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Register a new userAnomalous low temperature specific heat of He-3 inside nanotube bundles
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Helium atoms and hydrogen molecules can be strongly bound inside interstitial channels within bundles of carbon nanotubes. An exploration of the low energy and low temperature properties of He-3 atoms is presented here. Recent study of the analogous He-4 system has shown that the effect of heterogeneity is to yield a density of states N(E) that is qualitatively different from the one-dimensional (1D) form of N(E) that would occur for an ideal set of identical channels. In particular, the functional form of N(E) is that of a 4D gas near the very lowest energies and a 2D gas at somewhat higher energies. Similar behavior is found here for He-3. The resulting thermodynamic behavior of this fermi system is computed, yielding an anomalous form of the heat capacity and its dependence on coverage.
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Porous aerogel is a source of elastic scattering in superfluid 3He and modifies the properties of the superfluid, suppressing the transition temperature and order parameter. The specific heat jumps for the B-phase of superfluid 3He in aerogel have been measured as a function of pressure and interpreted using the homogeneous and inhomogeneous isotropic scattering models. The specific heat jumps for other p-wave states are estimated for comparison.
The specific heat of superfluid $^{3}$He, disordered by a silica aerogel, is found to have a sharp discontinuity marking the thermodynamic transition to superfluidity at a temperature reduced from that of bulk $^{3}$He. The magnitude of the discontinuity is also suppressed. This disorder effect can be understood from the Ginzburg-Landau theory which takes into account elastic quasiparticle scattering suppressing both the transition temperature and the amplitude of the order parameter. We infer that the limiting temperature dependence of the specific heat is linear at low temperatures in the disordered superfluid state, consistent with predictions of gapless excitations everywhere on the Fermi surface.
The low-temperature normal-state specific heat and resistivity curves of various nonmagnetic intermetallic compounds manifest an anomalous thermal evolution. Such an anomaly is exhibited as a break in the slope of the linearized C/T versus T^2 curve and as a drop in the R versus T curve, both at the same T_{beta}{gamma}. It is related, not to a thermodynamic phase transition, but to an anomaly in the density of states curves of the phonon or electron subsystems. On representing these two anomalies as additional Dirac-type delta functions, situated respectively at kB.{theta}_L (for lattice) and kB.{theta}_E (for electrons), an analytical expression for the total specific heat can be obtained. A least-square fit of this expression to experimental specific heat curves of various compounds reproduced satisfactorily all the features of the anomalous thermal evolution. The obtained fit parameters (in particular the Sommerfeld constant, {gamma}_{0}, and Debye temperatures, {theta}_D, compare favorably with the reported values. Furthermore, the analysis shows that (i) (T_{beta}{gamma}) / ({theta}_D) = 0.2(1pm1/surd6) and (ii) {gamma}_{0} {propto} ({theta}_D)^2; both relations are in a reasonable agreement with the experimental results. Finally, this analysis (based on the above arguments) justifies the often-used procedure that treats the above anomaly in terms of either a thermal variation of {theta}_D or an additional Einstein mode.
High resolution measurements of the specific heat of liquid $^{3}$He in the presence of a silver surface have been performed at temperatures near the superfluid transition in the pressure range of 1 to 29 bar. The surface contribution to the heat capacity is identified with Andreev bound states of $^{3}$He quasiparticles that have a range of half a coherence length.
Both amorphous and crystalline materials frequently exhibit low temperature specific heats in excess of what is predicted using the Debye model. The signature of this excess specific heat is a peak observed in $C/T^3$ textit{versus} $T$. To understand the curious absence of long-range ordering of local distortions in the crystal structure of pyrochlore Bi$_2$Ti$_2$O$_7$, we have measured the specific heat of crystalline Bi$_2$Ti$_2$O$_7$ and related compounds. We find that the peak in $C/T^3$ versus $T$ in Bi$_2$Ti$_2$O$_7$ falls at a substantially lower temperature than other similar compounds, consistent with the presence of disorder. This thermodynamic evidence for disorder in crystalline Bi$_2$Ti$_2$O$_7$ is consistent with quenched configurational disorder among Bi lone pairs produced by geometrical frustration, which could represent a possible realization of charge ice.
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