The single-particle spectral function for an incompressible fractional quantum Hall state in the presence of a scalar short-ranged attractive impurity potential is calculated via exact diagonalization within the spherical geometry. In…
Quantum embedding theories are promising approaches to investigate strongly-correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We…
We investigate the properties of electronic states in two and three-dimensional quasiperiodic structures: the generalized Rauzy tilings. Exact diagonalizations, limited to clusters with a few thousands sites, suggest that eigenstates are…
This paper describes how one can use four standing wave laser fields to realize a two dimensional optical quasicrystal with eight-fold symmetry, closely related to the well-known octagonal or Ammann-Beenker tiling quasicrystal. We describe…
A basic theoretical framework is developed in which elementary particles have a component of their wave function extending into higher spatial dimensions. This model postulates an extension of the Schrodinger equation to include a 4th and…