Temperature Fermi

For electrons in a metal, these velocities are on the order of 10 cm s . The Fermi temperature Tp is defined by the relation... 

The electronic heat capacity for the free electron model is a linear function of temperature only for T Tp = p / kp. Nevertheless, the Fermi temperature Tp is of the order of 105 K and eq. (8.46) holds for most practical purposes. The population of the electronic states at different temperatures as well as the variation of the electronic heat capacity with temperature for a free electron gas is shown in Figure 8.20. Complete excitation is only expected at very high temperatures, T>Tp. Here the limiting value for a gas of structureless mass points 3/2/ is approached. 

It follows fi om Eqns. 1-12 and 1-13 that the state density is half occupied by electrons with the remaining half vacant for electrons at the Fermi level, tt, as shown in Fig. 1-2. Since the Fermi temperature of electrons (Tc = Cf/A) in electron... 

However, the intra-atomic Coulomb interaction Uf.f affects the dynamics of f spin and f charge in different ways while the spin fluctuation propagator x(q, co) is enhanced by a factor (1 - U fX°(q, co)) which may exhibit a phase transition as Uy is increased, the charge fluctuation propagator C(q, co) is depressed by a factor (1 -H UffC°(q, co)) In the case of light actinide materials no evidence of charge fluctuation has been found. Most of the theoretical effort for the concentrated case (by opposition to the dilute one-impurity limit) has been done within the Fermi hquid theory Main practical results are a T term in electrical resistivity, scaled to order T/T f where T f is the characteristic spin fluctuation temperature (which is of the order - Tp/S where S is the Stoner enhancement factor (S = 1/1 — IN((iF)) and Tp A/ks is the Fermi temperature of the narrow band). 

A degenerate electron gas is an electron gas that is far below its Fermi temperature, thai is. which must be described by die Fermi distribution. The essential characteristic or this state is that a very large proportion of the electrons completely fill the lower energy levels, and are unable to lake pan in any physical processes until excited out of these levels. 

In order to identify the Feshbach shape resonance we have plotted in Fig. 14 the ratio Tc/TF(exp) for the aluminum doped case where TF is the Fermi temperature TF=eF/KB and eF=EA-EF is the Fermi energy of the holes in the a band, and Tc is the measured critical temperature. The TC/TF ratio is a measure of the pairing strength (kF o)1 where kF is the Fermi wavevector and is the superconducting coherence length. In fact in the single band BCS theory this ratio is given by TC/TF = 0.36/ , ,. ... 

Figure 1 2 14. The ratio Tc/TF(exp) (open squares) for the aluminium doped case where TF is the Fermi temperature TF=EF/KB for the holes in the o band and Tc is the measured critical temperature for A1 doped samples as a function of the reduced Lifshitz parameter z . The expected ratio Tc/TF(BCS) (open triangles) for the critical temperature in a BCS single s band, The ratio ATCITF = (7)(exp)- 7)(BCS)) /TF (solid dots) that measures the increase due to the...

For the compound UPt3, the value for y amounts to 420 mJ/mol K2, whereas the values for A and X depend on the direction in which the resistivity and the susceptibility have been measured, although these results do not differ more than roughly a factor of two. To illustrate these findings, the specific heat of an artificial heavy-fermion compound is shown in fig. 1 in a plot of c/T versus T2 and compared with the result for, again, an artificial normal metal. For the effective Fermi velocity, vF, one deduces values of order 5x103 m/sec and for the effective Fermi temperature values between 10 and 100 K. 

Typical for heavy-fermion systems is the large value for re that can take values which are several orders of magnitude larger than what is found in normal metals. It implies that the effective mass has a large volume dependence as does the effective Fermi temperature. 

Comparison of the Maxwell-Boltz-mann (MB) and Fermi-Dirac(FD) distributions, Eqs. (8.2.1) and (8.2.2), for the case T0= 100 7. Within the dimensionless abscissa parameterx, v2 is the independent variable. It is clearthatthe MB distribution peaks at very low velocities, while the FD occupancy is 1 (2 if you include spin) at lower temperatures, 0 at high temperatures, 1/2 at the Fermi temperature (at x = m Al2kBT = 100), and between 0 and 1 in a narrow x range around x=100. From Ashcroft and Mermin [4]. 

Now, typical Fermi temperatures in metals are of the order of 50 000 K. Thus, at room temperature, TIT is very small compared to one. So, one can ignore the Tdependence of p, to obtain... 

The result of the Hall coefficient gives a key to solve the present problem. We show in Fig.4 the temperature dependence of the Hall coefficient for 3N-G P-samples. The small resistivity for the H-sample corresponds to the small Hall coefficient, namely the large carrier concentration, as compared to the one for the L-sample. The Hall coefficients for the G-samples are temperature independent, showing a degenerate semiconductor. We can estimate the Fermi temperature, Tp, from the measured Hall coefficient under the assumption that the effective mass is equal to the free electron mass and the carrier is one kind, namely an electron. The Tp-value is ca. 600K for the G-samples. Therefore, the relatively large carrier concentration satisfies the degenerate condition. 

---