Cloning of Dirac fermions in graphene superlattices

Abstract

Lateral superlattices have attracted major interest as this may allow one to modify spectra of two dimensional (2D) electron systems and, ultimately, create materials with tailored electronic properties 1-8 . Previously, it proved difficult to realize superlattices with sufficiently short periodicity and weak disorder, and most of the observed features could be explained in terms of commensurate cyclotron orbits 1-4 . Evidence for the formation of superlattice minibands (so called Hofstadter's butterfly 9 ) has been limited to the observation of new low-field oscillations 5 and an internal structure within Landau levels 6-8 . Here we report transport properties of graphene placed on a boron nitride substrate and accurately aligned along its crystallographic directions. The substrate's moiré potential 10-12 leads to profound changes in graphene's electronic spectrum. Second-generation Dirac points 13-22 appear as pronounced peaks in resistivity accompanied by reversal of the Hall effect. The latter indicates that the sign of the effective mass changes within graphene's conduction and valence bands. Quantizing magnetic fields lead to Zak-type cloning 23 of the third generation of Dirac points that are observed as numerous neutrality points in fields where a unit fraction of the flux quantum pierces the superlattice unit cell. Graphene superlattices open a venue to study the rich physics expected for incommensurable quantum systems 7-9,22-24 and illustrate the possibility to controllably modify electronic spectra of 2D atomic crystals by using their crystallographic alignment within van der Waals heterostuctures 25 .Since the first observation of Weiss oscillations 1,2 , 2D electronic systems subjected to a periodic potential have been studied in great detail [3][4][5][6][7][8] . The advent of graphene has rapidly sparked interest in its superlattices, too [13][14][15][16][17][18][19][20][21][22] . The principal novelty in this case is the Dirac-like spectrum and the fact that charge carriers are not buried deep under the surface, allowing a relatively strong superlattice potential on a true nanometer scale. One promising avenue for making nanoscale graphene superlattices is the use of a potential induced by another crystal. For example, graphene placed on top of graphite or hexagonal boron nitride (hBN) exhibits a moiré pattern [10][11][12]26 , and graphene's tunneling density of states becomes strongly modified 12,26 indicating the formation of superlattice minibands. The spectral reconstruction occurs near the edges of superlattice's Brillouin zone (SBZ) that are characterized by wavevector G =4/ D and energy E S =v F G/2 (D is the superlattice period and v F graphene's Fermi velocity) 12,22 .To observe moiré minibands in transport properties, graphene has to be doped so that the Fermi energy reaches the reconstructed part of the spectrum. This imposes severe constraints on the misalignment angle  of graphene relatively to hBN. Indeed, D is given by  and the 1.8% difference between the two lattice constants ...

Artificial honeycomb lattices for electrons, atoms and photons

“…Works in this area started in the late eighties and enabled the observation of Weiss oscillations [29], novel conductance resonances due to quantization of the electron orbits in the 2D pattern in a magnetic field [30], chaotic dynamics, and, more recently, led to studies of Hofstadter butterfly phenomena [31,32]. Recently, similar effects have been observed in natural graphene where the 2D periodic potential (with periodicity of the order of ∼ 10 nm) was induced by placing it on h-BN [33][34][35].…”

Two-Dimensional MoS2-Graphene-Based Multilayer van der Waals Heterostructures: Enhanced Charge Transfer and Optical Absorption, and Electric-Field Tunable Dirac Point and Band Gap

“…These heterogeneous stacks have unusual properties that are not present in individual layers and encompass a wide spectrum of physical and chemical phenomena exemplified by new van Hove singularities [4][5][6][7] , Fermi velocity renormalization 8,9 , unconventional quantum Hall effects 10 , Hofstadter's butterfly pattern [11][12][13][14] , and others. Peculiar electronic [15][16][17] and optoelectronic properties 18,19 have been revealed in diverse 2D heterostructures based on layered materials such as GR, semiconducting transition metal dichalcogenides (TMDs) and insulating hexagonal boron nitride (h-BN).…”

Epitaxially Stabilized Oxide Composed of Twisted Triangular-Lattice Layers

“…The above result indicates that the new compound is composed of the triangular-lattice Rh In general, two triangular lattices coupled at a twist angle form a quasiperiodic structure that has no unit cell. [18][19][20][21] As evidenced by the in-plane x-ray and electron diffractions (Figures 2e and 3j), however, the new layered compound shows periodically modulated hexagonal patterns with the in-plane cell parameter of 8.05(±0.05) Å. The selected-area electron diffraction detects the single pattern from only one type of the two crystallographic domains, while their both patterns are observed in the entire-area in-plane XRD.…”

“…Actually, in the research field of atomic layer materials such as graphene or transition metal dichalcogenides, the twist angle has been recognized as a new important parameter for tuning electrical and optical properties of stacked layers. [18][19][20][21] In the following, we present a new compound with a twisted stack of oxide layers stabilized by epitaxy technique. For this purpose, we adopt a simple Bi-Rh-O system, because Bi with a relatively large ionic radius is expected to form a large triangular-lattice layer mismatched to the RhO 2 layer.…”