Magnetic subband structure of electrons in hexagonal lattices

Claro, F.; Wannier, Gregory H.

doi:10.1103/physrevb.19.6068

Cited by 233 publications

(159 citation statements)

References 18 publications

Supporting

Mentioning

154

Contrasting

Order By: Relevance

“…We now turn to the magnetotransport properties of STA bilayer graphene. The energy spectrum of a 2D electron system subject to a spatially periodic potential, and a perpendicular magnetic field (B) has a fractal structure known as the Hofstadter butterfly, characterized by two topological integers: ν, representing the Hall conductivity in units of e 2 /h, and s, the index of subband filling (31)(32)(33)(34). Gaps in the energy spectrum are observed when the density per moiré unit cell and the magnetic flux per moiré unit cell (ϕ ≡ BA) satisfy the following Diophantine equation:…”

Section: Resultsmentioning

confidence: 99%

Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene

Kim

DaSilva

Huang

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

541

408

View full text Add to dashboard Cite

According to electronic structure theory, bilayer graphene is expected to have anomalous electronic properties when it has long-period moiré patterns produced by small misalignments between its individual layer honeycomb lattices. We have realized bilayer graphene moiré crystals with accurately controlled twist angles smaller than 1°and studied their properties using scanning probe microscopy and electron transport. We observe conductivity minima at charge neutrality, satellite gaps that appear at anomalous carrier densities for twist angles smaller than 1°, and tunneling densities-of-states that are strongly dependent on carrier density. These features are robust up to large transverse electric fields. In perpendicular magnetic fields, we observe the emergence of a Hofstadter butterfly in the energy spectrum, with fourfold degenerate Landau levels, and broken symmetry quantum Hall states at filling factors ±1, 2, 3. These observations demonstrate that at small twist angles, the electronic properties of bilayer graphene moiré crystals are strongly altered by electron-electron interactions.moiré crystal | graphene | twisted bilayer | moiré band | Hofstadter butterfly M oiré patterns form when nearly identical two-dimensional (2D) crystals are overlaid with a small relative twist angle (1-4). The electronic properties of moiré crystals depend sensitively on the ratio of the interlayer hybridization strength, which is independent of twist angle, to the band energy shifts produced by momentum space rotation (5-12). In bilayer graphene, this ratio is small when twist angles exceed about 2°(10, 13), allowing moiré crystal electronic structure to be easily understood using perturbation theory (5). At smaller twist angles, electronic properties become increasingly complex. Theory (14, 15) has predicted that extremely flat bands appear at a series of magic angles, the largest of which is close to 1°. Flat bands in 2D electron systems, for example the Landau level bands that appear in the presence of external magnetic fields, allow for physical properties that are dominated by electron-electron interactions, and have been friendly territory for the discovery of fundamentally new states of matter. Here we report transport and scanning probe microscopy (SPM) studies of bilayer graphene moiré crystals with carefully controlled small-twist angles (STA), below 1°. We find that conductivity minima emerge in transport at neutrality, and at anomalous satellite densities that correspond to ±8 additional electrons in the moiré crystal unit cell, and that the conductivity minimum at neutrality is not weakened by a transverse electric field applied between the layers. Our observations can be explained only by strong electronic correlations. MethodsOur STA bilayer graphene samples are fabricated by sequential graphene and hexagonal boron-nitride (hBN) flake pick-up steps using a hemispherical handle substrate (16) that allows an individual flake to be detached from a substrate while leaving flakes in its immediate proximity intact. To...

show abstract

Section: Resultsmentioning

confidence: 99%

Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene

Kim

DaSilva

Huang

et al. 2017

Proc. Natl. Acad. Sci. U.S.A.

541

408

View full text Add to dashboard Cite

show abstract

“…For example, if we consider a standard tight-binding model, the energy spectrum displays a complex multifractal structure when varying the magnetic flux per unit cell as illustrated by the famous Hofstadter butterfly [1,2,3]. However, this spectrum is strongly geometry-dependent since even for periodic tilings, some anomalies can appear leading to interesting quantum interference phenomena [4,5].…”

Section: Introductionmentioning

confidence: 99%

Quasiperiodic tilings in a magnetic field

Vidal

Mosseri

2004

Journal of Non-Crystalline Solids

View full text Add to dashboard Cite

We study the electronic properties of a two-dimensional quasiperiodic tiling, the isometric generalized Rauzy tiling, embedded in a magnetic field. Its energy spectrum is computed in a tight-binding approach by means of the recursion method. Then, we study the quantum dynamics of wave packets and discuss the influence of the magnetic field on the diffusion and spectral exponents. Finally, we consider a quasiperiodic superconducting wire network with the same geometry and we determine the critical temperature as a function of the magnetic field.

show abstract

“…To determine the locations of these incompressible states, we need to know the particle densities n which completely fill an energy number of bands of the spectrum of CF's at flux n * φ . Generalizing from the continuum where the density of states in each LL is proportional to the flux density, an analysis of the spectrum leads to the conclusion that, when filling all states up to any given gap in the Hofstadter spectrum, the relation between n and n * φ remains linear [21,22], n = ν * n * φ + δ, with an offset δ. The coefficients ν * and δ can be determined from the Hofstadter spectrum by locating two points within the same gap.…”

mentioning

confidence: 99%

Composite Fermion Theory for Bosonic Quantum Hall States on Lattices

Möller¹,

2009

View full text Add to dashboard Cite

We study the groundstates of cold atomic gases on rotating optical lattices, as described by the Bose-Hubbard model in a uniform effective magnetic field. Mapping the bosons to composite fermions leads to the prediction of quantum Hall fluids that have no counterpart in the continuum. We construct trial wavefunctions for these phases, and perform numerical tests of the predictions of the composite fermion model. Our results establish the existence of strongly correlated phases beyond those in the continuum limit, and provide evidence for a wider scope of the composite fermion approach beyond its application to the lowest Landau-level.Ultra-cold atomic gases have become a very active field of study of strongly correlated quantum systems. While dilute Bose gases are typically in a weakly interacting regime, they can be driven into regimes of strong correlations by various means. The application of an optical lattice potential leads to a suppression of the kinetic energy relative to the interaction energy, and has allowed the experimental exploration of the quantum phase transition between Mott insulator and superfluid [1]. Rapid rotation of the atomic gas also leads to a quenching of the kinetic energy, into degenerate Landau levels [2], and a regime of strong interactions [3]. At low filling factor ν (defined as the ratio of the number of particles to the number of vortices) this is predicted to lead to very interesting strongly correlated phases [4] which can be viewed as bosonic versions of fractional quantum Hall effect (FQHE) states [5]. In order to access the low filling factor regime in experiment, it may be favourable to exploit the strong interactions that are available in optical lattice systems [6,7] for which methods exist in which to simulate uniform rotation (or equivalently a uniform magnetic field) [8][9][10]. This raises the interesting question: what are the correlated phases of atomic gases that are subjected both to an optical lattice and to rapid rotation?In this Letter, we study the interplay between the FQHE of bosons and the strong correlation imposed by an optical lattice potential. At sufficiently low particle density, the effect of the lattice has been shown to have negligible impact on the nature of the continuum Laughlin state at ν = 1 2 [7,10]. We focus on the possibility that there exist strongly correlated phases which have no counterpart in the continuum, but that appear as a direct consequence of both the lattice potential and rotation. To do so, we adapt the composite fermion (CF) theory [11,12] which has been shown to accurately describe rotating atomic Bose gases in the continuum [13,14], and apply this theory to rotating bosons on a lattice. Within mean-field theory, the lattice leads to the intricate Hofstadter spectrum for the composite fermions [15]. We predict a series of incompressible phases of bosons on the optical lattice, characterized by special relations of the flux density n φ and particle density n, and we construct trial wavefunctions describing these phases. Fro...

show abstract

Magnetic subband structure of electrons in hexagonal lattices

Cited by 233 publications

References 18 publications

Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene

Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene

Quasiperiodic tilings in a magnetic field

Composite Fermion Theory for Bosonic Quantum Hall States on Lattices

Contact Info

Product

Resources

About