Compressibility sum rule for the two-dimensional electron gas - art. no. 012103

The authors establish formulas for the isothermal compressibility and long- wavelength static density-density response function of a weakly correlated two-dimensional electron gas in the 1<<beta epsilon (F)<<infinity> and 0 le ss than or equal to beta epsilon (F)<<1 degeneracy domains; beta epsilon (F ) = pin (h) over bar (2)/(mk(B)T). The calculation of the pressure in the f ormer domain is based on the Isihara-Toyoda formula [A. Isihara and T. Toyo da, Phys. Rev. B 21, 3358 (1980)] for the exchange-correlation energy at fi nite temperature. The pressure calculation in the latter domain is based on the Totsuji classical cluster-expansion formula for the correlation energy [H. Totsuji, J. Phys. Sec. Jpn. 40, 857 (1976); Phys. Rev. A 19, 889 (1979 )].