arXiv subjects

A. P. Durajski

Publications and source records attributed to A. P. Durajski.

At least 19 recordsLinked to original sources

arXiv2021

Carbonaceous sulfur hydride system: the strong-coupled room-temperature superconductor with a low value of Ginzburg-Landau parameter

The superconducting state in Carbonaceous Sulfur Hydride (C-S-H) system is characterized by the record-high critical temperature of $288$~K experimentally observed at $\sim$267 GPa. Herein, we determined the properties of the \mbox{C-S-H} superconducting phase within the scope of both classical Eliashberg equations (CEE) and the Eliashberg equations with vertex corrections (VCEE). We took into account the scenarios pertinent to either the intermediate or the high value of electron-phonon coupling constant ($λ\sim 0.75$ or $λ\sim 3.3$, respectively). The scenario for the intermediate value, however, cannot be actually realized due to the anomally high value of logarithmic phonon frequency ($ω_{\rm ln}/k_{B}=7150$~K) it would require. On the other hand, we found it possible to reproduce correctly the value of $T_{C}$ and other thermodynamic quantities in the case of strong coupling. However, the vertex corrections lower the order parameter values within the range from $\sim 50$~K to $\sim275$~K. For the upper critical field $H_{C2}\sim 27$~T, the Ginzburg-Landau parameter $κ$ is of the order of $1.7$. This correlates well with the sharp drop of resistance observed by Hirsch and Marsiglio at the critical temperature. The strong-coupling scenario for C-S-H system is also suggested by the high values of $λ$ estimated for ${\rm H_{3}S}$ ($λ\sim 2.1$, $κ\sim 1.5$), ${\rm LaH_{10}}$ ($λ\sim 2.8$-$3.9$, $κ\sim 1.6$), and ${\rm YH_{6}}$ ($λ\sim 1.7$, $κ\sim 1.3$) compounds.

cond-mat.supr-con↗

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↗

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

From LaH10 to room-temperature superconductors

Thermodynamic parameters of the $\rm LaH_{10}$ superconductor were an object of our interest. $\rm LaH_{10}$ is characterised by the highest experimentally observed value of the critical temperature: $T^{a}_{C}=215$~K ($p_{a}=150$~GPa) and $T^{b}_{C}=260$~K ($p_{b}=190$~GPa). It belongs to the group of superconductors with a~strong electron--phonon coupling ($λ_{a}\sim 2.2$ and $λ_{b}\sim 2.8$). We calculated thermodynamical parameters of this superconductor and found that the values of the order parameter, the thermodynamic critical field, and the specific heat differ significantly from the values predicted by the conventional BCS theory. Due to the specific structure of the Eliashberg function for the hydrogenated compounds, the qualitative analysis suggests that the superconductors of the ${\rm La_δX_{1-δ}H_{10}}$--type (LaXH--type) structure, where ${\rm X}\in\{{\rm Sc},{\rm Y}\}$, would exhibit significantly higher critical temperature than $T_{C}$ obtained for $\rm LaH_{10}$. In the case of LaScH we came to the following assessments: $T^{a}_{C}\in\left<220,267\right>$~K and $T^{b}_{C}\in\left<263,294\right>$~K, while the results for LaYH were: $T^{a}_{C}\in\left<218,247\right>$~K and $T^{b}_{C}\in\left<261,274\right>$~K.

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↗

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↗

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

Migdal-Eliashberg equations - the effective model for superconducting state in H3S

The high-temperature superconducting state in sulfur trihydride ($T_{C}=203$~K) has been investigated in the context of the non-adiabatic and anharmonic effects. The Migdal-Eliashberg equations and the extended Eliashberg equations, which include the lowest-order vertex corrections, have been solved numerically in the self-consistent way. For $R3m$ crystal structure, the lowest-order vertex corrections decrease the value of the Coulomb pseudopotential from $0.123$ to $0.108$. The anharmonic effects work antagonistically in relation to the vertex corrections shifting the value of $μ^{\star}$ to $0.156$. The studies conducted for the structure $Im\overline{3}m$, where the Eliashberg function includes both the non-adiabatic and anharmonic effects, prove the even higher value of $μ^{\star}=0.185$. Independently of the assumed method of the analysis, the nearly identical no mean-field dependence of the order parameter on the temperature was obtained: $2Δ(0)/k_{B}T_{C}\sim 4.7$ - due to the significant strong-coupling and retardation effects: $λ\sim 2$ and $k_{B}T_{C}\slash ω_{\rm \ln}\sim 0.15$-$0.19$. It means that the classical equations of Migdal-Eliashberg can be treated as a correct effective model for the superconducting state in $\rm H_{3}S$. This paper has shown that the McMillan or Allen-Dynes formulas substantially lower the value of the critical temperature in relation to the result obtained with the Eliashberg equations.

cond-mat.supr-con↗

arXiv2016

Pseudogap in Eliashberg approach based on electron-phonon and electron-electron-phonon interaction

The properties of the superconducting and the anomalous normal state have been described by using the Eliashberg method. The pairing mechanism has been reproduced with help of the Hamiltonian, which models the electron-phonon and electron-electron-phonon interaction (EEPh). The set of the Eliashberg equations, which determines the order parameter function ($φ$), the wave function renormalization factor ($Z$), and the energy shift function ($χ$) has been derived. It has been proven that for the sufficiently large values of EEPh potential, the doping dependence of order parameter ($φ/Z$) has the analogous course to that observed experimentally in cuprates. The energy gap in the electron density of states is induced by $Z$ and $χ$ - the contribution from $φ$ is negligible. The electron density of states possesses the characteristic asymmetric form and the pseudogap is observed above the critical temperature.

cond-mat.supr-con↗

arXiv2016

Non-BCS temperature dependence of energy gap in thin film electron-doped cuprates

We investigate the dependence of the energy gap ($G$) on the temperature ($T$) for the electron-doped high-temperature superconductors. The following compounds, in the form of the thin films, have been taken into consideration: $\rm La_{2-x}Ce_xCuO_{4}$ (LCCO), $\rm Pr_{2-x}Ce_xCuO_{4}$ (PCCO), and $\rm Nd_{2-x}Ce_xCuO_4$ (NCCO). It was found that $G\left(T\right)$ deviates from the BCS prediction more, if a concentration of cerium assumes the lower values. For the lowest concentration (in the case of LCCO and NCCO), the function $G\left(T\right)$ is not quite like the BCS curve, which is connected with the existence of the residual Nernst region. Next, it has been pointed out that the NCCO superconductor becomes structurally unstable for the maximum concentration of cerium, which is leading to the anomalous dependence of the energy gap on the temperature and the induction of the wide Nernst region.

cond-mat.supr-con↗

arXiv2016

The isotope effect in H$\rm_{3}$S superconductor

The experimental value of ${\rm H_{3}S}$ isotope coefficient decreases from $2.37$ to $0.31$ in the pressure range from $130$ GPa to $200$ GPa. We have shown that the value of $0.31$ is correctly reproduced in the framework of the classical Eliashberg approach. On the other hand, the anomalously large value of the isotope coefficient ($2.37$) may be associated with the strong renormalization of the normal state by the electron density of states.

cond-mat.supr-con↗

arXiv2015

High-temperature study of superconducting hydrogen and deuterium sulfide

Hydrogen-rich compounds are extensively explored as candidates for a high-temperature superconductors. Currently, the measured critical temperature of $203$ K in hydrogen sulfide (H$_3$S) is among the highest over all-known superconductors. In present paper, using the strong-coupling Eliashberg theory of superconductivity, we compared in detail the thermodynamic properties of two samples containing different hydrogen isotopes H$_3$S and D$_3$S at $150$ GPa. Our research indicates that it is possible to reproduce the measured values of critical temperature $203$ K and $147$ K for H$_3$S and D$_3$S by using a Coulomb pseudopotential of $0.123$ and $0.131$, respectively. However, we also discuss a scenario in which the isotope effect is independent of pressure and the Coulomb pseudopotential for D$_3$S is smaller than for H$_3$S. For both scenarios, the energy gap, specific heat, thermodynamic critical field and related dimensionless ratios are calculated and compared with other conventional superconductors. We shown that the existence of the strong-coupling and retardation effects in the systems analysed result in significant differences between values obtained within the framework of the Eliashberg formalism and the prediction of the Bardeen-Cooper-Schrieffer 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

Anisotropy of the gap parameter in the hole-doped cuprates

The structure of the gap parameter ($Δ_{k}$) for the hole-doped cuprates has been studied. The obtained results indicate that the antinodal part of $Δ_{k}$ is very weakly temperature dependent and above the critical temperature ($T_{C}$), it extends into the anomalous normal state to the pseudogap temperature. On the other hand, the values of $Δ_{k}$, which are close to the nodal part, are strongly temperature dependent. The model has been tested for the ${\rm YBa_{2}Cu_{3}O_{7-δ}}$ superconductor. It has been shown that the theoretical results agree with the experimental data.

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

The thermodynamic properties of the high-pressure superconducting state in the hydrogen-rich compounds

The ab initio calculations suggest that the superconducting state in CaH6 under the pressure at 150 GPa has the highest critical temperature among the examined hydrogen-rich compounds. For this reason, the relevant thermodynamic parameters of the superconducting state in CaH6 have been determined; a wide range of the Coulomb pseudopotential has been assumed: $μ^{\star}\in\left<0.1,0.3\right>$. It has been found that: (i) The critical temperature (Tc) changes in the range from 243 K to 180 K. (ii) The values of the ratio of the energy gap to the critical temperature ($R_Δ\equiv 2Δ\left(0\right)/k_{B}T_{C}$) can be found in the range from 5.42 to 5.02. (iii) The ratio of the specific heat jump ($ΔC\left(T_{C}\right)$) to the value of the specific heat in the normal state ($C^{N}\left(T_{C}\right)$), which has been represented by the symbol Rc, takes the values from 3.30 to 3.18. (iv) The ratio $R_{H}\equiv T_{C}C^{N}\left(T_{C}\right)/H^{2}_{C}\left(0\right)$, where $H_{C}\left(0\right)$ denotes the critical thermodynamic field, changes from 0.122 to 0.125. The study has brought out the expressions that correctly predict the values of the thermodynamic parameters for the superconducting state in CaH6 and for the compounds: SiH4(H2)2, Si2H6, B2H6, SiH4, GeH4, and PtH. Next, in the whole family of the hydrogen-rich compounds, the possible ranges of the values have been determined for Tc, $R_Δ$, Rc, and $R_{H}$. It has been found that the maximum value of the critical temperature can be equal to 764 K, which very well correlates with Tc for metallic hydrogen (p=2 TPa). Other parameters ($R_Δ$, Rc, and $R_{H}$) should not deviate from the predictions of the BCS theory more than the analogous parameters for CaH6.

cond-mat.supr-con↗

arXiv2013

The high-pressure superconductivity in SiH4: the strong-coupling approach

In the paper, the thermodynamic parameters of the high-pressure superconducting state in the SiH$_4$ compound have been determined ($p=250$ GPa). By using the Eliashberg equations in the mixed representation, the critical temperature, the energy gap, and the electron effective mass have been calculated. It has been stated that the critical temperature ($T_{C}$) decreases from 51.65 K to 20.62 K, if the Coulomb pseudopotential increases ($μ^{\star}\in 0.1,0.3$). The dimensionless ratio $2Δ$0$/k_{B}T_{C}$ decreases from 4.10 to 3.84, where the symbol $Δ$0$$ denotes the value of the order parameter close to the zero temperature. The ratio of the electron effective mass to the band electron mass is high, and it reaches maximum equal to 1.95 for the critical temperature.

cond-mat.supr-con↗