Quantum Mechanics of an Abrikosov Vortex in Nanofabricated Pinning Potential

TL;DR

This work investigates whether an Abrikosov vortex in a type-II superconductor can be treated as a quantum mechanical quasiparticle by designing a Nb nanofabricated device that pins a single vortex in a central artificial defect. It combines time-dependent Ginzburg-Landau simulations to optimize geometry for robust single-vortex pinning at $B\approx 6\,\mathrm{T}$ with a 2D Schrödinger equation analysis for a vortex in a Gaussian-like pinning potential to obtain quantized energy levels as a function of the effective vortex mass $m_v$. The results show that ground and first excited states are distinguishable, with excitation energies remaining well above the $\mu\mathrm{eV}$ scale across mass ranges, suggesting feasibility of microwave spectroscopy; magnetic-field readouts via NV- or chip-scale magnetometers offer a plausible indirect measurement path. The study highlights a potential platform for probing quantum vortex dynamics with implications for cryogenic memory and quantum computing, while noting limitations related to dissipation and uncertain vortex mass in the pinned regime.

Abstract

A superconducting device is proposed for experimentally investigating whether an Abrikosov vortex can be modeled as a quantum mechanical quasiparticle. The design process of a type-II superconducting device capable of reliably pinning a single Abrikosov vortex is presented, creating a particle-in-a-box-like system. The proposed device consists of a cylindrically symmetric Nb film, 30 nm in diameter and 5 nm thick, with a 14 nm diameter artificial pinning center at its center. Time-dependent Ginzburg-Landau simulations indicate robust single-vortex pinning under an applied field of 6 T. The presumed quantized energy levels and associated quantum wavefunctions of the vortex quasiparticle are obtained by numerically solving the two-dimensional time-independent Schrödinger equation for this system. It is shown that distinguishing the ground and first excited states is experimentally feasible. Beyond fundamental physics studies, the application of the proposed device in cryogenic memory technology and quantum computing warrant further exploration.

Figures (7)

• Figure 1: A schematic illustration of the design of the Abrikosov vortex qubit device. In this work, we consider the optimization of the superconducting material along with the film thickness (d), the radius of the artificial pinning center ($R_\mathrm{pin}$), radius of the superconducting island ($R_\mathrm{dev}$) and the applied field ($B$) that enables single vortex entry and pinning in the proposed design.
• Figure 2: The zero temperature superconducting length scales as a function of Nb film thickness on silicon substrate: (a) The magnetic penetration depth according to the empirical model provided by Ilin et al.Ilin2004peculiarities. (b) The superconducting coherence length estimated by fitting a function $\xi_0(d)=k\cdot d^n$ to the experimental data provided by Pinto et al.Pinto2018dimensional, Zaytseva et al.Zaytseva2020upper and Draskovic et al.Draskovic2013measuring.
• Figure 3: The results of the time-dependent Ginzburg-Landau simulations for the optimized device ($R_\mathrm{dev}=15\,\mathrm{nm}$, $R_\mathrm{pin}=7\,\mathrm{nm}$, $d=5\,\mathrm{nm}$) at $B=6\,\mathrm{T}$ after 500 time steps, resulting in a steady state where a single vortex is trapped in the pinning center. (a) The magnitude of the order parameter and (b) the phase of the order parameter across the device.
• Figure 4: (a) The numerically calculated one-dimensional pinning potential based on Eqs. (\ref{['vortex_core_Eq']})--(\ref{['Chi_eq']}) (where $r=\sqrt{x^2+y^2}$ is expressed as $r=x$ at $y=0$) and a fit of a Gaussian potential $V(x)=a\cdot \mathrm{exp}(-\gamma x^2)$ via parameters $a$ and $\gamma$ to the numerical data. The fit resulted $a=-15.57$ and $\gamma=0.0015$. The gray region represents the scale of the device, corresponding to $x\in [-R_\mathrm{dev},\,R\mathrm{_\mathrm{dev}}]$. (b) The resulting cylindrically symmetric two-dimensional Gaussian potential based on the previous fit, that is used for solving the Schrödinger equation. The potential is set to $V=0$ when the distance from the origin is greater than $R_\mathrm{dev}=15\,\mathrm{nm}$.
• Figure 5: Visualizations of the ground state and the first excited state wavefunctions (continuous normalization) of the pinned vortex for different values of $m_\mathrm{v}$. The data is obtained from the numerical solutions of the time-independent Schrödinger equation for the Gaussian pinning potential illustrated in Fig. \ref{['Gaussian_fit_fig']}(b). The dashed white regions represent the dimensions of the pinning center ($R_\mathrm{pin}=7\,\mathrm{nm}$) and device ($R_\mathrm{dev}=15\,\mathrm{nm}$).