Quasiclassical theory for the superconducting proximity effect in Dirac materials

We derive the quasiclassical non-equilibrium Eilenberger and Usadel equations to first order in quantities small compared to the Fermi energy, valid for Dirac edge and surface electrons with spin-momentum locking, as relevant for topological insulators. We discuss in detail several of the key technical points and assumptions of the derivation, and provide a Riccati-parametrization of the equations. Solving first the equilibrium equations for S/N and S/F bilayers and Josephson junctions, we study the superconducting proximity effect in Dirac materials. Similarly to related works, we find that the effect of an exchange field depends strongly on the direction of the field. Only components normal to the transport direction lead to attenuation of the Cooper pair wavefunction inside the F. Fields parallel to the transport direction lead to phase-shifts in the dependence on the superconducting phase difference for both the charge current and density of states in an S/F/S-junction. Moreover, we compute the differential conductance in S/N and S/F bilayers with an applied voltage bias, and determine the dependence on the length of the N and F regions and the exchange field.Comment: 13 pages, 5 figures. Accepted for publication in Phys. Rev.

Particle Acceleration and Radiation associated with Magnetic Field Generation from Relativistic Collisionless Shocks

Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating through an ambient plasma with and without initial magnetic fields. We find only small differences in the results between no ambient and weak ambient magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates particles perpendicular and parallel to the jet propagation direction. The simulation results show that this instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields, which contribute to the electron's transverse deflection behind the jet head. The ``jitter'' radiation from deflected electrons has different properties than synchrotron radiation which is calculated in a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.Comment: 4 pages, 1 figure, submitted to Proceedings of 2003 Gamma Ray Burst Conferenc

Particle Acceleration in Relativistic Jets due to Weibel Instability

Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., the Buneman instability, two-streaming instability, and the Weibel instability) created in the shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating through an ambient plasma with and without initial magnetic fields. We find only small differences in the results between no ambient and weak ambient magnetic fields. Simulations show that the Weibel instability created in the collisionless shock front accelerates particles perpendicular and parallel to the jet propagation direction. While some Fermi acceleration may occur at the jet front, the majority of electron acceleration takes place behind the jet front and cannot be characterized as Fermi acceleration. The simulation results show that this instability is responsible for generating and amplifying highly nonuniform, small-scale magnetic fields, which contribute to the electron's transverse deflection behind the jet head. The ``jitter'' radiation (Medvedev 2000) from deflected electrons has different properties than synchrotron radiation which is calculated in a uniform magnetic field. This jitter radiation may be important to understanding the complex time evolution and/or spectral structure in gamma-ray bursts, relativistic jets, and supernova remnants.Comment: ApJ, in press, Sept. 20, 2003 (figures with better resolution: http://gammaray.nsstc.nasa.gov/~nishikawa/apjweib.pdf

Particle Acceleration and Magnetic Field Generation in Electron-Positron Relativistic Shocks

Shock acceleration is an ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., Buneman, Weibel and other two-stream instabilities) created in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic electron-positron jet front propagating into an ambient electron-positron plasma with and without initial magnetic fields. We find small differences in the results for no ambient and modest ambient magnetic fields. New simulations show that the Weibel instability created in the collisionless shock front accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction. Furthermore, the non-linear fluctuation amplitudes of densities, currents, electric, and magnetic fields in the electron-positron shock are larger than those found in the electron-ion shock studied in a previous paper at the comparable simulation time. This comes from the fact that both electrons and positrons contribute to generation of the Weibel instability. Additionally, we have performed simulations with different electron skin depths. We find that growth times scale inversely with the plasma frequency, and the sizes of structures created by the Weibel instability scale proportional to the electron skin depth. This is the expected result and indicates that the simulations have sufficient grid resolution. The simulation results show that the Weibel instability is responsible for generating and amplifying nonuniform, small-scale magnetic fields which contribute to the electron's (positron's) transverse deflection behind the jet head.Comment: 18 pages, 8 figures, revised and accepted for ApJ, A full resolution of the paper can be found at http://gammaray.nsstc.nasa.gov/~nishikawa/apjep1.pd

Particle acceleration, magnetic field generation, and emission in relativistic pair jets

Shock acceleration is a ubiquitous phenomenon in astrophysical plasmas. Plasma waves and their associated instabilities (e.g., Buneman, Weibel and other two-stream instabilities) created in collisionless shocks are responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic jet front propagating into an ambient plasma. We find that the growth times of Weibel instability are proportional to the Lorentz factors of jets. Simulations show that the Weibel instability created in the collisionless shock front accelerates jet and ambient particles both perpendicular and parallel to the jet propagation direction.Comment: 4 pages, 2 figures, submitted to Il nuovo cimento (4th Workshop Gamma-Ray Bursts in the Afterglow Era, Rome, 18-22 October 2004

Particle acceleration in electron-ion jets

Weibel instability created in collisionless shocks is responsible for particle (electron, positron, and ion) acceleration. Using a 3-D relativistic electromagnetic particle (REMP) code, we have investigated particle acceleration associated with a relativistic electron-ion jet fronts propagating into an ambient plasma without initial magnetic fields with a longer simulation system in order to investigate nonlinear stage of the Weibel instability and its acceleration mechanism. The current channels generated by the Weibel instability induce the radial electric fields. The z component of the Poynting vector (E x B) become positive in the large region along the jet propagation direction. This leads to the acceleration of jet electrons along the jet. In particular the E x B drift with the large scale current channel generated by the ion Weibel instability accelerate electrons effectively in both parallel and perpendicular directions.Comment: 2 pages, 1 figure, Proceedings for Astrophysical Sources of High Energy Particles and Radiation, AIP proceeding Series, eds . T. Bulik, G. Madejski and B. Ruda

Cavity-mediated superconductor\unicode{x2013}ferromagnetic insulator coupling

A recent proof of concept showed that cavity photons can mediate superconducting (SC) signatures to a ferromagnetic insulator (FI) over a macroscopic distance [Phys. Rev. B, 102, 180506(R) (2020)]. In contrast with conventional proximity systems, this facilitates long-distance FI\unicode{x2013}SC coupling, local subjection to different drives and temperatures, and studies of their mutual interactions without proximal disruption of their orders. Here we derive a microscopic theory for these interactions, with an emphasis on the leading effect on the FI, namely, an induced anisotropy field. In an arbitrary practical example, we find an anisotropy field of 14 \unicode{x2013} 16 $\mu$T, which is expected to yield an experimentally appreciable tilt of the FI spins for low-coercivity FIs such as Bi-YIG. We discuss the implications and potential applications of such a system in the context of superconducting spintronics.Comment: 17 pages, 8 figure