arXiv subjects

B. Ya. Shapiro

Publications and source records attributed to B. Ya. Shapiro.

At least 19 recordsLinked to original sources

arXiv2025

Maximal critical temperature dependence on number of layers due to phonon d-wave pairing in hole doped cuprates

Recently an apical oxygen atoms vibrations exchange mechanism of d-wave pairing in cuprates was proposed. The phonon mode in an insulating layer generates attraction of holes in metallic cuper oxygen planes. The pairing has a maximum at the crystallographic gamma point leading to d-wave channel. The idea is generalized here to include the in-plane breathers and half - breather modes in a multi-layer cuprate generating the pairing in an adjacent cuper oxygen layer of the same multi-layer. It is demonstrated that the phonon exchange and the spin fluctuation pairing constructively enhance each other since the paramagnon pairing peaks at crystallographic M point. The phonon contribution explains the maximal critical temperature dependence on the number of layers N. It rises equidistantly by 15K from N=1 to N=3 and then saturates. The strength of the onsite Coulomb on site repulsion at optimal doping is to obtain the observed values of maximal critical temperature in the intermediate range of the effective on-site repulsion U=(1.5-2) eV, smaller than commonly used in purely in-plane (spin fluctuation) theory of high temperature superconductivity.

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arXiv2023

Two step I to II type transitions in layered Weyl semi-metals and their impact on superconductivity

Novel "quasi two dimensional" typically layered (semi) metals offer a unique opportunity to control the density and even the topology of the electronic matter. Along with doping and gate voltage, a robust tuning is achieved by application of the hydrostatic pressure. In Weyl semi - metals the tilt of the dispersion relation cones, k , increases with pressure, so that one is able to reach type II k > 1 starting from the more conventional type I Weyl semi - metals k < 1. The microscopic theory of such a transition is constructed. It is found that upon increasing pressure the I to II transition occurs in two continuous steps. In the first step the cones of opposite chirality coalesce so that the chiral symmetry is restored, while the second transition to the Fermi surface extending throughout the Brillouin zone occurs at higher pressures. Flattening of the band leads to profound changes in Coulomb screening. Superconductivity observed recently in wide range of pressure and chemical composition in Weyl semi-metals of both types. The phonon theory of pairing including the Coulomb repulsion for a layered material is constructed and applied to recent extensive experiments on HfTe5.

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arXiv2023

Superconductivity in type II layered Weyl semi-metals

Novel quasi two dimensional typically layered semimetals offer a unique opportunity to control the density and even the topology of the electronic matter. In intercalated MoTe2 type II Weyl semimetal the tilt of the dispersion relation cones is so large that topologically of the Fermi surface is distinct from a more conventional type I. Superconductivity observed recently in this compound [Zhang et al, 2D Materials 9, 045027 (2022)] demonstrated two puzzling phenomena: the gate voltage has no impact on critical temperature, Tc, in wide range of density, while it is very sensitive to the interlayer distance. The phonon theory of pairing in a layered Weyl material including the effects of Coulomb repulsion is constructed and explains the above two features in MoTe2.The first feature turns out to be a general one for any type II topological material, while the second reflects properties of the intercalated materials affecting the Coulomb screening.

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arXiv2021

Origin of the maximal critical temperature disparities in one-layer cuprate superconductors

Recently a phonon exchange d - wave pairing mechanism in cuprates was proposed. The phonons are the lateral apical oxygen atoms vibrations. They generate the attractive pairing potential peaked at X point of the Brillouin zone, V (k) = exp [-2kda], where da is distance from the CuO planes. The model explains a rather paradoxical well known negative correlation of the optimal doping critical temperature Tcmax with da and increase of Tcmax with pressure. However the large disparities in Tcmax, especially in one - layer cuprate superconductors, from 39K for La2-xSrxCuO4, to 95K for HgBa2CuO4+x, cannot be attributed by differencies in da. Other important material parameters include the hopping amplitudes t; t0 and the on site Coulomb repulsion U. It is shown (within weak coupling)that Tcmax is highest for materials close to the topological (Lifshitz) transition from an open to a close Fermi surface. The transition occurss for t0 = -0.19t and rather small values of effective value of U = 2t at optimal doping. Analytic expressions for Tcmax are derived both near criticality and away from it.

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arXiv2021

Aslamazov Larkin Conductivity in Weyl Semimetals

The Aslamazov-Larkin conductivity (ALC) in the Weyl semi-metals is calculated both for Type-I and Type II for different dimensionality and magnetic fields. The ALC strongly depends on the tilt parameter of the dispersion relation cone. While the 3D and 2D the Aslamazov -Larkin conductivity slightly depends on tilt parameter in Type-I phase and increases in the Type-II phase the 1D ALC decreases in Type-I phase up to zero close to border between Type-I and Type-II phases. Results are discussed in light of the resent experiments on the layered HfTe5 Weyl semi-metals. It is concluded the one dimensional AL conductivity well explained the experimental data.

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arXiv2021

Apical oxygen vibrations dominant role in d-wave cuprate superconductivity and its interplay with spin fluctuations

Microscopic theory of a high Tc cuprate BiSCO based on main pairing channel of electrons in CuO planes due to 40meV lateral vibrations of the apical oxygen atoms in adjacent the SrO ionic insulator layer is proposed. The separation between the vibrating charged atoms and the 2D electron gas creates the forward scattering peak leading in turn to the d-wave pairing within Eliashberg formalism. The phonon mode naturally explain the kink in dispersion relation observed by ARPES and the and effect of the O16 to O18 isotope substitution in the normal state. To describe the pseudogap physics a single band fourfold symmetric Hubbard model, with the hopping parameters t' = - 0.17t and the on site repulsion U = 6t was used. It described the Mott insulator at low doping, while at higher dopping the pseudogap physics (still strongly correlated) can be be approximated by the symmetrized mean field model and with renormalized U incorporating screening. The location of the transition line between the locally antiferromagnetic pseudogap and the paramagnetic overdoped phases and susceptibility (describing spin uctuations coupling to 2DEG) are also obtained within this approximation. The superconducting d-wave gap mainly due to the phonon channel but is assisted by the spin fluctuations (15-20%). The dependence of the gap and Tc on doping and effect of the isotope substitution are obtained and is consistent with experiments.

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arXiv2021

The phonon mechanism explanation of the superconductivity dichotomy between FeSe and FeS monolayers on STO and other substrates

It was observed recently (K. Shigekawa et al, PNAS 116, 2470 (2019)) that while monolayer iron chalcigenide FeSe on SrTiO3 (STO) substrate has a very high critical temperature, its chemical and structural "twin" material FeS=STO has a very low Tc if any. To explain this the substrate interfacial phonon model of superconductivity in iron chalcogenides is further developed. The main glue is the oxygen ion (60mev) vibrations longitudinal optical (LO) mode. The mode propagates mainly in the TiO2 layer adjacent to the monolayer (and genrally present also in similar highly polarized ionic crystals like BaTiO3; rutile, anatase). It has stronger electron - phonon coupling to electron gas in FeSe than a well known (100mev) harder LO mode. It is shown that while (taking into account screened Coulomb repulsion efects) the critical temperature of FeSe on STO and TiO2 is above 65K, it becomes less than 5K for FeS due to two factors suppressing the electron - phonon coupling. The efective mass in the later is twice smaller and in addition the distance between the electron gas in FeSe to the vibrating substrate oxygen atoms is 15% smaller than in FeS reducinng the central peak in electron-phonon interaction. The theory is extended to other ionic insulating substrates.

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arXiv2019

Soft phonons in the interface layer of the STO substrate can explain high temperature superconductivity in one unit cell FeSe

Using a microscopic model of lattice vibrations in the STO(001) substrate, an additional 50 mev longitudinal optical (LO) interface mode is identified. The soft mode propagating mainly in the first TiO2 layer ("O chains") has stronger electron - phonon coupling to electron gas in FeSe than a well known 100 mev hard mode. The coupling constant, critical temperature, replica band are calculated. Although there exists a forward in the electron - phonon scattering peak, it is clearly not as sharp as assumed in recent theories (delta function - like). The satellite is broad and its peak appears at frequency much higher than the phonon frequency consistent with observations. Possible relation of the transverse counterpart of the surface LO soft mode with known phonons is discussed.

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arXiv2019

Intermediate State in Type I superconducting sphere: pinning and size effect

Simulations, based on the time dependent Ginzburg-Landau equations, show that the magnetization and spatial structure of the intermediate state strongly affected both by the radius of the sphere and by pinning center concentration. The intermediate states undergoes transformation from one-domain state in small clean sphere to multi-domain structure in big spheres. In spheres where part of the superconducting material replaced by the 0.5% randomly distributed normal phase (dirty case) the intermediate state demonstrates a well pronounced turbulence behavior.

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arXiv2018

Upper magnetic field in superconducting Dirac semi-metal

Temperature dependence of the upper critical field $H_{c2}$ of the Dirac semi - metal (DSM) with phonon mediated pairing is considered within semi - classical approximation. The low temperature dependence deviates from conventional BCS superconductor with parabolic dispersion relation\cite{WHH} even for large adiabaticity parameter, $γ=μ/\left( \hbar Ω\right) $., where $μ$ is the chemical potential and $Ω$ - Debye frequency. In particular the "reduced field", ratio of zero temperature $% H_{c2}$ to derivative at critical temperature, $h^{\ast }=H_{c2}\left( 0\right) /\left( -T\frac{dH_{c2}}{dT}\right) |_{T_{c}}$, depends on $γ$ and can be extended beyond the adiabatic limit. The reduced magnetic field ratio is universal (independent of the chemical potential, interaction strength etc.) and smaller than the Werthamer ratio for clean superconductors: $h^{\ast }=0.55$ for DSM, $h^{\ast }\left( 0\right) =0.69$ for parabolic band. The results are in good agreement compared with recent experiments on $TaP$.

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arXiv2018

Type I superconductivity in Dirac materials

Superconductivity of the second kind was observed in many 3D Weyl and Dirac semi-metals. However in PdT e2, superconductivity is clearly of the first kind. This is very rare in Dirac semi - metals, but is expected in clean conventional metallic superconductors with 3D parabolic dispersion relation. The conduction bands in this material exhibit the linear (Dirac) dispersion only along two directions, while in the third direction the dispersion is parabolic. Therefore the "hybrid" Dirac-parabolic material is intermediate between the two extremes. A microscopic pairing theory is derived for arbitrary tilt parameter of the 2D cone and used to determine anisotropic coherence lengths, the penetration depths and applied to recent extensive experiments. Magnetic properties of these superconductors are then studied on the basis of microscopically derived Ginzburg - Landau effective theory for the order parameter.

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arXiv2018

Magnetic properties of Type I and II Weyl Superconductors

Superconductivity was observed in certain range of pressure and chemical composition in Weyl semi-metals of both the type I and type II (when the Dirac cone tilt parameter $κ>1$). Magnetic properties of these superconductors are studied on the basis of microscopic phonon mediated pairing model. The Ginzburg - Landau effective theory for the order parameter is derived using Gorkov approach and used to determine anisotropic coherence length, the penetration depth determining the Abrikosov parameter for a layered material and applied to recent extensive experiments on $% MoTe_{2}$. It is found that superconductivity is of second kind near the topological transition at $κ=1$, but becomes first kind away from it. For the superconductors of the second kind the dependence of critical fields $H_{c2}$ and $H_{c1}$ on the tilt parameter $κ$ (governed by pressure) is compared with the experiments. Strength of thermal fluctuations is estimated and its is found that they are strong enough to cause Abrikosov vortex lattice melting near $H_{c2}$. The melting line is calculated and is consistent with experiments provided the fluctuations are three dimensional in the type I phase (large pressure) and two dimensional in the type II phase (small pressure).

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arXiv2017

Strong magnetic field induces superconductivity in Weyl semi - metal

Microscopic theory of the normal-to-superconductor coexistence line of a 2D two-band Weyl superconductor subjected to magnetic field is constructed. It is shown that a Weyl semi-metal that is nonsuperconducting or having a small critical temperature $T_{c}$ at zero field, might become a superconductor at higher temperature when the magnetic field is tuned to a series of quantized values $H_{n}$. The pairing occurs on Landau levels. It is argued that the phenomenon is much easier detectable in Weyl semi - metals than in parabolic band metals since the quantum limit already has been approaches in several Weyl materials.. An experimental signature of the superconductivity on Landau levels is the reduction of magnetoresistivity. This has already been observed in $Cd_{3}As_{2}$ and several other compounds. The novel kind of quantum oscillations of magnetoresistance detected in $ZrTe_{5}$ is discussed along these lines.

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arXiv2016

Superconductivity in 2D electron gas induced by high energy optical phonon mode and large polarization of the STO substrate

Theory of superconductivity generated in one atomic layer thick two dimensional electron gas by a single flat band of high energy longitudinal optical phonons is considered. The polar dielectric $SrTiO_{3}$ (STO) exhibits such an energetic phonon mode and the 2DEG is created both when one unit cell $FeSe$ layer is grown on its $\left( 100\right) $ surface and on the interface with another dielectric like $LaAlO_{3}$ (LAO). We obtain a quantitative description of both systems solving the gap equation for $T_{c}$ without making use of approximations like the Kirzhnits Ansatz for arbitrary chemical potential $μ$, electron-phonon coupling $λ$ and the phonon frequency $Ω$, and direct (RPA) electron-electron repulsion strength $α$. The high temperature superconductivity in 1UC$FeSe$/STO is possible due to a combination of three factors: high LO phonon frequency, large electron-phonon coupling $λ\sim 0.5$ and huge dielectric constant of the substrate suppression the Coulomb repulsion. It is shown that very low density electron gas in the interfaces is still capable of generating superconductivity of the order of $0.1$ K in LAO/STO. Superconductivity persists even on the band edge $μ=0$.

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arXiv2015

Collective modes, AC response and magnetic properties of the 3D Dirac semi-metal in the triplet superconducting state

It was recently shown that conventional phonon-electron interactions may induce a triplet pairing state in time-reversal invariant 3D Dirac semi - metals. Starting from the microscopic model of the isotropic Dirac semi-metal, the Ginzburg-Landau equations for the vector order parameter is derived using the Gor'kov technique. The collective modes including gapless Goldstone modes, and gapped Higgs modes of various polarizations are identified. They are somewhat analogous to the modes in the B phase of He3, although in the present case quantitatively there is a pronouneced difference between longitudinal and transverse components. The difference is caused by the vector nature of the order parameter leading to two different coherence lengths or penetration depths. The system is predicted to be highly dissipative due to the Goldstone modes. The time dependent Ginzburg - Landau model in the presence of external fields is used to investigate some optical and magnetic properties of such superconductors. The AC conductivity of a clean sample depends on the orientation of the order parameter. It is demonstrated that the difference between the penetration depths results in rotation of the polarization vector of microwave passing a slab made of this material. The upper critical magnetic field H_{c2} was found. It turns out that at fields close to H_{c2} the order parameter orients itself perpendicular to the field direction. In certain range of parameters the triplet superconducting phase persists at arbitrarily high magnetic field like in some p wave superconductors.

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arXiv2015

Chiral universality class of the normal-superconducting and the exciton condensation transition on the surface of topological insulator

New two dimensional systems like surface of topological insulator and graphene offer a possibility to experimentally investigate situations considered "exotic" just a decade ago. One of those is the quantum phase transition of the "chiral" type in electronic systems with relativistic spectrum. Phonon mediated ("conventional") pairing in the Dirac semimetal appearing on the surface of topological insulator leads to transition into a chiral superconducting state, while exciton condensation in these gapless systems has been envisioned long time ago in the physics of the narrow band semiconductors. Starting from the microscopic Dirac Hamiltonian with local attraction or repulsion, the BCS type gaussian approximation is developed in the framework of functional integrals. It is shown that due to an "ultra-relativistic" dispersion relation there is a quantum critical point governing the zero temperature transition to a superconducting or the exciton condensed state. The quantum transitions that have critical exponents very different from the conventional ones. They belong to the chiral universality class. We discuss the application of these results to recent experiments in which surface superconductivity was found in topological insulators and estimate feasibility of the phonon pairing.

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arXiv2014

Magnetic impurities make superconductivity in 3D Dirac semi-metal triplet

Conventional electron-phonon coupling induces either odd (triplet) or even (singlet) pairing states in a time reversal and inversion invariant Dirac semi - metal. In certain range of the chemical potential $μ$ and parameters characterizing the pairing attraction (effective electron-electron coupling constant $λ$ and the Debye energy $T_{D}$) the energy of the singlet although always lower, prevails by a very slim margin over the triplet. This means that interactions that are small but discriminate between the spin singlet and the spin triplet determine the nature of the superconducting order there. It shown that in materials close enough to the Dirac point ($μ\lesssim T_{D}$) magnetic impurities stabilize the odd pairing superconducting state.

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arXiv2014

Triplet superconductivity in 3D Dirac semimetal due to exchange interaction

Conventional phonon-electron interaction induces either triplet or one of two (degenerate) singlet pairing states in time reversal and inversion invariant 3D Dirac semi - metal. Investigation of the order parameters and energies of these states at zero temperature in wide range of values of chemical potential $μ$, the effective electron-electron coupling constant $λ$ and Debye energy $T_{D}$ demonstrates that when the exchange interaction is neglected the singlet always prevails, however in significant portions of the $\left( μ,λ,T_{D}\right) $ parameter space the energy difference is very small. This means that interactions that are small but discriminate between the spin singlet and the spin triplet are important in order to determine the nature of the superconducting order there. The best candidate for such an interaction in materials under consideration is the exchange (the Stoner term) characterized by constant $λ_{ex}$. We show that at values of $λ_{ex}$ much smaller then ones creating Stoner instability to ferromagnetism $λ_{ex}\sim 1$ the triplet pairing becomes energetically favored over the singlet ones for $μ<T_{D}$% . The 3D quantum critical point at $μ=0$ is considered in detail.

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