Related papers: The Hofstadter Spectrum and Photoluminescence
We develop a theory of photoluminescence using a time-dependent Hartree-Fock approximation that is appropriate for the two-dimensional Wigner crystal in a strong magnetic field. The cases of localized and itinerant holes are both studied.…
Motivated by recent experiments on radiative recombination of two-dimensional electrons in acceptor doped GaAs-AlGaAs heterojunctions as well as the success of a harmonic solid model in describing tunneling between two-dimensional electron…
We study the theory of itinerant-hole photoluminescence of two-dimensional electron systems in the regime of the magnetically induced Wigner crystal. We show that the exciton recombination transition develops structure related to the…
Recently, the Hofstadter spectrum of a twisted $\mathrm{WSe_2/MoSe_2}$ heterobilayer has been observed in experiment [C. R. Kometter, et al. Nat.Phys.19, 1861 (2023)], but the origin of Hofstadter states remains unclear. Here, we present a…
Electrons moving through a spatially periodic lattice potential develop a quantized energy spectrum consisting of discrete Bloch bands. In two dimensions, electrons moving through a magnetic field also develop a quantized energy spectrum,…
We develop a method to compute shakeup effects on photoluminescence from a strong magnetic field induced two-dimensional Wigner crystal. Only localized holes are considered. Our method treats the lattice electrons and the tunneling electron…
At very low density, the electrons in a uniform electron gas spontaneously break symmetry and form a crystalline lattice called a Wigner crystal. But which type of crystal will the electrons form? We report a numerical study of the density…
We study the effects of the Coulomb interactions between electrons on the Hofstadter butterfly, which characterizes the subband structure of the Landau levels of a two-dimensional electron gas in a perpendicular homogeneous magnetic field…
We study the spectral properties of a system of electrons interacting through long-range Coulomb potential on a one-dimensional chain. When the interactions dominate over the electronic bandwidth, the charges arrange in an ordered…
When the Coulomb repulsion between electrons dominates over their kinetic energy, electrons in two dimensional systems were predicted to spontaneously break continuous translation symmetry and form a quantum crystal. Efforts to observe this…
Hofstadter's butterfly, the predicted energy spectrum for non-interacting electrons confined to a two-dimensional lattice in a magnetic field, is one of the most remarkable fractal structures in nature. At rational ratios of magnetic flux…
We show that the photonic analogue of the Korringa-Kohn-Rostocker method is a viable alternative to the plane-wave method to analyze the spectrum of electromagnetic waves in a three-dimensional periodic dielectric lattice. Firstly, in the…
The studies of quantum states and optics in a {\it p}-type heterojunction with lateral surface quantum dot (antidot) superlattice and in the presence of perpendicular magnetic field are performed. For the first time the Azbel'-- Hofstadter…
The energy spectrum of a two-dimensional electron gas (2DEG) interacting with a valence-band hole is studied in the high magnetic field limit as a function of the filling factor nu and the separation d between the electron and hole layers.…
Eugene Wigner predicted long ago that when the Coulomb interactions between electrons become much stronger than their kinetic energy, electrons crystallize into a closely packed lattice. A variety of two-dimensional systems have shown…
We introduce a grating assisted tunneling scheme for tunable synthetic magnetic fields in photonic lattices, which can be implemented at optical frequencies in optically induced one- and two-dimensional dielectric photonic lattices. We…
We develop a method to compute shakeup effects on photoluminescence in a Wigner crystal from localized holes. Our method treats the lattice electrons and the tunneling electron on an equal footing, and uses a quantum-mechanical calculation…
The Hofstadter model allows to describe and understand several phenomena in condensed matter such as the quantum Hall effect, Anderson localization, charge pumping, and flat-bands in quasiperiodic structures, and is a rare example of…
The photoluminescence (PL) spectrum of a two-dimensional electron gas (2DEG) in the fractional quantum Hall regime is studied as a function of the separation $d$ between the electron and valence hole layers. The abrupt change in the…
Van der Waals heterostructures, which explore the synergetic properties of two-dimensional (2D) materials when assembled into three-dimensional stacks, have already brought to life a number of exciting new phenomena and novel electronic…