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arXiv:cond-mat/9610157 · Journal of Experimental and Theoretical Physics Letters

Poisson bracket scheme for vortex dynamics in superfluids and superconductors and the effect of the band structure of the crystal

Григорий Ефимович Воловик

Published Dec 1, 1996• 13 citations
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Abstract

Poisson brackets for the Hamiltonian dynamics of vortices are discussed for 3 regimes, in which the dissipation can be neglected and the vortex dynamics is reversible: (i) The superclean regime, in which the spectral flow is suppressed. (ii) The regime in which the fermions are pinned by the crystal lattice. This includes the regime of extreme spectral flow of fermions in the vortex core: these fermions are effectively pinned by the normal component. (iii) The case when the vortices are strongly pinned by the normal component. All these limits are described by the single parameter C 0 , the physical meaning of which is discussed for superconductors containing several bands of electrons and holes. The effect of the topology of the Fermi surface on the vortex dynamics is also discussed.

DOI
10.1134/1.567257

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Poisson brackets for the Hamiltonian dynamics of vortices are discussed for 3 regimes, in which the dissipation can be neglected and the vortex dynamics is reversible: (i) The superclean regime, in which the spectral flow is suppressed. (ii) The regime in which the fermions are pinned by the crystal lattice. This includes the regime of extreme spectral flow of fermions in the vortex core: these fermions are effectively pinned by the normal component. (iii) The case when the vortices are strongly pinned by the normal component. All these limits are described by the single parameter C 0 , the physical meaning of which is discussed for superconductors containing several bands of electrons and holes. The effect of the topology of the Fermi surface on the vortex dynamics is also discussed.
A non-dissipative force F nd acting on a vortex in Fermi superfluids and superconductors is calculated taking into account the spectral flow of fermion zero modes in the vortex core. The spectral-flow effect casts a new light on the problem of mutual friction in superfluids. We demonstrate that, for vortices in an isotropic system, the reactive mutual friction parameter D ' ( T ) is negative in the collisionless regime and it is positive in the hydrodynamic regime. This agrees with 3 He-B measurements, which thus give the experimental verification of the spectral-flow effect on the vortex dynamics.
In this thesis, we analytically and numerically study two different scenarios of vortex dynamics in a two-dimensional superfluid. The first system we explore is an expanding cluster of like-sign vortices, which recently suggested it could explain observations in a superfluid optomechanics experiment. We employ a recent theoretical model that approximates large collections of vortices as a fluid and present an analytic solution for its dynamics. Analysis suggests that as a cluster expands due to thermal friction, it forms a Rankine vortex (i.e., a top-hat distribution) that expands self-similarly in time regardless of initial vorticity distribution. Numerical simulations of point vortices confirm this universal expanding regime and further demonstrates vortex lattice formation that goes beyond the vortex fluid theory. We analyse correlations that emerge in the resulting lattices and observe decaying disorder as the cluster expands. Furthermore, we analyse experimental data from a quasi-two-dimensional 87Rb Bose-Einstein condensate, which supports the vortex fluid theory’s predictions.The second scenario considers the dynamics of a scattering event where a single quantum vortex interacts with a uniform, circular pinning potential in a steady two-dimensional superfluid flow. We first develop an approximate hydrodynamical model to understand the interaction between the vortex and the pinning potential in the conservative regime and find it is in good agreement with the mean-field Gross-Pitaevskii equation in the low-velocity limit. We further solve the Gross-Pitaevskii equation for higher background velocities to study how the vortex moves around pinning sites, interacts with it, and ultimately becomes pinned. We uncover four different regimes of vortex pinning, each marked with a characteristic emission of sound energy. Finally, we study how vortices become unpinned from a pinning site, revealing large vortex dipoles form to stabilise the system.Our work in this thesis takes significant steps towards advancing knowledge of both the collective dynamics of vortices and their individual interaction with defects upon surface substrates. Our numerical and analytical results opens up new avenues of exploration be it further understanding dissipation mechanisms in two-dimensional superfluids, or elucidating the nature of vortex pinning in systems such as neutron stars.
We consider a superfluid of trapped fermionic atoms and study the single vortex solution in the Ginzburg-Landau regime. We define simple analytical estimates for the main characteristics of the system, such as the vortex core size, temperature regimes for the existence of a vortex, and the effects of rotation and interactions with normal fermions. The parameter dependence of the vortex core size (healing length) is found to be essentially different from that of the healing length in metallic superconductors or in trapped atomic Bose-Einstein condensation in the Thomas-Fermi limit. This is an indication of the importance of the confining geometry for the properties of fermionic superfluids.
Superconductivity is an electronic state of matter arising from the existence of a common wave function with a coherent phase extending on a truly macroscopic scale. One major manifestation of this striking quantum phenomenon is the dissipationless transport of electrical current, an asset deserving particular attention in the present times where the efficient energy distribution has become of utmost importance. Unfortunately, the motion of quantum units of magnetic flux (so-called vortices or fluxons), which is an unavoidable side-effect found in superconductors in the presence of transport currents and magnetic fields, severely limits the conditions to preserve dissipationless transport. This poses a challenge for achieving the functionalization of superconducting materials and threatens their spectrum of applications. It is widely known that any inhomogeneities (either material imperfections, or ones made artificially), which locally suppress superconductivity on the scale comparable to the core of the vortex, can pin the vortex and delay the onset of the vortex motion to higher applied currents. In recent years a substantial effort has been made to minimize the effects of current-induced vortex motion by tailoring arrays of artificial pinning centers. Besides improving the critical parameters of the superconducting state, a pinning matrix can be used for the manipulation of vortex matter, thus directly affecting the vortex dynamics, such as rectification of vortex motion under an ac drive (vortex diode) by introducing asymmetric pinning landscapes. In the literature one can find that the realization of the anchoring of the vortices can be based on nanostructured arrays of perforations, chemically grown defects, permanent nanomagnets, or even pinning sites produced by heavy ion bombardment. All of those realizations are based on a permanent imprint on the superconductor, without any possibility for subsequent modifications in the distribution and strength of the pinning. The principal objective of this thesis is to investigate the dynamical behavior of vortex matter under an entirely new kind of pinning landscape consisting of spatial and temporal modulation of the superconducting condensate. A particular case of spatial modulation is considered in a constricted structure where current lensing can cause extremely high vortex velocities. Subsequently, a time-dependent thermal potential introduced to the superconducting condensate will cause stroboscopic resonances during the vortex motion - a phenomenon that cannot be observed in the systems with static pinning imprints. Finally, a study of electronic gating is presented, where the local properties of superconductor, such as mean free path, or electronic band structure in general, can be influenced electronically. This is a completely unexplored interdisciplinary research topic, which will eventually allow one to manipulate individual vortices in superconducting materials by means of spatially confined and temporally controlled thermal and electromagnetic excitations. Furthermore, such techniques can provide one fundamental insight in different states of the vortex matter with respect to variation of the transport current, highly relevant for understanding the resistive state of superconducting materials and their applications.
Excitations in vortex cores in superconductors and other Fermi superfluids are single-particle excitations with a peculiar energy spectrum. These excitations are responsible for many important thermodynamic properties such as specific heat, London penetration length, etc. They also determine the dynamic characteristics of superconductors and superfluids through their interaction with vortices. Flux flow resistance, the Hall effect in type II superconductors and the mutual friction in superfluids are the most important phenomena which strongly depend on vortex core excitations. These phenomena determine the electromagnetic responses of type II superconductors and the hydrodynamic behaviour of superfluids and are of great significance for practical applications of superconducting devices and for understanding the most fundamental properties of correlated electrons and other Fermi particles. In this review we consider the dynamic properties of superconductors and superfluids and outline the basic ideas and results on the vortex dynamics in clean superfluid Fermi systems. The forces acting on moving vortices are discussed including the problem of the transverse force which was a matter of confusion for quite some time. We formulate the equations of the vortex dynamics, which include all the forces and the inertial term associated with excitations bound to the moving vortex.