arXiv subjects

I. Shapiro

Publications and source records attributed to I. Shapiro.

At least 19 recordsLinked to original sources

arXiv2019

Increasing the Discovery Space in Astrophysics - A Collation of Six Submitted White Papers

We write in response to the call from the 2020 Decadal Survey to submit white papers illustrating the most pressing scientific questions in astrophysics for the coming decade. We propose exploration as the central question for the Decadal Committee's discussions.The history of astronomy shows that paradigm changing discoveries are not driven by well formulated scientific questions, based on the knowledge of the time. They were instead the result of the increase in discovery space fostered by new telescopes and instruments. An additional tool for increasing the discovery space is provided by the analysis and mining of the increasingly larger amount of archival data available to astronomers. Revolutionary observing facilities, and the state of the art astronomy archives needed to support these facilities, will open up the universe to new discovery. Here we focus on exploration for compact objects and multi messenger science. This white paper includes science examples of the power of the discovery approach, encompassing all the areas of astrophysics covered by the 2020 Decadal Survey.

astro-ph.GA↗

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.

cond-mat.supr-con↗

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.

cond-mat.supr-con↗

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).

cond-mat.supr-con↗

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.

cond-mat.supr-con↗

arXiv2017

Effect of the type I to type II Weyl semimetal topological transition on superconductivity

The influence of recently discovered topological transition between type I and type II Weyl semi-metals on superconductivity is considered. A set of Gorkov equations for weak superconductivity in Weyl semi-metal under topological phase transition is derived and solved. The critical temperature and superconducting gap both have spike in the point the transition point as function of the tilt parameter of the Dirac cone determined in turn by the material parameters like pressure. The spectrum of superconducting excitations is different in two phases: the sharp cone pinnacle is characteristic for a type I, while two parallel almost flat bands, are formed in type II. Spectral density is calculated on both sides of transition demonstrate different weight of the bands. The superconductivity thus can be used as a clear indicator for the topological transformation. Results are discussed in the light of recent experiments.

cond-mat.supr-con↗

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 $μ=0$.

cond-mat.supr-con↗

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.

cond-mat.supr-con↗

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.

cond-mat.supr-con↗

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.

cond-mat.supr-con↗

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.

cond-mat.supr-con↗

arXiv2014

Quantum critical point in the superconducting transition on the surface of topological insulator

Pairing in the Weyl semi - metal appearing on the surface of topological insulator is considered. 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 state. Starting from the microscopic Hamiltonian with local attraction, we calculated using the Gor'kov equations, the phase diagram of the superconducting transition at arbitrary chemical potential, its magnetic properties and critical exponents close to the quantum critical point. The Ginzburg - Landau effective theory is derived for small chemical potential allowing to consider effects of spatial dependence of order parameters in magnetic field. The GL equations are very different from the conventional ones reflecting the chiral universality class of the quantum phase transition. The order parameter distribution of a single vortex is found to be different as well. The magnetization near the upper critical field is found to be quadratic, not linear as usual. We discuss the application of these results to recent experiments in which surface superconductivity was found that some 3D topological insulators and estimate feasibility of the phonon pairing.

cond-mat.supr-con↗

arXiv2012

Majorana states in a p-wave superconducting ring

The spectrum of excitations of the chiral superconducting ring with internal and external radii, comparable with coherence length, trapping a unit flux is calculated. We find within the Bogoliubov-deGennes approach that there exists a pair of precisely zero energy states. They are not protected by topology, but are stable under certain deformations of the system. We discuss the ways to tune the system so that it grows into such a "Majorana disk". This condition has a character of a resonance phenomenon.

cond-mat.supr-con↗

arXiv2012

$p$-adic superspaces and Frobenius

The notion of a $p$-adic superspace is introduced and used to give a transparent construction of the Frobenius map on $p$-adic cohomology of a smooth projective variety over $\zp$ (the ring of $p$-adic integers), as well as an alternative construction of the crystalline cohomology of a smooth projective variety over $\fp$ (finite field with $p$ elements).

math.NT↗

arXiv2012

Isolating the vortex core Majorana state in p-wave superconductors

The spectrum of core excitations of the Abrikosov vortex pinned by a nanohole of the size of the coherence length is considered. While the neutral zero energy Majorana core state remains intact due to its topological origin, the energy of charged excitations is enhanced significantly compared to that in the unpinned vortex. As a consequence of the pinning the minigap separating the Majorana state from the charged levels increases to a signicant fraction of superconducting gap. Suppression of the thermodynamic and kinetic effects of the charged excitations allows to isolate the Majorana state so it can be used for quantum computation. It is proposed that thermal conductivity along the vortex cores is a sensitive method to demonstrate the minigap. We calculate, using Butticker-Landauer-Kopnin formula, the thermal conductance beyond linear response as function of the hole radius.

cond-mat.supr-con↗

arXiv2011

Thermomagnetic instability of standing flux-antiflux front in layered type-II superconductors

Stability of standing flux-antiflux front in anisotropic layered superconductors is considered. We describe two assisting mechanisms destabilizing the standing vortex-antivortex front. There are anisotropy of the layered superconductors and the heat, released by the vortex dynamics. We present the conditions of the front stability for various anisotropy and heating parameters. We predict that even small vortex-antivortex heating can result in front instability. The characteristic size of the unstable pattern is estimated.

cond-mat.supr-con↗

arXiv2009

Field cooling memory effect in Bi2212 and Bi2223 single crystals

A memory effect in the Josephson vortex system created by magnetic field in the highly anisotropic superconductors Bi2212 and Bi2223 is demonstrated using microwave power absorption. This surprising effect appears despite a very low viscosity of Josephson vortices compared to Abrikosov vortices. The superconductor is field cooled in DC magnetic field H_{m} oriented parallel to the CuO planes through the critical temperature T_{c} down to 4K, with subsequent reduction of the field to zero and again above H_{m}. Large microwave power absorption signal is observed at a magnetic field just above the cooling field clearly indicating a memory effect. The dependence of the signal on deviation of magnetic field from H_{m} is the same for a wide range of H_{m} from 0.15T to 1.7T.

cond-mat.supr-con↗

arXiv2008

BRST Reduction of the chiral Hecke Algebra

We explore the relationship between de Rham and Lie algebra cohomologies in the finite dimensional and affine settings. As an application, we describe the BRST reduction of the chiral Hecke algebra as a vertex super algebra.

math.RT↗