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R. Szczęśniak

Publications and source records attributed to R. Szczęśniak.

17 recordsLinked to original sources
arXiv2020

Chaotic evolution of the energy of the electron orbital and the hopping integral in diatomic molecule cations subjected to harmonic excitation

We analysed the dynamics of the positively charged ions of diatomic molecules (${\rm X_{2}^{+}}$ and ${\rm XY^{+}}$), in which the bond is realised by the single electron. We assumed that the atomic cores separated by the distance $R$ were subjected to the external excitation of the harmonic type with the amplitude $A$ and frequency $Ω$. We found the ground states of ions using the variational approach within the formalism of second quantization (the Wannier function was reproduced by means of Gaussian orbitals). It occurred that, on the account of the highly non-linear dependence of the total energy on $R$, the chaotic dynamics of cores induced the chaotic evolution of the electronic Hamiltonian parameters (i.e. the energy of the electron orbital $\varepsilon$ and the hopping integral $t$). Changes in cation masses or in the charge arrangement does not affect qualitatively the values of Lyapunov exponents in the $A$-$Ω$ parameter space.

physics.chem-ph↗
arXiv2020

Nonadiabatic superconductivity in Li-intercalated hexagonal boron nitride bilayer

In the case of Li-intercalated hexagonal boron nitride bilayer (Li-hBN), the vertex corrections of electron-phonon interaction cannot be omitted. This is evidenced by the very high value of the ratio $λω_{D}/\varepsilon_{F}\sim 0.46$, where $λ$ is the electron-phonon coupling constant, $ω_{D}$ is the Debye frequency, and the symbol $\varepsilon_{F}$ represents the Fermi energy. Due to the nonadiabatic effects, the phonon-induced superconducting state in Li-hBN is characterized by the much lower value of critical temperature ($T^{\rm LOVC}_{C}\in\{ 19.1, 15.5, 11.8\}$ K, for $μ^{\star}\in \{0.1, 0.14, 0.2\}$), than would result from calculations not taking this effect into account: $T^{\rm ME}_{C}\in\{ 31.9, 26.9, 21\}$ K. From the technological point of view, the low value of $T_{C}$ limits the possible applications of Li-hBN superconducting properties. The calculations were carried out under the classic Migdal-Eliashberg formalism (ME) and the Eliashberg theory with the lowest-order vertex corrections (LOVC).

cond-mat.supr-con↗
arXiv2018

Non-parametric application of Tsallis statistics to systems consisting of M hydrogen molecules

We have determined the entropy, the total energy, and the specific heat of the systems consisting of $M\geq 3$ hydrogen molecules. The calculations were conducted in the framework of the nonextensive Tsallis statistics. The relation between $M$ and the entropic index $q$ is given by $q = 1 + 1/M$, which results from the fact that the temperature of the nanosystems fluctuates around the temperature of the reservoir (Wilk and Włodarczyk, Phys. Rev. Lett. {\bf 84}, 2770 (2000)). The electron energy states of the hydrogen molecule have been determined with the help of the Hubbard Hamiltonian, which models all two-body interactions. The Hubbard Hamiltonian integrals have been calculated by using the variational method, whereas the Wannier function has been associated with $1s$ Slater-type orbitals. We have included the contributions to the energy of the hydrogen molecule coming from the oscillatory (either harmonic or anharmonic), rotational and translational degrees of freedom. In addition, we have investigated the impact of the external force ($F$) or the magnetic field ($h$) on the thermodynamic parameters of the systems. In each case the noticeable deviation from the results of the classical statistical physics can be observed for the systems consisting of $M<M_{c}\sim 10^{3}$ molecules.

cond-mat.mes-hall↗
arXiv2016

Pressure effects on the unconventional superconductivity of the noncentrosymmetric LaNiC2

The unconventional superconductivity in the noncentrosymmetric LaNiC$_2$, and its evolution with pressure, is analyzed basing on the {\it ab initio} computations and the full Eliashberg formalism. First principles calculations of the electronic structure, phonons and the electron-phonon coupling are reported in the pressure range 0-15 GPa. The thermodynamic properties of the superconducting state were determined numerically solving the Eliashberg equations. We found that already at $p=0$ GPa, the superconducting parameters deviate from the BCS-type, and a large value of the Coulomb pseudopotential $μ^{\star}=0.22$ is required to get the critical temperature $T_c = 2.8$~K consistent with experiment. If such $μ^{\star}$ is used, the Eliashberg formalism reproduces also the experimentally observed values of the superconducting order parameter, the electronic specific heat jump at the critical temperature, and the change of the London penetration depth with temperature. This shows, that deviation of the above-mentioned parameters from the BCS predictions do not prejudge on the triplet or multiple gap nature of the superconductivity in this compound. Under the external pressure, calculations predict continuous increase of the electron-phonon coupling constant in the whole pressure range 0-15~GPa, consistent with the experimentally observed increase in $T_c$ for the pressure range 0-4~GPa, but inconsistent with the drop of $T_c$ above 4~GPa and the disappearance of the superconductivity above 7~GPa, reported experimentally. The disappearance of superconductivity may be accounted for by increasing the $μ^{\star}$ to 0.36 at 7~GPa, which supports the hypothesis of the formation of a new high-pressure electronic phase, which competes with the superconductivity.

cond-mat.supr-con↗
arXiv2016

High-pressure superconducting state in hydrogen

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 $3.43$ $m_{e}$ to $6.88$ $m_{e}$), where $m_{e}$ 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: $2Δ\left(0\right)/k_{B}T_{C}\in\left<4.84,5.85\right>$. 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.

cond-mat.supr-con↗
arXiv2016

Superconducting properties of tin-copper amorphous thin films

The thermodynamic properties of the superconducting state in the amorphous ${\rm Sn_{1-x}Cu_{x}}$ thin films have been characterized. The concentration of copper changes in the range from $0.08$ to $0.41$. The calculations have been conducted in the framework of the strong-coupling formalism, wherein the Eliashberg functions determined in the tunnel experiment (Phys. Rev. B {\bf 51}, 685 (1995)) have been used. The value of the Coulomb pseudopotential equal to $0.1$ has been adopted. It has been found that the critical temperature ($T_{C}$) decreases from $7$ K to $3.9$ K. The ratio of the energy gap to the critical temperature: $R_Δ=2Δ\left(0\right)/k_{B}T_{C}$, differs significantly from the BCS value: $R_Δ\in\left<4.4,3.95\right>$. Similarly behaves the ratio of the specific heat jump to the specific heat of the normal state: $R_{C}=ΔC\left(T_{C}\right)/C^{N}\left(T_{C}\right)$, and the parameter: $R_{H}=T_{C}C^{N}\left(T_{C}\right)/H^{2}_{C}\left(0\right)$, where $H_{C}\left(0\right)$ is the thermodynamic critical field. In particular, $R_{C}\in\left<2.2,1.75\right>$ and $R_{H}\in\left<0.141,0.154\right>$.

cond-mat.supr-con↗
arXiv2016

Characteristics of the Eliashberg formalism on the example of high-pressure superconducting state in phosphor

The work describes the properties of the high-pressure superconducting state in phosphor: $p\in\{20, 30, 40, 70\}$ 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: (i) the observed not-high values of the critical temperature ($\left[T_{C}\right]_{p=30{\rm GPa}}^{\rm max}=8.45$ K) result not only from the low values of the electron - phonon coupling constant, but also from the very strong depairing Coulomb interactions, (ii) the inconsiderable strong - coupling and retardation effects force the dimensionless ratios $R_Δ$, $R_{C}$, and $R_{H}$ - 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.

cond-mat.supr-con↗
arXiv2013

Study of the superconducting state in the Cmmm phase of GeH4 compound

A superconducting state, that induces in ${\rm GeH_{4}}$ under the pressure at 20 GPa, is being characterized by a high critical temperature $T_{C}\in<54.54,31.23>$ K, for a wide range of the Coulomb pseudopotential $μ^{\star}\in<0.1,0.3>$. Other thermodynamic parameters for the considered range of the Coulomb pseudopotential significantly differ from the predictions of a classical BCS theory. In particular: (i) the ratio of the energy gap to the critical temperature ($R_Δ\equiv 2Δ(0)/k_{B}T_{C}$) changes from 4.07 to 3.88; (ii) the value of the parameter $R_{C}\equivΔC(T_{C})/C^{N}(T_{C})$ decreases from 1.85 to 1.69, where $ΔC$ denotes the specific heat's jump, and $C^{N}$ is the specific heat of the normal state; (iii) the ratio $R_{H}\equiv T_{C}C^{N}(T_{C})/H^{2}_{C}(0)$, where $H_{C}(0)$ represents the low - temperature thermodynamic critical field, increases from 0.147 to 0.155.

cond-mat.supr-con↗
arXiv2012

CaLi2 superconductor under the pressure of 100 GPa: the thermodynamic critical field and the specific heat

In the paper, the thermodynamic properties of the CaLi$_2$ superconductor have been studied. It has been assumed the high value of the pressure: $p=100$ GPa. The thermodynamic critical field ($H_{C}$) and the specific heats for the superconducting and normal state ($C^{S}$ and $C^{N}$) have been obtained. The calculations have been made within the framework of the Eliashberg approach for the wide range of the Coulomb pseudopotential: $μ^{\star}\in<0.1,0.3>$. It has been shown that the low-temperature critical field and the specific heat jump at $T_{C}$ strongly decrease if $μ^{\star}$ increases. The value of the dimensionless ratio $R_{C}\equiv(C^{S}-C^{N})/C^{N}$ at the critical temperature differs significantly from the value predicted by the BCS model. In particular, the parameter $R_{C}$ decreases from 1.83 to 1.73 with the increase of the Coulomb pseudopotential value. In the paper, the interpolation formulas for the functions $T_{C}(μ^{\star})$ and $R_{C}(μ^{\star})$ have been also given.

cond-mat.supr-con↗
arXiv2012

Electron-phonon pairing mechanism: cuprates with high value of the critical temperature

The model for the cuprates based on the modified electron-phonon pairing mechanism has been tested. For this purpose, the superconductors with high value of the critical temperature have been taken into consideration. In particular: ${\rm YBa_{2}Cu_{3}O_{7-y}}$, ${\rm HgBa_{2}CuO_{4+y}}$, ${\rm HgBa_{2}Cu_{1-x}Zn_{x}O_{4+y}}$, and ${\rm HgBa_{2}Ca_{2}Cu_{3}O_{8+y}}$. It has been shown that the dependence of the ratio $R_{1}\equiv 2Δ_{tot}^{(0)}/k_{B}T_{C}$ on the doping ($p$) can be properly predicted in the framework of the presented theory; the symbol $Δ_{tot}^{(0)}$ denotes the energy gap amplitude at the temperature of zero Kelvin, and $T_{C}$ is the critical temperature. The numerical results have been supplemented by the formula which describes the function $R_{1}(p)$.

cond-mat.supr-con↗
arXiv2012

The superconducting phase of Calcium under the pressure at 200 GPa: the strong-coupling description

The thermodynamic parameters of the superconducting state in Calcium under the pressure at 200 GPa have been determined. The numerical analysis by using the Eliashberg equations in the mixed representation has been conducted. It has been stated, that the critical temperature ($T_{C}$) decreases from 36.15 K to 20.79 K dependently on the assumed value of the Coulomb pseudopotential ($μ^{*}\in<0.1,0.3>$). Next, the order parameter near the temperature of zero Kelvin ($Δ(0)$) has been obtained. It has been proven, that the dimensionless ratio $2Δ(0)/k_{B}T_{C}$ decreases from 4.25 to 3.90 together with the growth of $μ^{*}$. Finally, the ratio of the electron effective mass to the electron bare mass ($m^{*}_{e}/m_{e}$) has been calculated. It has been shown, that $m^{*}_{e}/m_{e}$ takes the high value in the whole range of the superconducting phase's existence, and its maximum is equal to 2.23 for T=T_{C}.

cond-mat.supr-con↗
arXiv2011

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 ($μ^{\star}$) 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 $μ^{\star}$. The dimensionless ratios $r_{1}\equiv ΔC(T_{C})/C^{N}(T_{C})$ and $r_{2}\equiv T_{C}C^{N}(T_{C})/H^{2}_{C}(0)$ 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.

cond-mat.supr-con↗
arXiv2011

Properties of the superconducting state in molecular metallic hydrogen under pressure at 347 GPa

The thermodynamic properties of the superconducting state induced in metallic molecular hydrogen under the influence of pressure 347 GPa were determined. In particular, it has been shown that the critical temperature ($T_{C}$) changes in the range from 120 K to 90 K for $μ^{*}\in<0.08,0.15>$, where $μ^{*}$ is the value of the Coulomb pseudopotential. Next, the energy gap near the temperature of zero Kelvin ($2Δ(0)$) was calculated. It has been stated, that the dimensionless ratio $2Δ(0)/k_{B}T_{C}$ slightly decreases with the increase of $μ^{*}$ from 3.98 to 3.84. In the last step, the ratio of effective electron mass ($m^{*}_{e}$) to the bare electron mass ($m_{e}$)) was determined. It has been proved that $m^{*}_{e}/m_{e}$ takes its highest value equal to 1.96 for $T=T_{C}$.

cond-mat.supr-con↗
arXiv2011

Superconductivity of calcium under the pressure at 120 GPa

The properties of the superconducting state in calcium under the pressure at 120 GPa were analyzed. By using the imaginary axis Eliashberg equations it has been shown, that the Coulomb pseudopotential reaches the high value equal to 0.215. In the considered case, the critical temperature is not properly described by the Allen-Dynes formula and it should be calculated with an use of the modified expression. In the paper the exact solutions of the Eliashberg equations on the real axis were also obtained. On this basis it was stated, that the effective potential of the electron-electron interaction is attractive for the frequencies lower or equal to the maximum phonon frequency. Then, the dimensionless parameter 2Δ(0)/k_{B}T_{C}=4.10 was calculated. In the last step it has been proven, that the ratio of the electron effective mass to the bare electron mass is high and reaches its maximum equal to 2.36 for the critical temperature.

cond-mat.supr-con↗
arXiv2011

Properties of the superconducting state in compressed Sulphur

The thermodynamic properties of the superconducting state in Sulphur under the pressure at 160 GPa were determined. It has been shown that: (i) the critical value of the Coulomb pseudopotential is equal to 0.127; (ii) the critical temperature (T_{C} =17 K) should be calculated by using the modified Allen-Dynes formula; (iii) the effective electron-electron interaction is attractive in the range of frequencies from zero to the frequency slightly lesser than the maximum phonon frequency (~ 0.85Ω_{max}); (iv) the dimensionless ratios 2Δ(0)/k_{B}T_{C}, $ΔC(T_{C})/C^{N}(T_{C}) and T_{C}C^{N}(T_{C})/H^{2}_{C}(0) are equal to 3.7, 1.65 and 0.16 respectively; (v) the ratio of the effective to bare electron mass reaches maximum of 1.77 for T=T_{C}.

cond-mat.supr-con↗
arXiv2011

Specifc Heat and Thermodynamic Critical Field for Calcium under the Pressure at 120 GPa

The free energy difference between the superconducting and normal state for Calcium under the pressure at 120 GPa has been determined. The numerical calculations have been made in the framework of the imaginary axis Eliashberg approach. On the basis of the obtained results the specific heat in the superconducting C^{S}(T) and normal C^{N}(T) state, as well as, the thermodynamic critical field H_{C}(T) have been obtained. It has been shown that the characteristic values of the considered thermodynamic quantities do not obey the BCS universal laws. In particular, ΔC(T_{C})/C^N(T_{C})=2.48 and T_{C}C^{N}(T_{C})/H_{C}^{2}(0)=0.154.

cond-mat.supr-con↗