Wannier-Mott Excitons Research Articles

Optical Tamm states for the fabrication of polariton lasers

We propose to embed the ultrathin layer of an organic or inorganic material at the boundary between two specially designed periodic dielectric structures in order to achieve the strong coupling between Frenkel or Wannier-Mott excitons and optical Tamm states localized at the interface. This would allow the fabrication of polariton lasers without microcavities that could be easier from the technological point of view. Analytical formulas are given for the energies of optical Tamm states and the constant of their coupling to excitons.

ENERGY SPECTRUM OF MOTT–WANNIER EXCITON STUDIED BY VIRTUE OF THE EXCITON ENTANGLED STATE REPRESENTATION INSTEAD OF K·P PERTURBATION THEORY

We introduce the exciton entangled state. We show that the energy spectrum of Mott–Wannier exciton can be exactly derived by virtue of the entangled state representation. In contrast to the K · P perturbation theory this new approach seems non-perturbative, direct and exact.

Exciton–polaritons in nanostructured nitride superlattices

In this work we study the propagation of exciton–polaritons (bulk and surface modes) in a binary superlattice ABAB…, truncated at z=0, where z is defined as the growth axis. Here A is the spatially dispersive medium, which alternates with a common dielectric medium B (sapphire-Al2O3). The excitonic medium (A) is modelled by a semiconductor from the nitride's family (III–V semiconductor) that has, as a main characteristic, a wide-direct gap. The exciton-polariton spectrum is determined, in both s and p-polarization, by using standard electromagnetic boundary conditions, together with an additional boundary condition (ABC) for the Wannier–Mott excitons, employing a transfer-matrix formalism to simplify the algebra. The dispersion relation shows a bottleneck profile for the superlattice modes, whose behavior is similar to those found in the bulk crystal. Furthermore, interesting properties are revealed from the ABC as well as from different ratios of the thickness of the two superlattices alternating materials.

Interaction of quantum well excitons with a resonant localized excitation

We consider Wannier-Mott exciton in a semiconductor quantum well coupled via Coulomb interaction to a resonant localized excitation (a luminescent molecule or a quantum dot) placed nearby. As a result, the localized excitation can decay into the quantum well, which can be used for indirect pumping of Wannier excitons. On the other hand, Wannier excitons are scattered, and the scattering can be elastic or inelastic, depending on the strength of the dissipation in the molecule. We also show how the inelastic scattering transforms into the F\"orster picture of energy transfer when many molecules (quantum dots) with strong intrinsic dissipation are present.

The model of ultrafast light-induced insulator-metal phase transition in vanadium oxide

Ultrafast light-induced insulator-metal phase transitions (IM PT) in VO2 thin films was studied with use of a pump-probe technique. These studies show that the IM PT could be realized via an intermediate state. The relaxation processes after optical pumping are dependent on pump energy. The excitonic controlled model for such type of IM PT is proposed on this basis. The main channel for the ultrafast light-induced IM PT is the resonant transition between excited states of correlated vibronic Wannier-Mott excitons (WME) in insulator phase and the unoccupied excited states in metallic phase. The experiment observation, such as pump power drastic dependences of relaxation could be interpreted in the framework of the model.

On dispersion relations for optical media with spatial dispersion

An estimate of the ratio of the contributions of relativistic and nonrelativistic factors to the Kramers-Kronig relations for a medium with spatial dispersion is performed in a form taking into account the relativistic requirement of the finiteness of the velocity of propagation of a signal. Even under conditions of comparatively strong spatial dispersion, in the case of Wannier-Mott excitons in typical semiconductors, this ratio proves to be very small—of the order of 10−4, which justifies the conventional (nonrelativistic) form of the dispersion relations.

Michael Dudley Sturge

Michael Dudley Sturge, best known for his contributions to solid-state spectroscopy, died of leukemia on 13 July 2003 in Castleton, England.Born on 25 May 1931 in Bristol, England, Michael obtained his BA in engineering and physics (1952) and his PhD in physics (1957) at Cambridge University, where he worked on superconductors under Brian Pippard. After two years at Philips Labs outside London, Michael moved to the Royal Radar Establishment in Malvern, where he published, in Physical Review, his paper on the spectroscopy of gallium arsenide. That work included GaAs band structure parameters (most timely for the GaAs laser, invented in the same year) and the first observation of Wannier–Mott excitons in a III–V semiconductor. The paper became a citation classic and brought him international recognition.In 1961, Michael joined Bell Labs in Murray Hill, New Jersey. During his more than 20 years as a member of the technical staff, he grew into one of the leading experts on the optical properties of semiconductors and commanded a tremendous level of respect within that highly skilled community. His expertise, intense level of scientific curiosity, and personal and scientific integrity attracted many young scientists to Bell Labs, and he became a cherished mentor to many of them.In 1984, Michael joined Bell Communication Research in Murray Hill, an R&D firm that had split from Bell Labs. Two years later, he became a professor of physics at Dartmouth College.Michael first worked on the spec-troscopy of transition-metal ions in crystals, basic solid-state laser materials. By combining optical and electron paramagnetic resonance spectro-scopies, he identified the role of the dynamic Jahn–Teller effect in ion-level splitting and the collective Jahn–Teller effect in phase transitions of rare-earth perovskites. In the mid-1970s, Michael returned to the fundamental optical properties of semiconductors. He studied the excited states of excitons bound to isoelectronic nitrogen pairs in bulk gallium phosphide and classified them using the model of a tightly trapped electron and a hole orbiting the pair. When the interest of the semiconductor community turned to quantum wells and superlattices, he studied transport and cyclotron resonance in two-dimensional electron systems and participated in the discovery of minigaps in metal-oxide-semiconductor field effects and in the initial experiments on modulation-doped superlattices. In the early 1980s, Michael made important contributions to the spectroscopy of disordered semiconductor systems. By combining experiments of luminescence, resonant Rayleigh scattering, hole burning, and transient grating spectroscopy, he found clear evidence for a mobility gap in the spectrum of excitons in quantum wells. He also discovered a new type of exciton in short-period superlattices, which is indirect in both real and reciprocal spaces, and electric-field controlled switching between the direct and indirect band structures. Michael’s last work was on trions, complexes of a hole and two electrons similar to H− ions. He discovered a puzzling abrupt changeover in the magnetoluminescence from free-particle to bound-particle behavior when the lower electron Landau level becomes just filled. That observation proved that a “hidden symmetry,” known for strong magnetic fields, surprisingly manifests itself in moderate-to-weak fields.Michael always set the highest standards for his work. He perceived science in its unity and applied that approach when composing, with one of us (Rashba), the volume Excitons (North-Holland, 1982), which included reviews of excitons. As the general editor of the Journal of Luminescence from 1985 to 1990, Michael expanded its scope to embrace modern research areas. At Dartmouth, he brought the same standards to his teaching, which he continued after retiring from the college in 1998. To introduce students to the dramatic history of physics during the 20th century, Michael worked with them on factual and moral problems raised by Michael Frayn’s play Copenhagen. He also wrote a textbook on statistical physics that included many recently studied systems.To honor Michael’s scientific achievements and his leadership, the International Conference on Dynamical Processes in Excited States of Solids has established the Sturge Prize for outstanding contributions to solid-state spectroscopy made by young scientists. The prize will be awarded for the first time in 2005.Michael enjoyed sailing and hiking and had a deep knowledge of history, politics, and philosophy. When visiting Jerusalem in 1972, Michael, in a quiet and almost shy way, kept correcting the old professional guide about historical facts. In 1987, at the Triniti-Sergey Monastery museum near Moscow, Michael noticed that an exhibit designated as “A prayer book of the Czar Ivan the Terrible” was actually published after Ivan’s death. The astonished guide explained that the original book was lost, and Michael was the first visitor to notice the inconsistency. Michael commented that it was merely his professional habit to pay attention to details and notice anomalies.Michael was a prominent researcher and a person of extraordinary standards and integrity. His family, colleagues, and friends will miss him.Michael Dudley SturgePPT|High resolution© 2004 American Institute of Physics.

Effects of structural disorder and temperature on the distribution of exciton binding energy in poly(phenylene vinylene) films

Luminescence quenching experiments on oriented and drop-cast poly(phenylene vinylene) (PPV), films identify the excitons in these polymer films as Wannier–Mott excitons. The data are interpreted in terms of a distribution of exciton binding energies ( E b). We find that the width of this distribution is well correlated with the degree of structural disorder. The relatively small mean E b, approximately 60 meV, results in field-induced exciton disociations that limits the quantum efficiency obtained from polymer-based light emitting diodes (PLEDs) which typically are operated at applied fields of 10 6 V/cm or greater where the field-induced exciton disociations is significant. We present data and analysis that support these conclusions, as well as a discussion on the implications of our findings on polymer-based display technology.

Motion of a 3D exciton in a magnetic field: Exciton-magnetoexciton “phase” transition

A rearrangement of the ground state of a Wannier-Mott exciton upon an increase in its momentum is considered. The phase diagram of the electron and the hole experiencing the Coulomb interaction on the magnetic momentum-external magnetic field plane is investigated. A jumplike exciton-magnetoexciton “phase” transition is observed upon an increase in the momentum in fields B weaker than a certain value B 0 even for B→0. At the point of transition, the exciton energy-momentum relation changes jumpwise from a quadratic law to a relation virtually independent of the momentum. For B<Btr1, the exciton-magnetoexciton transition becomes blurred.

Collective optical excitations in one-dimensional porphyrin assemblies

The collective electronic oscillator (CEO) method allows to analyze the electronic excitations in molecular systems. Using this technique the excitations are directly connected to the corresponding one-electron transition density matrices, obtained as eigenmodes of the time dependent Hartree–Fock (TDHF) Liouville operator, which represent motions of electron–hole (e–h) pairs. Two-dimensional plots of the density matrices establish the connection between the electronic spectra and the electronic rearrangement due to the photon absorption. In this paper, we use the CEO procedure to study the nature of the electronic excitations on three series of one-dimensional porphyrin systems, showing through the analysis of the CEO eigenmodes how they can be described in terms of Frenkel or Wannier–Mott excitons.

Stark effect and resonances in the ionization continuum for hydrogen atom and Wannier–Mott excitons in a DC electric field

Stark effect and resonances in the ionization continuum for hydrogen atom and Wannier–Mott excitons in a DC electric field

The Effects of Structural Disorder on the Luminescence Quenching in Poly(phenylene vinylene)

AbstractLuminescence quenching experiments on oriented and drop-cast poly(phenylene vinylene), (PPV), films identify the excitons in these polymer films as Wannier-Mott excitons. The data are interpreted in terms of a distribution of exciton binding energies (Eb). We find that the width of this distribution is well correlated with the degree of structural disorder. The relatively small mean EbEb, approximately 60 meV, results in field-induced exciton disociation that limits the quantum efficiency obtained from polymer-based light emitting diodes (PLEDs) which typically are operated at applied fields of 106 V/cm or greater where the field-induced exciton disociation is significant. We present data and analysis that support these conclusions, as well as a discussion on the implications of our findings on polymer-based display technology.

Theoretical and computational studies of excitons in conjugated polymers

We present a theoretical and computational analysis of excitons in conjugated polymers. We use a tight-binding model of $\ensuremath{\pi}$-conjugated electrons, with $1/r$ interactions for large r. In both the weak-coupling limit (defined by $W\ensuremath{\gg}U)$ and the strong-coupling limit (defined by $W\ensuremath{\ll}U),$ where W is the bandwidth and U is the on-site Coulomb interaction, we derive and analyze effective-particle models. We compare these to density matrix renormalization group (DMRG) calculations, and find good agreement in the extreme limits. We use these analytical results to interpret the DMRG calculations in the intermediate-coupling regime (defined by $W\ensuremath{\sim}U),$ most applicable to conjugated polymers. We make the following conclusions. (1) In the weak-coupling limit the bound states are Mott-Wannier excitons, i.e., conduction-band electrons bound to valence-band holes. Singlet and triplet excitons whose relative wave functions are odd under a reflection of the relative coordinate are degenerate. Thus, the $2{}^{1}{A}_{g}^{+}$ and $1{}^{3}{A}_{g}^{\ensuremath{-}}$ states are degenerate in this limit. (2) In the strong-coupling limit the bound states are Mott-Hubbard excitons, i.e., particles in the upper Hubbard band bound to holes in the lower Hubbard band. These bound states occur in doublets of even and odd parity excitons. Triplet excitons are magnons bound to the singlet excitons, and hence are degenerate with their singlet counterparts. (3) In the intermediate-coupling regime Mott-Wannier excitons are the more appropriate description for large dimerization, while for the undimerized chain Mott-Hubbard excitons are the correct description. For dimerizations relevant to polyacetylene and polydiacetylene both Mott-Hubbard and Mott-Wannier excitons are present. (4) For all coupling strengths an infinite number of bound states exist for $1/r$ interactions for an infinite polymer. As a result of the discreteness of the lattice and the restrictions on the exciton wave functions in one dimension, the progression of states does not follow the Rydberg series. In practice, excitons whose particle-hole separation exceeds the length of the polymer can be considered unbound. (5) The DMRG calculated exciton excitation energies scale as the inverse of the chain length for short chains and the inverse of the square of the chain length for long chains. This fits the effective-particle-in-a-box model.

ZnO as a Material Mostly Adapted for Realisation of Room-Temperature Polariton Lasers

Wannier-Mott excitons in the wurzite-type semiconductor material ZnO are stable at room temperature, have an extremely large oscillator strength and emit purple light. This makes ZnO an excellent potential candidate for the fabrication of room-temperature lasers where the coherent light amplification is ruled by the fascinating mechanism of the Bose-condensation of the exciton-polaritons. We first report on the direct optical measurement of the exciton oscillator strength f in ZnO. The longitudinal transverse splitting of the exciton resonances Γ 5 (B) and Γ 1 (C) are found to achieve record values of 5 and 7 meV, respectively, that is two orders of magnitude larger than that in GaAs. Secondly, we propose a model ZnO-based microcavity structure that is found to be the most adapted structure for the observation of the polariton laser effect. We thus can compute the phase diagram of the lasing regimes. A record value of the threshold power of 2 mW per device (at power density of 3000 W/cm 2 ) at room temperature is found for the model laser structure.

Wannier–Mott excitons formed by electrons in a quantum wire and holes in a perpendicular quantum layer

We analyze Wannier–Mott excitons in which the electrons are constrained in one-dimensional quantum wires and the holes in two-dimensional quantum layers perpendicular to the wires. The resulting three-dimensional exciton Schrödinger equation in the laboratory frame of reference is solved in terms of the common 3D exciton states in the center of mass frame.

ZnO as a material mostly adapted for the realization of room-temperature polariton lasers

Wannier-Mott excitons in the wurzite-type semiconductor material ZnO are stable at room temperature, have an extremely large oscillator strength, and emit blue light. This makes ZnO an excellent potential candidate for the fabrication of room-temperature lasers where the coherent light amplification is ruled by the fascinating mechanism of the Bose condensation of the exciton polaritons. We report the direct optical measurement of the exciton oscillator strength f in ZnO. The longitudinal transverse splitting of the exciton resonances Γ 5 (B) and Γ 1 (C) are found to achieve record values of 5 and 7 meV, respectively, that, is two orders of magnitude larger than in GaAs. Second, we propose a model ZnO-based microcavity structure that is found to be the most adapted structure for the observation of the polariton laser effect. We thus can compute the phase diagram of the lasing regimes. A record value of the threshold power of 2 mW per device (at power density of 3000 W/cm 2 ) at room temperature is found for the model laser structure.

Exciton formed by electron and hole separated in concentric quantum rings

We analyze a Wannier–Mott exciton in which the electron is constrained to move in a quantum ring and the hole moves in another concentric quantum rings. We expand the electron–hole interaction potential in terms of multipoles by assuming that both the electron and hole experience transverse harmonic confinements in the ρ and z directions, both being in their respective transverse groundstates. For the resulting φ-dependent Schrödinger equation we calculate the lowest exciton eigenenergies and eigenfunctions.

Charged Frenkel excitons in organic crystals

In molecular crystals a charge carrier and a molecular (Frenkel) exciton are attracted to each other. This attraction arises from the increase of the molecular static polarizability upon electronic excitation, and may be responsible for the formation of a two-particle bound state of the exciton and the free charge. Such charged Frenkel excitons are analogous to trions (bound states of a Wannier–Mott exciton and a charge carrier) in inorganic semiconductors. In this paper we develop a theory of charged excitons in molecular crystals, and apply this theory to study the spectra of charged Frenkel excitons in two-dimensional structures, which serve as a rather good approximation for layered crystals like anthracene, tetracene. We show that the binding energy of charged Frenkel excitons can be of the order of several hundred cm −1. Thus, they may be stable at room temperatures, in contrast to trions in inorganic semiconductors. Particularly interesting is the possibility of forming charged triplet excitons in the crystal of tetracene where the energy of the lowest triplet exciton is much smaller than the energy of the lowest excitation in ions. This circumstance prevents the transformation of charged triplet excitons into an ion excitation with short lifetime and promotes the formation of rather stable charged triplet excitation. We briefly discuss the optical properties of charged Frenkel excitons and the effects of a static electric field.

Point-dipole approximation of the exciton coupling model versus type of bonding and of excitons in porphyrin supramolecular structures.

The application of the exciton coupling model to interacting porphyrin chromophores is discussed. Covalently bonded systems and ionic or electrostatically bonded homoassociates require different orientations of the transition dipole moments in order to explain the experimental results: according to the symmetry of the assembly for covalently bonded porphyrins, and assuming isolated chromophores for ionic bonded porphyrins. Further, for covalently bonded systems, an extended exciton coupling has been demonstrated, but the ionic systems are in agreement with non-extended couplings. The relation of these facts to a molecular description of solid-state Wannier-Mott or Frenkel excitons is briefly discussed.

Two-dimensional Wannier-Mott exciton in a uniform electric field

A new treatment of the problem of a two-dimensional Wannier-Mott exciton in a uniform electric field, based on the parabolic coordinates, is presented. The quasi-stationary Hamiltonian is regularized, and the efficient numerical methods are applied. The dependence of the exciton binding energy on the electric field is computed. The results are very close to those obtained by the perturbation theory calculations.