Daniel Hone

Charge renormalization, osmotic pressure, and bulk modulus of colloidal crystals: Theory

The interactions between charged colloidal particles with sufficient strength to cause crystallization are shown to be describable in terms of the usual Debye–Huckel approximation, but with a renormalized charge. The effective charge in general is smaller than the actual charge. We calculate the relationship between the actual charge and the renormalized charge by solving the Boltzmann–Poisson equation numerically in a spherical Wigner–Seitz cell. We then relate the numerical solutions and the effective charge to the osmotic pressure and the bulk modulus of the crystal. Our calculations also reveal that the renormalization of the added electrolyte concentration is negligible, so that the effective charge computations are useful even in the presence of salts.

Theory of charge exchange scattering from surfaces

We present a simple model calculation of the charge exchange probability for ions scattering from solid surfaces, including interactions with both broad band delocalized electrons and with localized core electrons within an Anderson type Hamiltonian with time dependent parameters. The results exhibit some of the major observed experimental features, including characteristic oscillations as a function of incident velocity (from quasi-resonant electron interchange with the core levels) and overall exponential decay ∼exp(−Av), with v the incident ion velocity, from interactions with the broad band electrons.

The phase diagram of charged colloidal suspensions

The thermodynamics of a system of identical electrically charged spheres in colloidal suspension in a polar fluid (typically, H2O), are calculated within a model of point particles interacting via a screened Coulomb (Yukawa) potential of suitably renormalized strength. The particles are taken to be sufficiently massive that a classical theory is appropriate. The free energies of the crystalline phases are calculated within a mean field theory which is an extension of the self‐consistent harmonic approximation. The melting curve is estimated from the semiempirical Lindemann rule, with mean squared displacements again calculated self‐consistently. As functions of the relevant parameters: electrical charge of each sphere, density of spheres and added salt concentration, stable predicted phases include fcc and bcc crystals and a disordered fluid. Under suitable circumstances a reentrant bcc→fcc→bcc transition is predicted as salt is added, and bcc is predicted always likely to be the stable phase just below t...

Theory of light emission from small particle tunnel junctions

We study a simple model of light emission from inelastic electron tunneling into small metallic particles, here represented as spheres. Within a quasistatic approximation for the induced polarization in the electrodes, we calculate the radiated intensity as a function of frequency and direction.

BCC-FCC, melting and reentrant transitions in colloidal crystals

Abstract Charged colloids exhibit a variety of order—disorder and structural transitions. If the interactions can be treated in a Debye-Huckel approximation and if the dielectric constant of the solvent arises from free dipoles and follows a Curie law, the partition function is temperature independent and the system is athermal. If the dielectric constant of the solvent increases faster than linearly with inverse temperature (as is the case for H2O) then the high-entropy phase occurs upon either heating or cooling from the more—ordered phase. As an illustration of these effects the FCC-BCC transition of colloidal crystals as a function of density and screening length is calculated.

ac-Field-controlled Anderson localization in disordered semiconductor superlattices.

An ac field, tuned exactly to resonance with the Stark ladder in an ideal tight binding lattice under strong dc bias, counteracts Wannier-Stark localization and leads to the emergence of extended Floquet states. If there is random disorder, these states localize. The localization lengths depend non-monotonically on the ac field amplitude and become essentially zero at certain parameters. This effect is of possible relevance for characterizing the quality of superlattice samples, and for performing experiments on Anderson localization in systems with well-defined disorder.

Time-dependent Floquet theory and absence of an adiabatic limit

Quantum systems subject to time periodic fields of finite amplitude \ensuremath{\lambda} have conventionally been handled either by low-order perturbation theory, for \ensuremath{\lambda} not too large, or by exact diagonalization within a finite basis of

Localization effects in ac-driven tight-binding lattices

N

ac Stark effects and harmonic generation in periodic potentials.

states. An adiabatic limit, as \ensuremath{\lambda} is switched on arbitrarily slowly, has been assumed. But the validity of these procedures seems questionable in view of the fact that, as

Time-periodic behavior of multiband superlattices in static electric fields.

N\ensuremath{\rightarrow}\ensuremath{\infty},