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ELTE Fizika Tanszekcsoport


                             ORTVAY KOLLOKVIUM

                    2005. marcius 17. , csutortok, 15 orakor
  Az ELTE Pazmany Peter s. 1/A alatti epuleteben a foldszinti 0.83 eloadoban

                                 FIB Williams 
             (SPEC, CEA-Saclay, France es SZFKI, MTA-Budapest  ): 
    " From Classical Coulomb Crystal to Quantum Wigner Transition - in 2-D" 

Kivonatos ismertetes:

Electrons in a metal behave as a conducting Fermi liquid; the interaction 
with 
the underlying lattice of ions is felt mostly as renormalised mass and the 
mutual interaction is hardly felt at all. As early as 1934, Wigner pointed 
out 
that if electrons were heavier, or more dilute, the ground state should be 
not 
a liquid but a (now called Wigner) crystal of electrons. Usually extrinsic 
disorder is stronger than the mutual Coulomb interaction at the low densities 
at which this would occur and the electrons get stuck in the disorder 
potential 
instead of crystallising. In the absence of disorder, the quantum kinetic 
(Fermi) energy favours the more delocalised liquid configuration and the 
criterion determining which configuration is more favourable compares Fermi 
energy with Coulomb energy: r_s=W(Coulomb)/W(Fermi)=(e^2/a)/(h^2/ma^2)=a/a_B, 
where a is the mean distance between electrons. In usual metals, r_s~1 
whereas 
the crystalline ground state is only expected for r_s > 10^2 in 3 dimensions. 
It was another 45 years before experimentalists found a system satisfying 
this 
and the disorder criterion. 

The first, very classical, Coulomb crystal was seen in 1979 in the very low 
disorder system of electrons on the cold surface of liquid helium, at 
r_s~1000. 
This very classical system is an ideal test bed for classical melting in 2 
dimensions. Experiments have been possible on structure, spatial 
fluctuations, 
transverse phonons and thermodynamics, all of which point to melting by 
separation of dislocation pairs, a mechanism proposed for 2-D melting by 
Kosterlitz and Thouless. 

Nine years later the quantum melting transition was observed for electrons 
constrained to 2-D by a high quality (low disorder) GaAs/GaAlAs 
heterojunction. 
Despite r_s~3, the quantum fluctuations could be reduced by the application 
of 
a strong magnetic field perpendicular to the plane of the dynamics. As one 
raises the magnetic field in this system one observes the integral then the 
fractional quantum Hall effects before the fluctuations are reduced 
sufficiently that, at sufficiently low temperature, the charges crystallise. 
In 
this system, the background disorder is no longer negligible and leads to 
collective pinning and non-linear longitudinal and Hall conductivity. This 
aspect of the problem, a periodic elastic network in a random field, 
resembles 
the problem of vortices in superconductors and in particular in very 
anisotropic quasi-2-D high Tc superconductors like BSCCO on which non linear 
conduction in the "free flux flow" regime of the vortex solid phase has 
recently been investigated at the SZFKI. 

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