Camel's back excitons in GaP

The influence of the recently proposed camel's back structure of the GaP conduction band edge on the exciton spectrum is investigated theoretically. The results are in good agreement with differential absorption data and strongly support a camel's back structure, with a 4 meV central hump. The computed exciton binding energy is 18.5 meV, and when combined with recent experimental data, indicates a binding of about 32 meV for the electron-hole liquid.     

Camel's back structure of the conduction band in GaP

A simple k · p theory based on Si and the ionic X gap is applied to the conduction band of GaP. It is found that recent evidence may indicate a location of the absolute minima away from the zone boundary. In the directions parallel to 〈100〉, the band structure is highly nonparabolic for carrier energies in the range 1–50 meV.     

Indirect exciton dispersion in III–V semiconductors: “Camel's back” in GaP

A new perturbation approach to exciton dispersion in indirect gap semiconductors is developed. For GaP and AlSb existence of the “camel's back” in exciton dispersion is confirmed, and a precise value of the “camel's back” parameter for X^c₁-minima in GaP is reported: E(X^c₁)?E_min(Δ^c₁)=3.5±0.3 meV. At the X-point the 21.44 and 19.48 meV exciton binding energies in GaP are obtained. The corresponding valley-anisotropy splitting is 1.96 meV.     

Theory of donor states in GaP: The role of the camel's back

We present a theoretical study of the influence of the camel's back structure on the low lying excited states of the donors in GaP. Based on comparison with the observed spectrum, we conclude that the appropriate values for the parameters describing the camel's back are $\text{Δ}\text{E}\text{= 3.2}\text{meV and k}{}_{\mathrm{o}}\text{= 0.083 (}\text{a}{}_{\mathrm{o}}\text{2π}\text{)}$.     

Thermodynamics of electron-hole liquids in graphene

The impact of Coulomb interactions on the chemical potential, heat capacity, and oscillating magnetic moment is studied. The cases of low and high temperatures are considered. At low temperatures, doped graphene behaves as the common Fermi liquids with the power temperature laws for thermodynamic properties. However, at high temperatures and relatively low carrier concentrations, it exhibits the collective electron-hole behavior: the chemical potential tends to its value in the undoped case going with the temperature to the charge neutrality point. Simultaneously, the electron contribution into the heat capacity tends to the constant value as in the case of the Boltzmann statistics.     

Dynamic structural correlations and Van Hove's correlation function for liquids

The stochastic model for liquids, developed previously and applied to the evaluation of static correlations, is extended to the evaluation of the dynamic pair correlation function. This extension can be achieved by a generalization of the width function W, characterizing the spread in the distribution of correlated local structures, from a piecewise linear function of r to a piecewise linear function in the (r, t) plane.     

On the possibility of superconductivity in electron-hole liquids

It is shown that an electron-hole liquid under suitable conditions can become superconducting. This conclusion is reached by using an effective electron-electron interaction which includes vertex corrections and multiple electron-hole scattering. The mechanism for superconductivity is novel. The intermediate bosons responsible for the superconducting pairing are not acoustic plasmons but correlated pair excitations from the Fermi sea of the holes. Some materials are proposed for an experimental verification of the ideas presented here.     

Relation between bulk compressibility and surface energy of electron-hole liquids

Attention is drawn to the existence of an empirical relation χσ/a_B¹ ～ 1 between the compressibility, the surface energy and the excitonic radius in electron-hole liquids.     

A possible unification of Newton's and Coulomb's forces

We have considered electric charge as the fourth component of the particle momentum in five-dimensional space–time. The fifth dimension has been compactified on a circle with an extremely small radius determined from the fundamental physics constants. First, we have given equations in the framework of five-dimensional special relativity and determined the corresponding reduction to four-dimensional space–time. Then, in order to obtain an appropriate charge-to-mass ratio and to avoid the Fourier modes problem, we have considered the propagation of an off-mass shell particle in the five-dimensional space–time which can be interpreted as the motion of an on-mass shell particle in the four-dimensional world we experience. As an example, we have discussed the five-dimensional kinematic equations associated with the electron-positron annihilation process into two photons. Finally, the consequences on the gravitational interaction between two elementary charged particles has been studied. As a main result, we have obtained a unification of Newton's gravitational and Coulomb's electrostatic forces.     

Weyl's association,Wigner's function and affine geometry

According to Weyl one may associate a function with a dynamical operator; these functions depend on the parameters p and q and can be displayed in a p, q manifold, the W space. In the classical limit the W space becomes the phase space parametrised by the canonical variables. The function associated in this manner with the density operator is Wigner's function. It turns out that if Wigner's function is a delta function it cannot represent the density operator of a physically realisable state unless the argument of the delta-function is linear in the parameters a and q. In all other cases Wigner's function associated with a physically realisable state has a finite width, proportional to $\text{h}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$. Consequently straightness (linear combination of p and q) has a fundamental significance in the W space. Since this property is preserved under linear inhomogeneous transformations the W space will have a geometry generated by these transformations, the affine geometry of Euler, Moebius and Blaschke. In the present note we show how this comes about, how it simplifies the semiclassical approximations of Wigner's function, and makes one understand how in the classical limit this geometry is lost, allowing to be replaced by the geometry of canonical transformations.