Quasiparticle Tunneling in the Fractional Quantum Hall State

Marc A. Kastner, Massachusetts Institute of Technology, DMR 1104394

In high magnetic fields a two-dimensional electron gas forms a quantum Hall state that is an insulator in its interior, but is metallic at its edges. The =5/2 state may be useful for quantum computing if its statistics are non-abelian. Theory predicts tunneling of particles from one edge to another in a quantum point contact QPC (sketch) that gets weaker as more current is passed through the edge states, and it relates the dependence of tunneling on temperature and current to two parameters, e* and g. For tunneling through the long QPC (applying negative voltage to gates labeled G1-G4 all others grounded) we find the error contours shown in the lower left and for a short QPC (voltage applied to G1, G2 and A2 all others grounded) the contours in the lower right. Both give e* close to ¼ as predicted by theory, but the long QPC favors one of the abelian states, whereas the short favors a non-abelian state. If the state depends on the size of the QPC, this could have important implications for applications to quantum computing.

Sketch of edge states and tunneling

(dashed line)Micrograph of

gate electrodes

Error contours for long (left) and short (right) QPCs. The contours 1, 1.1 and 1.2 are labeled by

the error levels relative to the noise. The black circle is the best fit, the open circles are theoretical predictions for states that are non-abelian, and the

red circle is for one that is abelian

0.8

0.6

0.4

0.2

0.0g

0.80.60.40.2

e*

(1/4, 1/2)

(1/4, 1/4)

(1/4, 3/8)

1.2 1.1

1

0.8

0.6

0.4

0.2

0.0

g

0.80.60.40.2

e*

(1/4, 1/2)

(1/4, 1/4)

(1/4, 3/8)

1.2

1.1 1

Quasiparticle Tunneling in the Fractional Quantum Hall State

Marc A. Kastner, Massachusetts Institute of Technology, DMR 1104394

Marc Kastner speaks frequently to MIT alumni about the importance of basic research to the US economy and national security. Often these are selected alumni, who are founders of companies and investors, and are highly influential.

Kastner’s former students are employed in large and small companies, research universities and teaching colleges. They have learned an appreciation of applied as well as fundamental research.