# Zero-bias Shapiro steps in asymmetric pinning nanolandscapes

## TL;DR

This paper investigates zero-bias Shapiro steps in asymmetric nanostructures by combining theoretical modeling and experiments, revealing how dc bias influences vortex dynamics and produces rectified voltages.

## Contribution

It introduces the first experimental observation and theoretical explanation of zero-bias Shapiro steps in asymmetric pinning nanolandscapes.

## Key findings

- Zero-bias Shapiro steps are observed experimentally.
- Dc bias can reverse the rectified voltage.
- Theoretical model explains the emergence of zero-bias steps.

## Abstract

The coherent nonlinear dynamics of Abrikosov vortices in asymmetric pinning nanolandscapes is studied by theoretical modeling and combined microwave and dc electrical resistance measurements. The problem is considered on the basis of a single-vortex Langevin equation within the framework of a stochastic model of anisotropic pinning. When the distance over which Abrikosov vortices are driven during one half ac cycle coincides with one or a multiple of the nanostructure period, Shapiro steps appear in the current-voltage curves (CVCs) as a general feature of systems whose evolution in time can be described in terms of a particle moving in a periodic potential under combined dc and ac stimuli. While a dc voltage appears in response to the ac drive, the addition of a dc bias allows one to diminish the rectified voltage and eventually to change its sign when the extrinsic dc bias-induced asymmetry of the pinning potential starts to dominate the intrinsic one. This rectified negative voltage in the CVCs becomes apparent as \emph{zero-bias} Shapiro steps, which are theoretically predicted and experimentally observed for the first time.