# Search for Composite Fermions at Filling Factor 5/2: Role of Landau Level and Subband Index

## TL;DR

This study investigates the presence and properties of composite fermions at filling factor 5/2 in different Landau levels and subbands, revealing their absence in the N=1 level and differences in mean-free-path and anisotropy in the N=0 level.

## Contribution

The paper provides the first direct geometric resonance measurements of CFs at 5/2, demonstrating their absence in the N=1 LL and highlighting the impact of Landau level and subband index on CF properties.

## Key findings

- No geometric resonances for CFs at 5/2 in the N=1 LL.
- Clear CF signatures observed in the N=0 LL when 5/2 is in the anti-symmetric subband.
- CFs in N=1 LL have significantly smaller mean-free-path than in N=0 LL.

## Abstract

The pairing of composite fermions (CFs), electron-flux quasi-particles, is commonly proposed to explain the even-denominator fractional quantum Hall state observed at $\nu=5/2$ in the first excited ($N=1$) Landau level (LL) of a two-dimensional electron system (2DES). While well-established to exist in the lowest ($N=0$) LL, much is unknown about CFs in the $N=1$ LL. Here we carry out geometric resonance measurements to detect CFs at $\nu=5/2$ by subjecting the 2DES to a one-dimensional density modulation. Our data, taken at a temperature of 0.3 K, reveal no geometric resonances for CFs in the $N=1$ LL. In stark contrast, we observe clear signatures of such resonances when $\nu=5/2$ is placed in the $N=0$ LL of the anti-symmetric subband by varying the 2DES width. This finding implies that the CFs' mean-free-path is significantly smaller in the $N=1$ LL compared to the $N=0$ LL. Our additional data as a function of in-plane magnetic field highlight the role of subband index and establish that CFs at $\nu=5/2$ in the $N=0$ LL are more anisotropic in the symmetric subband than in the anti-symmetric subband.