Detecting half-quantum superconducting vortices by spin-qubit relaxometry

Abstract

Half-quantum vortices in spin-triplet superconductors are predicted to harbor Majorana zero modes and may provide a viable avenue to topological quantum computation. Here, we introduce a novel approach for directly measuring the half-integer-quantized magnetic fluxes, $Φ= h / (4e)$, carried by such half-quantum vortices via spin-qubit relaxometry. We consider a superconducting strip with a narrow pinch point at which vortices cross quasi-periodically below a spin qubit as a result of a bias current. We demonstrate that the relaxation rate of the spin qubit exhibits a pronounced peak if the vortex-crossing frequency matches the transition frequency of the spin qubit and conclude that the magnetic flux $Φ$ of a single vortex can be obtained by dividing the corresponding voltage along the strip with the transition frequency. We discuss experimental constraints on implementing our proposed setup in spin-triplet candidate materials like UTe$_2$, UPt$_3$, and URhGe.

Figures (4)

• Figure 1: Proposed setup for determining the magnetic flux $\Phi$ carried by a single superconducting vortex. The application of a sufficiently large bias current $I$ leads to quasi-periodic vortex crossing across the pinch point and, hence, a finite voltage $V$ along the superconducting strip of thickness $D$. Magnetic-field modulations induced by subsequent vortex-crossing events lead to a pronounced peak in the relaxation rate $1/T_1$ of the spin qubit at height $d$ above the strip when the vortex-crossing frequency $V / \Phi$ is commensurate with the transition frequency $f_0$ of the spin qubit. Each vortex nucleated at the smaller constriction on the top edge is focused toward the larger constriction at the bottom edge as a result of current crowding (red curves) and passes below the spin qubit with the same speed $v$.
• Figure 2: Nonzero components (a) $B_y (t)$ and (b) $B_z (t)$ of the time-dependent magnetic field at the spin qubit during a single vortex-crossing event for different ratios between the distance $d$ of the spin qubit and the thickness $D$ of the superconductor.
• Figure 3: (a) Schematic form of the time-dependent magnetic field $\bar{B} (t)$ at the spin qubit during a series of vortex-crossing events at $t = t_m$ separated by an approximately constant time difference $T \pm \tau$ with $\tau \ll T$. (b) Schematic form of the resulting relaxation rate $\Gamma \equiv 1/T_1$ against the transition frequency $f_0$ with a sequence of well-defined peaks at integer multiples of $1/T$.
• Figure 4: Dimensionless function $G (\alpha, \Phi f_0 / V)$ against the voltage $V$ for different ratios $\alpha = \tau / T$ between the variation $\tau$ and the mean $T$ of the approximately constant time difference separating subsequent vortex-crossing events.