1. 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. APS March Meeting 2008

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

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

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

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

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

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

8. Effect of Disorder  Dopants form a smooth disorder potential inducing puddles of charge.  This disorder excites meron-meron pairs and unbinds them in the system.  Merons and antimerons can diffuse in the system independently.  There 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

9. Chern-Simon Dynamics of Merons  Any current distribution in a bilayer can be divided into a parallel (coflow) and counterflow.  The parallel flow (CS boson flow) will interact with the attached CS flux of merons.  Merons are charged  They carry CS flux.  The 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) :

10. Drag and Drive Activation Energies  Direct consequence: For Drag experiments the force on merons with only one sign of dipole moment is nonzero !  Can show this results in voltage drop in only drive layer. Antisymmetric behavior of activation energy.  Merons with opposite vorticity and dipole moment attract each other.  Secondary 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 !

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

13. 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=1.0l B.

14. 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. Conclusion