We present a minimalistic equilateral triangular lattice model, from which we derive electron and exciton band structures for semiconducting transition-metal dichalcogenides. With explicit consideration of the exchange interaction, this model is appropriate across the spectrum from Wannier to Frenkel excitons. The single-particle contributions are obtained from a nearest-neighbor tight-binding model parameterized using the effective mass and spin-orbit coupling. The solutions to the characteristic equation, computed in direct space, are in qualitative agreement with first-principles calculations and highlight the inadequacy of the two-dimensional hydrogen model to describe the lowest-energy exciton bands. The model confirms the lack of subshell degeneracy and shows that the A-B exciton split depends on the electrostatic environment as well as the spin-orbit interaction.
With the ever-growing interest in quantum computing, understanding the behaviour of excitons in monolayer quantum dots has become a topic of great relevance. In this paper, we consider a Wannier exciton confined in a triangular quantum dot of hexagonal Boron Nitride. We begin by outlining the adequate basis functions to describe a particle in a triangular enclosure, analyzing their degeneracy and symmetries. Afterwards, we discuss the excitonic hamiltonian inside the quantum dot and study the influence of the quantum dot dimensions on the excitonic states.
Dirac particles, massless relativistic entities, obey linear energy dispersions and hold important implication in particle physics. Recent discovery of Dirac fermions in condensed matter systems including graphene and topological insulators raises great interests to explore relativistic properties associated with Dirac physics in solid-state materials. In addition, there are stimulating research activities to engineer Dirac paricles to eludicte their physical properties in a controllable setting. One of the successful platforms is the ultracold atom-optical lattice system, whose dynamics can b…
Excitonic properties in the Kagome lattice system, which is produced by quantum wires on semiconductor surfaces, are investigated by using the exact diagonalization of a tight binding model. It is shown that due to the existence of flat bands the binding energy of exciton becomes remarkably large in the two-dimensional Kagome lattice compared to that in one-dimensional lattice, and the exciton Bohr radius is quite small as large as a lattice constant. We also discuss the magnetic field effects on the exciton binding energy and the stability of exciton against the creation of charged exciton an…
We study transport of indirect excitons in GaAs/AlGaAs coupled quantum wells in linear lattices created by laterally modulated gate voltage. The localization-delocalization transition (LDT) for transport across the lattice was observed with reducing lattice amplitude or increasing exciton density. The exciton interaction energy at the transition is close to the lattice amplitude. These results are consistent with the model, which attributes the LDT to the interaction-induced percolation of the exciton gas through the external potential. We also discuss applications of the lattice potentials fo…
We report a two-dimensional artificial lattice for dipolar excitons confined in a GaAs double quantum well. Exploring the regime of large fillings per lattice site, we verify that the lattice depth competes with the magnitude of excitons repulsive dipolar interactions to control the degree of localisation in the lattice potential. Moreover, we show that dipolar excitons radiate a narrow-band photoluminescence, with a spectral width of a few hundreds of micro-eV at 340 mK, in both localised and delocalised regimes. This makes our device suitable for explorations of dipolar excitons quasi-conden…
We report on a method for the realization of two-dimensional electrostatic lattices for excitons using patterned interdigitated electrodes. Lattice structure is set by the electrode pattern and depth of the lattice potential is controlled by applied voltages. We demonstrate square, hexagonal, and honeycomb lattices created by this method.
The effects of substrate on electronic and optical properties of triangular and hexagonal graphene nanoflakes with armchair edges are investigated by using a configuration interaction approach beyond double excitation scheme. The quasiparticle correction to the energy gap and exciton binding energy are found to be dominated by the long-range Coulomb interactions and exhibit similar dependence on the dielectric constant of the substrate, which leads to a cancellation of their contributions to the optical gap. As a result, the optical gaps are shown to be insensitive to the dielectric environmen…
Moiré superlattices formed in van der Waals bilayers have enabled the creation and manipulation of new quantum states, as is exemplified by the discovery of superconducting and correlated insulating states in twisted bilayer graphene near the magic angle. Twisted bilayer semiconductors may lead to tunable exciton lattices and topological states, yet signatures of moiré excitons have been reported only in closely angularly-aligned bilayers. Here we report tuning of moiré lattice in WS$_{2}$ /MoSe$_{2}$ bilayers over a wide range of twist angles, leading to the continuous tuning of moiré lattice…
We investigate the interaction of excitons in a two dimensional lattice and photons in a planar cavity in the presence of disorder. The strong exciton-photon coupling is described in terms of polariton quasi-particles, which are scattered by a disorder potential. We consider three kinds of disorder: (a) inhomogeneous exciton energy, (b) inhomogeneous exciton-photon coupling and (c) deviations from an ideal lattice. These three types of disorder are characteristic of different physical systems, and their separate analysis gives insight on the competition between randomness and light-matter coup…
We present a method for determining correlations in a gas of indirect excitons in a semiconductor quantum well structure. The method involves subjecting the excitons to a periodic electrostatic potential that causes modulations of the exciton density and photoluminescence (PL). Experimentally measured amplitudes of energy and intensity modulations of exciton PL serve as an input to a theoretical estimate of the exciton correlation parameter and temperature. We also present a proof-of-principle demonstration of the method for determining the correlation parameter and discuss how its accuracy ca…
We propose a way to directly excite compact localized condensates in a nearly flat band of the exciton-polariton Lieb lattice by short Laguerre-Gaussian pulses and investigate the dynamics of these condensates in the presence of repulsive polariton-polariton interaction and distributed losses in the lattice. The evolution of a low-density compact polariton condensate shows fast Rabi oscillations between its excitonic and photonic components, with slow beatings of the Rabi oscillation amplitude. Both oscillations and beatings are suppressed at higher condensate densities due to polariton-polari…
We study nonlinear dynamics of exciton-polaritons in an incoherently pumped semiconductor microcavity with embedded weak-contrast lattice and coupled to an exciton reservoir. We elucidate fundamental features of non-equilibrium exciton-polariton condensate trapped in one-dimensional periodical potential close to zero momentum (so-called "Zero-state") and to the state at the boundary of Brillouin zone ("$π$-state"). Within the framework of the mean-field theory, we identify different regimes of both relaxation and oscillatory dynamics of coherent exciton-polaritons governed by superpositions of…
We describe the possibility for topologically robust edge states existing on interfaces of triangular lattices which are supported by rotational symmetries that are sensitive to boundary conditions. Such states are trivial from the perspective of Berry curvature, but result instead from an interplay between crystalline symmetries and finite boundary effects. Regardless, we show such states are in a distinct topological phase, provided the gauge-dependent symmetries are maintained. Such a model describes a number of recent bosonic experimental demonstrations on triangular lattices, the physics …
In the present paper, the mean of Lyapunov exponents for the Azbel-Hofstadter model on the triangular lattice is calculated. It is recently proposed that [Phys. Rev. Lett. {\bf 85}, 4920 (2000)], for the case of the square lattice, this quantity can be related to the logarithm of the partition function of the two dimensional Ising model and has a connection to the asymptotic bandwidth. We find that the correspondence of this quantity to the logarithm of the partition function of the two dimensional Ising model is not complete for the triangular lattice. Moreover, the detailed connection betwee…
The microwave (MW) photoresistance has been measured on a high-mobility two-dimensional electron gas patterned with a shallow triangular antidot lattice, where both the MW-induced resistance oscillations (MIRO) and magnetoplasmon (MP) resonance are observed superposing on sharp commensurate geometrical resonance (GR). Analysis shows that the MIRO, MP, and GR are decoupled from each other in these experiments.
Pristine graphene is a semimetal and thus does not have a band gap. By making a nanometer scale periodic array of holes in the graphene sheet a band gap may form; the size of the gap is controllable by adjusting the parameters of the lattice. The hole diameter, hole geometry, lattice geometry and the separation of the holes are parameters that all play an important role in determining the size of the band gap, which, for technological applications, should be at least of the order of tenths of an eV. We investigate four different hole configurations: the rectangular, the triangular, the rotated…
A simple method to create and control magnetic potentials onto coupled quantum wells is demonstrated for indirect-exciton magnetic confinement. Localized inhomogeneous magnetic potentials with periodically distributed local minima and maxima, known as magnetic lattices, are projected into the plane of the coupled quantum wells and used for the spatially distributed two-dimensional indirect-exciton trapping, in which case localized indirect-excitons are observed. The indirect-exciton trapping mechanism is examined by controlling external magnetic field bias resulting in a shift of the localized…
Rotational excitation of polar molecules trapped in an optical lattice gives rise to rotational excitons. Here we show that non-linear interactions of such excitons can be controlled by an electric field. The exciton--exciton interactions can be tuned to induce exciton pairing, leading to the formation of biexcitons. Tunable non-linear interactions between excitons can be used for many applications ranging from the controlled preparation of entangled quasiparticles to the study of polaron interactions and the effects of non-linear interactions on quantum energy transport in molecular aggregate…
The concept of quantum plasmonic excitations in plasmonic lattices, which similarly to Frenkel excitons in molecular crystals propagate by hopping from one nanoparticle to another, is introduced. A consistent quantum theory of such plasmonic excitons, beginning with the quantization of localized surface plasmons in a metal nanoparticle and including the radiative relaxation in both 1D and 2D lattices near a reflective substrate surface, is developed. A possible room-temperature Bose-Einstein condensation in the quantum gas of plasmonic excitons is also discussed.
Dark and bright excitons are shown to appear naturally in a linear atomic super-lattice with two atoms per unit cell. In bringing the super-lattice into a strong coupling regime with a one-dimensional nanophotonic waveguide, bright excitons and photons are coherently mixed to form polaritons. Treating excitons as bosons implies a mechanism that forbids two excitations from being at the same atomic state, which is included here through a bosonization procedure with kinematic interactions. Interestingly these interactions couple dark and bright excitons, and which we exploit as a new tool for ex…
In the present work we discuss the propagation of excitons across a one-dimensional Su-Schrieffer-Heeger lattice, which possesses both harmonic oscillations and weak quartic anharmonicities. When quantizing these vibrational degrees of freedom we identify several phonon-conserving nonlinearities, each one with a different impact on the excitonic transport. Our analysis identifies a dominant nonlinear correction to the phonon hopping which leads to a strong enhancement of exciton conduction compared to a purely linear vibrational dynamics. Thus quartic lattice nonlinearities can be exploited to…
We propose a new model to implement organic exciton-semiconductor exciton hybridization by embedding a semiconductor quantum dot array into an organic medium. A Wannier-Mott transfer exciton is formed when the exciton in each semiconductor dot interacts via the multipole-multipole coupling with other excitons in the different dtos of the array. A new hybrid exciton appears in the system owing to strong dipole-dipole interaction of the Frenkel exciton of the organic molecules with the Wannier Mott transfer exciton of the quantum dot array. This hybrid exciton has both a large oscillator strengt…
We report resonant Raman spectroscopy of neutral excitons X$^0$ and intravalley trions X$^-$ in hBN-encapsulated MoS$_2$ monolayer embedded in a nanobeam cavity. By temperature tuning the detuning between Raman modes of MoS$_2$ lattice phonons and X$^0$/X$^-$ emission peaks, we probe the mutual coupling of excitons, lattice phonons and cavity vibrational phonons. We observe an enhancement of X$^0$-induced Raman scattering and a suppression for X$^-$-induced, and explain our findings as arising from the tripartite exciton-phonon-phonon coupling. The cavity vibrational phonons provide intermedia…
We show theoretically that a lattice of exciton-polaritons can behave as a life-like cellular automaton when simultaneously excited by a continuous wave coherent field and a time-periodic sequence of non-resonant pulses. This provides a mechanism of realizing a range of highly sought spatiotemporal structures under the same conditions, including: discrete solitons, oscillating solitons, rotating solitons, breathers, soliton trains, guns, and choatic behaviour. These structures can survive in the system indefinitely, despite the presence of dissipation, and allow universal computation.
Bose-Einstein condensation in strongly correlated lattices provides the possibility to coherently generate macroscopic quantum states, which have attracted tremendous attention as ideal platforms for quantum simulation. Ultracold atoms in optical lattices are one of such promising systems, where their realizations of different phases of matter exhibit promising applications in condensed matter physics, chemistry, and cosmology. Nevertheless, this is only accessible with ultralow temperatures in the nano to micro Kelvin scale set by the typical inverse mass of an atom. Alternative systems such …
We study the Kondo Lattice and Hubbard models on a triangular lattice for band filling factor 3/4. We show that a simple non-coplanar chiral spin ordering (scalar spin chirality) is naturally realized in both models due to perfect nesting of the Fermi surface. The resulting triple-Q magnetic ordering is a natural counterpart of the collinear Neel ordering of the half-filled square lattice Hubbard model. We show that the obtained chiral phase exhibits a spontaneous quantum Hall-effect with sigma_{xy}= e^2/h.
We investigate topological states of two-dimensional (2D) triangular lattices with multi-orbitals. Tight-binding model calculations of a 2D triangular lattice based on $\emph{p}_{x}$ and \emph{p}_{y} orbitals exhibit very interesting doubly degenerate energy points at different positions ($Γ$ and K/K$^{\prime}$) in momentum space, with quadratic non-Dirac and linear Dirac band dispersions, respectively. Counterintuitively, the system shows a global topologically trivial rather than nontrivial state with consideration of spin-orbit coupling due to the "destructive interference effect" between t…
Engineering non-linear hybrid light-matter states in tailored optical lattices is a central research strategy for the simulation of complex Hamiltonians. Excitons in atomically thin crystals are an ideal active medium for such purposes, since they couple strongly with light and bear the potential to harness giant non-linearities and interactions while presenting a simple sample-processing and room temperature operability. We demonstrate lattice polaritons, based on an open, high-quality optical cavity, with an imprinted photonic lattice strongly coupled to excitons in a WS$_{2}$ monolayer. We …
Excitons with a radius of a few lattice constants can be affected by strong central-cell corrections, leading to significant deviations of the optical spectrum from the hydrogen-like Rydberg series, and also to an enhancement of the exciton mass. We present an approach to this situation based on a lattice model that incorporates the effects of a non-parabolic band structure, short distance corrections to the Coulomb interaction between electrons and holes, spin-orbit and exchange coupling. The lattice model allows for observation of the crossover from large radius Wannier to small radius Frenk…
A harmonic triangular lattice with a vacancy under imposed volumetric strain is considered. Simple asymptotic formula for the displacement field is derived. The formula has reasonable accuracy at all lattice nodes. Strain concentration factor, defined as the ratio of the maximal deformation of the bonds adjacent to the vacancy to the deformations of bonds at infinity, is calculated. It is shown that the asymptotic formula predicts the strain concentration factor with 4% accuracy. The results are compared with predictions of continuum elasticity theory. Effective diameter of the vacancy is calc…
We propose a tight binding model for the quantum spin Hall system on triangular optical lattice and we determined the edge state spectrum which contains gap traversing states as the hallmark of $\mathds{Z}_{2}$ topological insulator. The advantage of this system is the possibility of implementing it in the fermionic ultracold atomic system whose nearly free electron limit is proposed by B. Béri and N. R. Cooper, Phys. Rev. Lett. {\bf 107}, 145301 (2011).
