On monday I am giving a talk at the Indian Institute for Science Education and Research (IISER ) Pune.

Here is the current version of the slides.

## Friday, September 23, 2016

## Wednesday, September 21, 2016

### A minor detail that matters in organic charge transfer salts

One helpful way to think about condensed matter is in terms of relative energy scales. This can help one decide what is important and what is not.

However, this does not always work, particularly in complex systems where new low energy scales can emerge.

For a long time there has been a "minor detail" about organic charge transfer salts based on the BEDT-TTF molecule that I have found rather annoying and puzzling.

It concerns the role of ethylene end groups on the molecule and their possible different conformations (eclipsed vs. staggered).

Why should the conformations matter?

I would think not. The overlap of the relevant electronic molecular orbitals which are largely centred on sulphur atoms are negligible as seen below in the HOMO (Highest Occupied Molecular Orbital) for a BEDT-TTF dimer.

The figures are taken from this paper by Edan Scriven and Ben Powell.

However, things are more subtle than I would have thought.

Here are some of the significant effects that result from these two different conformations. They have different energies and by thermal annealing in a crystal you can convert between them.

As a result disorder in a crystal can be controlled by varying the cooling rate.

In some materials there is even a glass transition around 80 Kelvin.

Examples of the dramatic effects of the disorder can be seen.

Resistance vs. temperature curve (see for example the figure below taken from here).

Suppression of the superconducting transition temperature.

This can be seen in the curves above.

Electrical noise experiments

Another dramatic effect of the ethylene groups that is much larger than most people expect is

Isotopic substitution of the hydrogen with deuterium in the ethylene groups can drive the Mott metal-insulator transition.

This somehow arises from a geometrical isotope effect associated with hydrogen bonds between the ethylene groups and the anion.

It turns out that changing the conformation of the end group can have a significant effect on the parameters in the Hubbard model, that is the simplest possible effective Hamiltonian for these materials.

This is shown in this recent paper which estimates these parameters using DFT-based electronic structure calculations and Wannier orbitals to map onto a tight-binding model.

Influence of molecular conformations on the electronic structure of organic charge transfer salts Daniel Guterding, Roser Valentí, and Harald O. Jeschke .

In particular in going from Eclipsed (E) to Staggered (S) or visa versa is enough to cross the Mott insulator-metal phase boundary.

This provides a framework to understand the experimental puzzles discussed above.

The authors estimate the Hubbard paper U (Coulomb interaction) for two holes on a BEDT-TTF dimer with a formula which is only valid in a particular limit.

The general formula for the energy of two electrons on a two site Hubbard model is

where Um is the Hubbard interaction on a single dimer, V is the inter site Coulomb repulsion and t is the intersite hopping. The authors are assuming that Um - Vm is much larger than 4t which Scriven and Powell argue is not the case.

This will lead to quantitative changes but not change the main point that the conformational changes can produce a significant change in the Hubbard model parameters; particularly a large enough change to cross the Mott insulator-metal phase boundary.

Later I will write about the noise measurements (which I puzzled about before) which turn out to be a very sensitive probe of these two molecular conformations and their interconversion.

I thank Jens Muller for very helpful discussions about this work.

However, this does not always work, particularly in complex systems where new low energy scales can emerge.

For a long time there has been a "minor detail" about organic charge transfer salts based on the BEDT-TTF molecule that I have found rather annoying and puzzling.

It concerns the role of ethylene end groups on the molecule and their possible different conformations (eclipsed vs. staggered).

Why should the conformations matter?

I would think not. The overlap of the relevant electronic molecular orbitals which are largely centred on sulphur atoms are negligible as seen below in the HOMO (Highest Occupied Molecular Orbital) for a BEDT-TTF dimer.

The figures are taken from this paper by Edan Scriven and Ben Powell.

However, things are more subtle than I would have thought.

Here are some of the significant effects that result from these two different conformations. They have different energies and by thermal annealing in a crystal you can convert between them.

As a result disorder in a crystal can be controlled by varying the cooling rate.

In some materials there is even a glass transition around 80 Kelvin.

Examples of the dramatic effects of the disorder can be seen.

Resistance vs. temperature curve (see for example the figure below taken from here).

Suppression of the superconducting transition temperature.

This can be seen in the curves above.

Electrical noise experiments

Another dramatic effect of the ethylene groups that is much larger than most people expect is

Isotopic substitution of the hydrogen with deuterium in the ethylene groups can drive the Mott metal-insulator transition.

This somehow arises from a geometrical isotope effect associated with hydrogen bonds between the ethylene groups and the anion.

It turns out that changing the conformation of the end group can have a significant effect on the parameters in the Hubbard model, that is the simplest possible effective Hamiltonian for these materials.

This is shown in this recent paper which estimates these parameters using DFT-based electronic structure calculations and Wannier orbitals to map onto a tight-binding model.

Influence of molecular conformations on the electronic structure of organic charge transfer salts Daniel Guterding, Roser Valentí, and Harald O. Jeschke .

In particular in going from Eclipsed (E) to Staggered (S) or visa versa is enough to cross the Mott insulator-metal phase boundary.

This provides a framework to understand the experimental puzzles discussed above.

*One minor quibble.*The authors estimate the Hubbard paper U (Coulomb interaction) for two holes on a BEDT-TTF dimer with a formula which is only valid in a particular limit.

The general formula for the energy of two electrons on a two site Hubbard model is

where Um is the Hubbard interaction on a single dimer, V is the inter site Coulomb repulsion and t is the intersite hopping. The authors are assuming that Um - Vm is much larger than 4t which Scriven and Powell argue is not the case.

This will lead to quantitative changes but not change the main point that the conformational changes can produce a significant change in the Hubbard model parameters; particularly a large enough change to cross the Mott insulator-metal phase boundary.

Later I will write about the noise measurements (which I puzzled about before) which turn out to be a very sensitive probe of these two molecular conformations and their interconversion.

I thank Jens Muller for very helpful discussions about this work.

## Monday, September 19, 2016

### SciPost is a great initiative towards restoring science to journals

"SciPost is a a complete scientific publication portal managed by active professional scientists."

It is worth checking out.

SciPost addresses many concerns I have about the current sorry state of science and publishing. These include that journals becoming redundant and counter productive and so we need alternative publication models, particularly not involving for-profit companies.

One thing I particularly like is the transparency. All the referee reports are public and referees have the option of being anonymous or not. Furthermore, anyone can write a report. Authors responses to the reports are also public.

I think this public accountability may raise standards significantly.

I hope you (and I) will consider supporting it by

- submitting articles

- writing referee reports (either on request or volunteering)

- writing commentaries

- being willing to serve on the Editorial College

Jean-Sebastien Caux is to be commended for all the work he has put into this.

I thank Matt Davis for bringing this significant initiative to my attention.

It is worth checking out.

SciPost addresses many concerns I have about the current sorry state of science and publishing. These include that journals becoming redundant and counter productive and so we need alternative publication models, particularly not involving for-profit companies.

One thing I particularly like is the transparency. All the referee reports are public and referees have the option of being anonymous or not. Furthermore, anyone can write a report. Authors responses to the reports are also public.

I think this public accountability may raise standards significantly.

I hope you (and I) will consider supporting it by

- submitting articles

- writing referee reports (either on request or volunteering)

- writing commentaries

- being willing to serve on the Editorial College

Jean-Sebastien Caux is to be commended for all the work he has put into this.

I thank Matt Davis for bringing this significant initiative to my attention.

## Friday, September 16, 2016

### A basic quantum concept: energy level repulsion (avoided crossings)

When I learnt and later taught basic quantum mechanics I don't think the notion of energy level repulsion (or equivalently avoided crossings) was emphasised (or even discussed?).

Much later I encountered the idea in advanced topics in theoretical physics such as random matrix theory and in theoretical chemistry (non-adiabatic transitions and conical intersections).

Yet level repulsion is a very simple phenomena that can be illustrated with just a two by two matrix describing two coupled quantum states, as nicely discussed on the Wikipedia page.

Last semester when I was teaching Solid State Physics I realised just how central and basic the phenomena is and that the students did not appreciate this.

Level repulsion is the origin of several key phenomena in chemistry and physics.

In solid state physics, it is the origin of the appearance of band gaps at the zone boundary and thus the all important distinction between metals and insulators.

Previously, I posted how Chemistry is quantum science because chemical bonding (the lowering of energy due to interacting atoms) arises due to the superposition principle. This could also be viewed as level repulsion.

Another key idea in chemistry is that of transition states and activation energies for chemical reactions. When one uses a diabatic state picture, particularly as emphasised by Shaik and Warshel, the transition state emerges naturally in terms of level repulsion.

Much later I encountered the idea in advanced topics in theoretical physics such as random matrix theory and in theoretical chemistry (non-adiabatic transitions and conical intersections).

Yet level repulsion is a very simple phenomena that can be illustrated with just a two by two matrix describing two coupled quantum states, as nicely discussed on the Wikipedia page.

Last semester when I was teaching Solid State Physics I realised just how central and basic the phenomena is and that the students did not appreciate this.

Level repulsion is the origin of several key phenomena in chemistry and physics.

In solid state physics, it is the origin of the appearance of band gaps at the zone boundary and thus the all important distinction between metals and insulators.

Previously, I posted how Chemistry is quantum science because chemical bonding (the lowering of energy due to interacting atoms) arises due to the superposition principle. This could also be viewed as level repulsion.

Another key idea in chemistry is that of transition states and activation energies for chemical reactions. When one uses a diabatic state picture, particularly as emphasised by Shaik and Warshel, the transition state emerges naturally in terms of level repulsion.

The figure is taken from here.

Can you think of any other nice examples?

Labels:
chemistry,
conical intersection,
diabatic states,
key concepts,
PHYS4030,
teaching

## Wednesday, September 14, 2016

### Relating the Hall coefficient to thermodynamic quantities

Previously, I have posted about how in certain contexts one can relate non-equilibrium transport quantities to equilibrium thermodynamic quantities. This is particularly nice because for theorists it is usually a lot easier to calculate the latter than the former.

But, it should be stressed that all of these results are an approximation or only hold in certain limits.

Here are some examples.

The thermoelectric power can be related to the temperature derivative of the chemical potential through the Kelvin formula (illuminated by Peterson and Shastry).

A paper argues that the Weidemann-Franz ratio in a non-Fermi liquid can be related to the ratio of two different susceptibilities.

Work of Shastry showing that the high frequency limit of the Hall coefficient, Lorenz ratio and thermopower can be related to equilibrium correlation functions.

It has been suggested that the transverse thermoelectric conductivity (Nernst signal) due to superconducting fluctuations is closely related to the magnetisation.

Haerter, Pederson, and Shastry conjectured that for a doped Mott insulator on a triangular lattice that the Hall coefficient can be related to the temperature dependence of diamagnetic susceptibility.

Here I want to discuss some interesting results for the Hall coefficient R_H.

First, remember that in a simple Fermi liquid (or a classical Drude model) with only one species of charge carrier of charge q and density n that

R_H=1/q n

Clearly this is a case where a rather complex transport quantity (which is actually a correlation function involving three currents) reduces to a simple thermodynamic quantity.

But, what about in strongly correlated systems?

There is a rarely cited paper from 1993

Sign of equilibrium Hall conductivity in strongly correlated systems

A. G. Rojo, Gabriel Kotliar, and G. S. Canright

It gives an argument of just a few lines that relates the Hall coefficient to the orbital magnetic susceptibility (Landau diamagnetism)

BTW. I think there is a typo in the very last equation. It should also contain a factor of the charge compressibility.

I am a bit puzzled by the derivation, because it appears to be completely rigorous and general. The derivation of the Kelvin formula for thermopower, also has this deceptive general validity. It turns out that "devil in the details" turns out to be that the two limits of sending frequency and wave vector to zero do not commute.

A related paper shows that with a certain limiting procedure the Hall response (at zero temperature) is related to the derivative of the Drude weight with respect to the density.

Reactive Hall Response

X. Zotos, F. Naef, M. Long, and P. Prelovšek

This is valuable because it gives a simple explanation of why in a doped Mott insulator the Hall coefficient can change sign as the doping changes.

But, it should be stressed that all of these results are an approximation or only hold in certain limits.

Here are some examples.

The thermoelectric power can be related to the temperature derivative of the chemical potential through the Kelvin formula (illuminated by Peterson and Shastry).

A paper argues that the Weidemann-Franz ratio in a non-Fermi liquid can be related to the ratio of two different susceptibilities.

Work of Shastry showing that the high frequency limit of the Hall coefficient, Lorenz ratio and thermopower can be related to equilibrium correlation functions.

It has been suggested that the transverse thermoelectric conductivity (Nernst signal) due to superconducting fluctuations is closely related to the magnetisation.

Haerter, Pederson, and Shastry conjectured that for a doped Mott insulator on a triangular lattice that the Hall coefficient can be related to the temperature dependence of diamagnetic susceptibility.

Here I want to discuss some interesting results for the Hall coefficient R_H.

First, remember that in a simple Fermi liquid (or a classical Drude model) with only one species of charge carrier of charge q and density n that

R_H=1/q n

Clearly this is a case where a rather complex transport quantity (which is actually a correlation function involving three currents) reduces to a simple thermodynamic quantity.

But, what about in strongly correlated systems?

There is a rarely cited paper from 1993

Sign of equilibrium Hall conductivity in strongly correlated systems

A. G. Rojo, Gabriel Kotliar, and G. S. Canright

It gives an argument of just a few lines that relates the Hall coefficient to the orbital magnetic susceptibility (Landau diamagnetism)

I am a bit puzzled by the derivation, because it appears to be completely rigorous and general. The derivation of the Kelvin formula for thermopower, also has this deceptive general validity. It turns out that "devil in the details" turns out to be that the two limits of sending frequency and wave vector to zero do not commute.

A related paper shows that with a certain limiting procedure the Hall response (at zero temperature) is related to the derivative of the Drude weight with respect to the density.

Reactive Hall Response

X. Zotos, F. Naef, M. Long, and P. Prelovšek

This is valuable because it gives a simple explanation of why in a doped Mott insulator the Hall coefficient can change sign as the doping changes.

Labels:
charge transport,
Fermi liquids,
strong correlations

## Monday, September 12, 2016

### Mental illness IS irrational

That is the point!

Mentally healthy people are rational and reasonable (within the bounds of human fallibility!).

They are

Yet, often people struggle to understand and/or be empathetic with someone suffering from mental illness because they are not thinking and/or acting in a "rational" manner.

This dismissal or diminishing of what is going on can even be done by a sufferer themself, "I know I am having all these crazy thoughts and feelings, but I know they are crazy so it does not matter.... I don't need to get help."

or...

The person is so far gone that they actually think that their irrational thoughts are rational. It is everyone else who is crazy...

Here two good recent articles about mental health by physicists.

The plight of the postdocs: Academia and mental health

There’s an awful cost to getting a PhD that no one talks about

Mentally healthy people are rational and reasonable (within the bounds of human fallibility!).

They are

**not driven or paralysed**by amplified anxieties, phobias, mood swings, suicidal thoughts, depression, "black clouds", ...Yet, often people struggle to understand and/or be empathetic with someone suffering from mental illness because they are not thinking and/or acting in a "rational" manner.

This dismissal or diminishing of what is going on can even be done by a sufferer themself, "I know I am having all these crazy thoughts and feelings, but I know they are crazy so it does not matter.... I don't need to get help."

or...

The person is so far gone that they actually think that their irrational thoughts are rational. It is everyone else who is crazy...

Here two good recent articles about mental health by physicists.

The plight of the postdocs: Academia and mental health

There’s an awful cost to getting a PhD that no one talks about

## Friday, September 9, 2016

### Talk advice, especially for the inexperienced

There is nothing new in this post. But the issue keeps coming up.

I have written many posts about this before.

My last one was Advice to undergrads giving research talks.

Perhaps the following basic point gets lost in all the suggestions.

In almost every situation, most of your audience knows very little about your specific research topic. In some cases, they know virtually nothing about your actual research field.

Thus, you need to cut out almost all the technical details and give plenty of background and motivation.

But again, you need to realistic. Don't kid yourself that in 5 minutes you are going to teach them Density Functional Theory or Two-dimensional NMR spectroscopy.

Teach the audience some interesting science.

Convince them that your topic/field is interesting and important.

Show them you have achieved something concrete and interesting.

Don't bore people.

But perhaps, these are ambitious goals because most talks I hear don't achieve them!

I have written many posts about this before.

My last one was Advice to undergrads giving research talks.

Perhaps the following basic point gets lost in all the suggestions.

**Keep it simple.**In almost every situation, most of your audience knows very little about your specific research topic. In some cases, they know virtually nothing about your actual research field.

Thus, you need to cut out almost all the technical details and give plenty of background and motivation.

But again, you need to realistic. Don't kid yourself that in 5 minutes you are going to teach them Density Functional Theory or Two-dimensional NMR spectroscopy.

**Have modest goals.**Teach the audience some interesting science.

Convince them that your topic/field is interesting and important.

Show them you have achieved something concrete and interesting.

Don't bore people.

But perhaps, these are ambitious goals because most talks I hear don't achieve them!

Subscribe to:
Posts (Atom)