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Register a new userQuantum Hall transport as a probe of capacitance profile at graphene edges
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Added by
Ivan Jesus Vera-Marun
Publication date
2011
fields
Physics
and research's language is
English
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The quantum Hall effect is a remarkable manifestation of quantized transport in a two-dimensional electron gas. Given its technological relevance, it is important to understand its development in realistic nanoscale devices. In this work we present how the appearance of different edge channels in a field-effect device is influenced by the inhomogeneous capacitance profile existing near the sample edges, a condition of particular relevance for graphene. We apply this practical idea to experiments on high quality graphene, demonstrating the potential of quantum Hall transport as a spatially resolved probe of density profiles near the edge of this two-dimensional electron gas.
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The unique capabilities of capacitance measurements in bilayer graphene enable probing of layer-specific properties that are normally out of reach in transport measurements. Furthermore, capacitance measurements in the top-gate and penetration field geometries are sensitive to different physical quantities: the penetration field capacitance probes the two layers equally, whereas the top gate capacitance preferentially samples the near layer, resulting in the near-layer capacitance enhancement effect observed in recent top-gate capacitance measurements. We present a detailed theoretical description of this effect and show that capacitance can be used to determine the equilibrium layer polarization, a potentially useful tool in the study of broken symmetry states in graphene.
We demonstrate experimentally that graphene quantum capacitance $C_{mathrm{q}}$ can have a strong impact on transport spectroscopy through the interplay with nearby charge reservoirs. The effect is elucidated in a field-effect-gated epitaxial graphene device, in which interface states serve as charge reservoirs. The Fermi-level dependence of $C_{mathrm{q}}$ is manifested as an unusual parabolic gate voltage ($V_{mathrm{g}}$) dependence of the carrier density, centered on the Dirac point. Consequently, in high magnetic fields $B$, the spectroscopy of longitudinal resistance ($R_{xx}$) vs. $V_{mathrm{g}}$ represents the structure of the unequally spaced relativistic graphene Landau levels (LLs). $R_{xx}$ mapping vs. $V_{mathrm{g}}$ and $B$ thus reveals the vital role of the zero-energy LL on the development of the anomalously wide $ u=2$ quantum Hall state.
The structure of edge modes at the boundary of quantum Hall (QH) phases forms the basis for understanding low energy transport properties. In particular, the presence of ``upstream modes, moving against the direction of charge current flow, is critical for the emergence of renormalized modes with exotic quantum statistics. Detection of excess noise at the edge is a smoking gun for the presence of upstream modes. Here we report on noise measurements at the edges of fractional QH (FQH) phases realized in dual graphite-gated bilayer graphene devices. A noiseless dc current is injected at one of the edge contacts, and the noise generated at contacts at $L= 4,mu$m or $10,mu$m away along the upstream direction is studied. For integer and particle-like FQH states, no detectable noise is measured. By contrast, for ``hole-conjugate FQH states, we detect a strong noise proportional to the injected current, unambiguously proving the existence of upstream modes. The noise magnitude remaining independent of length together with a remarkable agreement with our theoretical analysis demonstrates the ballistic nature of upstream energy transport, quite distinct from the diffusive propagation reported earlier in GaAs-based systems. Our investigation opens the door to the study of upstream transport in more complex geometries and in edges of non-Abelian phases in graphene.
We study the effect of backward scatterings in the tunneling at a point contact between the edges of a second level hierarchical fractional quantum Hall states. A universal scaling dimension of the tunneling conductance is obtained only when both of the edge channels propagate in the same direction. It is shown that the quasiparticle tunneling picture and the electron tunneling picture give different scaling behaviors of the conductances, which indicates the existence of a crossover between the two pictures. When the direction of two edge-channels are opposite, e.g. in the case of MacDonalds edge construction for the $ u=2/3$ state, the phase diagram is divided into two domains giving different temperature dependence of the conductance.
The quantum localization in the quantum Hall regime is revisited using Graphene monolayers with accurate measurements of the longitudinal resistivity as a function of temperature and current. We experimentally show for the first time a cross-over from Efros-Shklovskii Variable Range Hopping (VRH) conduction regime with Coulomb interactions to a Mott VRH regime without interaction. This occurs at Hall plateau transitions for localization lengths larger than the interaction screening length set by the nearby gate. Measurements of the scaling exponents of the conductance peak widths with both temperature and current give the first validation of the Polyakov-Shklovskii scenario that VRH alone is sufficient to describe conductance in the Quantum Hall regime and that the usual assumption of a metallic conduction regime on conductance peaks is unnecessary.
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