I consider electrodynamics and the problem of knotted solitons in two-component superconductors. Possible existence of knotted solitons in multicomponent superconductors was predicted several years ago. However their basic properties and stability in these systems remains an outstandingly difficult question both for analytical and numerical treatment. Here I propose a new perturbative approach to treat self-consistently all the degrees of freedom in the problem. I show that there exists a length scale for a Hopfion texture where the electrodynamics of a two-component superconductor is dominated by a self-induced Faddeev term, which is a stark contrast to the Meissner electrodynamics of single-component systems. I also show that at certain short length scales knotted solitons in two-component Ginzburg-Landau model are not described by a Faddeev-Skyrme-type model and are unstable. However these solitons can be stable at some intermediate length scales. I argue that configurations with a high topological charge may be more stable in this system than low-topological-charge configurations. In the second part of the paper I discuss qualitatively different physics of the stability of knotted solitons in a more general Ginzburg-Landau model and point out the physically relevant terms which enhance or suppress stability of the knotted solitons. With this argument it is demonstrated that the generalized Ginburg-Landau model possesses stable knotted solitons.
Theory and experiment on the London moment is reviewed. A simple mathematical model is motivated and then used to study the responses of a spherical superconductor to an external field and to rotation. It reveals a connection between perfect diamagnetism (Meissner effect) and the London moment. In the model neither of these are exact but the deviation from B=0 internal field in the former and from $B=(2mc/e)Ω$ in the latter case is described by the same dimensionless parameter. Apart from its pedagogical values the model might throw some light on the controversy surrounding the correction to t…
Based on an analytic scheme and neglecting the back reaction effect several crucial properties of holographic $ s $- wave superconductors have been investigated in the presence of an external magnetic field in the background of a $ D $ dimensional Schwarzschild AdS space time. Inspired by low energy limit of heterotic string theory, in the present paper we replace the conventional Maxwell action by a Power Maxwell action. Immersing the holographic superconductors in an external static magnetic field the spatially dependent condensate solutions have been obtained analytically. Interestingly eno…
Electrodynamics of superconductors is primarily the electrodynamics of the Meissner state, a state characterized by zero magnetic induction of a superconducting fraction of conduction electrons. Simultaneously, the Meissner state is characterized by zero resistivity and zero entropy of these electrons. The latter means that the temperature of an ensemble of superconducting electrons is zero as well. Understanding properties of the Meissner state provides a key to understand and predict these and other equilibrium and non-equilibrium properties of superconductors, e.g., properties of the interm…
We discuss topological aspects of two-gap superconductors with and without Josephson coupling between gaps. We address nontrivial topological aspects of the dual superconductors and its connections to Meissner effect and flux quantization. The topological knotted string geometry is also discussed in terms of the Hopf invariant, curvature and torsion of the strings associated with U(1)$\times$U(1) gauge group.
In this paper we have studied the onset of holographic $s$-wave condensate in the $(4+1)$ dimensional planar Gauss-Bonnet-AdS black hole background with several non-linear corrections to the gauge field. In the probe limit, performing explicit analytic computations, with and without magnetic field, we found that these higher order corrections indeed affect various quantities characterising the holographic superconductors. Also, performing a comparative study of the two non-linear electrodynamics it has been shown that the exponential electrodynamics has stronger effects on the formation of the…
The Meissner effect and the Spin Meissner effect are the spontaneous generation of charge and spin current respectively near the surface of a metal making a transition to the superconducting state. The Meissner effect is well known but, I argue, not explained by the conventional theory, the Spin Meissner effect has yet to be detected. I propose that both effects take place in all superconductors, the first one in the presence of an applied magnetostatic field, the second one even in the absence of applied external fields. Both effects can be understood under the assumption that electrons expan…
From the outset of superconductivity research it was assumed that no electrostatic fields could exist inside superconductors, and this assumption was incorporated into conventional London electrodynamics. Yet the London brothers themselves initially (in 1935) had proposed an electrodynamic theory of superconductors that allowed for static electric fields in their interior, which they unfortunately discarded a year later. I argue that the Meissner effect in superconductors necessitates the existence of an electrostatic field in their interior, originating in the expulsion of negative charge fro…
We report here the frequency-dependent optical response of a nearly ferroelectric superconductor (NFE-SC), like Na$_{x}$WO$_3$, or n-SrTiO$_3$. From $ω=0$, up to a critical frequency $ ω_{c1}$, Meissner-like field extinction occurs as in a usual superconductor. In the "anomalous" region $ω_{c1}<ω<ω_{TO}$ (the TO frequency of the NFE) the field propagates as in a dielectric. For $ω>ω_{TO}$ Meissner damping recurrs, then at higher $ω$, dielectriclike propagation is found. New optical anomalies (peaks in transmission) are predicted for a film of NFE-SC below the soft mode frequency $ω_{TO}$. Thes…
The proximity coupled topological insulator / superconductor (TI/SC) bilayer system is a representative system to realize topological superconductivity. In order to better understand this unique state and design devices from the TI/SC bilayer, a comprehensive understanding of the microscopic properties of the bilayer is required. In this work, a microwave Meissner screening study, which exploits a high-precision microwave resonator technique, is conducted on the SmB6/YB6 thin film bilayers as an example TI/SC system. The study reveals spatially dependent electrodynamic screening response of th…
Traditionally, superconductors are categorized as type-I or type-II. Type-I superconductors support only Meissner and normal states, while type-II superconductors form magnetic vortices in sufficiently strong applied magnetic fields. Recently there has been much interest in superconducting systems with several species of condensates, in fields ranging from Condensed Matter to High Energy Physics. Here we show that the type-I/type-II classification is insufficient for such multicomponent superconductors. We obtain solutions representing thermodynamically stable vortices with properties falling …
We have directly imaged the anisotropic nonlinear Meissner effect in an unconventional superconductor through the nonlinear electrodynamic response of both (bulk) gap nodes and (surface) Andreev bound states. A superconducting thin film is patterned into a compact self-resonant spiral structure, excited near resonance in the radio-frequency range, and scanned with a focused laser beam perturbation. At low temperatures, direction-dependent nonlinearities in the reactive and resistive properties of the resonator create photoresponse that maps out the directions of nodes, or of bound states assoc…
The discovery of the Meissner effect was a turning point in the history of superconductivity. It demonstrated that superconductivity is an equilibrium state of matter, thus allowing to use thermodynamics for its study. This provided a justification for the two-fluid model of Gorter and Casimir, a seminal thermodynamic theory founded on a postulate of zero entropy of the superconducting (S) component of conduction electrons. It also demonstrated that, apart from zero resistivity, the S phase is also characterized by zero magnetic induction, used as a basic postulate in the theory of Londons und…
We derive general frequency dependencies of the surface impedance modulus for conductors without the dc dissipation, i. e. for superconductors or perfect conductors. The frequency-dependent surface impedance was applied for the solutions corresponding to the spatially dispersive eigenvalues of the permittivity operator for conductors. We demonstrate that appropriately taken into account effects of the spatial dispersion can give the general frequency dependence of the surface impedance for the obtained solutions including that for superconductor. It is shown that an incorporation of the spatia…
In recent work we formulated a new set of electrodynamic equations for superconductors as an alternative to the conventional London equations, compatible with the prediction of the theory of hole superconductivity that superconductors expel negative charge from the interior towards the surface. Charge expulsion results in a macroscopically inhomogeneous charge distribution and an electric field in the interior, and because of this a spin current is expected to exist. Furthermore, we have recently shown that a dynamical explanation of the Meissner effect in superconductors leads to the predicti…
We study the metastability of the superheated Meissner state in type II superconductors with k >> 1 beyond Ginzburg-Landau theory, which is applicable only in the vicinity of the critical temperature. Within Eilenberger's semiclassical approximation, we use the local electrodynamic response of the superconductor to derive a generalized thermodynamic potential valid at any temperature. The stability analysis of this functional yields the temperature dependence of the superheating field. Finally, we comment on the implications of our results for superconducting cavities in particle accelerators.
We review recent developments concerning non-equilibrium quantum dynamics and many-body physics with light, in superconducting circuits and Josephson analogues. We start with quantum impurity models summarizing the effect of dissipation and of driving the system. We mention theoretical and experimental efforts to characterize these non-equilibrium quantum systems. We show how Josephson junction systems can implement the equivalent of the Kondo effect with microwave photons. The Kondo effect is characterized by a renormalized light-frequency and a peak in the Rayleigh elastic transmission of a …
We study the electrodynamics of spin triplet superconductors including dipolar interactions, which give rise to an interplay between the collective spin dynamics of the condensate and orbital Meissner screening currents. Within this theory, we identify a class of spin waves that originate from the coupled dynamics of the spin-symmetry breaking triplet order parameter and the electromagnetic field. In particular, we study magnetostatic spin wave modes that are localized to the sample surface. We show that these surface modes can be excited and detected using experimental techniques such as micr…
