Session V54: Superconductivity: Magnetic Field Effects Including Vortex Related Phenomena (Theory)

Vortex Dynamics in Ferromagnetic Superconductors: Excitations of Domain Walls and Enhanced Viscosity

As more and more superconductors with coexisting magnetic order are found in the last decades, understanding of the vortex dynamics in these superconductors becomes a relevant issue [1, 2]. We investigate vortex dynamics in ferromagnetic superconductors both numerically and analytically. Driven by the Lorentz force, the vortices perturb the magnetic moments and excite magnons. At some velocities, the motion of vortices is resonant with magnetic moments, and the amplitude of magnon excitation is enhanced. When the relaxation rate of magnon is smaller than the pumping rate, the magnon becomes unstable and domain walls are created. The domain walls interact strongly with vortices motion and greatly enhance the viscosity of vortices. Depending on the density of vortices, the vortex configuration may be modulated by the magnetic system. The underlying dynamics of the vortices and magnetic moments can be probed by transport measurement. \\[4pt] [1] L. N. Bulaevskii, A. I. Buzdin, M. L. Kulic, and S. V. Panjukov, Adv. Phys. 34, 175 (1985).\\[0pt] [2] A. Shekhter, L. N. Bulaevskii, and C. D. Batista, Phys. Rev. Lett. 106, 037001 (2011).   

The effect of impurities on the Superheating field of Type II superconductors

We calculate the superheating field $H_s(T)$, the maximum field at which the Meissner state exists, for a type-II, single band s-wave superconductor with nonmagnetic and magnetic impurities. $H_s(T)$ was calculated for the entire temperature region $0c_g$, the quasiparticle gap $E_g(c)$ appears at $H=H_s$ so that $E_g \sim 0.410\Delta$ in the dirty limit. This feature can be important for the nonlinear surface resistance at strong rf fields $H\sim H_s$.   

Gap structure probed by field-angle resolved thermal oscillations in CeCoIn5 superconductor

We calculate the angle-resolved oscillations of the specific heat and thermal conductivity in a rotating in-plane magnetic field in the multiband superconductor CeCoIn$_5$ using realistic tight-binding Fermi surfaces. We find that an electron pocket at the $M$ point and a hole pocket at the $\Gamma$ point of the Brillouin zone yield sufficiently large Fermi surface anisotropies to produce fourfold oscillations not only for $d$-wave pairing, but also for $s$-wave pairing in the regime where our approximations are valid for both nodal and isotropic gap, namely near the upper critical field $H_{c2}$ and down to fields of order $H_{c2}/2$. More importantly, in this region we find a sign reversal in the oscillations as a function of temperature and fixed field for all gap symmetries investigated. We compare our results with available data on CeCoIn$_5$ and CeIrIn$_5$ and discuss how Fermi surface anisotropies affect the identification of gap structures and symmetries.   

Pnictide Half-Dirac Nodal Quasiparticle Scaling Properties in Vortex State

We investigate the scaling properties of quasiparticles of Pnictide with ``half-Dirac'' node under magnetic field in vortex state. By computing the density of states, we aim to find in vortex state the form of non-Simon-Lee scaling predicted for such system by several recent works in non-vortex state. We find by exact diagonalization of the BdG Hamiltonian and finite size scaling a $N(E)\sim \sqrt{E}$ power law in the case without magnetic field which agrees with analytical prediction. We consider the vortex state by first studying the hypothetical situation of uniform magnetic field without vortices and then we properly treat the magnetic field-induced vortex lattice by expressing the BdG Hamiltonian in terms of superfluid velocity and Berry's gauge field. The two calculations are shown to agree with each other. We then analyze quantitatively, the effects of anisotropic dispersion to the quasiparticles scaling properties in vortices. A very crucial prediction is also made on an upper bound to the value of ``anomalous dimension'' $\delta$ of density of states scaling with magnetic field, a quantity that can be measured experimentally.   

Vortex-assisted photon counts and their magnetic field dependence in superconducting nano-wire single-photon detectors

We argue that photon counts in a superconducting nano-wire single-photon detector (SNSPD) are caused by the transition from a current-biased metastable superconducting state into the normal state. Such a transition is triggered by photons with the frequency $\omega$ above the critical frequency $\omega_c$ or by photons with the frequency $\omega<\omega_c$ and subsequent vortex crossing from one edge of the superconducting strip to the other. The vortex is pushed across the strip due to the Lorentz force in the presence of the bias current $I$. We calculate the efficiency of photon counts as a function of $\omega$, $I$, bath temperature, and the strip geometry. We derive the dependence of the rate of vortex-assisted photon counts on the bias current at given $\omega$ and strip geometry. The resulting photon count rate has a plateau at high currents, close to the critical current, and drops as a power-law with high exponent at lower currents. While a magnetic field applied perpendicular to the superconducting strip does not affect the formation of hot spots by photons, it increases the rate of vortex crossings (with and without photons). We show that by applying a magnetic field one may identify the origin of dark and photon-assisted counts.   

Type-1.5 superconductivity: effects of interband interactions and Semi-Meissner State

A conventional superconductor is described by a single complex order parameter field which has two fundamental length scales, the magnetic field penetration depth $\lambda$ and the coherence length $\xi$. Their ratio $\kappa$ determines the response of a superconductor to an external field, sorting them into two categories as follows; type-I when $\kappa <1/\sqrt{2}$ and type-II when $\kappa >1/\sqrt{2}$. Multicomponent systems can possess three or more fundamental length scales and allow a separate ``type-1.5'' superconducting state when $\xi_1<\sqrt{2}\lambda<\xi_2$. In that state, as a consequence of the extra fundamental length scale vortices attract one another at long range but repel at shorter ranges. As a consequence the system should form an additional Semi-Meissner state. In that state vortices form clusters in low magnetic fields. In the vortex clusters the component with larger coherence length is depleted and consequently its current is mostly concentrated on the boundaries of the vortex cluster, thus resembling the screening currents in type-I superconductors. We discuss how the vortex clusters and type-1.5 regimes are affected by various interband couplings in multiband superconductors.   

Length scales, collective modes, and type-1.5 regimes in three-band superconductors

The recent discovery of iron pnictide superconductors has resulted in a rapidly growing interest in multiband models with more than two bands. We derive normal modes and characteristic length scales in the conventional $U(1)$ three-band Ginzburg-Landau model as well as in its time-reversal symmetry-broken counterpart with $U(1)\times Z_2$ symmetry. We show that, in the latter case, the collective modes are associated with the mixed phase-density modes and thus are different from the Leggetts modes in two band superconductors. Next we show that gradients of densities and phase differences can be inextricably intertwined in vortex excitations in three-band models. This can lead to very long-range attractive intervortex interactions and the appearance of type-1.5 regimes even when the intercomponent Josephson coupling is large. We next show that field-induced vortices can lead to a change of broken symmetry from $U(1)$ to $U(1)\times Z_2$ in the system. In the type-1.5 regime, it results in a semi-Meissner state where the system has a macroscopic phase separation in domains with broken $U(1)$ and $U(1) \times Z_2$ symmetries.   

Molecular Dynamics of Type-1.5 Superconductors

In multi-component superconductors and structures of interlaced layered type-I type-II layers there exists a range of parameters where inter-vortex interaction is repulsive at short ranges and attractive at long range. Such regimes were termed ``type-1.5 superconductivity'' recently. This vortex interaction leads to a microscopic phase separation in Meissner and vortex droplets. In this talk, we utilize molecular dynamics to investigate the magnetic response of such superconductors in the type-1.5 regimes.   

Stabilization of a vortex-antivortex lattice created by a magnetic-field pulse

Using the time-dependent Ginzburg-Landau approach, we theoretically investigate the formation and evolution of vortex-antivortex patterns, which are created in a thin superconducting film by a single pulse of an inhomogeneous magnetic field. The field pulse is induced by a periodic square array of current loops, where the current direction is either the same for all the loops or changes from one loop to another in the checkerboard order. In an ideally homogeneous superconductor film, the vortices and antivortices, generated by an applied magnetic field pulse, fully recombine within a relatively short time interval after switching off the current in the loops. We demonstrate that in the presence of- even relatively weak- pinning centers the vortex-antivortex distributions, induced by a short magnetic-field pulse, can eventually evolve into vortex-antivortex lattices, which remain stable for an arbitrarily long time. This work was supported by the Methusalem Funding of the Flemish Government, the NES-ESF program, the Belgian IAP, the Fund for Scientific Research-Flanders (FWO- Vlaanderen).   

Topological solitons in three-band superconductors with broken time reversal symmetry

We report that three-band superconductors with Broken Time Reversal Symmetry allow magnetic field-induced topological solitons. When time reversal symmetry is broken, ground state exhibits $\mbox{U(1)}\times Z_2$ symmetry. Domain-wall, are natural solutions when theories exhibit such a discrete symmetry. Closed domain-walls are unstable to collapse because of their line tension. We show that closed domain-walls can be stabilized by confining vortices. The resulting topological solitons are stable and can be induced by fluctuations or quenching the system through a phase transition. This new kind of solitons can provide an experimental signature of the Time Reversal Symmetry Breakdown. Based on : J. Garaud, J. Carlstr\"om, and E. Babaev, Phys. Rev. Lett. 107, 197001 (Nov 2011).   

Vortex dynamics in Superconducting Corbino Disks: Molucular Dynamics and Heat Transport Simulations

Understanding vortex dynamics is important for application of superconductivity, because vortex motion causes resistive state of superconductors and controlling vortex motion is useful for superconducting devices. Also vortex dynamics shows much variety of phenomena. In a corbino disk geometry, where electric current is injected at the center of the disk and flows toward the perimeter of the disk, vortex moves circular by the Lorentz force from this current. But the Lorentz force depend on the distance from the center as $1/r$, and therefore the vortex velocity faster in the center region than those in the perimeter region. Then vortex motion generates heat and causes non-uniform temperature distribution. Non-uniform temperature distribution causes further vortex motion. Therefore in the superconducting corbino disk, vortex dynamics is not a simple problem. In order to investigate this vortex dynamics, we combine the molecular dynamics and the heat transport simulations. Our simulation results show that dynamical structure of vortices depends on the heat resistance between the superconductor and a substrate as well as the heat capacity and heat conductance of superconductors. Especially there is a transition from laminar flow to the spiral or non-uniform flow.   

$\Phi_{0}$ as a smallest unit of the intermediate state of a type-I superconductor: Revelation through nonlinear dynamics

We study by time-dependent Ginzburg-Landau simulations the nonlinear dynamics of the intermediate state in a current-carrying type-I superconductor. The stray magnetic field of the current induces the intermediate state, where nucleation of flux domains is \textit{discretized to a single fluxoid at a time}, while their final shape (tubular or laminar), size and nucleation rate depend on applied current and edge conditions. The current induces opposite flux domains on opposite sides of the sample, and subsequently drives them to annihilation -- which is \textit{also discretized}, as a sequence of vortex-antivortex pairs. Discretization of both nucleation and annihilation leave measurable traces in the voltage signal across the sample. These dynamic phenomena provide an unambiguous proof of a flux quantum being the smallest building block of the intermediate state in type-I superconductors.   

Nucleation and development of dendritic flux avalanches in superconducting films

The stability of superconducting films is threatened by thermomagnetic runaways commonly observed as abrupt dendritic flux avalanches. We report numerical simulations of the electrodynamics and thermal behavior of superconducting films, where the gradual flux penetration is interrupted by such avalanches. The simulation formalism is based on an efficient method for treating the nonlinear and nonlocal electrodynamics, and it handles both the slow flux creep dynamics prior to the avalanches and the transition to the many orders of magnitude faster instability regime. Then the temperature rises quickly above the critical temperature, and the avalanche develops fully in less than 100 nanoseconds, with an initial velocity of approximately 100 km/s. Both the morphology and speed of the avalanches are in excellent agreement with results from magneto-optical imaging experiments. The sample is seeded with randomly distributed disorder, which results in a significantly reduced threshold for onset of avalanches. Interaction with the material disorder also contributes to branching and irreprodusibility of the flux structures. However, disorder is not the main mechanism behind branching and dendritic structures are also found to develop in completely uniform samples.   

Josephson and pancake vortices in Bi-2212 with anti-dots array

Josephson and pancake vortices in Bi-2212 with anti-dots (holes) array have been studied with measuring the flow-resistance and the c-axis resistance. The samples for the measurements were prepared by a focused ion-bean milling with a diameter of 200 nm and 1000 nm pitch hole-array and in the in-line structure. Angular dependence of the flow-resistance does not show lock-in phenomenon as usually observed in the behaviors of Josephson vortices in Bi-2212. Instead, there are several peaks observed in the flow-resistance. A couple of peak can be explained with the matching field effect of pancake vortices to the array, but the others not. The c-axis transport measurements show characteristic transitions near the matching fields and between them in the c-axis resistance with the perpendicular field to the superconducting layers. This is related to the accommodation rate of pancake vortices into the holes and to the interaction between/among the vortices outside the holes and the trapped vortices.   

Effect of pinning force on critical current using molecular dynamic simulation

Molecular dynamics have been used to study the effect of pinning force on the critical current at different temperatures. Our simulation is built on assuming a two dimensional periodic arrays of vortices and pins at different sites. The critical current density has been studied at different temperatures by solving the over damped equation of vortex motion taking into account the vortex-vortex interaction, the thermal force, the vortex-pinning interaction as well as the driving Lorentz force. The results show a second phase transition at specific low temperature at all pinning forces with a definite pinning size.