Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9906100

Ionization degree of the electron-hole plasma in semiconductor quantum wells

M. E. Portnoi·I. Galbraith
View original source ↗Read source document ↗Export metadata ↓

Abstract

The degree of ionization of a nondegenerate two-dimensional electron-hole plasma is calculated using the modified law of mass action, which takes into account all bound and unbound states in a screened Coulomb potential. Application of the variable phase method to this potential allows us to treat scattering and bound states on the same footing. Inclusion of the scattering states leads to a strong deviation from the standard law of mass action. A qualitative difference between mid- and wide-gap semiconductors is demonstrated. For wide-gap semiconductors at room temperature, when the bare exciton binding energy is of the order of T, the equilibrium consists of an almost equal mixture of correlated electron-hole pairs and uncorrelated free carriers.

Explore related subjects

cond-mat.stat-mechcond-mat.str-el

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

M. E. Portnoi, I. Galbraith. 1999-06-07. Ionization degree of the electron-hole plasma in semiconductor quantum wells. https://doi.org/10.1103/physrevb.60.5570

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Direct Experimental Test of Conformal Invariance via Grazing Scattering: A Proposal for X-ray and Neutron Experiments

We propose a test of conformal invariance in critical phenomena based on the study of a two-point correlation function in the presence of a boundary. This two-point function can be studied using X-ray or neutron scattering in the conditions of total reflection (so-called grazing scattering). The conformal Ward identity in momentum space is here expressed as a differential constraint on the scattering cross-section, as a function of the momentum transfer and the scattering angle. Experimental verification using X-rays and binary alloys appears well within the existing techniques, while feasibility for neutron scattering requires further study. This would be the first direct experimental test of conformal invariance in critical phenomena, a symmetry widely assumed but never directly verified.

cond-mat.stat-mech↗
arXiv2026

Thermodynamic and statistical properties of a multifractional modified dispersion relation via the grand-canonical ensemble

We study the thermodynamic and statistical properties of a gas governed by a multifractional modified dispersion relation of the form $ω^{2}=k^{2}+4E_{*}^{-1/2}k^{5/2}$, where $E_{*}$ sets the characteristic scale of the multifractional correction. Working within the grand-canonical ensemble, we derive the modified density of states, the grand potential, the partition function, and the main thermodynamic quantities for both bosonic and fermionic sectors. The deformation changes the available phase-space distribution and produces nonstandard thermal scalings controlled by the ratio $T/E_{*}$. In the infrared regime, the usual relativistic gas behavior is recovered with leading corrections proportional to powers of $(T/E_{*})^{1/2}$. In the ultraviolet regime, the density of states scales as $\varrho(ω)\propto ω^{7/5}$, corresponding to an effective density-of-states dimension $d_{\mathrm{eff}}=12/5$. As a consequence, the Stefan-Boltzmann law is deformed from $u\propto T^{4}$ to $u\propto E_{*}^{3/5}T^{17/5}$, while the equation-of-state parameter approaches $w=5/12$ instead of the standard radiation value $w=1/3$. We also analyze thermal stability, particle number and energy fluctuations, Bose-Einstein condensation, and the degenerate Fermi gas limit. The multifractional correction increases the critical temperature of a conserved bosonic gas and modifies the Fermi energy, pressure, sound speed, and low-temperature heat capacity of degenerate fermions. A direct fit to the COBE/FIRAS monopole spectrum yields $E_{*}>0.36\,\mathrm{MeV}$ at $95\%$ CL, while the conservative GWTC--3 propagation constraint gives $E_{*}>1.18\times10^{19}\,\mathrm{GeV}$ at $90\%$ credibility when the dispersion relation is assumed to be universal.

cond-mat.stat-mech↗
arXiv2026

Foundations of Many-Body Theory of Quantum Unified Statistics: Green functions and Linear Response Theory

We develop a comprehensive many-body theory for systems of particles obeying quantum unified statistics, or quons. After exploring the properties of the Fock space of this system, we formulate a systematic S-matrix expansion and a generalized Wick's theorem. A consistent Green-function formalism is constructed at both zero and finite temperatures, accompanied by a generalized Wick's theorem appropriate for infinite-statistics operator algebras. Within this framework, we establish diagrammatic rules for interacting quon systems. Employing the random phase approximation, we derive the dielectric function and reveal the emergence of anomalous plasmon modes that have no direct counterpart in conventional Bose or Fermi systems. We further analyze the ground-state energy, energy-loss function, generalized Thomas-Fermi screening wave vectors, and Friedel oscillations, elucidating how infinite statistics qualitatively modifies collective behavior and screening properties.

cond-mat.stat-mech↗