Ben Powell gave a short survey of work that has been recently published by him and Ross H. McKenzie (PRL 94, 047004 (2005), PRL 98, 027005 (2007) and J. Phys.: Condens. Matter 18 R827 (2006)). A paper on similar grounds has been published by J.Y. Gan, Yan Chen, Z.B. Su, F.C. Zhang (PRL 94, 067005 (2005)). The work concerns the kappa- and beta phases of (BEDT-TTF)_2X, a layered organic superconductor. Here, X is an anion complex such as Cu[N(CN)_2]Cl. Ben discussed the pressure-temperature phase diagram which reveals an insulator -> metal transition for increasing pressure (the pressure is supposed to be related to t/U in a Hubbard-like model, see below). At low temperature, a transition from an antiferromagnetic insulator (AFI) to a superconducting state (SC) is seen. At higher temperature, the AFI is replaced by a paramagnetic insulator and the SC takes a transition to a Fermi liquid. At even higher temperature, a "bad metal" is observed. A pseudo gap phase (PG) seems to be present above the SC at the low pressure side.
John Mydosh: does the PG end at the "bad metal". --- Ben: Yes.
Ben then presented a sketch of log(T_c) versus log(lambda) with slope -3 which is still a puzzling observation (BJP and R.H: McKenzie, J. Phys.: Condens. Matter 16, L367 (2004)).
The organic molecules are placed on a unit cell whereby two of the molecules (a pair) takes a lattice site. The transfer energy within each pair is the largest energy scale so that in the kappa and beta phases, they present a dimer. Then there is hopping t between adjacent dimers and a hopping parameter t' between one pair of diagonal dimers (the second diagonal hopping is much smalller and may be neglected. In the kappa phase t'/t ≤ 1 and in the beta phase t'/t > 1. The band structure may be described by a half-filled tight-binding model, with each site representing a dimer. For his modelling, Ben proposes a Hubbard-Heisenberg model with parameter space (t,t',J,J',U). A RVB-evaluation with a projected BCS ground state is set up.
Hartmut Monien: Doping dependence? --- Ben: The system stays basically undoped. The calculation is therefore at half-filling.
The evaluation of the Z-factor (which is 8(1-2d)d, where d is the average number of doubly occupied sites) displays a first order Mott transition with increasing U/t. With increasing t'/t, the transition is shifted towards larger U/t. The calculated phase diagram (U/t versus t'/t) is then as follows: For large values of U/t a Mott insulator is established. The peak in the fluctuations switches from wave vector (pi,pi) at small t'/t to some incommensurate value (q,q) close to t'/t=1 to (pi/2, pi/2) at larger t'/t. For sufficiently small U/t various superconducting phases are identified. For small t'/t <> 1 a d_xy -s phase is found. They are representations of the c_2v symmetry. For t'/t equal to 1 the symmetry group is c_6v and a d+id phase is expected. Numerical work and GL expansion suggests that it is stabilized in a finite interval. Finally, Ben expects that, with a lowering of the symmetry, a splitting of the SC transition may be observed for t'/t close to 1. First a d-wave state is stabilized and then, with lower temperature the d+id state. As this parameter regime is realized for the organic systems with X=[Cu(CN)_3], Ben proposes to search for such a phase transition scenario, for example, measure the state with broken time reversal symmetry with muSR.
John Mydosh commented: The anomalous Nernst effect is observed in the SC at sufficiently low pressure but is lost when you move to higher pressure (that is, also to different compounds).
Claudio Castellani asked: Is there a coupling to the lattice observed with the phase transitions?
Ben: A jump in the lattice constants has not been clearly observed. However in Raman frequency shifts of the modes have been seen.
Claudio Castellani: Comparison with the cuprates? Ben: you would have to introduce a new axis t/U in the phase diagram, pointing vertically from the undoped system.
Wednesday, August 29, 2007
Posted by Thilo Kopp at 6:24 PM