Minibands in twisted bilayer graphene probed by magnetic focusing

Abstract

Magnetic fields force ballistic electrons injected from a narrow contact to move along skipping orbits and form caustics. This leads to pronounced resistance peaks at nearby voltage probes as electrons are effectively focused inside them, a phenomenon known as magnetic focusing. This can be used not only for the demonstration of ballistic transport but also to study the electronic structure of metals. Here we use magnetic focusing to probe narrow bands in graphene bilayers twisted at ~2°. Their minibands are found to support long-range ballistic transport limited at low temperatures by intrinsic electron-electron scattering. A voltage bias between the layers causes strong valley splitting and allows selective focusing for different valleys, which is of interest for using this degree of freedom in frequently-discussed valleytronics.Crystallographic alignment of atomically thin crystals stacked together in a van der Waals heterostructure is a powerful tool that enables fine tuning of their electronic spectra. For crystals with similar honeycomb lattices the spectra are modified by the presence of a long-range interference (moiré) pattern with a period lS dependent on the twist angle θ between the layers (1-18), see Fig 1A. The additional spatial periodicity reduces the size of the Brillouin zone and introduces secondary Dirac points, as illustrated in Fig. 1B. So far, the most pronounced twist-engineered changes in the electronic properties of 2D crystals have been achieved in twisted bilayer graphene (TBG), where the twist at discrete 'magic' angles results in narrow bands, periodically modulated interlayer hybridisation and strong enhancement of electron correlations, leading to superconductivity and Mott insulator transitions (6-8). At larger θ, the TBG spectrum corresponds to a metal with several minibands at each K and K' valley in the Brillouin zone (Fig. 1B). Electronic properties of such a metal are expected to be quite different from the behaviour of Dirac electrons in monolayer or bilayer (aligned to Bernal stacking) graphene but so far remain largely unexplored. Here we use transverse focusing of electrons in a perpendicular magnetic field (TMF) (12,(19)(20)(21)(22)(23) to probe the properties of moiré minibands in TBG and demonstrate an exceptionally high quality of the 'artificial metal' in TBG, as well as a possibility to use vertical displacement field, D, to break the valley degeneracy in the two constituent layers and selectively enhance transport in one of the valleys.

Valley splitter and transverse valley focusing in twisted bilayer graphene

“…Furthermore, as time-reversal symmetry is effectively broken within a single valley of TBG, the layer-locked current for a given valley attains a net transverse deflection, giving rise to transverse valley currents [36]. The magnitude of deflection can be controlled by the slope of the potential and hence this effect, which we call transverse valley focusing, can be thought of as an electronic counterpart of transverse magnetic focusing [37,38].…”

Precision measurement of electron-electron scattering in GaAs/AlGaAs using transverse magnetic focusing

“…). This suggests that the ratio of subsequent TMF maxima values R n , is not a good measure to infer specularity of the boundary as has been used by various works 32 , 33 , 38 .

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“…The decay in R n with increasing scattering has been observed to be exponential and to possess a characteristic decay length 34 , 35 , in early work associated with (with no reference to ). The increase in scattering can be effectuated by increasing T as has been noted in graphene 32 , 33 . In this work, we address the problem to relate MC scattering and specifically to the decay in R n , simultaneously underlining the importance of MC scattering in ballistic transport and introducing a sensitive approach to quantify .…”

“…MR scattering (mediated by lattice defects and phonons) is responsible for dissipation of the system’s momentum to the lattice. TMF is usually applied to study the ballistic nature of carriers and characterize the shape of the Fermi surface in 3D solids 26 , 27 and in 2DESs 28 – 33 . In the presence of a magnetic field B applied normal to the plane of the 2DES, electrons injected from a point contact (PC) follow semiclassical skipping cyclotron orbits of diameter d c = 2 ℏ k F / e B to focus on a collector PC at a distance L c = n d c , where n is an integer.…”

Combined Minivalley and Layer Control in Twisted Double Bilayer Graphene

“…Perfect minivalley polarization can be achieved when the Fermi level is tuned into the band gap at κ or κ 0 by tuning the displacement field. This is in contrast with TBG where only partial minivalley polarization can be reached [24]. Contrary to κ and κ 0 states, carriers stemming from the γ points occupy all layers [ Fig.…”