Hydrogenation of the Transition Metal Dichalcogenide Superconductors

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 T_c versus x plot in Figure . In both figures T_c 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. ( T_c ;SPM_lt; 0.5 K for H_0.87TaS₂.[179]. This data point is not shown in Figure .) T_c also increases slightly for NbSe₂ when a small amount of hydrogen is added.[179]

  
Figure: T_c 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, T_c ;SPM_lt; 0.5 K (not shown). b) From Ref. [90]. T_CDW is the CDW onset temperature, while T_c is the usual superconducting transition temperature. 4H _b and 2H are TaS₂ polytypes with different crystal structures.

The resemblance between the C₈KH_x and the TMDC data turns out to be mostly coincidence since the causes are probably quite different. The hydrogen-induced T_c 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 T_c 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 Nb_1-xTi_xSe₃. NbSe₃ has T_c < 50 mK, whereas the compound with x = 0.001 has T_c 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 T_c 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 T_c enhancement with pressure. Since NbS₂ is also the only material which does not have a CDW transition, its comparatively small dT_c/dP ( only 5× 10^-6 K/bar) is evidence that CDW suppression is the cause of the dT_c/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 T_c up to the point where the CDW is suppressed, whereas they affect T_c only slowly above the CDW transition. For example, NbSe₂ has a large dT_c/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 dT_c/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 T_c.[91] By ``intrinsic'', one means the T_c value that would be expected from the usual theories given theta_D, Lambda_ep, etc. Further application of the perturbation may then either increase or decrease T_c, 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) Delta_s², where Delta_s 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) Delta_CDW² (with some additional multiplicative factors),[204] where Delta_CDW 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 T_c 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 T_c is the CDW-suppressed superconducting transition temperature, T_c0 is the intrinsic transition temperature, T_CDW 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 T_CDW(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 T_c(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 T_c. The enhancement of T_c 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 T_c 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.