Value Of Coulomb Pseudopotential Research Articles

Anomalously high value of Coulomb pseudopotential for the H5S2 superconductor

The H5S2 and H2S compounds are the two candidates for the low-temperature phase of compressed sulfur-hydrogen system. We have shown that the value of Coulomb pseudopotential (μ*) for H5S2 ([TC]exp = 36 K and p = 112 GPa) is anomalously high. The numerical results give the limitation from below to μ* that is equal to 0.402 (μ* = 0.589), if we consider the first order vertex corrections to the electron-phonon interaction). Presented data mean that the properties of superconducting phase in the H5S2 compound can be understood within the classical framework of Eliashberg formalism only at the phenomenological level (μ* is the parameter of matching the theory to the experimental data). On the other hand, in the case of H2S it is not necessary to take high value of Coulomb pseudopotential to reproduce the experimental critical temperature relatively well (μ* = 0.15). In our opinion, H2S is mainly responsible for the observed superconductivity state in the sulfur-hydrogen system at low temperature.

On the high-pressure superconducting phase in platinum hydride

Motivated by the ambiguous experimental data for the superconducting phase in silane (SiH4), which may originate from platinum hydride (PtH), we provide a theoretical study of the superconducting state in the latter alloy. The quantitative estimates of the thermodynamics of PtH at 100 GPa are given for a wide range of Coulomb pseudopotential values () within the Eliashberg formalism. The obtained critical temperature value ( for ) agrees well with the experimental TC for SiH4, which may be ascribed to PtH. Moreover, the calculated characteristic thermodynamic ratios exceed the predictions of the Bardeen–Cooper–Schrieffer theory, implying the occurrence of strong-coupling and retardation effects in PtH. We note that our results may be of high relevance for future theoretical and experimental studies on hydrides.

Study of the superconducting phase in silicene under biaxial tensile strain

The electron-doped silicene under the influence of the biaxial tensile strain is predicted to be the phonon-mediated superconductor. By using the Eliashberg formalism, we investigate the thermodynamic properties of the superconducting silicene in the case when the tension is 5% and the electron doping equals 3.5×1014cm−2. Under such conditions, silicene monolayer is expected to exhibit the highest superconducting transition temperature (TC). In particular, based on the electron–phonon spectral function and assuming a wide range of the Coulomb pseudopotential values (μ⋆∈〈0.1,0.3〉) it is stated that the superconducting transition temperature decreases from 18.7K to 11.6K. Similar behavior is observed in the case of the zeroth temperature superconducting energy gap at the Fermi level: 2Δ(0)∈〈6.68,3.88〉 meV. Other thermodynamic parameters differ from the predictions of the Bardeen–Cooper–Schrieffer theory. In particular, the ratio of the energy gap to the critical temperature changes in the range from 4.14 to 3.87. The ratio of the specific heat jump to the specific heat in the normal state takes the values from 2.19 to 2.05, and the ratio of the critical temperature and specific heat in the normal state to the thermodynamic critical field increases from 0.143 to 0.155. It is also determined that the maximum value of the electron effective mass equals 2.11 of the electron band mass.

Strong-coupling superconductivity in CaLi2 under the pressure of 100 GPa

In presented paper the superconducting properties of compressed CaLi2 compounds have been calculated for P21/c phase. Energy gap, critical temperature and electron effective mass are analyzed within the framework of the strong-coupling Eliashberg theory for a wide range of Coulomb pseudopotential μ⋆∈〈0.1,0.3〉. It has been stated that Δ(0) decreases from 6.01meV to 3.62meV, TC decreases from 29.31K to 18.16K and dimensionless ratio 2Δ(0)/kBTC decreases from 4.76 to 4.64 dependently on the assumed value of the Coulomb pseudopotential. Moreover, it has been proved, that the ratio of the electron effective mass to the electron band mass me⋆/me is high in the whole range of the superconducting phase existence and reaches its maximum equal to 3.73 for the critical temperature regardless of the value of Coulomb pseudopotential.

Thermodynamics of the superconducting phase in compressed [formula omitted

Recent studies on the hydrogen-rich metals are mainly stimulated by the fact that these superconductors are supposed to exhibit the high value of the critical temperature (TC). The thermodynamic properties of GeH4(H2)2 hydride under the pressure at 250GPa have been studied in the present paper. The calculations have been conducted in the framework of the Eliashberg approach for the wide range of the Coulomb pseudopotential values: μ⋆∈〈0.1,0.3〉. It has been found that the critical temperature is high in the entire range of the Coulomb pseudopotential: TC∈〈128.5,69.8〉K. The values of the thermodynamic dimensionless ratios, namely RΔ≡2Δ(0)/kBTC, RC≡ΔC(TC)/CN(TC), and RH≡TCCN(TC)/HC2(0), differ from the predictions of the Bardeen–Cooper–Schrieffer theory. In particular, RΔ∈〈4.30,4.08〉, RC∈〈1.91,1.58〉, and RH∈〈0.151,0.154〉. Finally, the ratio of the electron effective mass (me⋆) to the electron band mass (me) reaches the maximum at the critical temperature, where me⋆/me=2.45.

Superconducting state above the boiling point of liquid nitrogen in the GaH3 compound

The thermodynamic parameters of the superconducting state in the GaH3 compound under a pressure of 120 GPa have been determined. A wide range of Coulomb pseudopotential values has been taken into account: μ⋆∈〈0.1,0.2〉. It has been shown that, for the considered values of μ⋆, the superconducting state is characterized by a critical temperature which is higher than the boiling temperature of liquid nitrogen: TC∈(122.99,89.78) K. Other parameters significantly deviate from the predictions of BCS theory. In particular, the ratio of the energy gap to the critical temperature (RΔ ≡ 2Δ(0)/kBTC) changes in the range from 4.15 to 4.03. The ratio of the specific heat jump to the specific heat in the normal state (RC ≡ ΔC(TC)/CN(TC)) takes values from 1.87 to 1.58. The parameter , where HC is the thermodynamic critical field, is characterized in the following manner: RH∈〈0.147,0.150〉. Finally, it has been proven that the maximum value of the electron effective mass () equals 2.66me, where the symbol me denotes the electron band mass.

On the critical temperature and the energy gap in dense [formula omitted]([formula omitted])2 at 250 GPa

The critical temperature (TC) and the energy gap (2Δ(T)) for the superconductor SiH4(H2)2 at 250GPa have been calculated. The wide range of the Coulomb pseudopotential's values has been considered: μ⋆∈〈0.1,0.3〉. It has been stated that TC decreases together with the increase of μ⋆ from 129.83K to 81.40K. The low-temperature energy gap (T∼0 K) decreases together with the increase of the Coulomb pseudopotential from 50.96meV to 30.12meV. The high values of 2Δ(0) mean that the dimensionless ratio RΔ≡2Δ(0)/kBTC significantly exceeds the value predicted by the classical BCS theory. In the considered case: RΔ∈〈4.55,4.29〉. Due to the unusual dependence of the critical temperature and the energy gap on μ⋆, the analytical expressions for TC(μ⋆) and Δ(μ⋆) have been given.

Thermodynamics of the Superconducting State in Calcium at 200 GPa

The thermodynamic parameters of the superconducting state in Calcium under the pressure at 200 GPa were calculated. The Coulomb pseudopotential values (μ ⋆) from 0.1 to 0.3 were taken into consideration. It has been shown that the specific heat’s jump at the critical temperature and the thermodynamic critical field near zero Kelvin strongly decrease with μ ⋆. The dimensionless ratios r 1≡ΔC(T C)/C N(T C) and \(r_{2}\equiv T_{\mathrm{C}}C^{N}(T_{\mathrm{C}})/H^{2}_{\mathrm{C}}(0)\) significantly differ from the predictions based on the BCS model. In particular, r 1 decreases from 2.64 to 1.97 with the Coulomb pseudopotential; whereas r 2 increases from 0.140 to 0.157. The numerical results have been supplemented by the analytical approach.

The superconducting state in metallic hydrogen under pressure at 2000 GPa

In this study, we have analysed the properties of the superconducting phase in metallic hydrogen under pressure at 2000 GPa. In particular, we have calculated the dependence of the basic thermodynamic quantities on the value of Coulomb pseudopotential ( μ ∗ ). The main results are the following: (i) The critical temperature ( T C ) is large even for high values of μ ∗ . (ii) The values of the ratios R 1 ≡ 2 Δ ( 0 ) / k B T C , R 2 ≡ Δ C ( k B T C ) / C N ( k B T C ) and R 3 ≡ T C C N ( k B T C ) / H C 2 ( 0 ) differ from the BCS values. (iii) The electron effective mass is large and reaches its maximum value for T = T C . Additionally, we have given the analytical formulas for T C , R 1 and R 2 which reproduce results originating from exact numerical calculations very well.

Upper bound on the specific-heat jump: Application to the high-Tc oxides.

We establish an upper limit on the normalized specific-heat jump $\frac{\ensuremath{\Delta}C}{\ensuremath{\gamma}(0){T}_{c}}$ at ${T}_{c}$, for the case of an isotropic Eliashberg superconductor. Functional derivative results for $\frac{\ensuremath{\Delta}C}{\ensuremath{\gamma}(0){T}_{c}}$, in the case of realistic electron-phonon spectral densities, lead us to consider a model delta-function spectrum which, we can prove, gives a local maximum in $\frac{\ensuremath{\Delta}C}{\ensuremath{\gamma}(0){T}_{c}}$ for some low but finite phonon energy. The value of the maximum depends somewhat on the value of Coulomb pseudopotential (${\ensuremath{\mu}}^{*}$) used, but is always surprisingly small. As an example for ${\ensuremath{\mu}}^{*}=0.15$, $\frac{\ensuremath{\Delta}C}{\ensuremath{\gamma}(0){T}_{c}}\ensuremath{\le}3.73$ with the inequality holding for realistic spectra. This is smaller than some recent experimental values published for ${\mathrm{La}}_{1.85}$${\mathrm{Sr}}_{0.15}$Cu${\mathrm{O}}_{4}$.