Is there more than one way to get grounded?

Thinking more about my earlier post, Key questions about organometallic materials for LEDs, I realised there is a subtlety that is sometimes overlooked when interpreting experimental data on these materials. The radiative and non-radiative decay rates of the emitting state are never directly measured. Rather, one actually measures the total lifetime tau (or decay rate) of the emitting state and the PLQY (PhotoLuminescence Quantum Yield). This is the ratio of the number of emitted photons to the number of absorbed photons (see the blue and red arrows below).

One then uses the following two equations to deduce the radiative and non-radiative decay rates.

For just one of many examples, of how this is done, see this paper, by Lawrence Lo and collaborators.

However, this analysis assumes that one hundred per cent of the 1MCLT state decays to the 3MLCT state. i.e., that there is NO significant non-radiative decay of this state via other channels (e.g., the MC state shown above).

Its all about entropy (again)

Tomorrow's lecture is on chemical equilibrium. A few key ideas are:

• chemical reactions never proceed to completion because of the entropy of mixing
• the equilibrium constant quantifies how far the reaction proceeds.
  
• measuring its temperature dependence allows one to determine the enthalpy change of the reaction. (and consequently also the entropy change).

Some cool videos I show are from the Chemistry Comes Alive series produced by the Journal of Chemical Education. These include lots of good ones on thermodynamics and phase transitions.

Student problem set in quantum many-body theory

Learning basic concepts in quantum many-body theory and starting to do actual calculations is not easy. Furthermore, understanding the relationship between its formulation and application in quantum chemistry and solid state physics is even harder.

A few years colleagues and I ran a series of summer schools for graduate students in physics and chemistry to help them get started. As usual, I think some of us lecturers actually learnt more than the students.

Here are some "basic" problems that I set.

One facet of saving the planet

Today Max Lu is giving the weekly Physics Colloquium. No doubt, one thing he will talk about is how his group was able to grow large single crystals of the anatase form of TiO2 (titanium dioxide) with a large percentage of reactive facets. (It is described in this Nature paper). A key component of that work was that DFT calculations helped guide the chemical synthesis strategy.

A really nice exposition of this work and its significance is given by Annabella Selloni in a Nature Materials News and Views. It contains the Figure above.

Key questions about organometallic LED materials

The figure below, taken from a JACS paper, is a possible schematic for photo-physics of the excited states of Ru(bpy)3 which is a model compound for attempting to understand materials used in phosphorescent organic LEDs.

My 5 biggest questions concerning this class of materials are:

1. What is the character of the triplet emitting state?

To what extent is it a metal-to-ligand charge transfer state (MLCT) and to what extent is it ligand centred (LC)?

2. What is the non-radiative decay path from the emitting state?

What are the relevant vibrational co-ordinates?

3. What is the physical mechanism for the ultra-fast (tens of fsec) transition from the singlet to the triplet MLCT state?

Is there are conical intersection associated with this intersystem crossing?

4. Are the excited states delocalised over all the ligands or localised on single ligands?

For example, the equation below (from the same JACS) suggests that the singlet state is delocalised and the triplet is localised on a single ligand.

5. Is there a metal-centred (MC) state that is relevant to the non-radiative decay, as suggested by the above figure?

The idea of a t2g->eg state being relevant has recently been proposed, and has some support from quantum chemistry calculations, described here. Hopefully, I will blog about this later.

Mott transition into a spin liquid state

The Figure below shows the phase diagram of the Hubbard model on the anisotropic triangular lattice at half filling.as a function of temperature and t/U obtained from cluster DMFT. The figure is taken from this PRB by Liebsch, Ishida, and Merino.

As U/t increases there is a first order phase transition from a metallic to and Mott insulating phase. This first order line ends at a critical point.

(a) and (b) are for t'/t=0.8 and 1, respectively.

Note that the slope of the line at low temperatures depends on the ratio t'/t, reflecting the effect of frustration.

The Clausius-Clapeyron equation and the positive slope of the phase boundary implies that for t'=t that the insulating state has a larger entropy than the metallic state, even at low temperatures. The calculated diagram for t'=0.8t is in semi-quantitative agreement with the observed temperature-pressure phase diagram of a range of organic charge transfer salts. The diagram for t'=t is consistent with that observed for kappa-(ET)2(CN)3, which may have a spin liquid ground state.

The calculated values of the critical temperature Tc = 40-50 K, at which the first order line terminates, are comparable to experimental values.

Furthermore, the Figure shows how frustation can produce a Mott insulating state in which the entropy at low temperatures is larger than that of the metallic state. Such a large entropy is characteristic of a spin liquid.

This leads to a first-order phase boundary which has a positive slope.

In contrast, in a two-dimensional antiferromagnetic Heisenberg model on the square lattice [which have a Neel ordered ground state] at low temperatures has an entropy that is proportional to T^2. At low enough temperature this will always be less than the entropy of a Fermi liquid which is proportional to temperature.

One dimension is different

This weeks reading from Phillips, Advanced Solid State Physics, is Section 8.4, on the dielectric response function. This is calculated at the level of the Random-Phase-Approximation (RPA) for a Fermi liquid (weakly interacting fermion gas). One finds the density-density response function. The imaginary part is related to the structure factor (via a fluctuation-dissipation relation). This can be thought of as an effective density of states for particle-hole excitations.

In three-dimensions these excitations are gapless for all wavevectors. However, one dimension is different. The shaded area in Figure (b) above shows the relevant excitations for on one-dimensional fermion gas. This Figure is taken from a seminal paper by Haldane, who emphasized the distinct difference from higher dimensions.

The fact that there is a well defined dispersion for low momenta, shown above means that density fluctuations are well-defined quasi-particles in the one dimensions. This is the basis of bosonisation and the Luttinger liquid, discussed in Chapter 9.