Quantifying electronic correlations in simple metals

Considering natural orbitals in quantum chemistry this week reminded me of a key property of Fermi liquids: the existence of a discontinuity in the wavevector dependence of the Fourier transform of the one-electron reduced density matrix n(k).

The figure below is taken from a PRB paper by Paola Gori-Giorgi and Paul Ziesche. It shows the wavevector dependence of n(k) for a uniform electron liquid (at density corresponding to an interparticle spacing of rs=5, comparable to a typical metal). k=1 corresponds to the Fermi wavevector.

For a non-interacting fermion system n(k)=1 for k less than 1 and 0 for k >1.

The figure below shows the magnitude of zF, the jump in n(k) at k=1, as a function of rs. Increasing rs corresponds to decreasing electron density and increasing correlation effects. This quantity zF can be related to the quasi-particle weight associated with the pole in the one-electron Greens function. The smaller zF the larger the effective mass of the quasi-particles.

In a few weeks we will be looking at all this in the Quantum Many-Body Theory reading group.

How wrong about the future can you be?

Distinguished scientists trying to predict the future direction of a field of study is a dangerous (but fascinating) exercise. I have on my desk four such articles. I hope to comment on each in turn, but it is interesting to compare them since they are all very different, have had different impacts, and in hindsight some were pre-scient and others off track. Here they are in chronological order:

Niels Bohr, Light and Life, given at the International Congress of Light Therapy in 1932, and published in two parts in Nature in 1933 (Part 1 and Part 2).

Charles Coulson, Present State of Molecular Structure Calculations,

Given as an "after-dinner" speech at a quantum chemistry conference in 1959.

Brian Pippard, The Cat and the Cream, 1961

A conference banquet speech at a conference held at IBMs new lab at Yorktown Heights, and later published in Physics Today.

Serge Haroche and Jean-Michel Raimond, Quantum Computing: Dream or Nightmare? Physics Today, 1996.

Entanglement in quantum chemistry

Today I gave a talk at the weekly UQ Condensed Matter Theory group meeting (cake meeting because someone always brings a cake!) on the possible role of entanglement measures in quantum chemistry. I only got through the first half of these notes and so will continue next week.

Any comments welcome.

Quick to save the planet

A fundamental question concerning dye-sensitized solar cells is what determines the speed and efficiency with which charge is injected from the dye to the semiconductor (such as titanium oxide) on which it is absorbed?

A nice review by Liu and Andersen contains the summary diagram.

One important point I learnt is that (at least in some dyes) the ultrafast injection (~tens fsec) from the singlet excited state of the organometallic dye complex (such as those shown above) competes with intersystem crossing to the triplet excited state, from which injection can also occur but not as quickly.

Simplifying the Theory of Everything

This weeks reading from Advanced Solid State Physics by Philip Phillips is Chapter 2, The Born-Oppenheimer [BO] Approximation.

This reflects a key idea in quantum many-body theory: when there is a clear separation of energy scales one can often simplify the theory greatly and identify distinct quasi-particles [e.g., phonons and electronic quasi-particles] corresponding to the different energy scales.

Without BO there would be no quantum chemistry and no quantum theory of electronic properties of crystals.

BO is a consequence of the fact that electrons are much lighter than nuclei. Consequently, electrons in a molecule or solid have average velocities that are typically orders of magnitude faster than the nuclei.

Equation (2.1) is the Hamiltonian

The symbols Zα and Mα are the atomic number and mass of the α^th nucleus, Rα is the location of this nucleus, e and m are the electron charge and mass, r _j is the location of the j ^th electron, and ℏ is Planck's constant.

If we could solve this Hamiltonian we would have Laughlin and Pines Theory of Everything.

Equations (2.10) and (2.14) are the key results of the chapter.

But there are many interesting and important situations where BO breaks down. Cases for molecules are discussed here.

Anderson's radical idea

In a 1987 Science paper Phil Anderson made a radical proposal, stimulated by the discovery of high-Tc superconductivity in layered copper oxides. [A meausure of the influence of Anderson's paper is that it has been cited more than 4000 times]. My version of Anderson's proposal is:

The fluctuating spin singlet pairs [produced by the exchange interaction] in the [Mott] insulating state become charged superconducting pairs when the insulating state is destroyed by doping, frustration or reduced correlations.

These fluctuations are enhanced by spin frustration and low dimensionality.

To me the idea is radical and rather counter-intuitive because in one sense insulating and superconducting states are so different. One has infinite conductivity and the other zero.

Ben Powell and I have been invited to write a review article for Reports in Progress in Physics concerning organic charge transfer salts which can be described by a Hubbard model on the anisotropic triangular lattice. [An earlier review of related materials is here].

A key issue is whether these materials can be used as tuneable systems to test ideas about the interplay of superconductivity, Mott insulation, quantum fluctuations and spin frustration.

A cautionary word about email

I was going to write a post about email and then remembered I wrote a post Think twice before you send that email in the early days of this blog. It says much of what I wanted to say again.

Think twice (or cool off) before you hit Reply or Send or Forward.

It is also worth reading some of the lists of "email etiquette" on the web. Here is one that I thought was pretty could.

Some of this may seem obvious and common sense. But to quote Steven Covey, "Common sense is not necessarily common practice."