Abstract
The nearly roomtemperature superconductivity that had been predicted theoretically for lanthanum and yttrium superhydrides at megabar pressures has been recently achieved experimentally in several superhydride compounds, including lanthanum decahydride with \(T _{c}\) of about 250 K under high pressure of about 150 GPa. Though superconductivity should be governed by the phonon mechanism in these compounds, which is evident due to the measured deuterium isotope effect in LaD_{10}, we believe that the choice of small values of the effective Coulomb constant, used in theoretical calculations of the critical temperature, merits farther substantiation. We discuss the possibility for the collective acoustic electronic excitations (acoustic plasmons) to appear in the collective spectra of superhydrides thus facilitating the suppression of the Coulomb repulsion. In LaH_{10} the conditions for such mechanism arise due to the hybridization of La 4f and H 1s states near the Fermi level in the vicinity of the Lpoint of the Brillouin zone. A simple model approximation for the resulting conducting band allows us to show that in a certain portion of quasimomentum space an acoustic branch should appear in the spectrum of the collective electronic excitations in LaH_{10}, arguably reducing the effective Coulomb constant.
Article highlights

We discuss the possibility for the acoustic plasmons to appear in superhydrides and to influence the superconducting properties of these materials.

Analytical expression (the “extended” Lindhard formula) is derived for the 3D polarization operator in the case of anisotropic uniaxial effective mass.

The possible change of the Fermi energy due to a slight deviation from stoichiometry is shown to have a potential to facilitate higher T_{c} in superhydrides.
Introduction
In 1968 Neil Ashcroft predicted superconductivity with high critical temperature for hypothetical metallic hydrogen [1]. As an advantage of this candidate for high\(T_{c}\) superconductors Ashcroft mentioned the high Debye phonon frequency, which enters the preexponent in the BCS formula for \(T_{c}\). But he also estimated, using the spherical Fermi surface and static screening in the Thomas–Fermi model, that in the metallic hydrogen the Coulomb repulsion, represented by the Coulomb constant (pseudopotential) \(\mu ^{*}\), should be very weak in comparison with the Fröhlich phonon attraction described by the phonon coupling constant \(\lambda\). The significance of this observation is obvious if we look at any expression for \(T_{c}\), that takes into account the strong electronphonon coupling along with the Coulomb repulsion, for example
or
These formulas represent results obtained for different models of the phonon spectrum in [2, 3], respectively, both based on the Eliashberg equation accounting for the strong retarded electron–phonon interaction. In the above formulas \(\omega _{0}\) is a characteristic phonon frequency, \(\lambda ,\; \lambda _{0} ,\; \lambda _{\infty }\) are electronphonon coupling constants defined in respective models, and \(\mu ^{*}\) is the Bogoliubov–Tolmachov–Morel–Anderson pseudopotential.
A new step towards the achievement of the hydrogenbased superconductivity was made again by Ashcroft in 2004, who suggested that the high pressure needed for the formation of metallic hydrogen may be lowered by chemical bond with metal atoms in compounds with a significant predominance of hydrogen atoms [4]. Later this approach was substantiated in [5,6,7,8,9] by the firstprinciple calculations of the electron band structure and phonon spectra for superhydrides of several lanthanoid elements at megabar pressures, as well as for the vanadium hydrides [10] and hydrogen sulfide \(\hbox {H}_{{3}}\)S [11]. In these calculations very high values of the coupling constant \(\lambda\) and critical temperature \(T_{c}\) were predicted within the Migdal–Eliashberg theory. Finally, this approach was implemented experimentally by two groups led by Hamley (in the USA) [12] and Eremets (in Germany) [13]. Superconductivity at 250 K has been achieved in lanthanum decahydride \(\mathrm {LaH}_{10}\) under high pressure of about 150 GPa.
The strong electron–phonon interaction and high phonon frequencies make the phonon mechanism virtually the sole candidate for the explanation of the high values of the temperature of superconducting transition in superhydrides. At the same time, these high values of \(T_{c}\) were obtained in theoretical calculations [5, 6] with the choice of small values of the effective Coulomb constant \(\sim 0.1\), which in our opinion needs farther justification. We intend to discuss below the effects that the peculiar features of the oneparticle electronic spectra of the rareearth superhydrides may play in the achieving of such Coulomb constant and in the increasing of the values of critical temperature.
It should be noticed that in the same 1968 year one of us (E.A.P.) suggested a possible nonphononic mechanism of hightemperature superconductivity (HTS) [14], where the Cooper pairing of the charge carriers was brought about by interaction with the socalled acoustic plasmons—the collective excitations arising in solids with two subsystems of degenerate charge carriers with significantly different effective masses (light and heavy) [15].
In the Eliashberg theory of superconductivity [16] the electron–phonon interaction constant is determined by the momentumaveraged spectral function \(\alpha ^{2} F\left( \nu \right)\) of this interaction:
In the case of the plasmonmediated interaction between the charge carriers the spectral function of the electronplasmon interaction (the retarded screened Coulomb interaction) is defined by means of the Coulomb matrix element \(V_{C} \left( q\right)\) and frequency and momentumdependent dielectric function \(\varepsilon \left( \nu ,q\right)\):
where \(\nu\) and q are transferred frequency and momentum.
With the discovery of HTS in cuprates in 1986 several authors [17,18,19] suggested plasmonic mechanism as a reason for increased \(T_{c}\). On the other hand, Abrikosov in [20] emphasized the crucial role of the so called “extended saddle points”, observed near the Fermi level in the cuprate metaloxides [20, 21], stating that they should be responsible for high values of \(\textit{T}_{c}\) even in the case of standard phonon mechanism. We have shown in a series of publications [22,23,24,25] that significant anisotropy of the Fermi velocity along quasi2D Fermi surface (FS) of cuprates, caused by these features of the oneparticle spectra, should bring about the emergence of acoustic plasmon branch even in the case of a singleconnected FS, when the roles of “heavy” and “light” carriers are played by the quasiparticles, belonging to the FS in the vicinity of the “extended saddle points” and away from them, respectively. As the result, due to the symmetry of the Fermisurface, the acoustic plasmonic excitations contribute in cuprates to the Cooper pairing in the dwave channel.
Though the rareearth superhydrides are completely different from HTS cuprate metaloxides, there is some similarity in singleelectron spectrum feature near Fermi level in both cases. The electronic bands of \(\mathrm {LaH}_{10}\) at pressure of 300 GPa, calculated in [5], are shown in Fig. 1 (Fig. 6b in [5]). Of the bands, crossing the Fermi level, of special interest for us is the one showing almost “flat” dispersion in the vicinity of the Fermi level. This band is shown schematically in Fig. 2 and has open FS with eight “necks” at \(\mathrm {L}\)points of the fcc Brillouin zone (BZ). A slight “doping” with hydrogen vacancies may lead to a downward shift of the Fermi level (FL) without affecting the band structure. In this case additional hole pockets in the form of oblate ellipsoids may appear inside the “necks” of the FS. All these band features are due to the hybridization of La 4f and H 1s states near the FL in the vicinity of the Lpoint of the BZ [5]. The existence of such a band in the electronic spectrum of \(\mathrm {LaH}_{10}\) allowed us to put forward in [26] a supposition about the appearance of the acoustic plasmon excitations in the collective electronic spectra of this system and their influence on the superconducting critical temperature.
In the present paper we are going to expand upon the points made in [26] and in the next section will give the detailed analytical expression for the polarization operator for the system with uniaxially anisotropic effective mass. In Sect. 2 we introduce a simple analytical model for the conduction band describing the mentioned peculiarities and present the results of the numerical calculations of polarization operator, dielectric function and acoustic plasmon dispersion for such a band. We also study the effects of the small changes of the Fermi level and emphasize their potential role in the increasing of the critical temperature. In the final section we summarize the main results of this paper.
Polarization operator
The branches of the collective electronic spectrum are determined by zeroes of the frequency and momentumdependent dielectric permittivity (dielectric function)
which implies that we need to know the retarded polarization operator (PO),
in our case—in the presence of an open Fermi surface, described above. In (3) \(\xi\) denotes the quasiparticle energy, f stands for Fermi distribution function and \(\delta\) is a positive infinitesimal value.
For preliminary analytical estimates, the polarization operator for such a Fermi surface was represented as a superposition, with a certain weight, of the polarization operator for a sphere and the contributions from eight “necks” of the Fermi surface, which were approximated by onesheet hyperboloids of revolution in the vicinity of the \(\mathrm {L}\)points of the Brillouin zone.
For this purpose, we have extended the Lindhard formula for the 3D PO [27] to the case of anisotropic uniaxial effective mass and obtained a general analytical expression for a band, characterized by dispersion
which corresponds to a Fermi surface in the form of a spheroid or hyperboloid of revolution, depending on the sign in (4). Here \(p_{\bot }\) is the transvers 2D component of the momentum in the isotropic plane, \(p_{\parallel }\) is the momentum component along the third (rotational) axis, while \(m_{\bot }\) and \(m_{\parallel }\) are the respective masses. The result of integration in eq. (3) with spectrum (4) over the transverse momentum \(d^{2} p_{\bot }\) may be written in the form
here we have introduced several functions dependent on the parameter of mass anisotropy \(\eta =\, \sqrt{{m_{\bot } \big / m_{\parallel } } }\) and polar angle \(\vartheta\) (\({\pi \big / 2} \le \vartheta \le {\pi \big / 2}\)), measured from the plane perpendicular to the rotation axis (\(q_{\bot } \equiv q\cos \vartheta\), \(q_{\parallel } \equiv q\sin \vartheta\)):
where \({\alpha _ \pm } = {\cos ^2}\vartheta \pm {\eta ^2}{\sin ^2}\vartheta\), \({z_ \pm } = \frac{\displaystyle {q{{\mid {{\alpha _ \pm }} \mid }^{{1 \big / 2}}}}}{\displaystyle {2p_{F \bot }^{\left( \pm \right) }}}\), \({u_ \pm } = \frac{\displaystyle \nu }{\displaystyle {q{{\mid {{\alpha _ \pm }} \mid }^{{1 \big / 2}}}V_{F \bot }^{\left( \pm \right) }}}\), \(p_{F\bot }^{\left( \pm \right) }\) and \(V_{F\bot }^{\left( \pm \right) }\)—Fermi momentum and velocity, lying in transversal plane, and ± signs correspond to those in (4). For the spheroid FS the integration limit \(\gamma _{+}\) in (5) is ultimately determined by the maximal value of the Fermi momentum in the direction of the rotation axis, \(p_{F\parallel }^{\left( +\right) } =\eta ^{1} \cdot p_{F\bot }^{\left( +\right) }\), and reads as \(\gamma _{+} =\eta ^{1}\). In the case of the open FS in the form of onesheet hyperboloid the choice of \(\gamma _{}\) is somewhat arbitrary, as formally there is no such a limiting value as \(p_{F\parallel }^{\left( \right) }\). In reality this maximal value may not exceed the size of the BZ and should be determined by the “length” of the “necks” of the FS within the BZ.
If we choose for the hyperboloid case \(\gamma _{} =\eta ^{1}\), just as for the spheroid one, then the universal “anisotropic Lindhard” expressions for the real and imaginary parts of polarization operator read as:
where \(\theta \left( x\right)\) is the Heaviside step function.
In the case of onesheet hyperboloid, if \(\vartheta \rightarrow \pm \mathop {\mathrm{arccot}}\nolimits \left( \eta \right)\) (the momentum belongs to the asymptotic conical surface), we have \(\alpha _{} \rightarrow 0\), \(\mathop {\mathrm{Im}}\nolimits \Pi _{3D}^{\left(  \right) } \rightarrow 0\) and \(\mathop {\mathrm{Re}}\nolimits \Pi _{3D}^{\left(  \right) } \rightarrow {\sqrt{m_{\bot } m_{\parallel }}\, p_{F \bot }^{\left(  \right) } \big / 2\pi ^{3} }\).
Finally, if for \({\Pi _{3D}^{\left( \right) } \big / \gamma _{} }\) we formally set \(\gamma _{} \rightarrow 0\), then for \(\vartheta =0\) the classical Stern result [28] for 2D degenerate electron gas with \(m_{2D} =m_{\bot }\) and \(p_{F}^{(2D)} =p_{F \bot }^{\left(  \right) }\) is obtained from (5):
Note that the expressions, derived here, may be applied to the description of dynamic screening in degenerate multivalley semiconductors (ellipsoid of revolution) and on the surfaces (1,1,1) of noble metals (onesheet hyperboloid).
For the parameters extracted from the calculated singleparticle spectra, we constructed polarization operator as a superposition of the polarization operator for a sphere and the contributions from eight “necks” of the Fermi surface. It appears, that even such a crude model approximates the polarization operator quite satisfactory (dielectric and spectral functions obtained in this way are shown with thin lines on Fig. 4 below) and confirms the possibility of the existence of acoustic plasmons in a certain range of solid angles.
Numerical calculation of the polarization operator and plasmon dispersion
For a more detailed numerical calculations, we propose the following approximation of the band dispersion in the vicinity of the \(\mathrm {L}\)points in the Brillouin zone, which models the result of hybridization of La 4f and H 1s states:
here the momentum component \(p_\parallel\) is along the \(\Gamma\) – \(\mathrm {L}\) direction, while \(p_{\bot }\) lies in the plain of the hexagonal edge of BZ. This expression is merged with a usual tightbindingapproximation formula, based on s orbitals, away from the \(\mathrm {L}\)points:
where \(\varepsilon _{TB}\approx 8\) eV is the width of the band and a is the lattice constant of the cubic fcc lattice.
The obtained model band dispersion and density of states (DOS) are shown in Fig. 3, alongside with these characteristics for the “row” tightbinding band (10). We should mention in passing that aside from providing conditions for the appearance of the collective acoustic chargedensity excitations, which we are going to discuss now, the oneparticle spectrum feature that we are describing here also provides for the increased DOS near the FL. The higher DOS mean higher values of phonon coupling constant, thus increasing superconducting critical temperature.
On Fig. 4 the results of numerical calculation of dielectric permittivity and spectral function of the screened Coulomb interaction for the model band described above, are shown with thick lines. In this computations we first calculated the imaginary part of the polarization function (3) and then obtained the real part of the dielectric function by means of the Kramers–Kronig relation. The computation of the energysurface integrals for the imaginary part of (3) was done by covering the BZ with a mesh of tetrahedral cells (see e.g. [29, 30]), with the density of mesh point been adaptively increased when approaching the integration surface. The number of tetrahedra crossed by the integration surface was in the range of \(10^{7}\) in the highly parallelized GPU computation. The quasimomentum \(q=0.05{\pi \big / a}\) for this calculation lies in the plain of the hexagonal edge of the Brillouin zone and its direction is given by angle \(\varphi =30{}^\circ\) (see Fig. 2).
There is a lowfrequency zero (at about 0.12 eV in this case), corresponding to the peak in spectral function, and describing the additional branch of collective charge excitations (the highfrequency zero of the dielectric function, corresponding to the usual plasma frequency, lies far beyond the frequency range of this Figure). This additional branch appears due to the significant Fermivelocity anisotropy of the conduction band, caused by “flat” portions of the band spectrum, as was discussed in the Introduction, which can be seen from Fig. 5, where we compare the dielectric permittivity and spectral function, calculated for our model band (solid curve on Fig. 3), with those of a conduction band of an fcc metal, obtained within the tightbinding approximation (dashed curve on Fig. 3). It should be noted that the acoustic plasmonic branch appears only in a portion of the phase space, and for some directions of quasimomentum it is much more pronounced then in the others. One of this favorite directions is defined by the diagonal of the cubic cell of the reciprocal bcc lattice, so for the Fig. 5 we made calculation with the same model band as for the Fig. 4, but with quasimomentum lying in this direction—to emphasize the welldefined additional zeroes of dielectric function for our model band (thick curves) and their absence in the case of a basic tightbinding band.
Finally, dispersion and attenuation of acoustic plasmons with momenta lying in the plane of the hexagonal edge of the Brillouin zone are shown on Fig. 6. The frequency values were determined by the positions of the maximum of the spectral function for corresponding momenta and attenuation was estimated as the halfwidth of the plasmonic peak.
In Introduction we have mentioned a possibility for the composition of a superhydride to deviate slightly from stoichiometry. For example, a small number of hydrogen vacancies in lanthanum decahydride, \(\mathrm {LaH}_{10x}\) with \(x \ll 1\), should lead to a slight lowering of the Fermi level with no significant effect on the band structure. Up until now we have dealt with the FL position corresponding to the ideal \(\mathrm {LaH}_{10}\), but here, toward the end of the paper, we’ll touch upon the effects connected to the change in the position of the FL.
The change of the FS as the result of a shift of the Fermi level by \(0.08\) eV is illustrated in Fig. 7. The main result of this change is the appearance of the additional holelike “pockets” of the Fermi surface, which implies farther increase in the system’s anisotropy, not only through the variation of the Fermi velocity over the singlyconnected FS, but also through the variation of the masses on the various sheets of the FS. As we mentioned earlier, such anisotropy facilitates the appearance of acoustic plasmons.
The dielectric permittivity and Coulomb spectral function calculated with this FL position are shown on Fig. 8. We see that the maximum of the resulting plasmonic spectral function drifts to the left with redistribution of its weight towards the lower frequencies, simultaneously contributing to the increase of the electron–electron attraction constant and decrease of the Coulomb repulsion constant.
Conclusion
The experimental measurement of the exponent of the isotope effect was performed in [13] with substitution of deuterium for hydrogen in \({{{{{\mathop {\mathrm{LaD}}\nolimits } }_{10}}} \big / {{{{\mathop {\mathrm{LaH}}\nolimits } }_{10}}}}\). The result was rather close to the classical value \(\beta ={1\big / 2}\) obtained in the model of the pure Fröhlich electronphonon attraction. On the one hand, this is a strong experimental suggestion that the electronphonon interaction plays the predominant role in superconductivity of the rareearth superhydrides. On the other hand, using the formulas for isotopeeffect exponent, which are derived from (1) and (2) (see [2, 31], respectively):
we may conclude that the effective Coulomb constant \(\mu ^{*}\) must be negligibly small. Our analytical and numerical results suggest that lowfrequency acoustic collective electronic excitations (acoustic plasmons) may appear in superhydrides due to the peculiarities of the oneparticle band spectra of these compounds. We believe that the existence of these excitations bring about the additional suppression of the Coulomb repulsion, thus constituting the “plasmonic” mechanism of the increasing of \(T_{c}\). As was mentioned in [26], in \(\mathrm {LaH}_{10}\) the preconditions for such mechanism arise due to the hybridization of La 4f and H 1s states near the Fermi level in the vicinity of the \(\mathrm {L}\)point of the BZ [5]. It should be noted that these conditions are absent in the cases of another lanthanide superhydrides’ electron spectra, such as \(\mathrm {YbH}_{10}\) and \(\mathrm {LuH}_{8}\) under the same megabar pressure calculated in [8], with essentially lower predicted \(T_c\) of 102.1 K and 86.2 K, respectively. On the other hand, the conditions for the “plasmonic” mechanism in \(\mathrm {LaH}_{10}\) appear to be even more favorable in the case of a slight downward sift of the FL (induced by the presence of a small amount of hydrogen vacancies in the decahydride structure) due to the enhancement of the lowfrequency part of acoustic plasmon spectral function.
Of course, the overall Coulomb interaction remains repulsive and the plasmonic attraction is effective in a limited portion of the phase volume. Nevertheless, the interaction is isotropized in all directions due to the swave symmetry of pairing, which obviously occurs in the case of superhydrides under pressure (in contrast with the HTS cuprates demonstrating dwave pairing), and the additional plasmon attraction leads to the suppression of the Coulomb pseudopotential and to the increase in the superconducting critical temperature of superhydrides such as \(\mathrm {LaH}_{10}\).
Data availability
Not applicable.
Code availability
Not applicable.
References
Ashcroft NW (1968) Metallic hydrogen: a hightemperature superconductor? Phys Rev Lett 21:1748–1749. https://doi.org/10.1103/PhysRevLett.21.1748
McMillan WL (1968) Transition temperature of strongcoupled superconductors. Phys Rev 167:331–344. https://doi.org/10.1103/PhysRev.167.331
Medvedev MV, Pashitskii EA, Pyatiletov YS (1974) Effect of the lowfrequency peaks of the phonon state density on the critical temperature of superconductors. Sov Phys JETP 38:587–592 (original publication in Russian: Zh. Eksp. Teor. Fiz. 65, 1186–1197 (1973))
Ashcroft NW (2004) Hydrogen dominant metallic alloys: high temperature superconductors? Phys Rev Lett 92:187002. https://doi.org/10.1103/PhysRevLett.92.187002
Liu H, Naumov II, Hoffmann R, Ashcroft NW, Hemley RJ (2017) Potential high\(T_{c}\) superconducting Lanthanum and Yttrium hydrides at high pressure. Proc Natl Acad Sci USA 114:6990–6995. https://doi.org/10.1073/pnas.1704505114
Liu H, Naumov II, Geballe ZM, Somayazulu M, Tse JS, Hemley RJ (2018) Dynamics and superconductivity in compressed Lanthanum superhydride. Phys Rev B 98:100102. https://doi.org/10.1103/PhysRevB.98.100102
Durajski AP, Szczȩśniak R, Li Y, Wang C, Cho JH (2020) Isotope effect in superconducting lanthanum hydride under high compression. Phys Rev B 101:214501. https://doi.org/10.1103/PhysRevB.101.214501
Sun W, Kuang X, Keen HDJ, Lu C, Hermann A (2020) Second group of highpressure hightemperature lanthanide polyhydride superconductors. Phys Rev B 102:144524. https://doi.org/10.1103/PhysRevB.102.144524
Durajski AP, Wang C, Li Y, Szczȩśniak R, Cho JH (2021) Evidence of phononmediated superconductivity in LaH\(_{10}\) at high pressure. Ann Phys (Berlin) 533:2000518
Li X, Peng F (2017) Superconductivity of pressurestabilized vanadium hydrides. Inorg Chem 56:13759–13765. https://doi.org/10.1021/acs.inorgchem.7b01686
Szczȩśniak R, Durajski AP (2018) Unusual sulfur isotope effect and extremely high critical temperature in H\(_3\)S superconductor. Sci Rep 8:6037. https://doi.org/10.1038/s41598018244428
Somayazulu M, Ahart M, Mishra AK, Geballe ZM, Baldini M, Meng Y, Struzhkin VV, Hemley RJ (2019) Evidence for superconductivity above 260 K in Lanthanum superhydride at megabar pressures. Phys Rev Lett 122:027001. https://doi.org/10.1103/PhysRevLett.122.027001
Drozdov AP, Kong PP, Minkov VS, Besedin SP, Kuzovnikov MA, Mozaffari S, Balicas L, Balakirev FF, Graf DE, Prakapenka VB, Greenberg E, Knyazev DA, Tkacz M, Eremets MI (2019) Superconductivity at 250 K in lanthanum hydride under high pressures. Nature 569:528–531. https://doi.org/10.1038/s4158601912018
Pashitskii EA (1969) “Plasmon’’ mechanism of superconductivity in degenerated semiconductors and semimetals. Sov Phys JETP 28:1267–1271 (original publication in Russian: Zh. Eksp. Teor. Fiz. 55, 2387–2394 (1968))
Pines D (1956) Electron interaction in solids. Can J Phys 34:1379–1394
Eliashberg GM (1960) Interactions between electrons and lattice vibrations in a superconductor. Sov Phys JETP 11:696–702 (original publication in Russian: Zh. Eksp. Teor. Fiz. 38, 148–160 (1960))
Ruvalds J (1987) Plasmons and hightemperature superconductivity in alloys of copper oxides. Phys Rev B 35:8869–8872. https://doi.org/10.1103/PhysRevB.35.8869
Kresin VZ (1987) Critical temperatures of superconductors with low dimensionality. Phys Rev B 35:8716–8719. https://doi.org/10.1103/PhysRevB.35.8716
Pashitskii EA (1993) Plasmon mechanism of hightemperature superconductivity in cuprate metaloxide compounds. JETP 76:425–444 (original publication in Russian: Zh. Eksp. Teor. Fiz. 103, 867–909 (1993))
Abrikosov AA, Campuzano JC, Gofron K (1993) Experimentally observed extended saddle point singularity in the energy spectrum of \({\rm Y} {\rm Ba}_{2} Cu _{3}{\rm O} _{6.9}\) and \({\rm Y}{\rm Ba}_{2}{\rm Cu}_{4}{\rm O}_{8}\) and some of the consequences. Physica C 214:73–79. https://doi.org/10.1016/09214534(93)901094
Gofron K, Campuzano JC, Abrikosov AA, Lindroos M, Bansil A, Ding H, Koelling D, Dabrowski B (1994) Observation of an “extended’’ Van Hove singularity in \({\rm Y}{\rm Ba}_{2}{\rm Cu}_{4}{\rm O}_{8}\) by ultrahigh energy resolution angleresolved photoemission. Phys Rev Lett 73:3302–3305. https://doi.org/10.1103/PhysRevLett.73.3302
Pashitskii EA, Pentegov VI, Semenov AV, Abraham E (1998) Acoustic plasmons and high\(T_{c}\) superconductivity of cuprates with extended saddle point singularity in electron spectrum. Int J Mod Phys B 12:2946–2949. https://doi.org/10.1142/S0217979298001824
Semenov AV (1998) The simple generalized BCStype model for the acoustic plasmon induced \(d\)wave superconductivity in high\(T_{c}\) layered cuprate compounds. Int J Mod Phys B 12:3141–3145. https://doi.org/10.1142/S0217979298002234
Pashitskii EA, Pentegov VI, Semenov AV, Abraham E (1999) On the role of the Coulomb interaction in the mechanism of \(d\)wave cooper pairing in the high\(T_{c}\) superconductors. JETP Lett 69:753–761. https://doi.org/10.1134/1.568086 ([original publication in Russian: Pis’ma ZhETF 69, 703710 (1999)])
Pashitskii EA, Pentegov VI (2008) On the plasmon mechanism of high\(T_{c}\) superconductivity in layered crystals and twodimensional systems. Low Temp Phys 34:113–122. https://doi.org/10.1063/1.2834256 (original publication in Russian: Fiz. Nizk. Temp. 34, 148–160 (2008))
Pashitskii EA, Pentegov VI, Semenov AV (2022) Possibility for the anisotropic acoustic plasmons in LaH\(_{10}\) and their role in enhancement of the critical temperature of superconducting transition. Low Temp Phys 48:26–31. https://doi.org/10.1063/10.0008960
Lindhard J (1954) On the properties of a gas of charged particles. Kgl Danske Videnskab Selskab Math Fys Medd 28:8
Stern F (1967) Polarizability of a twodimensional electron gas. Phys Rev Lett 18:546–548. https://doi.org/10.1103/PhysRevLett.18.546
Jepson O, Anderson OK (1971) The electronic structure of h.c.p. Ytterbium. Solid State Commun 9:1763–1767. https://doi.org/10.1016/00381098(71)903139
Lehmann G, Taut M (1972) On the numerical calculation of the density of states and related properties. Phys Status Solidi B 54:469–477. https://doi.org/10.1002/pssb.2220540211
Pan VM, Pashitskii EA, Prokhorov VG (1974) On calculating electron–phonon interaction constant in strong coupling superconductors. Ukr J Phys 19:1298–1302 (publication in Russian with English Abstract)
Acknowledgements
This work was supported by the Grant of the National Academy of Science of Ukraine Grant No. B/193.
Funding
This work was supported by the grant of the National Academy of Science of Ukraine (Grant Number B/193).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors have no relevant financial or nonfinancial interests to disclose.
Ethical approval
Not applicable.
Consent to participate
All the authors give their consent to participate in the open access publication
Consent for publication
All the authors give their consent for publication
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Pashitskii, E.A., Pentegov, V.I. & Semenov, A.V. Collective acoustic electronic excitations in LaH_{10} as a factor in boosting of the critical temperature of superconducting transition. SN Appl. Sci. 4, 195 (2022). https://doi.org/10.1007/s4245202205077x
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s4245202205077x
Keywords
 Roomtemperature superconductivity
 Rareearth superhydrides
 Polarization operator
 Acoustic plasmons