The impact of hydrogen on superconductivity in the transition
metals bears some resemblance to the effect hydrogen has on
the KH-GIC's. To be convinced of this, compare Figure
a) with the Tc versus x plot in Figure
.
In both figures Tc at first rises with increasing
H content, reaching its maximum near x 0.1, and then falls to
an unmeasurably low level at high x. ( Tc
;SPMlt; 0.5 K for
H0.87TaS2.[179]. This data point is not shown
in Figure
.) Tc also
increases slightly for NbSe2 when a small amount
of hydrogen is added.[179]
Figure: Tc increase in
TaS2 induced by a) hydrogenation and b) pressure.
a) From Ref. [179]. The
error bars represent the transition width, while the circles
are the volume % superconducting. This experiment was
performed on a powder sample. At a hydrogen concentration
ofu.87, Tc ;SPMlt; 0.5 K (not shown).
b) From Ref. [90].
TCDW is the CDW onset temperature, while
Tc is the usual superconducting transition
temperature. 4H b and 2H are TaS2
polytypes with different crystal structures.
The resemblance between the C8KHx and
the TMDC data turns out to be mostly coincidence since the
causes are probably quite different. The hydrogen-induced
Tc enhancement in the TMDC's TaS2 and
NbSe2 is now known to be due to suppression of a
charge-density wave transition that occurs in the
unhydrogenated materials.[179,90] The charge-density wave can
also be suppressed (and consequently Tc can be
increased) by intercalation, pressure, or dopants beside
hydrogen.[90] CDW
destruction by intercalation was briefly mentioned in Section
. CDW
suppression by pressure is illustrated in Figure
b) for TaS2. CDW suppression by pressure is a
general phenomenon for the CDW's of the layered TMDC's.[90] CDW destruction by
impurities is exemplified in the system
Nb1-xTixSe3.
NbSe3 has Tc < 50 mK, whereas
the compound with x = 0.001 has Tc 2.1 K.[91] The extreme sensitivity of the
CDW to impurities has understandably resulted in great
reproducibility problems with superconductivity in the
TMDC's.[91]
The CDW-based explanation for Tc enhancement in
the TMDC's is fairly well-established because of the
observation of a CDW in several different experiments. For
example, Figure show discontinuities in
the resistivity of TaSe2 due to a CDW
transition.[264] There can
be no doubt that these high-temperature resistivity anomalies
are due to CDW formation since the associated periodic
lattice distortion has been directly observed using TEM,
neutron scattering, and x-ray diffraction.[90,264]
Figure: In-plane resistivity
discontinuities in TaSe2 associated with CDW
formation. From Ref. [264]. 1T- and 2H- refer to
different polytypes (crystal structures). The CDW transitions
occur at 473 K in 1T-TaSe2 and at 117 K in
2H-TaSe2, respectively. Notice that
1T-TaSe2 has a higher resistivity below its
transition, whereas the resistivity of 2H-TaSe2
decreases at its transition.
Except for 2H-NbS2, the CDW phenomenon occurs in all polytypes of all members of the class MX2, where M = V, Nb, or Ta, and X = S or Se.[90] Of these materials, only 2H-NbS2 does not show a large Tc enhancement with pressure. Since NbS2 is also the only material which does not have a CDW transition, its comparatively small dTc/dP ( only 5× 10-6 K/bar) is evidence that CDW suppression is the cause of the dTc/dP in the other MX2 materials.[90,217] A host of experiments show that perturbations (such as pressure, hydrogen, and impurities) tend to rapidly increase Tc up to the point where the CDW is suppressed, whereas they affect Tc only slowly above the CDW transition. For example, NbSe2 has a large dTc/dP (4.95 × 10 -5 K/bar) for pressures below 35 kbar, the pressure where the CDW is completely suppressed. Above 35 kbar, the slope is only dTc/dP = 2.8 × 10-6 K/bar, even smaller than that in NbS2.[217] Obviously this is no coincidence.
The thrust of many of the superconductivity experiments on the TMDC's is that there is a competition between the superconducting and CDW transitions, so that preventing one condensed state encourages the other one. This line of reasoning says that once the CDW is completely suppressed by a perturbation, a material reaches its intrinsic magnitude of Tc.[91] By ``intrinsic'', one means the Tc value that would be expected from the usual theories given thetaD, Lambdaep, etc. Further application of the perturbation may then either increase or decrease Tc, depending on the properties of the individual superconductor.
The reason that CDW's and superconductivity compete with one another is quite simple. In the BCS theory of superconductivity,[16] the condensation energy of the superconducting state is 1/2 N(0) Deltas2, where Deltas is the superconducting energy gap. In a similar mean-field theory of the charge-density wave transition, the condensation energy is also proportional to N(0) DeltaCDW2 (with some additional multiplicative factors),[204] where DeltaCDW is now the CDW energy gap. The juxtaposition of these two expressions for the condensation energy immediately shows why the two phases tend not to coexist: they both need to create a gap at the Fermi surface. Once the Fermi surface has a gap above it, any further phase transition driven by an instability of the Fermi sea is completely suppressed.
In real metals, a CDW transition tends to gap only a portion of the Fermi surface, leaving some condensation energy available for use in a superconducting transition. Thus a high-temperature CDW transition tends merely to lower Tc and not to altogether prevent superconductivity. Bilbro and McMillan found a relationship between the amount that the superconducting transition temperature is lowered by a higher-temperature CDW phase transition and the amount of Fermi surface which is removed in that transition.[23] The relationship is:
where Tc is the CDW-suppressed superconducting
transition temperature, Tc0 is the intrinsic
transition temperature, TCDW is the CDW onset
temperature, and N1/N is the fraction of the
density-of-states removed in the CDW transition. Fuller,
Chaikin, and Ong[91]
obtained N1/N as a function of pressure P in
NbSe3 by measuring the size of the resistivity
discontinuity at TCDW(P). The result is
N1/N = (0.6 - 0.18p), where p is the pressure in
kbar. Fuller and coauthors[91] used these numbers in
conjunction with Eqn. to fit their
Tc(P) data, and found good agreement at low
pressures.
This agreement is convincing evidence that CDW-suppression of superconductivity is indeed due to the competition of the two condensed phases for the Fermi surface. Any perturbation of the materials that tends to suppress the CDW, such as pressure, hydrogenation, or intercalation, will therefore also tend to increase Tc. The enhancement of Tc by hydrogenation in the TMDC's obviously is due to a very different mechanism than that which has been put forward for the transition metals and the alkali-metal GIC's. Since hydrogen first increases and then depresses Tc in C8K, one might wonder whether CDW's might also play a role. This possibility is discussed below in connection with the results on the KHg-GIC's. Before relating the outcome of the hydrogenation experiments on the KHg-GIC's, the details of the experiments are briefly described.