Activation energies and dissipation in biased quantum Hall

bilayer systems at .

B. Roostaei [1] , H. A. Fertig [2,3], K. J. Mullen [1] , S. Simon [4]

[1] Department of Physics, University of Oklahoma, Norman, OK

[2] Department of Physics, Indiana University, Bloomington, IN

[3] Technion, Haifa,Israel

[4] Lucent Tech., Murray Hill, NJ

1T

Supported by : NSF and the Center for Semiconductor Physics in Nanostructures (NSF-MRSEC)

OSCER : OU Supercomputer Center .

APS March Meeting 2007

Outline :

Merons as Pseudospin excitations of double layer quantum Hall systems .

Meron flavors.

Experimental results of transport in separately contacted bilayers .

Disorder and effect of merons on transport .

Numerical HF results of activation energies of merons

Model of meron-edge interaction ( ongoing work) .

Anisotropic Heisenberg magnet in long wavelength approximation :

deEmrdrmrdmrdH zxSASE ,1

422

2

2

Double layer electron gas in strong magnetic field :

Pseudospin formalism :

U

L

ULS

ULA

AlGaAs GaAsEnergy

d

Typical separation between electrons

Two electron gases form a quantum coherent liquid when :

eB

~

Quantum Coherence

1 RLT

~d

Pseudospin-z Pseudospin Excitations

Uniform State

1T

Charged Excitations

Topological Excitations :

Bimerons : Meron-Meron Pairs

They carry electric charge

Their projection in the plane is a vortex-antivortex pair.

e

1T

U

L

ULS

ULA

LUzS

Meron Flavors

Charge :

qmnv

2/e

2/1zS

vorticity :

0.4

0.2

0

0.2

0.4

0.4

0.2

0

0.2

0.4

00.050.1

0.150.2

LUzS

UL

1

In real experiment disorder/Temperature likely to unbind merons.

Each meron carries half electronic charge and an electric dipole moment.

Vorticity Electric Dipole moment

Charge

+1 +1/2 -e/2

-1 +1/2 +e/2

+1 -1/2 +e/2

-1 -1/2 -e/2

L

U

Image from Senthil et al., Science 2004.

Cartoon Picture of a Meron

Transport Experiments : Drag and Drive V

V

R. Wiersma, et. Al. PRL 93,266805(2004)

Drag: symmetric in bias

Drive: antisymmetric in bias

• Measured activation energies behave differently with respect to bias for drag and drive layer !

•This may be due to dissipation caused by merons.

Activation energies

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

1020

3040

10203040

0.20

0.2

0.20

0.2

1020

3040

10203040

0.0010

0.001

0.0010

0.001Checkerboard Bias

Pseudospin-z

Calculation of Activation barrier using meron lattice

We can model the activation barrier using our lattice of merons in the Hartree-Fock approximation :

We apply a checkerboard bias potential to the lattice , in-phase and out of phase.

Analogy to spin in magnetic field :

bias zero bias rdcheckerboa)( EEV

The activation barrier is :

VEVE E 0)(

LUzS

L. Brey, H.A. Fertig, R. Cote, and A.H. MacDonald, PRB 54, 16888 (1996)

0 0.02 0.04 0.06 0.08 0.1L UT

0.2

0

0.2

0.4

EK

0EE phasein

0EE phaseout

.0,2.1,9.0/ SASd The energy is linear in interlayer bias.

Estimation of activation energies are higher than observation.

HF Approximation over-estimates the exchange energy.

The results are depends on the shape and width of the potential .

0 0.02 0.04 0.06 0.08 0.10

0.05

0.1

0.15

0.2

0.25

0,8.0/,2.1 SAST d T

UL

Narrow potential

W < (meron radius)

)(KE10

203040

10203040

0.0010

0.001

0.0010

0.001

W

W ~ (meron radius)

Next question : Why the behavior of activation energy for drag and drive layer is so different ?

Model of interaction of merons with the edge and its dynamics :

R. Wiersma, et. Al. PRL 93,266805(2004)

•Counterflow current drives merons to the edges.

•Merons can dissipate edge current in drag and drive layer depending on their charge and electric dipole moment. V A

A

V A

A

-e/2

+e/2

-e/2

-e/2

Vorticity Electric Dipole moment

Charge

+1 +1/2 -e/2

-1 +1/2 +e/2

+1 -1/2 +e/2

-1 -1/2 -e/2antisymmetric

symmetric

Ongoing work :

V

V

Summary

Drag and drive layer resistivities are observed to be activated.

The activation energies for drag and drive layer behave differently as overall bias changes.

Activated behavior may be caused by mobile topological excitations of the bilayer system.

These topological excitations have pseudospin nature( merons and antimerons) .

Behavior of activation energies can be understood by the fact that merons have electric dipole moment and charge.

A model of interaction of the merons with edge electrons may explain the activated behavior consistently.