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arXiv:cond-mat/9605197 · Physical review. B, Condensed matter

Spectral flow, Magnus force, and mutual friction via the geometric optics limit of Andreev reflection

Michael Stone

Published Nov 1, 1996• 138 citations
arXivHTMLPDF

Abstract

The notion of spectral flow has given new insight into the motion of vortices in superfluids and superconductors. For a BCS superconductor the spectrum of low energy vortex core states is largely determined by the geometric optics limit of Andreev reflection. We use this to follow the evolution of the states when a stationary vortex is immersed in a transport supercurrent. If the core spectrum were continuous, spectral flow would convert the momentum flowing into the core via the Magnus effect into unbound quasiparticles---thus allowing the vortex to remain stationary without a pinning potential or other sink for the inflowing momentum. The discrete nature of the states, however, leads to Bloch oscillations which thwart the spectral flow. The momentum can escape only via relaxation processes. Taking these into account permits a physically transparent derivation of the mutual friction coefficients. \textcopyright{} 1996 The American Physical Society.

DOI
10.1103/physrevb.54.13222

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Spectral Flow, Magnus Force and Mutual Friction Via the Geometric Optics Limit of Andreev Reflection

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The notion of spectral flow has given new insight into the motion of vortices in superfluids and superconductors. For a BCS superconductor the spectrum of low energy vortex core states is largely determined by the geometric optics limit of Andreev reflection. We use this to follow the evolution of the states when a stationary vortex is immersed in a transport supercurrent. If the core spectrum were continuous, spectral flow would convert the momentum flowing into the core via the Magnus effect into unbound quasi-particles — thus allowing the vortex to remain stationary without a pinning potential or other sink for the inflowing momentum. The discrete nature of the states, however, leads to Bloch oscillation which thwart the spectral flow. The momentum can escape only via relaxation processes. Taking these into account permits a physically transparent derivation of the mutual friction coefficients.

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The notion of spectral flow has given new insight into the motion of vortices in superfluids and superconductors. For a BCS superconductor the spectrum of low energy vortex core states is largely determined by the geometric optics limit of Andreev reflection. We use this to follow the evolution of the states when a stationary vortex is immersed in a transport supercurrent. If the core spectrum were continuous, spectral flow would convert the momentum flowing into the core via the Magnus effect into unbound quasiparticles---thus allowing the vortex to remain stationary without a pinning potential or other sink for the inflowing momentum. The discrete nature of the states, however, leads to Bloch oscillations which thwart the spectral flow. The momentum can escape only via relaxation processes. Taking these into account permits a physically transparent derivation of the mutual friction coefficients. \textcopyright{} 1996 The American Physical Society.
The notion of spectral flow has given new insight into the motion of vortices in superfluids and superconductors. For a BCS superconductor the spectrum of low energy vortex core states is largely determined by the geometric optics limit of Andreev reflection. We use this to follow the evolution of the states when a stationary vortex is immersed in a transport supercurrent. If the core spectrum were continuous, spectral flow would convert the momentum flowing into the core via the Magnus effect into unbound quasi-particles — thus allowing the vortex to remain stationary without a pinning potential or other sink for the inflowing momentum. The discrete nature of the states, however, leads to Bloch oscillation which thwart the spectral flow. The momentum can escape only via relaxation processes. Taking these into account permits a physically transparent derivation of the mutual friction coefficients.
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.
Abstract There are four forces acting on a vortex moving with respect to normal and superfluid components of the liquid: three reactive forces (Magnus, Iordanskii, and Kopnin forces) and the Stokes friction force. The Iordanskii force comes from the analog of the gravitational Aharonov–Bohm effect and are discussed later in the book. The Kopnin or spectral flow force appears only in fermionic superfluids. This chapter discusses the Kopnin force acting on a singular vortex. The origin of this force is the phenomenon of chiral anomaly, but as distinct from the force acting on continuous vortex discussed in Chapter 18, the Adler–Bell–Jackiw equation for chiral anomaly is not applicable. The anomaly is now related to the spectral flow of fermion zero modes in the vortex core, which is caused by motion of the vortex with respect to the normal component. The spectral flow leads to generation of linear momentum by a vortex core, which is then transferred to the normal component. This process is similar to the generation of baryonic charge by the cores of cosmic strings and serves as the analog of Callan–Harvey mechanism of cancellation of anomalies. The temperature dependence of the spectral flow force is obtained from solution of kinetic equation for fermion zero modes. The resulting force acting on a vortex has been measured in experiments on vortex dynamics in 3He-B. Existence of two forces in addition to conventional Magnus and friction forces — Iordanskii and Kopnin forces – has been verified.
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.
We investigate the two-dimensional motion of a single vortex orbiting a pinned anti-vortex in a unitary Fermi superfluid. By analyzing its trajectory, we measure the yet-unknown longitudinal and transverse mutual friction coefficients, which quantify the vortex-mediated coupling between the normal and superfluid components. Both coefficients increase while approaching the superfluid transition. They provide access to the vortex Hall angle, which is linked to the relaxation time of the localized quasiparticles occupying Andreev bound states within the vortex core, and to the vortex Reynolds number Reα associated with the transition from laminar to quantum turbulent flows. We compare our results with numerical simulations and an analytic model originally formulated for superfluid 3He, finding good agreement. Our work suggests that vortex dynamics in unitary Fermi superfluids is essentially affected by the interplay between delocalized thermal excitations and vortex-bound quasiparticles. Further, it provides a novel testbed for studying vortex dynamics at finite temperatures. Vortex dynamics and mutual friction in quantum fluids are intimately connected to the fundamental properties of superfluids. Here, the authors reveal previously unexplored mechanisms underlying the mutual friction coefficients in ultracold Fermi superfluids in the unitary limit, suggesting bound quasiparticles within the vortex core play a significant role.
Abstract The physical origin of mutual friction in quantum fluids is deeply connected to the fundamental nature of superfluidity. It stems from the interaction between the superfluid and normal components, mediated by the dynamics of quantized vortices that induce the exchange of momentum and energy. Despite the complexity of these interactions, their essential features can be effectively described by the dissipative point vortex model—an extension of classical vortex dynamics that incorporates finite-temperature dissipation. Mutual friction is parametrized by the longitudinal (dissipative) coefficient α\alphaα α and the transverse (reactive) coefficient α′\alpha 'α′ α ′ . Accurate measurement of these parameters provides critical insights into the microscopic mechanisms governing vortex motion and dissipation in quantum fluids, serving as a key benchmark for theoretical models. In this work, we employ the dissipative point vortex model to study how fluctuations in the initial conditions influence the inference of α\alphaα α and α′\alpha 'α′ α ′ from the time evolution of the vortex trajectories. Using experimentally realistic parameters, we show that fluctuations can introduce significant biases in the extracted values of the mutual friction coefficients. We compare our findings with recent experimental measurements in strongly interacting atomic superfluids. Applying this analysis to our recent experimental results allowed us to account for fluctuations in the correct determination of α\alphaα α and α′\alpha 'α′ α ′ .