**Are you an EPFL student looking for a semester project?**

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

Concept# Random phase approximation

Summary

The random phase approximation (RPA) is an approximation method in condensed matter physics and in nuclear physics. It was first introduced by David Bohm and David Pines as an important result in a series of seminal papers of 1952 and 1953. For decades physicists had been trying to incorporate the effect of microscopic quantum mechanical interactions between electrons in the theory of matter. Bohm and Pines' RPA accounts for the weak screened Coulomb interaction and is commonly used for describing the dynamic linear electronic response of electron systems.
In the RPA, electrons are assumed to respond only to the total electric potential V(r) which is the sum of the external perturbing potential Vext(r) and a screening potential Vsc(r). The external perturbing potential is assumed to oscillate at a single frequency ω, so that the model yields via a self-consistent field (SCF) method a dynamic dielectric function denoted by εRPA(k, ω).
The contribution to the dielectric function from

Official source

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications

Loading

Related people

Loading

Related units

Loading

Related concepts

Loading

Related courses

Loading

Related lectures

Loading

Related people

Related publications (12)

No results

Loading

Loading

Loading

Related units

Related concepts

No results

No results

Related courses (1)

PHYS-317: Optics I

L'optique est un vieux domaine qui touche à beaucoup de sujets modernes, des techniques expérimentales aux applications courantes. Ce premier cours traite plusieurs aspects de base de l'optique: propagation, dispersion, interférence, diffraction, polarisation, modulation, guidage, etc.

Related lectures (1)

This thesis work contains an experimental study of many-body and cooperative effects in quantum wells. Many-body effects prove important for an understanding of the physical and specifically optical properties of semiconductors. The Coulomb interaction between electrons profoundly modifies the electronic states and the light-matter interaction, leading to a number of density-dependent effects that can not be accounted for in the one-electron picture which is the starting point of most textbooks on the subject. The simplest of these modifications is the exciton, the bound state of one electron and one hole which leads to the emergence of two-particle states energetically below the continuous band electron-hole states. Optical excitation in the band continuum is possibly followed by the formation of excitons upon release of the excess energy to the lattice vibrations. Chapter 5 contains an experimental analysis of the dynamics of this process. A high quality single In0.05Ga0.95As/GaAs quantum well sample allows us to separately study the temporal evolution of the continuum photoluminescence on the one hand and the excitonic photoluminescence on the other. The results indicate a rather fast formation process, leading to the establishment of a species interconversion equilibrium between free pairs and bound pairs at higher density. However, at the lowest excitation density, we found evidence for a non-equilibrium species repartition. At high electron-hole pair density, the two-particle bound exciton state disappears due to the screening of the Coulomb interaction by the surrounding carriers as well as the blocking of the constituting states according to the Pauli exclusion principle. The transition from an excitonic population to a free carrier plasma is referred to as excitonic Mott transition. Chapter 6 reports an experimental investigation of the repercussions of this transition on the optical spectra, performed on the In0.05Ga0.95As/GaAs quantum well of chapter 5. The time-resolved spectra do not show an abrupt change of photoluminescence intensity or spectral form when transforming gradually from an exciton dominated spectrum to free plasma photoluminescence, indicating a rather gradual transition. The separate visibility of continuum and excitonic PL contributions below the transition density reveals the total absence of exciton binding energy variations, indicating a very low exciton ionization degree in contrast to theoretical work on the subject. Another high-density effect arising from the particle interactions is the energetic lowering of the electronic states due to screening and correlation, denoted as band gap renormalization (BGR). Chapter 7 presents measurements of BGR using a single GaAs/Al0.25Ga0.75As quantum well of 60 Å width. We obtain good agreement with calculations of the carrier self energy within the framework of the random phase approximation. The last part of this thesis (chapter 8) reports an experimental test of the possibility of cooperative spontaneous emission, often denoted as superradiance, from a high-density electron-hole plasma. This effect has been extensively studied in optically excited atomic gases, where it leads under certain conditions to the reemission of the stored energy in a single coherent radiation burst instead of the slow exponential decay according to the spontaneous radiation of a single atom. We find no evidence for the occurrence of this effect in our samples, probably due to the fast incoherent polarization decay in the carrier plasma.

In a recent paper [Phys. Rev. B 90, 125102 ( 2014)], we showed that the random phase approximation with exchange (RPAx) gives accurate total energies for a diverse set of systems including the high and low density regime of the homogeneous electron gas, the N-2 molecule, and the H-2 molecule at dissociation. In this paper, we present results for the van der Waals bonded Ar-2 and Kr-2 dimers and demonstrate that the RPAx gives superior dispersion forces as compared to the RPA. We then show that this improved description is crucial for the bond formation of the Mg-2 molecule. In addition, the RPAx performs better for the Be-2 dissociation curve at large nuclear separation but, similar to the RPA, fails around equilibrium due to the build up of a large repulsion hump. For the strongly correlated LiH molecule at dissociation we have also calculated the RPAx potential and find that the correlation peak at the bond midpoint is overestimated as compared to the RPA and the exact result. The step feature is missing and hence the delocalization error is comparable to the RPA. This is further illustrated by a smooth energy versus fractional charge curve and a poor description of the LiH dipole moment at dissociation.

,

Calculations of exact-exchange (EXX) and random phase approximation (RPA)-correlation energies within the formally exact adiabatic connection fluctuation-dissipation theorem formalism have recently been carried out for a number of isolated and condensed systems. Unfortunately, most of the applications have been done in a non-self-consistent procedure, and for several systems it has been found that RPA correlation energies may significantly depend on the choice of input single-particle wave functions. In this work, we develop an efficient approach to compute the EXX/RPA total energy self-consistently. We derive an expression for the RPA self-consistent potential based on the density functional perturbation theory and dielectric matrix approaches and implemented it within the plane-wave pseudopotential framework. The efficiency of this approach is greatly improved by exploiting an iterative procedure to compute the inverted Kohn-Sham density-density response function. We apply our implementation to study the binding energy curves and the structural properties of rare gasses such as Ar and Kr and alkaline-earth Be dimers. In addition, the EXX and RPA-correlation potentials of these systems at different dissociation distances are analyzed.