# Non-trivial quantum oscillation geometric phase shift in a trivial band

## TL;DR

This study reveals a non-trivial geometric phase shift in a trivial band of ABA-trilayer graphene, caused by the influence of a nearby Dirac band with non-trivial Berry's phase, highlighting complex band interactions.

## Contribution

It demonstrates how non-trivial Berry's phase effects can manifest in trivial bands due to inter-band constraints in multi-band topological materials.

## Key findings

- Observed anomalous phase shift in quadratic band oscillations
- Linked phase shift to non-trivial Berry's phase of Dirac band
- Showed multi-band interactions reveal subtle topological effects

## Abstract

The accumulation of non-trivial geometric phases in a material's response is often a tell-tale sign of a rich underlying internal structure. Studying quantum oscillations provides one of the ways to determine these geometrical phases, such as Berry's phase, that play a central role in topological quantum materials. We report on magneto-transport measurements in ABA-trilayer graphene, the band structure of which is comprised of a weakly gapped linear Dirac band, nested within a trivial quadratic band. Here we show Shubnikov-de Haas (SdH) oscillations of the quadratic band shifted by a phase that sharply departs from the expected 2$\pi$ Berry's phase. Our analysis reveals that, surprisingly, the anomalous phase shift is non-trivial and is inherited from the non-trivial Berry's phase of the linear Dirac band due to strong filling-enforced constraints between the linear and quadratic band Fermi surfaces. Given that many topological materials contain multiple bands, our work indicates how additional bands, which are thought to obscure the analysis, can actually be exploited to tease out the subtle effects of Berry's phase.