Session C2: Invited Session: Coulomb Drag and Exciton Condensation in Semiconductor and Graphene Double Layers

Exciton Transport and Perfect Coulomb Drag

Exciton condensation is realized in closely-spaced bilayer quantum Hall systems at $\nu_T =1$ when the total density in the two 2D electron layers matches the Landau level degeneracy. In this state, electrons in one layer become tightly bound to holes in the other layer, forming a condensate similar to the Cooper pairs in a superconductor. Being charge neutral, these excitons ought to be free to move throughout the bulk of the quantum Hall fluid. One therefore expects that electron current driven in one layer would spontaneously generate a ``hole'' current in the other layer, even in the otherwise insulating bulk of the 2D system. We demonstrate precisely this effect, using a Corbino geometry to defeat edge state transport. Our sample contains two essentially identical two-dimensional electron systems (2DES) in GaAs quantum wells separated by a thin AlGaAs barrier. It is patterned into an annulus with arms protruding from each rim that provide contact to each 2DES separately. A current drag geometry is realized by applying a drive voltage between the outer and inner rim on one 2DES layer while the two rims on the opposite layer are connected together in a closed loop. There is no direct electrical connection between the two layers. At $\nu_T =1$ the bulk of the Corbino annulus becomes insulating owing to the quantum Hall gap and net charge transport across the bulk is suppressed. Nevertheless, we find that in the drag geometry appreciable currents do flow in each layer. These currents are almost exactly equal magnitude but, crucially, flow in opposite directions. This phenomenon reflects exciton transport within the $\nu_T=1$ condensate, rather than its quasiparticle excitations. We find that quasiparticle transport competes with exciton transport at elevated temperatures, drive levels, and layer separations. This work represents a collaboration with A.D.K. Finck, J.P. Eisenstein, L.N. Pfeiffer and K.W. West.   

Coulomb Drag and Magnetotransport in Graphene Double Layers

Graphene double layers, a set of two closely spaced graphene monolayers seperated by an ultra-thin dielectric, represent an interesting electron system to explore correlated electron states. We discuss the fabrication of such samples using a layer-by-layer transfer approach, the electron transport in individual layers at zero and in a high magnetic field, and Coulomb drag measurements. Coulomb drag, probed by flowing a drive current in one layer, and measuring the voltage drop in the opposite layer provides a direct measurement of the electron-electron scattering between the two layers, and can be used to probe the electron system ground state. Coulomb drag in graphene, measured as a function of both layer densities and temperature reveals two distinct regimes: (i) diffusive drag at elevated temperatures, above 50 K, and (ii) mesoscopic fluctuations-dominated drag at low temperatures [1, 2]. A second topic discussed here is a technique that allows a direct measurement of the Fermi energy in an electron system with an accuracy independent of the sample size, using a graphene double layer heterostructure. The underlying principle of the technique is that an interlayer bias applied to bring the top layer to the charge neutrality point is equal to the Fermi energy of the bottom layer, which in effect renders the top graphene layer a resistively detected Kelvin probe [3]. We illustrate this method by measuring the Fermi velocity, Landau level spacing, and Landau level broadening in monolayer graphene. Work done in collaboration with S. Kim, I. Jo, J. Nah, D. Dillen, K. Lee, B. Fallahazad, Z. Yao, and S. K. Banerjee. \\[4pt] [1] S. Kim \textit{et al.}, \textit{Phys. Rev. B }\textbf{83}, 161401 (2011).\\[0pt] [2] S. Kim, E. Tutuc, \textit{Sol. State Comm}. \textbf{152}, 1283 (2012).\\[0pt] [3] S. Kim \textit{et al.},\textit{ Phys. Rev. Lett. }\textbf{108}, 116404 (2012).   

Interaction phenomena and Coulomb drag in graphene-based heterostructures

Double-layer graphene heterostructures with boron nitride as a thin insulating barrier allow us to achieve a strongly interacting regime such that the two Dirac liquids effectively nest within the same plane but can be tuned and measured independently. The experiment reveals many unexpected features that are related to strong excitonic effects and mutual polarization of the graphene layers, which will be discussed in this talk.   

Interlayer Coherence and Transport in Quantum Hall Bilayers and Dirac Materials

I will discuss two phenomenological descriptions of low-current transport in bilayer quantum Hall system with exciton condensates [1], one based on a Landauer-Buttiker description of Andreev scattering at contacts to coherent bilayers, and one based on a simplified single-parameter p-ology description of the weak to strong interlayer coupling crossover. The Andreev scattering phenomenology is intended to apply when the condensate is well developed and is used to predict current-voltage relationships for a variety of two-contact geometries. I will also apply this formalism to circumstances in which the tunnel current exceeds its critical value and the condensate is time-dependent. The p-ology approach will establish the universal development of large longitudinal drags, even in homogeneous coherent samples, as the condensate weakens and the Hall drag is reduced. Further, I will discuss the interaction-enhanced coherence in layered Dirac systems: two graphene or topological insulator surface-state layers, and the estimates of its strength based on the imaginary-axis gap equations in the random phase approximation [2]. Using a self-consistent treatment of dynamic screening of Coulomb interactions in the gapped phase, I will show that the excitonic gap can reach values on the order of the Fermi energy at strong interactions. The gap will turn out to be a discontinuous function of the interlayer separation and effective fine structure constant, revealing a first-order phase transition between effectively incoherent and interlayer coherent phases. \\[4pt] [1] D. A. Pesin and A. H. MacDonald, Phys. Rev. B 84, 075308 (2011)\\[0pt] [2] Inti Sodemann, D. A. Pesin, and A. H. MacDonald, Phys. Rev. B 85, 195136 (2012)