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Register a new userEdge Channels of Broken-Symmetry Quantum Hall States in Graphene probed by Atomic Force Microscopy
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The quantum Hall (QH) effect, a topologically non-trivial quantum phase, expanded and brought into focus the concept of topological order in physics. The topologically protected quantum Hall edge states are of crucial importance to the QH effect but have been measured with limited success. The QH edge states in graphene take on an even richer role as graphene is distinguished by its four-fold degenerate zero energy Landau level (zLL), where the symmetry is broken by electron interactions on top of lattice-scale potentials but has eluded spatial measurements. In this report, we map the quantum Hall broken-symmetry edge states comprising the graphene zLL at integer filling factors of $ u=0,pm 1$ across the quantum Hall edge boundary using atomic force microscopy (AFM). Measurements of the chemical potential resolve the energies of the four-fold degenerate zLL as a function of magnetic field and show the interplay of the moire superlattice potential of the graphene/boron nitride system and spin/valley symmetry-breaking effects in large magnetic fields.
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The flat bands in bilayer graphene(BLG) are sensitive to electric fields Ebot directed between the layers, and magnify the electron-electron interaction effects, thus making BLG an attractive platform for new two-dimensional (2D) electron physics[1-5]. Theories[6-16] have suggested the possibility of a variety of interesting broken symmetry states, some characterized by spontaneous mass gaps, when the electron-density is at the carrier neutrality point (CNP). The theoretically proposed gaps[6,7,10] in bilayer graphene are analogous[17,18] to the masses generated by broken symmetries in particle physics and give rise to large momentum-space Berry curvatures[8,19] accompanied by spontaneous quantum Hall effects[7-9]. Though recent experiments[20-23] have provided convincing evidence of strong electronic correlations near the CNP in BLG, the presence of gaps is difficult to establish because of the lack of direct spectroscopic measurements. Here we present transport measurements in ultra-clean double-gated BLG, using source-drain bias as a spectroscopic tool to resolve a gap of ~2 meV at the CNP. The gap can be closed by an electric field Ebot sim13 mV/nm but increases monotonically with a magnetic field B, with an apparent particle-hole asymmetry above the gap, thus providing the first mapping of the ground states in BLG.
We realize p-p-p junctions in few-layer black phosphorus (BP) devices, and use magneto-transport measurements to study the equilibration and transmission of edge states at the interfaces of regions with different charge densities. We observe both full equilibration, where all edge channels equilibrate and are equally partitioned at the interfaces, and partial equilibration, where only equilibration only takes place among modes of the same spin polarization. Furthermore, the inner p-region with low-doping level in the junction can function as a filter for highly doped p-regions which demonstrates gate-tunable transmission of edge channels.
We present low temperature transport measurements on dual-gated suspended trilayer graphene in the quantum Hall (QH) regime. We observe QH plateaus at filling factors { u}=-8, -2, 2, 6, and 10, in agreement with the full-parameter tight binding calculations. In high magnetic fields, odd-integer plateaus are also resolved, indicating almost complete lifting of the 12-fold degeneracy of the lowest Landau levels (LL). Under an out-of-plane electric field E, we observe degeneracy breaking and transitions between QH plateaus. Interestingly, depending on its direction, E selectively breaks the LL degeneracies in the electron-doped or hole-doped regimes. Our results underscore the rich interaction-induced phenomena in trilayer graphene.
Understanding the mechanisms governing the optical activity of layered-stacked materials is crucial to the design of devices aimed at manipulating light at the nanoscale. Here, we show that both twisted and slid bilayer graphene are chiral systems that can deflect the polarization of linear polarized light. However, only twisted bilayer graphene supports circular dichroism. Our calculation scheme, which is based on the time-dependent Schrodinger equation, is particularly efficient for calculating the optical-conductivity tensor. Specifically, it allows us to show the chirality of hybridized states as the handedness-dependent bending of the trajectory of kicked Gaussian wave packets in bilayer lattices. We show that nonzero Hall conductivity is the result of the noncanceling manifestation of hybridized states in chiral lattices. We also demonstrate the continuous dependence of the conductivity tensor on the twist angle and the sliding vector.
Strong confinement of charges in few electron systems such as in atoms, molecules and quantum dots leads to a spectrum of discrete energy levels that are often shared by several degenerate quantum states. Since the electronic structure is key to understanding their chemical properties, methods that probe these energy levels in situ are important. We show how electrostatic force detection using atomic force microscopy reveals the electronic structure of individual and coupled self-assembled quantum dots. An electron addition spectrum in the Coulomb blockade regime, resulting from a change in cantilever resonance frequency and dissipation during tunneling events, shows one by one electron charging of a dot. The spectra show clear level degeneracies in isolated quantum dots, supported by the first observation of predicted temperature-dependent shifts of Coulomb blockade peaks. Further, by scanning the surface we observe that several quantum dots may reside on what topologically appears to be just one. These images of grouped weakly and strongly coupled dots allow us to estimate their relative coupling strengths.
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