We have performed a theoretical study of the effects of pinning potential and dissipation on vortex tunneling in superconductors. Analytical results are obtained in various limits relevant to experiment. In general we have found that pinning and dissipation tend to suppress the effect of the vortex velocity dependent part of the Magnus force on vortex tunneling.
We have performed a theoretical study of the effects of pinning potential and dissipation on vortex tunneling in superconductors. Analytical results are obtained in various limits relevant to experiment. In general we have found that pinning and dissipation tend to suppress the effect of the vortex velocity dependent part of the Magnus force on vortex tunneling.
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.
The tunneling rate ${t}_{v}∕\ensuremath{\hbar}$ of a vortex between two pinning sites (of strength V separated by d) is computed using the Bogoliubov expansion of vortex wave-functions overlap. For BCS vortices, tunneling is suppressed beyond a few Fermi wavelengths. For Bose condensates, ${t}_{v}=\overline{V}\phantom{\rule{0.2em}{0ex}}\mathrm{exp}(\ensuremath{-}\ensuremath{\pi}{n}_{s}{d}^{2}∕2)$, where ns is the boson density. The analogy between vortex hopping in a superconducting film and two-dimensional electrons in a perpendicular magnetic field is exploited. We derive the variable range hopping temperature, below which vortex tunneling contributes to magnetoresistance. Using the ``quantum Hall insulator'' analogy we argue that the Hall conductivity (rather than the inverse Hall resistivity) measures the effective carrier density in domains of mobile vortices. Details of vortex wave functions and overlap calculations, and a general derivation of the Magnus coefficient for any wave function on the sphere, are provided in appendixes.
We give a general review of recent developments in the theory of vortices in superfluids and superconductors, discussing why the dynamics of vortices is important, and why some key results are still controversial. We discuss work that we have done on the dynamics of quantized vortices in a superfluid. Despite the fact that this problem has been recognized as important for forty years, there is still a lot of controversy about the forces on and masses of quantized vortices. We think that one can get unambiguous answers by considering a broken symmetry state that consists of one vortex in an infinite ideal system. We argue for a Magnus force that is proportional to the superfluid density, and we find that the effective mass density of a vortex in a neutral superfluid is divergent at low frequencies. We have generalized some of the results for a neutral superfluid to a charged system.
The transverse force acting on a quantized vortex in a superfluid is a problem that has eluded a complete understanding for more than three decades. In this Letter I calculate the superfluid velocity part of the transverse force in a way closely related to Laughlin's argument for the quantization of conductance in the quantum Hall effect. A combination of this result, the vortex velocity part of the transverse force found by Thouless, Ao, and Niu [Phys. Rev. Lett. 76, 3758 (1996)], and Galilean invariance shows that there cannot be a transverse force proportional to the normal fluid velocity.
Starting from the time-dependent version of the Feynman-Hellmann theorem, the Magnus force acting on a vortex in fermion superfluid is expressed via the adiabatic curvature over the space of vortex positions. With use of the Bogoliubov--de Gennes approximation, the Magnus force in a homogeneous superfluid at T=0 is shown to originate from virtual transitions between the lowest quasiparticle core bound states. Nonadiabatic corrections to the curvature are obtained to second order in vortex velocity. The adiabatic approximation is shown to break down at a critical velocity equal to the vortex velocity in the first Landau level. The effect of elastic scattering on the Magnus force is discussed in terms of the relaxation-time approximation. It is suggested that this approximation is appropriate only for a large-scale vortex motion. In this case, the effective Magnus force is drastically reduced when the elastic-scattering rate exceeds the core excitation frequency. We conjecture that quantum vortex tunneling is governed by a local Magnus force obtained from the Berry phase approach.
We characterize the mechanisms of vortex pinning in a superfluid thin film described by the two-dimensional Gross-Pitaevskii equation. We consider a vortex "scattering experiment" whereby a single vortex in a superfluid flow interacts with a circular, uniform pinning potential. By an analogy with linear dielectrics, we develop an analytical hydrodynamic approximation that predicts vortex trajectories, the vortex fixed point and the unpinning velocity. We then solve the Gross-Pitaevskii equation to validate this model, and build a phase portrait of vortex pinning. We identify two different dynamical pinning mechanisms marked by distinctive phonon emission signatures: one enabled by acoustic radiation and another mediated by vortex dipoles nucleated within the pin. Relative to obstacle size, we find that pinning potentials on the order of the healing length are more effective for vortex capture. Our results could be useful in mitigating the negative effects of drag due to vortices in superfluid channels, in analogy to maximizing supercurrents in type-II superconductors.