Superconducting state in the atomic metallic hydrogen just above the pressure of the molecular dissociation

̧śniak, R. Szcze; ̧śniak, D. Szcze; Drzazga, E.A.

doi:10.1016/j.ssc.2012.08.022

Cited by 36 publications

(26 citation statements)

References 47 publications

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“…The latter one can be calculated as follows: The order parameter and the renormalization functions have been determined by solving the imaginary axis Eliashberg equations [9]. These complicated calculations have been made by using the iterative methods presented in the papers [10] and [11]. In the considered case, we have assumed that M = 1100, in order to ensure the stability of the numerical solutions for T ≥ T 0 ≡ 5 K.…”

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confidence: 99%

Thermodynamic Critical Magnetic Field for Chlorine Halide Superconductor at High Pressure

Szczęśniak¹,

Szczȩśniak

2014

Acta Phys. Pol. A

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At present, hydrides are considered as a one of the most interesting high-temperature superconductors with the classical electron-phonon pairing mechanism. In the present paper, we have analyzed the dependence of the thermodynamic critical magnetic eld (Hc) on the temperature for the chlorine halide superconductor. The calculations have been made in the framework of the Eliashberg formalism for the following pressure values: p1 = 320 GPa and p2 = 360 GPa. We have shown that Hc increases strongly with the increase of the pressure: [Hc (0) In recent years, hydrides have gained much attention as possible pressure-induced high-temperature superconductors with the conventional electron-phonon pairing mechanism [1,2]. This interest stems from the fact that, in hydrides, it is theoretically possible to obtain a high critical temperature (T c ) at the pressure (p) which is much lower than the metallization pressure (∼ 400 GPa) for the pure metallic hydrogen [3,4]. In certain cases, like for example in the case of Si 2 H 6 , the critical temperature is expected, on the basis of the theoretical calculations [5], to be as high as 173 K at p = 275 GPa. Please note that this value of T C is even higher than for the cuprate superconductor HgBa 2 Ca 2 Cu 3 O 8+y , where the maximal critical temperature is equal to 164 K at p = 31 GPa [6]. Thus, it is important to examine the promising superconducting properties of such hydrogen compounds.In the presented work, we have studied the dependence of the thermodynamic critical magnetic eld (H C ) on the temperature for the chlorine halide (HCl) superconductor. Despite of the fact that HCl contains a smaller number of the H atoms than the hydrogen-rich materials, the hitherto determined superconducting properties of this material are promising [7].The analysis of the HCl compound (within the P 2 1 /m crystal structure) has been carried out for the pressure values p 1 = 320 GPa and p 2 = 360 GPa. In the considered cases, the electron-phonon coupling constants In the paper, we have assumed that the electronphonon interaction is modeled by the Eliashberg functions originally calculated in [7], whereas the Coulomb pseudopotential (µ ) takes a typical value of 0.1.The critical magnetic eld at a given temperature can be calculated by using the expression (the CGS unit system) [9]:where ρ(0) stands for the value of the electron density of states at the Fermi level, and ∆F denotes the free energy dierence between the normal and the superconducting state. The latter one can be calculated as follows: The order parameter and the renormalization functions have been determined by solving the imaginary axis Eliashberg equations [9]. These complicated calculations have been made by using the iterative methods presented in the papers [10] and [11]. In the considered case, we have assumed that M = 1100, in order to ensure the stability of the numerical solutions for T ≥ T 0 ≡ 5 K.In the bottom panel of Fig. 1, we have presented the dependence of ∆F/ρ(0) on the temperature for the (344)

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confidence: 99%

Thermodynamic Critical Magnetic Field for Chlorine Halide Superconductor at High Pressure

Szczęśniak¹,

Szczȩśniak

2014

Acta Phys. Pol. A

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“…The Eliashberg equations on the imaginary axis have been solved for 1100 Matsubara frequencies (M = 1100). We have taken the advantage of the numerical methods described and used in the works: [28][29][30][31][32][33]. The functions ∆ n and Z n are stable for the temperature higher than T 0 = 1.5 K. It is assumed that the cut-off energy is equal to 5Ω max , where the exact values of the Debye energy are collected in Table I.…”

Section: Thermodynamics Of High-pressure Superconducting State In Phomentioning

confidence: 99%

Characteristics of the Eliashberg Formalism on the Example of High-Pressure Superconducting State in Phosphor

et al. 2016

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The work describes the properties of the high-pressure superconducting state in phosphor: p ∈ {20, 30, 40, 70} GPa. The calculations were performed in the framework of the Eliashberg formalism, which is the natural generalization of the BCS theory. The exceptional attention was paid to the accurate presentation of the used analysis scheme. With respect to the superconducting state in phosphor it was shown that the observed not-high values of the critical temperature ([TC] max p=30 GPa = 8.45 K) result not only from the low values of the electron-phonon coupling constant, but also from the very strong depairing Coulomb interactions. Additionally the inconsiderable strong-coupling and retardation effects force the dimensionless ratios R∆, RC, and RH -related to the critical temperature, the order parameter, the specific heat, and the thermodynamic critical field -to take the values close to the BCS predictions. Hamiltonian and fundamental equations of BCS model and Eliashberg formalismThe first microscopic theory of the superconducting state was formulated in 1957 by Bardeen, Cooper and Schrieffer (the so-called "BCS model") [1,2]. In the framework of the method of the second quantization the BCS Hamiltonian can be written with the following formula [3,4]:where the function ε k represents the electron band energy, V is the effective pairing potential, whose value is determined by the matrix elements of the electronphonon interaction, the electron band energy and the phonon energy. The symbols c † kσ and c kσ represent the creation and annihilation operator of the electron state in the momentum representation (k) for the spin σ ∈ {↑, ↓}. It should be noted that the sum denoted by the sign ought to be calculated only for those values of the momenta, for which the condition −Ω max < ε k < Ω max is fulfilled, where Ω max represents the Debye energy. In the considered case the effective pairing potential is positive, which allows the formation of the superconducting condensate. The fundamental equation of the BCS theory for the order parameter (∆ ≡ V k c −k↓ c k↑ ) is derived directly from Hamiltonian (1) using the mean field approximation to the interaction term. As a result the following can be obtained:) * corresponding author; e-mail: aduda@wip.pcz.pl where k B is the Boltzmann constant. Let us notice that Eq. (2) cannot be solved analytically. However, in the limit cases T → T C and T → 0 K the relatively simple calculations allow us to obtain the formulae for the critical temperature and the value of the order parameter k B T C = 1.13Ω max exp (−1/λ), ∆ (0) = 2Ω max exp (−1/λ). The electron-phonon coupling constant λ in the BCS model is given by λ ≡ ρ (0) V (the quantity ρ (0) represents the electron density of states on the Fermi surface). The BCS theory predicts the existence of the universal thermodynamic ratios, which are defined below:andThe symbols appearing in the formulae (4) and (5) denote respectively: C S -the specific heat of the superconducting state, C N -the specific heat of the normal state, and ...

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“…The Eliashberg equations were solved for M = 1100, which ensured the stability of the functions φ m and Z m for the temperatures larger than, or equal to T 0 = 50 K. The numerical modules described and tested in the papers: [22], [24], [29], [30], [31], [32], and [33] were used.…”

Section: The Formalismmentioning

confidence: 99%

“…In particular, for the molecular phase of hydrogen (p ∈ 400, 500 GPa), the critical temperature grows rapidly from about 80 K to 350 K [21], [22], [23], and [24]. Above 500 GPa, the value of T C stabilizes in the range from ∼ 300 K to ∼ 470 K, whereas for 2 TPa, the maximum of the critical temperature able to reach even the value of 630 K is predicted [10], [11].…”

Section: Introductionmentioning

confidence: 96%

“…The thermodynamics of the superconducting state in hydrogen has been studied for the few selected pressures [11], [22], [24]. The obtained results suggest that, due to the significant strong-coupling and retardation effects, the description with the use of the BCS theory [25], [26] is not sufficient and the Eliashberg method should be used instead [27].…”

Section: Introductionmentioning

confidence: 99%

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High-pressure superconducting state in hydrogen

Duda

Szczȩśniak

Sowińska

et al. 2016

Solid State Communications

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The paper determines the thermodynamic parameters of the superconducting state in the metallic atomic hydrogen under the pressure at 1 TPa, 1.5 TPa, and 2.5 TPa. The calculations were conducted in the framework of the Eliashberg formalism. It has been shown that the critical temperature is very high (in the range from 301.2 K to 437.3 K), as well as high are the values of the electron effective mass (from 3.43 me to 6.88 me), where me denotes the electron band mass. The ratio of the low-temperature energy gap to the critical temperature explicitly violates the predictions of the BCS theory: 2∆ (0) /kBTC ∈ 4.84, 5.85 . Additionally, the free energy difference between the superconducting and normal state, the thermodynamic critical field, and the specific heat of the superconducting state have been determined. Due to the significant strong-coupling and retardation effects those quantities cannot be correctly described in the framework of the BCS theory.

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Superconducting state in the atomic metallic hydrogen just above the pressure of the molecular dissociation

Cited by 36 publications

References 47 publications

Thermodynamic Critical Magnetic Field for Chlorine Halide Superconductor at High Pressure

Thermodynamic Critical Magnetic Field for Chlorine Halide Superconductor at High Pressure

Characteristics of the Eliashberg Formalism on the Example of High-Pressure Superconducting State in Phosphor

High-pressure superconducting state in hydrogen

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