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Register a new userDensity of states of Dirac-Landau levels in a gapped graphene monolayer under strain gradient
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We study a gapped graphene monolayer in a combination of uniform magnetic field and strain-induced uniform pseudomagnetic field. The presence of two fields completely removes the valley degeneracy. The resulting density of states shows a complicated behaviour that can be tuned by adjusting the strength of the fields. We analyze how these features can be observed in the sublattice, valley and full density of states. The analytical expression for the valley DOS is derived.
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The wavefunction of massless Dirac fermions is a two-component spinor. In graphene, a one-atom-thick film showing two-dimensional Dirac-like electronic excitations, the two-component representation reflects the amplitude of the electron wavefunction on the A and B sublattices. This unique property provides unprecedented opportunities to image the two components of massless Dirac fermions spatially. Here we report atomic resolution imaging of the two-component Dirac-Landau levels in a gapped graphene monolayer by scanning tunnelling microscopy and spectroscopy. A gap of about 20 meV, driven by inversion symmetry breaking by the substrate potential, is observed in the graphene on both SiC and graphite substrates. Such a gap splits the n = 0 Landau level (LL) into two levels, 0+ and 0-. We demonstrate that the amplitude of the wavefunction of the 0- LL is mainly at the A sites and that of the 0+ LL is mainly at the B sites of graphene, characterizing the internal structure of the spinor of the n = 0 LL. This provides direct evidence of the two-component nature of massless Dirac fermions.
We investigate the electrostatic confinement of charge carriers in a gapped graphene quantum dot in the presence of a magnetic flux. The circular quantum dot is defined by an electrostatic gate potential delimited in an infinite graphene sheet which is then connected to a two terminal setup. Considering different regions composing our system, we explicitly determine the solutions of the energy spectrum in terms of Hankel functions. Using the scattering matrix together with the asymptotic behavior of the Hankel functions for large arguments, we calculate the density of states and show that it has an oscillatory behavior with the appearance of resonant peaks. It is found that the energy gap can controls the amplitude and width of these resonances and affect their location in the density of states profile.
We present the results of an experimental study of the interaction of quantized Landau level (LL) edge-states at the physical edge of graphene by using a graphene pn junction device with a ring-shaped geometry for the channel. The unique device geometry allows the interactions between edge-states to be probed at both electrostatic edges defined by pn junctions and at the graphene physical edge. Measurements show that while the lowest LL edge-state is decoupled from the other LLs along the electrostatic junction, all the edge-states strongly equilibrate at the graphene physical edge despite the relatively short distance that they travel along the edge in our device. These findings are fundamental for the engineering of future high-performance graphene field-effect transistors based upon electron optics.
As a canonical response to the applied magnetic field, the electronic states of a metal are fundamentally reorganized into Landau levels. In Dirac metals, Landau levels can be expected without magnetic fields, provided that an inhomogeneous strain is applied to spatially modulate electron hoppings in a similar way as the Aharonov-Bohm phase. We here predict that a twisted zigzag nanoribbon of graphene exhibits strain-induced pseudo Landau levels of unexplored but analytically solvable dispersions at low energies. The presence of such dispersive pseudo Landau levels results in a negative strain resistivity characterizing the $(1+1)$-dimensional chiral anomaly if partially filled and can greatly enhance the thermopower when fully filled.
We study RKKY interactions for magnetic impurities on graphene in situations where the electronic spectrum is in the form of Landau levels. Two such situations are considered: non-uniformly strained graphene, and graphene in a real magnetic field. RKKY interactions are enhanced by the lowest Landau level, which is shown to form electron states binding with the spin impurities and add a strong non-perturbative contribution to pairwise impurity spin interactions when their separation $R$ no more than the magnetic length. Beyond this interactions are found to fall off as $1/R^3$ due to perturbative effects of the negative energy Landau levels. Based on these results, we develop simple mean-field theories for both systems, taking into account the fact that typically the density of states in the lowest Landau level is much smaller than the density of spin impurities. For the strain field case, we find that the system is formally ferrimagnetic, but with very small net moment due to the relatively low density of impurities binding electrons. The transition temperature is nevertheless enhanced by them. For real fields, the system forms a canted antiferromagnet if the field is not so strong as to pin the impurity spins along the field. The possibility that the system in this latter case supports a Kosterlitz-Thouless transition is discussed.
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