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Register a new userLandau level splitting due to graphene superlattices
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The Landau level spectrum of graphene superlattices is studied using a tight-binding approach. We consider non-interacting particles moving on a hexagonal lattice with an additional one-dimensional superlattice made up of periodic square potential barriers, which are oriented along the zig-zag or along the arm-chair directions of graphene. In the presence of a perpendicular magnetic field, such systems can be described by a set of one-dimensional tight-binding equations, the Harper equations. The qualitative behavior of the energy spectrum with respect to the strength of the superlattice potential depends on the relation between the superlattice period and the magnetic length. When the potential barriers are oriented along the arm-chair direction of graphene, we find for strong magnetic fields that the zeroth Landau level of graphene splits into two well separated sublevels, if the width of the barriers is smaller than the magnetic length. In this situation, which persists even in the presence of disorder, a plateau with zero Hall conductivity can be observed around the Dirac point. This Landau level splitting is a true lattice effect that cannot be obtained from the generally used continuum Dirac-fermion model.
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We report the observation of the resonant excitation of edge photocurrents in bilayer graphene subjected to terahertz radiation and a magnetic field. The resonantly excited edge photocurrent is observed for both inter-band (at low carrier densities) and intra-band (at high densities) transitions between Landau levels (LL). While the intra-band LL transitions can be traced to the classical cyclotron resonance (CR) and produce strong resonant features, the inter-band-LL resonances have quantum nature and lead to the weaker features in the measured photocurrent spectra. The magnitude and polarization properties of the observed features agree with the semiclassical theory of the intra-band edge photogalvanic effect, including its Shubnikov-de-Haas oscillations at low temperatures.
The quantum Hall (QH) effect in two-dimensional (2D) electrons and holes in high quality graphene samples is studied in strong magnetic fields up to 45 T. QH plateaus at filling factors $ u=0,pm 1,pm 4$ are discovered at magnetic fields $B>$20 T, indicating the lifting of the four-fold degeneracy of the previously observed QH states at $ u=pm(|n|+1/2)$, where $n$ is the Landau level index. In particular, the presence of the $ u=0, pm 1$ QH plateaus indicates that the Landau level at the charge neutral Dirac point splits into four sublevels, lifting sublattice and spin degeneracy. The QH effect at $ u=pm 4$ is investigated in tilted magnetic field and can be attributed to lifting of the spin-degeneracy of the $n=1$ Landau level.
Interaction driven integer quantum Hall effects are anticipated in graphene bilayers because of the near-degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance signal will appear at some odd-integer filling factors, accompanied by collective modes which are nearly gapless and have approximate $k^{3/2}$ dispersion. We speculate on the possibility of unususal localization physics associated with these modes.
We have measured a strong increase of the low-temperature resistivity $rho_{xx}$ and a zero-value plateau in the Hall conductivity $sigma_{xy}$ at the charge neutrality point in graphene subjected to high magnetic fields up to 30 T. We explain our results by a simple model involving a field dependent splitting of the lowest Landau level of the order of a few Kelvin, as extracted from activated transport measurements. The model reproduces both the increase in $rho_{xx}$ and the anomalous $ u=0$ plateau in $sigma_{xy}$ in terms of coexisting electrons and holes in the same spin-split zero-energy Landau level.
Landau level gaps are important parameters for understanding electronic interactions and symmetry-broken processes in bilayer graphene (BLG). Here we present transport spectroscopy measurements of LL gaps in double-gated suspended BLG with high mobilities in the quantum Hall regime. By using bias as a spectroscopic tool, we measure the gap {Delta} for the quantum Hall (QH) state at filling factor { u}={pm}4 and -2. The single-particle gap for { u}=4 scales linearly with magnetic field B and is independent of the out-of-plane electric field E. For the symmetry-broken { u}=-2 state, the measured values of gap are 1.1 meV/T and 0.17 meV/T for singly-gated geometry and dual-gated geometry at E=0, respectively. The difference between the two values arises from the E-dependence of the gap, suggesting that the { u}=-2 state is layer polarized. Our studies provide the first measurements of the gaps of the broken symmetry QH states in BLG with well-controlled E, and establish a robust method that can be implemented for studying similar states in other layered materials.
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