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M. W. Jarosik

Publications and source records attributed to M. W. Jarosik.

14 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↗
arXiv2019

The unbalanced phonon-induced superconducting state on a square lattice beyond the static boundary

The paper presents our verification of induction of the superconducting state on a square lattice by the linear electron-phonon interaction for values of the unbalance parameter ($γ=λ_{D}/λ_{ND}$) less than $γ_{C}=0.42$. Symbols $λ_{D}$ and $λ_{ND}$ denote the values of the coupling constant in the diagonal and the non-diagonal channel of the self-energy. Calculations were carried out using the Eliashberg equations, in which the order parameter ($Δ_{\bf k}\left(iω_{n}\right)$) and the wave function renormalising factor ($Z_{\bf k}\left(iω_{n}\right)$) depend explicitly on the Matsubara frequency ($ω_{n}$) and the wave vector (${\bf k}$). The value of $γ_{C}$ in the static boundary ($Δ_{\bf k}\left(iω_{n}\right)\rightarrow Δ_{\bf k}\left(iω_{n=1}\right)$), equal to ($0.93$), is significantly greater than the obtained limit value of $0.42$. Values of the thermodynamic functions of the superconducting state determined for our assumptions are significantly different from the values calculated in accordance with the BCS theory. The results were obtained for the electron-phonon interaction function explicitly dependent on the momentum transfer between electron states.

cond-mat.supr-con↗
arXiv2019

Interaction of the hydrogen molecule with the environment: stability of the system

We study the stability of the hydrogen molecule interacting with the environment according to the balanced gain and loss energy scheme. We determined the properties of the molecule taking into account all electronic interactions, where the parameters of the Hamiltonian have been computed by using the variational method. The interaction of the hydrogen molecule with the environment was modeled parametrically ($γ$) with the help of the non-hermitian operator. We have shown that the hydrogen molecule is dynamically unstable. The dissociation time ($T_{D}$) decreases, if the $γ$ parameter increases (for $γ\rightarrow 0$, we get $T_{D}\rightarrow +\infty$). At the dynamic instability of the hydrogen molecule overlaps its static instability as the coupling constant $γ$ increases. We observed the decrease in the dissociation energy and the existence of the metastable state of the molecule ($γ_{MS}=0.659374$~Ry). The hydrogen molecule is statically unstable for $γ>γ_{D}=1.024638$~Ry. One can also observed the $\mathcal{PT}$ symmetry breaking effect for the electronic Hamiltonian ($γ_{\mathcal {PT}}=0.520873$~Ry). However, it does not affect the properties of the hydrogen molecule, such as: the electronic Hamiltonian parameters, the phonon and rotational energy, and the values of the electron-phonon coupling constants.

quant-ph↗
arXiv2018

Description of the thermodynamic properties of $\rm{BiH_{5}}$ and $\rm{BiH_{6}}$ superconductors beyond the mean-field approximation

The ab initio calculations suggest (Y. Ma et al.), that the high-pressure ($p=200$~GPa) superconducting state in $\rm{BiH_{5}}$ and $\rm{BiH_{6}}$ compounds characterizes with a high value of the critical temperature ($T_{C}\sim 100$~K). Due to the large value of the electron-phonon coupling constant ($λ\sim 1.2$), the thermodynamic parameters of the superconducting phase in $\rm{BiH_{5}}$ and $\rm{BiH_{6}}$ have been determined beyond the mean-field approximation - in the framework of the Eliashberg equations formalism. We have calculated the dependence of the order parameter ($Δ$) and the wave function renormalization factor on the temperature. Then we have estimated the free energy difference between the superconducting state and the normal state, the thermodynamic critical field ($H_{C}$) and the specific heat of the superconducting state ($C^{S}$) and the normal state ($C^{N}$). The values of the dimensionless ratios $R_Δ=2Δ\left(0\right)/k_{B}T_{C}$, $R_{C}=ΔC\left(T_{C}\right)/C^{N}\left(T_{C}\right)$ and $R_{H}=T_{C}C^{N}\left(T_{C}\right)/H^{2}_{C}\left(0\right)$ are equal $R_{Δ_{\rm BiH_{5}}}=4.17$ and $R_{Δ_{\rm BiH_{6}}}=4.20$, $R_{C_{\rm BiH_{5}}}=2.54$ and $R_{C_{\rm BiH_{6}}}=2.58$, $R_{H_{\rm BiH_{5}}}=0.146$ and $R_{H_{\rm BiH_{6}}}=0.146$ respectively.

cond-mat.supr-con↗
arXiv2017

Strong-coupling superconductivity induced by calcium intercalation in bilayer transition-metal dichalcogenides

We theoretically investigate the possibility of achieving a superconducting state in transition-metal dichalcogenide bilayers through intercalation, a process previously and widely used to achieve metallization and superconducting states in novel superconductors. For the Ca-intercalated bilayers MoS$_2$ and WS$_2$, we find that the superconducting state is characterized by an electron-phonon coupling constant larger than $1.0$ and a superconducting critical temperature of $13.3$ and $9.3$ K, respectively. These results are superior to other predicted or experimentally observed two-dimensional conventional superconductors and suggest that the investigated materials may be good candidates for nanoscale superconductors. More interestingly, we proved that the obtained thermodynamic properties go beyond the predictions of the mean-field Bardeen--Cooper--Schrieffer approximation and that the calculations conducted within the framework of the strong-coupling Eliashberg theory should be treated as those that yield quantitative results.

cond-mat.supr-con↗
arXiv2017

Characteristics of superconducting state in vanadium: the Eliashberg equations and semi-analytical formulas

The superconducting state in vanadium characterizes with the critical temperature ($T_{c}$) equal to $5.3$~K. The Coulomb pseudopotential, calculated with the help of the Eliashberg equations, possesses anomalously high value $μ^{\star}\left(3Ω_{\rm max}\right)=0.259$ or $μ^{\star}\left(10Ω_{\rm max}\right)=0.368$ ($Ω_{\rm max}$ denotes the maximum phonon frequency). Despite the relatively large electron-phonon coupling constant ($λ=0.91$), the quantities such as: the order parameter ($Δ$), the specific heat ($C$), and the thermodynamic critical field ($H_{c}$) determine the values of the dimensionless ratios not deviating much from the predictions of the BCS theory: $R_Δ=2Δ\left(0\right)/ k_{B}T_{c}=3.68$, $R_{C}=ΔC\left(T_{c}\right)/ C^{N}\left(T_{c}\right)=1.69$, and $R_{H}=T_{c}C^{N}\left(T_{c}\right)/ H^{2}_{c}\left(0\right)=0.171$. This result is associated with the reduction of the strong-coupling and the retardation effects by the high value of the Coulomb pseudopotential. It has been shown that the results of the Eliashberg formalism can be relatively precisely reproduced with the help of the semi-analytical formulas, if the value of $μ^{\star}$ is determined on the basis of the $T_{c}$-Allen-Dynes expression ($μ^{\star}_{AD}=0.198$). The attention should be paid to the fact that in the numerical and in the semi-analytical approach the comparable values of the thermodynamic parameters for the same $μ^{\star}$ have been obtained only in the vicinity of the point $μ^{\star}=0.1$.

cond-mat.supr-con↗
arXiv2014

The correlation between the energy gap and the pseudogap temperature in cuprates: the YCBCZO and LSHCO case

The paper analyzes the influence of the hole density, the out-of-plane or in-plane disorder, and the isotopic oxygen mass on the zero temperature energy gap ($2Δ\left(0\right)$) for $\rm{Y}_{1-x}\rm{Ca}_{x}\rm{Ba}_2\left(\rm{Cu}_{1-y}\rm{Zn}_{y}\right)_{3}\rm{O}_{7-δ}$ (YCBCZO) and $\rm{La}_{1.96-x}\rm{Sr}_{x}\rm{Ho}_{0.04}\rm{CuO}_{4}$ (LSHCO) superconductors. It has been found that the energy gap is visibly correlated with the value of the pseudogap temperature ($T^{\star}$). On the other hand, no correlation between $2Δ\left(0\right)$ and the critical temperature ($T_{C}$) has been found. The above results mean that the value of the dimensionless ratio $2Δ\left(0\right)/k_{B}T_{C}$ can vary very strongly together with the chemical composition, while the parameter $2Δ\left(0\right)/k_{B}T^{\star}$ does not change significantly. In the paper, the analytical formula which binds the zero temperature energy gap and the pseudogap temperature has been also presented.

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

The Properties of the Superconducting State in YNi2B2C: The One-Band Eliashberg Approach

The basic thermodynamic parameters of the superconducting state in $\rm{YNi_{2}B_{2}C}$ were calculated in the framework of the one-band Eliashberg model. The effective Eliashberg function, determined on the basis of the transport function (R.S. Gonnelli, {\it et al.}, Physica C \textbf{341}, 1957 (2000)), was used during calculations. It was shown that the dimensionless ratios are equal to: $R_{1}\equiv 2Δ(0)/k_{B}T_{C}=3.87$, $R_{2}\equivΔC(T_{C})/C^{N}(T_{C})=1.79$ and $R_{3}\equiv T_{C}C^{N}(T_{C})/H_{C}^{2}(0)=0.159$. The value $R_{1}$ fairly agrees with the experimental data whereas $R_{2}$ and $R_{3}$ agree very well.

cond-mat.supr-con↗
arXiv2011

Specific heat and thermodynamic critical field for the molecular metallic hydrogen

In the framework of the Eliashberg formalism the free energy difference between the superconducting and normal state for the molecular metallic hydrogen was calculated. The pressure values $p_{1}=347$ GPa and $p_{2}=428$ GPa were taken into consideration. It has been shown, that together with the increase of the pressure, grows the value of the specific heat jump at the critical temperature and the value of the thermodynamic critical field near zero Kelvin: $[ΔC(T_{C})]_{p2}/[ΔC(T_{C})]_{p1}\simeq 2.33$ and $[H_{C}(0)]_{p2}/[H_{C}(0)]_{p1}\simeq 1.74$. Next, it has been stated, that the ratio $ΔC(T_{C})/C^{N}(T_{C})$ also increases from 1.91 to 2.39; whereas $T_{C}C^{N}(T_{C})/H^{2}_{C}(0)$ decreases from 0.152 to 0.140. The last results prove that the considered parameters significantly diverge from the prediction based on the BCS model.

cond-mat.supr-con↗
arXiv2011

Strong-coupling description of the high-temperature superconductivity in the molecular hydrogen

The detailed study of the selected thermodynamic properties of the superconducting phase in the molecular hydrogen under the pressure at 428 GPa has been presented. For the increasing value of the Coulomb pseudopotential, $μ^{*}\in<0.08,0.15>$, the following results have been obtained: (i) the critical temperature decreases from 179 K to 141 K, (ii) the ratio $R_{1}\equivΔ(0)/k_{B}T_{C}$ differs noticeably from the BCS value: $R_{1}\in<4.71,3.60>$; (iii) the electron effective mass is large and grows slightly together with the temperature ($[m^{*}_{e}/m_{e}]_{\rm max} = 2.2$ for $T = T_{C}$).

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↗