arXiv subjects

R. Szczȩśniak

Publications and source records attributed to R. Szczȩśniak.

15 recordsLinked to original sources

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

Superconducting properties of under- and over-doped Ba$_{x}$K$_{1-x}$BiO$_{3}$ perovskite oxide

In the present study, we investigate the thermodynamic properties of the Ba$_{x}$K$_{1-x}$BiO$_{3}$ (BKBO) superconductor in the under- ($x=0.5$) and over-doped ($x=0.7$) regime, within the framework of the Migdal-Eliashberg formalism. The analysis is conducted to verify that the electron-phonon pairing mechanism is responsible for the induction of the superconducting phase in the mentioned compound. In particular, we show that BKBO is characterized by the relatively high critical value of the Coulomb pseudopotential, which changes with doping level and does not follow the Morel-Anderson model. In what follows, the corresponding superconducting band gap size and related dimensionless ratio are estimated to increase with the doping, in agreement with the experimental predictions. Moreover the effective mass of electrons is found to take on high values in the entire doping and temperature region. Finally, the characteristic dimensionless ratios for the superconducting band gap, the critical magnetic field and the specific heat for the superconducting state are predicted to exceed the limits set within the Bardeen-Cooper-Schrieffer theory, suggesting pivotal role of the strong-coupling and retardation effects in the analyzed compound. Presented results supplement our previous investigations and account for the strong-coupling phonon-mediated character of the superconducting phase in BKBO at any doping level.

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↗

arXiv2015

Thermodynamics of the hydrogen dominant potassium hydride superconductor at high pressure

In the present paper we report comprehensive analysis of the thermodynamic properties of novel hydrogen dominant potassium hydride superconductor (KH$_{6}$). Our computations are conducted within the Eliashberg theory which yields quantitative estimations of the most important thermodynamic properties of superconducting phase. In particular, we observe, that together with the increasing pressure all the thermodynamic properties decrease, e.g. $T_{C} \in \left< 72.91 , 55.50 \right>$ K for $p \in \left< 166 , 300 \right>$ GPa. It is predicted that such decreasing behavior corresponds to the decreasing hydrogen lattice molecularization with increasing pressure value. Futhermore, by calculating the dimensionless thermodynamic ratios, familiar in the Bardeen-Cooper-Schrieffer theory (BCS), it is proved that KH$_{6}$ material is a strong-coupling superconductor and cannot be quantitatively described within the BCS theory.

cond-mat.supr-con↗

arXiv2015

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 $3.5\times10^{14}~{\rm cm^{-2}}$. Under such conditions, silicene monolayer is expected to exhibit the highest superconducting transition temperature ($T_C$). In particular, based on the electron-phonon spectral function and assuming wide range of the Coulomb pseudopotential values ($μ^{\star}\in\left\langle0.1,0.3\right\rangle$) it is stated that the superconducting transition temperature decreases from $18.7$ K to $11.6$ K. Similar behavior is observed in the case of the zeroth temperature superconducting energy gap at the Fermi level: $2Δ(0)\in\left\langle6.68, 3.88\right\rangle$ 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.

cond-mat.supr-con↗

arXiv2015

Quantum conductance of silicon-doped carbon wire nanojunctions

The unknown quantum electronic conductance across nanojunctions made of silicon-doped carbon wires between carbon leads is investigated. This is done by an appropriate generalization of the phase field matching theory for the multi-scattering processes of the electronic excitations at the nanojunction, and the use of the tight-binding method. Our calculations of the electronic band structures for carbon, silicon and diatomic silicon carbide, are matched with the available corresponding density functional theory results to optimize the required tight-binding parameters. The silicon and carbon atoms are treated on the same footing by characterizing each with their corresponding orbitals. Several types of nanojunctions are analyzed to sample their behavior under different atomic configurations. We calculate for each nanojunction the individual contributions to the quantum conductance for the propagating $σ$, $π$, and $σ^{*}$ electrons incident from the carbon leads. The calculated results show a number of remarkable features, which include the influence of the ordered periodic configurations of silicon-carbon pairs, and the suppression of the quantum conductance due to minimum substitutional disorder and to artificially organized symmetry on these nanojunctions. Our results also demonstrate that the phase field matching theory is an efficient tool to treat the quantum conductance of complex molecular nanojunctions.

cond-mat.mes-hall↗

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↗

arXiv2014

Influence of lithium doping on the thermodynamic properties of graphene based superconductors

It has been recently observed that the conventional electron-phonon mediated superconducting phase in graphene can be easily induced by doping its surface with the lihitum adatoms. Due to the emerging interest in this field of research we present our theoretical discussion of the thermodynamic properties of this novel structures within the strong-coupling limit. We show, that together with the increase of the adatom doping, from one (LiC$_{6}$) to two (Li$_{2}$C$_{6}$) lithium atoms per unit cell, the critical temperature ($T_C$) changes from 8.55 K to 21.83 K. Such trend is also observed for other thermodynamic properties which moreover differ from the predictions of the Bardeen-Cooper-Schrieffer theory. In particular, the zero-temperature energy gap to the critical temperature ratio: R$_Δ^{{\rm LiC}_6}$=3.72 and R$_Δ^{{\rm Li}_{2}{\rm C}_6}$=4.21; the ratio of the specific heat for superconducting and the normal state: R$_{\rm C}^{{\rm LiC}_6}$=1.47 and R$_{\rm C}^{{\rm Li}_{2}{\rm C}_6}$=1.79; and the parameter connected with the zero-temperature thermodynamic critical field: R$_{\rm H}^{{\rm LiC}_6}$=0.167 and R$_{\rm H}^{{\rm Li}_{2}{\rm C}_6}$=0.144. Finally the electron effective mass at $T_c$ is calculated to be: $(1.62m_e)_{{\rm LiC}_6}$ and $(2.48m_e)_{{\rm Li}_{2}{\rm C}_6}$.

cond-mat.supr-con↗

arXiv2013

Description of the superconducting state in the high-pressure fcc phase of platinum-hydride

The thermodynamic parameters of the superconducting state in PtH at the pressure 76 GPa have been examined. The calculations have been carried out in the framework of the Eliashberg formalism. It has been found that the critical temperature changes in the range from 30.6 K to 16.8 K, depending on the assumed value of the Coulomb pseudopotential (0.1, 0.2 and 0.3). The other thermodynamic quantities differ significantly from the predictions of the classical BCS theory. In particular: (i) The parameter which corresponds to the superconducting band gap reaches the values from 4.25 to 3.98. (ii) The ratio of the specific heat jump to the specific heat in the normal state takes the values from 2.07 to 1.97. (iii) Finally, the parameter for the low-temperature thermodynamic critical field is in the range from 0.145 to 0.156.

cond-mat.supr-con↗

arXiv2012

The characterization of high-pressure superconducting state in Si2H6 compound: the strong-coupling description

The thermodynamic parameters of the superconducting state, that induces in ${\rm Si_{2}H_{6}}$ under the pressure at 275 GPa, have been calculated. In the framework of the Eliashberg formalism, it has been shown that the critical temperature can attain extremely high values: $T_{C}(μ^{\star})\in<173.36, 99.99>$ K, where the Coulomb pseudopotential $(μ^{\star})$ belongs to the range from 0.1 to 0.3. The ratio of the energy gap to the critical temperature ($R_Δ$) significantly exceeds the value predicted by the BCS theory: $R_Δ(μ^{\star})\in<4.40, 4.04>$. Additionally, it has been stated that in the whole range of the superconducting state's existence, the electron effective mass ($m^{\star}_{e}$) is large; $[m^{\star}_{e}]^{\rm max}_{T=T_{C}}=2.397m_{e}$, where the symbol $m_{e}$ denotes the electron band mass.

cond-mat.supr-con↗

arXiv2012

Multigap superconducting state in molecular metallic hydrogen

The thermodynamic parameters of the superconducting state, that gets induced in the metallic molecular hydrogen under the influence of the pressure at 414 GPa ($T_{C}=84$ K), have been determined. The calculations have been conducted in the framework of the three-band Eliashberg equations. The order parameters ($Δ^α$) and the wave function renormalization factors ($Z^α$) have been derived; the symbol $α$ denotes the band index: $α\in{a,b,c}$. It has been stated that the dimensionless ratios $2Δ^α(0)/k_{B}T_{C}$ are equal to: 5.55, 3.96 and 3.53, respectively. Next, the total normalized function of the density of states, the free energy, the thermodynamic critical field and the specific heat have been determined. The obtained results differ significantly from the results achieved in the framework of the one-band Eliashberg model for the comparable value of the pressure ($p=428$ GPa). In the last step, the values of the wave function renormalization factors have been estimated for $T_{C}$. It allowed us to calculate the maximum value of the electron effective mass in a given band [($[m^{\star}_{e}]_α$). The following results have been achieved: $[m^{\star}_{e}]_{a}=2.99 [m_{e}]_{a}$, $[m^{\star}_{e}]_{b}=2.10 [m_{e}]_{b}$ and $[m^{\star}_{e}]_{c}=1.94 [m_{e}]_{c}$, where $[m_{e}]_α$ stands for the electron band mass.

cond-mat.supr-con↗

arXiv2012

On the critical temperature and the energy gap in dense SiH4(H2)2 at 250 GPa

The critical temperature ($T_{C}$) and the energy gap ($2Δ(T)$) for the superconductor SiH$_4$(H$_2$)$_2$ at 250 GPa have been calculated. The wide range of the Coulomb pseudopotential's values has been considered: $μ^{\star}\in<0.1,0.3>$. It has been stated that $T_{C}$ decreases together with the increase of $μ^{\star}$ from 129.83 K to 81.40 K. The low-temperature energy gap ($T\sim 0$ K) decreases together with the increase of the Coulomb pseudopotential from 50.96 meV to 30.12 meV. The high values of $2Δ(0)$ mean that the dimensionless ratio $R_Δ\equiv 2Δ(0)/k_{B}T_{C}$ significantly exceeds the value predicted by the classical BCS theory. In the considered case: $R_Δ\in<4.55,4.29>$. Due to the unusual dependence of the critical temperature and the energy gap on $μ^{\star}$, the analytical expressions for $T_{C}(μ^{\star})$ and $Δ(μ^{\star})$ have been given.

cond-mat.supr-con↗

arXiv2012

Characterization of the high-pressure superconductivity in the Pnma phase of calcium

The thermodynamic parameters of the superconducting state in calcium under the pressure at 161 GPa have been calculated within the framework of the Eliashberg approach. It has been shown that the value of the Coulomb pseudopotential is high (0.24) and the critical temperature (25 K) should be determined from the modified Allen-Dynes formula. In addition, it has been found that the basic dimensionless ratios of the thermodynamic parameters significantly diverge from the BCS predictions, and take the following values: (i) The zero temperature energy gap to the critical temperature(R1) is equal to 4.01. (ii) The ratio R2 equals 2.17. (iii) The quantity R3=0.158. Finally, it has been proven that the electron effective mass is large and takes the maximum of 2.32*me at TC.

cond-mat.supr-con↗

arXiv2011

The toy model for the high-Tc superconductivity

The simple microscopic model for the high-T_{C} superconductors based on the electron-phonon (EPH) and electron-electron-phonon (EEPH) interactions has been presented. On the {\it fold} mean-field level, it has been shown, that the obtained model supplements the predictions based on the BCS van Hove scenario. In particular: (i) For strong EEPH coupling and T<T_{C} the energy gap (Δ_{tot}) is very weak temperature dependent; up to the critical temperature Δ_{tot} extends into the anomalous normal state to the Nernst temperature. (ii) The model explains well the experimental dependence of the ratio R_{1}\equiv 2Δ_{tot}^{(0)}/k_{B}T_{C} on doping for the reported superconductors in the terms of the few fundamental parameters.

cond-mat.supr-con↗