Superconductivity in the Potassium-Hydrogen GIC's

The effect of hydrogen on superconductivity in C₈K must be a balance of opposing tendencies since hydrogen can either raise or lower T_c. From the discussion above concerning the transition metals, one might anticipate that the opposing factors might be the decrease in carrier density and increase in electron-phonon coupling that are generally associated with hydrogenation of metals.[233] The T_c's of hydrogenated K-GIC's are collected in Table .

  
Table: Superconducting transition temperatures of the KH-GIC's and C₈K. Two methods of preparation are possible: direct intercalation of KH powder into graphite,[76] and intercalation of K into graphite to form C₈K, followed by hydrogen chemisorption.[78] Single-phase specimens are difficult to obtain because of slow hydrogen sorption kinetics.[231,78]

The situation in the KH-GIC's is complicated by the presence of multiple phases, just as in the KHg-GIC's. In the KH-GIC's, both alpha ( I_c = 8.43-8.53 Å) and beta ( I_c = 9.13 Å) phases can coexist in a given sample.[213,231] The structure and stoichiometry of these phases is uncertain.[171] To complicate matters further, staging disorder is also a common feature of the KH-GIC's, unlike the KHg-GIC's, which are nearly always single-stage. One reason for the staging disorder in the chemisorbed compounds is the complex behavior as a function of hydrogen stoichiometry. Starting with a C₈K sample, hydrogen goes into interstitial sites in C₈K up to x = 0.1. For x > 0.1, the stage II compound, also denoted C₈KH_x, begins to form. Stage I and stage II coexist until x = 0.67, when the last stage I material transforms to stage II.[153] Other reasons for disorder are the large number of steps that go into the reaction and the fairly complicated final structure.

Despite all this complexity, Enoki et al. have done an admirable job of making sense out of the numbers in Table . Their interpretation, which is based on specific heat and conductivity measurements, is summarized by Figure below. The decline in Gamma with increasing x shows that H is lowering the carrier density and must have at least a partially ionic character. The lower density of states in the KH-GIC's as compared to the K-GIC's is also seen in Shubnikov-deHaas[79] and optical measurements.[62] The sequential increase and decrease in theta_D and T_E shows that hydrogen first stiffens and then softens both the acoustic and optic modes in C₈K.

  
Figure: Hydrogen stoichiometry dependence of the superconducting transition temperature T_c, Debye temperature theta_D, the Einstein temperature T_E, and the linear specific heat coefficient Gamma in C₈KH_x and C₈RbH_x. From Ref. [78]. The label F(x)/F(0) indicates that each of the quantities is plotted normalized to 1.0 at x = 0.

The data shown in Figure can be analyzed to produce the numbers listed in Table , which is adapted from Ref. [78]. The conclusions one draws from examination of this table are similar to those from study of the transition metal hydrides, but with some important differences. As noted in Ref. [78], the main effect of hydrogen is that as a function of x the electron-phonon coupling parameter increases and the density of states at the Fermi level decreases. The T_c enhancement with hydrogenation is therefore accounted for mostly by a larger Lambda. The increase in Lambda_ep with x is overwhelmed at large x by the decrease in carrier density that is reflected by the fall in the DOS.

  
Table: Parameters relevant to superconductivity in the KH- and RbH-GIC's. Adapted from Ref. [78]. The density of states has been corrected for the electron-phonon coupling. ^dagger means a calculated parameter; ? means not measured.

None of the previous statements is at all surprising in light of the results of hydrogenation on the transition metals. What is a little bit hard to account for is the mechanism by which Lambda_ep increases. According to Equation , the hydrogen-induced rise in theta_D and T_E in the KH-GIC's should lower rather than raise Lambda_ep. The source of the T_c increase in the KH-GIC's may be the optic modes associated with the hydrogen atoms, just as in the hydrogenated transition metals.[77] The very slight metallic character of H in KH-GIC's[171,75] could contribute to the enhancement of the electron-phonon coupling. Evidence for the hydrogen hole band near the Fermi level comes from electron spin resonance, thermopower, and conductivity measurements.[171,75] The schematic density of states of C₈K before and after hydrogenation is shown in Figure . The reasonableness of the optic-mode explanation for the hydrogen-induced T_c increase is hard to judge, but further experiments are underway.

  
Figure: Schematic density-of-states for a) C₈K and b) C₈KH_0.55. From Ref. [171]. Note the very small hole band near E_F in b).

Superconductivity in the KH-GIC's is not completely understood, but there are several generalizations that can be made. Firstly, hydrogenation tends to decrease the density of states at the Fermi level by putting carriers into low-lying hydrogen bands. Secondly, hydrogenation strongly increases the electron-phonon coupling, although how exactly it does so is not clear. Whether the optic phonons associated with hydrogen are crucial for the KH-GIC's, as they are in the transition metals, is not yet certain.

Besides the KH-GIC's, another group of materials with much in common with the KHg-GIC's is the transition metal dichalcogenides. The effect of hydrogenation on superconductivity in the TMDC's is discussed below.