Thermal properties in mesoscopics: physics and ... - ResearchGate

e 2 R /Δ T 2 (0)(×10 -2 Q&Q&
)
6
k T/Δ(0) = 0.4
B
3
0
6
-3
3
= 1
0.94
¡ = 1
0.98
0.96
0.96
0.98
(a)
Q& (nW/μm
A
2 )(×10 2 )
-6
0
0.0
-9
0.0
0.94
0.4
kBT/Δ(0) 0.5
0.8
1.0 1.5
eV/Δ(0)
8
7
6
5
4
3
k T/ Δ (0)=0.4
2 B
1
0
¢ = 1
0.98
0.96
0.94
25
20
15
10
5
0.0 0.4 0.8 0
k T/Δ(0)
B
0.3
0.2
0.15
0.94 0.96 0.98 1.00
FIG. 31 (Color in online edition) (a) Calculated heat current
˙ Q of a SF junction vs bias voltage V at T = Te,F =
Te,S = 0.4 ∆(0)/kB for several spin polarizations P. The inset
shows the same quantity calculated at the optimal bias
voltage against temperature for some values of P. (b) Calculated
maximum cooling power surface density ˙ QA versus
P for various temperatures. The inset shows the coefficient
of performance η calculated at the optimal bias voltage versus
temperature for some P values. Adapted from (Giazotto
et al., 2002, 2005).
a possible higher-temperature first stage in cascade cooling
(for instance, over or around 1 K), where it could
dominate over the large thermal coupling to the lattice
characteristic for such temperatures.
The results given above point out the necessity of
strongly spin-polarized ferromagnets for a proper operation
of the SF refrigerator. Among the predicted
half-metallic candidates it is possible to indicate CrO2
(Brener et al., 2000; Kämper et al., 1987; Schwartz,
1986), for which values of P in the range 85...100% have
been reported (Coey et al., 1998; Dedkov et al., 2002; Ji
et al., 2001; Parker et al., 2002), (Co1−xFex)S2 (Mazin,
2000), NiMnSb (de Groot et al., 1983), Sr2FeMoO6
(Kobayashi et al., 1998) and NiMnV2 (Weht and Pickett,
1999). So far no experimental realizations of SF structures
for cooling applications have been reported.
5. HTc NIS systems
Heat transport in high-critical temperature (HTc) NIS
junctions was theoretically addressed by Devyatov et al.
(2000). In these systems the cooling power depends on
interface transmissivity as well as on orientation of the
superconductor crystal axes and temperature. In particular,
these authors showed that the maximum positive
heat current in these structures can be achieved
in junctions with zero superconducting crystallographic
angle, at temperature T = 0.45 Tc and bias voltage
V ≈ 0.8 ∆(0)/e. The behavior of ˙ Q(V ) turns out to
be qualitatively similar to that of NIS junctions based
on low-critical temperature superconductors (see Fig.
26(a)), and with comparable values (in relative units).
P
η (%)
(b)
40
From this it follows that the cooling power of electronic
refrigerators based on HTc materials is approximately
two orders of magnitude larger than in NIS junctions
based on low-critical temperature superconductors (at
much lower temperatures).
A somewhat different cooling effect in HTc superconductors
was predicted by Svidzinsky (2002), who showed
that an adiabatic increase of the supercurrent in a ring
(or cylinder) made from a HTc superconductor may lead
to a cooling effect. The maximum cooling occurs if the
supercurrent is equal to its critical value. For a clean
HTc superconductor, the minimum achievable temperature
(Tmin) was found to be around Tmin = T 2 0 /Tc, with
T0 the initial temperature of the ring, thus meaning that
substantial cooling can be achieved using large Tc values.
Experimentally, Fee (1993) realized a Peltier refrigerator
junction exploiting a HTc superconductor and operating
around liquid nitrogen temperatures. In particular,
his device consisted of a BiSb alloy and YBa2Cu3O7−δ
superconducting rods connected by a small copper plate
which acted as the cold junction of the device. The latter
showed a maximum cooling of 5.35 K below the bath
temperature T0 = 79 K. The figure of merit of the junction,
Z, was estimated to be as large as 2.0 × 10 −3 K −1 .
6. Application of (SI)NIS structures to lattice refrigeration
One well established application of SINIS refrigerators
concerns lattice cooling (Clark et al., 2005; Luukanen
et al., 2000; Manninen et al., 1997). As a matter
of fact, while NIS tunneling directly cools the electron
gas of the normal electrode, the phonon system can be
refrigerated through the electron-phonon coupling (see
Eq. (24)). The latter, however, is typically very small at
the lowest temperatures, thus limiting the heat transfer
from the surroundings to the electrons. This situation
normally happens whenever the metal to be cooled is in
direct contact with a thick substrate, for instance, oxidized
Si (Leivo et al., 1996; Nahum et al., 1994): only the
electrons of the N region cool down while the metal lattice
presumably remains at the substrate temperature. The
metal lattice can be refrigerated considerably if the thermal
resistance between the phonons and the substrate
is not negligible compared to that between the electrons
and the phonons. One effective choice to meet this requirement,
that was indeed suggested at the beginning
of cooling experiments (Fisher et al., 1995; Nahum et al.,
1994) as well as for detector applications (Deiker et al.,
2004; Doriese et al., 2004; Irwin et al., 1996; Nahum and
Martinis, 1995; Pekola et al., 2004b; Ullom et al., 2004),
is to exploit a thermally isolated thin dielectric membrane
on which the N region of the cooler is extended.
In this way, tunneling through the NIS junction will
cool down the electrons of the metal, then the phonons
of the metal (via electron-phonon coupling) that subsequently
will refrigerate the membrane phonons (Clark
et al., 2005; Luukanen et al., 2000; Manninen et al., 1997)