Bottom arm gate Top arm gate
6.4 Tunneling and Counterflow with Zero Parallel FieldField
6.4.4 Corbino Counterflow
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Figure 6.8: (a) Circuit for Corbino counterflow measurement, with floated shunt.
Ohmic contact 2 is along the outer edge of the annulus while ohmic contacts 5 and 6 are along the inner edge. (b) Corbino counterflow measurementI1(V) at d/`= 1.49, T = 25 mK, and θ = 0. The I −V trace for tunneling Itunneling(V) using the same currents leads (but no interlayer shunt) is also shown.
layers seems to imply that counterflow currents are once again propagating through the sample from the current leads to the shunt. But this time no edge channel connects the current leads with the shunt resistance. What then accounts for the enhanced current I1 at large bias? Due to the charge gap, one would expect that electrical currents through the bulk between the current leads and the shunt should be highly suppressed.
Instead, we assert that counterflow currents are propagating through the bulk in the form of excitons rather than charged currents flowing independently in the two layers. The flow of neutral excitons is unaffected by the large perpendicular magnetic field and thus counterflow transport should have a large bulk conductivity σCFxx . In fact, in the limit of zero current the excitons should ideally exhibit superfluidity and have infinite conductance.
Although the data in figure 6.8b suggest that the presence of the shunt can dra- matically change the I −V curve, it does not tell us the whole story of what is occurring within the sample during counterflow. For example, we cannot yet rule out the possibility that some unusual tunneling process allowed by the shunt is taking place. Furthermore, it is unclear if the charge gap is not disrupted by the applied in- terlayer bias. Indeed, we will show later on that parallel Corbino conductanceσxx|| can rise and become nonnegligible at a sufficiently large DC bias. Thus, it is conceivable that charged excitations might still be flowing during the counterflow measurement and explain our results instead.
To support the case of neutral exciton transport, we use a modification of the Corbino counterflow circuit. This modified circuit is shown in figure 6.9a. Here, we still drive current into the top layer at contact 5 and measure the current I1 flowing from the bottom layer via contact 6. However, we now shunt the two layers together at the opposite edge using an exterior 50 kΩ shunt resistor connected to the top layer at contact 2 and to the bottom layer at contact 1. This exterior shunt resistor is located outside of the dilution refrigerator and kept at room temperature. By
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measuring the voltage drop across the exterior shunt resistor, we can learn the actual current going through the shunt. Also, we connect one end of the exterior shunt resistor to the input of a current preamp, providing a low impedance (2 kΩ) path to ground. The current preamp will report the current I2 that is flowing through this alternative path to ground. If the enhanced counterflow currents are due to charged excitations in its bulk, then one would expect this additional current preamp will short-out the original preamp recording I1. That is, nearly all of the current flowing through the shunt would leak to ground at the second current preamp, and very little should return to the sample to complete the counterflow path, resulting in I1 ≈0.
In figure 6.9b, we show the results from this unusual counterflow circuit while d/` = 1.49, T = 25 mK, and tilt angle θ = 0. We plot the three recorded currents I1, I2, and IS along with the tunneling current that is observed while no shunt is present. At low applied bias, the counterflow current I1 is identical to IT unneling and bothIS andI1are zero. Once more, this is consistent with strong interlayer tunneling preventing any current from reaching the shunt. At large bias, we see thatI1 diverges from the tunneling I−V. This is coincident with the shunt current IS beginning to grow in magnitude. Thus, counterflow currents are propagating all the way through the bulk of the νT = 1 system in order to deliver the energy that is dissipated across the shunt resistance. Tunneling alone can not explain the large I1.
We also notice that the current I2 is much smaller than any of the other currents.
This result is quite remarkable; it implies that a relatively large amount of current is flowing through the shunt yet most of it prefers to return to the sample to be detected the I1 preamp. Even in the absence of a completely incompressible QH state, the return path through the sample should have a much larger resistance than the input impedance of the current preamplifier. Another unusual consequence of I2 = 0 is that when a positive voltage is applied to contact 5, any current flowing through the shunt resistance and past the grounding point provided by the current preamp would require that contact 1 be at a negative voltage. We observe this behavior even when the second current preamp is replaced by a simple physical connection to ground.
The small size of the current I2 leaking to ground from the shunt demonstrates
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Figure 6.9: (a) Circuit for Corbino counterflow measurement with exterior shunt resistor. (b) Corbino counterflow measurement atd/`= 1.49, T = 25 mK, andθ = 0.
Current leads (I1) are on the inner edge and an exterior shunt resistor (IS) is placed between the layers using contacts on the outer edge. One end of the exterior shunt resistor is grounded using a current preamp (I2). The I −V trace for tunneling Itunneling(V) using the same currents leads (but no interlayer shunt) is also shown.
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that parallel currents are still suppressed within theνT = 1 system during the Corbino counterflow measurement. In order to allow I2 6= 0, net charge would have to flow from one edge of the annulus to another. That would require parallel currents to transport the charge across the bulk. However, only counterflow currents are allowed in the bulk of theνT = 1 state. This is an important point to emphasize, because one might suggest that during the counterflow measurement there are certain regions in the bulk where more current is flowing in the top layer than in the bottom layer and that there are other regions where the reverse is true. In this scenario, one would only require that thetotal current flowing through the top layer be equal in magnitude to the total current flowing through the bottom layer. Such a hypothesis permits there to be charged excitations in the bulk of the sample that are localized in one layer or another. However, such charged excitations requires the presence of bulk parallel currents. As we have shown, those parallel currents are still suppressed during the counterflow measurement. Everywhere within the bulk the current in the top layer must be equal in magnitude and opposite in direction as the current in the bottom layer. Therefore, figure 6.9b demonstrates that counterflow currents can carry energy through the bulk of the νT = 1 annulus without a net transfer of charge. These two characteristics are key properties of exciton flow.