Saturday, November 20, 2010

The Fermi surface of overdoped cuprates

When I was in Bristol a few months ago Nigel Hussey gave me a proof copy of a nice paper that has just appeared in the New Journal of Physics,
A detailed de Haas–van Alphen effect study of the overdoped cuprate Tl2Ba2CuO6+δ
by P M C Rourke, A F Bangura, T M Benseman, M Matusiak, J R Cooper, A Carrington and N E Hussey

Here are a few things I found particularly interesting and significant about the paper.
1. It is beautiful data!
2. Estimating the actual doping level and "band filling" in cuprates is a notoriously difficult problem. But, measuring the dHvA oscillation frequency gives a very accurate measure of the Fermi surface area (via Onsager's relation). Luttingers theorem then gives the doping level. [see equation 15 in the paper].
3. The intralayer Fermi surface and anisotropy of the interlayer hopping determined are consistent with independent determinations from Angle-Dependent MagnetoResistance (ADMR) performed by Hussey's group earlier. This increases confidence in the validity of both methods. Aside: It should be stressed that both are bulk low-energy probes, whereas ARPES and STM are surface probes. 
4. The effective mass m*(therm) determined from the temperature dependence of the oscillations agrees with that determined from the specific heat and from ARPES. This is approximately 3 times the band mass, showing the presence of strong correlations, even in overdoped systems. The effective mass does not vary significantly with doping [see my earlier post on this].
5. The presence of the oscillations put upper bounds on the amount of inhomogeneity in these samples, ruling out some claims concerning inhomogeneous doping.
6. The Figure above shows how well the observed Fermi surface agrees with that calculated from the Local Density Approximation (LDA) of Density Functional Theory (DFT). I think this means that the momentum dependence of the real part of the self energy on the Fermi surface must be small.
7. The "spin zeroes" allow one to determine the "effective mass" m*(susc) associated with the Zeeman splitting. [This could also be viewed as a effective g-factor g*]. 
A few small comments:
a. The equation below relates the specific heat coefficient gamma to the effective mass determined from dHvA
This is often derived for a parabolic band. It is not widely that this is a very general relationship which holds for any quasi-two-dimensional band structure. Furthermore, the formula for the effective mass in terms of the derivative of the area of the Fermi surface gives this formula too. Hence, taking that derivative numerically, as done by Rourke et al., is unnecessary. This is shown and discussed in detail in a paper I wrote with Jaime a decade ago, Cyclotron effective masses in layered metals.
b.  The ratio of the two effective masses, m*(susc) and m*(therm) equals the Sommerfeld-Wilson ratio, something I pointed out  in a preprint [but was not able to publish] long ago. 

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