Canonical behavior of the
specific heat
W. H. Lien and N. E. Phillips, Phys. Rev. 118, 958 (1960)
Less canonical behavior of C(T)—notice a pronounced T 3 ln T term.
Such a term, however, is still within the Fermi-liquid theory.
G. Stewart, Rev. Mod. Phys. 56, 755 (1984)
Non-Fermi-liquid behavior of the specific heat
Amitsuka et al. Physica B 206&207, 461 (1995)
Interaction-induced renormalizaton
of the Fermi-gas parameters
kF l ; 1
χ*/χ
rs ≡ m0 e 2 1/ π n
rs
Resistive transition
Si-MOSFET
Pudalov at al. (2001)
interaction
Qualtitatively similar results
on n- and p-GaAs
Linear T-dependence of the resistivity:
understood cases
Interaction of electrons
with lattice vibrations
(phonons)
Linear T-dependence of the resistance:
mysterious cases
• Some heavy-fermion compounds
• High-Tc superconductors in the normal
phase
Resistivity as a function of T in a heavy-fermion compound
YbRh 2 ( Si 0.95Ge0.95 ) 2
J. Custers, PhD thesis 2004
TU Dresden
Cannot be phonons (too low T)
Slope of
ρ = AT a
Origin of the linear T
dependence:
most likely not phonons
T term in the resistivity of Al
2
Landau Fermi-liquid theory (1958):
1
τ e− e
T2
∝ T
2
T2
2
ρ
=
AT
law
Another example of the
K. E. Andres, J. E. Graebner, and H. R. Ott
Phys. Rev. Lett. 35, 1779 (1975)
Quantum ferromagnetic phase
transition in NiPd alloy
• Adding non-magnetic Pd to magnetic Ni, one
destroys ferromagnetism (FM).
• This destruction happens at a well defined
concentration of Pd, where the critical temperature
of the FM transition vanishes.
• Points where a phase transformation occurs at zero
temperature due to tuning of some control
parameter are called Quantum Phase Transitions.
• Experiments are performed at finite temperatures
—signatures in C(T), resistivity, etc.
A dissenting opinion: P. Allen from Stony Brook [Nature, 412, 494 (2001)]
argues that this linear-in-T dependence can be well explained by phonons.
Hall Effect
Al
Graphite, S. Tongay et al. arXiv:0907.1111
your next homework
Weak-field limit
RH = R1
ρ
(ρ1+
2
2
ρ 2)
2
+ R2
ρ
(ρ1+
2
1
ρ 2)
2
Bi @ T=25 mK
Bompadre, Biagini, Maslov, and Hebard, Phys. Rev. B
Quantum magnetoscillations
in HTc superconductors
http://en.wikipedia.org/wiki/Quantum_Hall_effect