An important step in modelling complex materials is writing down effective Hamiltonians which capture the essential physics. One approach to estimating model parameters for a specific material is to calculate them using methods from electronic structure theory.
About ten years ago, following earlier work by Kino and Fukuyama, I wrote a
review arguing that the relevant Hamiltonian for the kappa-(BEDT-TTF)2X family of superconducting organic charge transfer salts was a Hubbard model on the anisotropic triangular lattice at half filling.
A recent
PRL by a group from Goethe Universitat Frankfurt is of particular interest to me because it describes state-of-the-art calculations based on density functional theory. For three different anions X and two different pressures, the authors calculate the parameters t and t' which define the band structure. Figure 4 from the paper gives a nice summary of the results.
[Similar results were obtained at the same time by a group in Japan and reported
here.]
The ratio t'/t has a significant effect on the ground state of the system, as can be seen in the proposed phase diagram from a
PRL by Ben Powell and I.
A few specific things that stood out to me about the results:
1. The ratio t'/t does vary significantly with anion X.
X, t'/t , experimental ground state at ambient pressure
Cu[N(CN)2]Cl, 0.44 +- 0.05, antiferromagnetic Mott insulator
Cu(SCN)2, 0.58 +- 0.05, superconductor
Cu2(CN)3, 0.83 +- 0.08, spin liquid Mott insulator
This variation can explain why one does see a "chemical pressure" effect. i.e., the anion does have a significant effect on the ground state.
2. The level of DFT used (LDA vs. GGA) does not seem to have a large effect (less than ten per cent) on the results, increasing confidence that the results are somewhat robust.
3. The calculated magnitudes of t~0.05-0.07 eV are comparable to those estimated from comparision of the experimental optical conductivity to that calculated using dynamical mean-field theory (see this
PRL).
4. The values of t and t' can be used to estimate the bare density of states at the Fermi energy. Comparison with measurements of the cyclotron effective mass and the specific heat coefficient gamma provides a means to estimate the renormalisation of these by many body effects. This is discussed in great detail in this
paper.
5. The value of t1 (the intradimer hopping) ~ 0.2 eV is comparable to that estimated from the intradimer transition in the optical conductivity.
6. The authors estimate U ~ 2t1, where t1 is the intradimer hopping, following what I did a decade ago. However, this is only true in the limit that 2t1 >> U0, the single molecule U. This turns out not to be justified and is discussed in
this review.
7. The authors calculate that t varies by as much as 30 per cent as the pressure increases to 0.75 GPa ( 7.5 kbar). This can explain why the ground state does change with pressure (e.g., from Mott insulator to superconductor to metal). When I wrote my review a decade ago this was an unsolved problem.
8. The value for X=Cu2(CN)3 of t'/t = 0.83 +- 0.08 means in the relevant Heisenberg model that describes the spin degrees of freedom in the Mott insulator, J'/J ~0.6, a value comparable to that at which magnetic order disappears, as calculated in this
paper.
One question I have is:
What is the physical basis of the chemical pressure effect?
