APS March Meeting 2008 Activation energies and dissipation

APS March Meeting 2008 Activation energies and dissipation in biased quantum Hall bilayer systems at . B. Roostaei [1, 2] , H. A. Fertig [3, 4], K. J. Mullen [2] , S. Simon [5] [1] Department of Physics, Case Western University, Cleveland, OH [2] Department of Physics, University of Oklahoma, Norman, OK [3] Department of Physics, Indiana University, Bloomington, IN [4] Technion, Haifa, Israel [5] Lucent Tech. , Murray Hill, NJ Supported by : NSF and the Center for Semiconductor Physics in Nanostructures (NSF-MRSEC) OSCER : OU Supercomputer Center.

Double layer electron gas in strong magnetic field : Quantum Coherence Typical separation between electrons Two electron gases form a quantum coherent liquid when : Pseudospin formalism : Analogy with easy-plane ferromagnet Energy Al. Ga. As

Exciton Superfluidity At total filling factor one the electrons in one layer can pair with holes in another layer. electron hole ØThe coherent state of the bilayer can be interpreted as the condensed state of the exciton gas. ØA counterflow current can couple to this excitonic superfluid. M. Kellogg, J. P. Eisenstein, L. N. Pfeifer, and K. W. West, Phys. Rev. Lett. 93, 036801 (2004)

Pseudospin Excitations Uniform State Charged Excitations n. T =1 Topological Excitations : Bimerons : Meron-Meron Pairs They carry electric charge Their projection in the plane is a vortex-antivortex pair. Pseudospin-z

Topological Structure: Individual Meron ØBimeron is composed of two bound merons. ØEach meron has charge ±e/2, electric dipole moment and vorticity. ØAt large separations exchange energy is low enough to let the meron binding decrease.

Meron Flavors In real experiment disorder/Temperature likely to unbind merons. Charge : Each meron carries electrostatic charge and an electric dipole moment. For equal densities in each layer Vorticity +1 -1 Electric Dipole moment Charge +1/2 -1/2 -e/2 +e/2 -e/2 U L vorticity :

Puzzle in Excitonic Superfluid : Drag and Drive Ø Measured activation energies behave differently with respect to bias for drag and drive layer ! Drag activation: symmetric in bias Drive activation: antisymmetric in bias The Hall resistance is still quantized. R. Wiersma, et. Al, PRL 93, 266805(2004) R. Wiersma, et. Al. PRL 93, 266805(2004)

Effect of Disorder Ø Dopants form a smooth disorder potential inducing puddles of charge. Ø This disorder excites meron-meron pairs and unbinds them in the system. Ø Merons and antimerons can diffuse in the system independently. + + ØThere is a barrier for merons in hopping over an incompressible region from one puddle to the other. H. A. Fertig, G. Murthy, PRL 95 (2005) + + + Incompressible barrier + +

Chern-Simon Dynamics of Merons q Merons are charged They carry CS flux. q Any current distribution in a bilayer can be divided into a parallel (coflow) and counterflow. ØThe parallel flow (CS boson flow) will interact with the attached CS flux of merons. ØThe counterflow ( exciton superfluid flow) will interact with merons via magnus force. The total force on the meron from an arbitrary current distribution ( Roostaei, Fertig, Mullen, Simon, unpublished) :

Drag and Drive Activation Energies ØDirect consequence: For Drag experiments the force on merons with only one sign of dipole moment is nonzero ! ØCan show this results in voltage drop in only drive layer. Antisymmetric behavior of activation energy. ØMerons with opposite vorticity and dipole moment attract each other. ØSecondary merons will be dragged by driven merons inducing a much smaller voltage drop in the drag layer. Since the barriers are much smaller than meron size, the Drag activation energy would be maximum of the two. Symmetric !

ØWe model this barrier by adding a self-consistent potential on meron location and off the meron location. ØCalculate the difference in meron energy. ØWe use our lattice of merons to perform this calculation. Off Barrier On Barrier

Hopping energy of a meron for barrier height of V=0. 0061 e 2/l. B at different layer separations. Hopping energy of a meron for barrier height of V=0. 0057 e 2/l. B at layer separation d=1. 0 l. B.

Conclusion • Free Charged topological excitations of bilayer quantum Hall system may be the source of dissipation in this excitonic superfluid. • Because of meron’s electric dipole moment two activation energies is observed in drag geometry. • Hartree-Fock approximation is able to capture this behavior qualitatively but is off in about a factor of two in energy. • Since experiments are performed close to phase boundary, Quantum fluctuations need to be taken into account for a more accurate estimate of energies.