Bulk valley transport and Berry curvature spreading at the edge of flat bands

Subhajit Sinha,Pratap Chandra Adak,L D Varma Sangani,R S Surya Kanthi,Kenji Watanabe,Jeil Jung,Mandar M Deshmukh,Bheema Lingam Chittari,Takashi Taniguchi

doi:10.1038/s41467-020-19284-w

Abstract

2D materials based superlattices have emerged as a promising platform to modulate band structure and its symmetries. In particular, moiré periodicity in twisted graphene systems produces flat Chern bands. The recent observation of anomalous Hall effect (AHE) and orbital magnetism in twisted bilayer graphene has been associated with spontaneous symmetry breaking of such Chern bands. However, the valley Hall state as a precursor of AHE state, when time-reversal symmetry is still protected, has not been observed. Our work probes this precursor state using the valley Hall effect. We show that broken inversion symmetry in twisted double bilayer graphene (TDBG) facilitates the generation of bulk valley current by reporting experimental evidence of nonlocal transport in a nearly flat band system. Despite the spread of Berry curvature hotspots and reduced quasiparticle velocities of the carriers in these flat bands, we observe large nonlocal voltage several micrometers away from the charge current path — this persists when the Fermi energy lies inside a gap with large Berry curvature. The high sensitivity of the nonlocal voltage to gate tunable carrier density and gap modulating perpendicular electric field makes TDBG an attractive platform for valley-twistronics based on flat bands.

Highlights

The advancement in twistronics has opened up new avenues to study electron correlations physics, such as Mott insulator states[1,2,3], superconductivity[3,4], and orbital ferromagnetism[5,6] in twisted bilayer graphene (TBG)
The nonzero Berry curvature can manifest itself in bulk valley transport via valley Hall effect (VHE), as electrons from two valleys are deflected to two opposite directions perpendicular to the in-plane electric field[26,27]
twisted double bilayer graphene (TDBG) offers a unique platform since it provides electrical control over the flatness of Chern bands through vF and the band gap it hosts

Summary

Introduction

The advancement in twistronics has opened up new avenues to study electron correlations physics, such as Mott insulator states[1,2,3], superconductivity[3,4], and orbital ferromagnetism[5,6] in twisted bilayer graphene (TBG). The observation of anomalous Hall state in TBG5,6 has been explained by spontaneous symmetry breaking of degenerate Chern bands[20,21] Such observations point to rich topology in twisted systems governed by nonzero Berry curvature and understanding these topological aspects is currently at the frontier[22,23,24]. The nonzero Berry curvature can manifest itself in bulk valley transport via valley Hall effect (VHE), as electrons from two valleys are deflected to two opposite directions perpendicular to the in-plane electric field[26,27] In systems such as graphene with small intervalley scattering, the valley current can be detected by an inverse VHE at probes away from the charge current path in the form of a nonlocal resistance[28,29,30]. Twistronic system, like the one we present, offers two key knobs for bulk valleytronics—firstly, the magnitude of Berry curvature is inversely related to the gap, and secondly, the tunability of Fermi velocity tunes the sharpness of the Berry curvature hotspot

Methods

Results

Conclusion