Bottom arm gate Top arm gate
6.6 Corbino Counterflow with Weaker Interlayer CorrelationsCorrelations
6.6.1 Elevated Temperature
Thermal fluctuations destroy the correlated state atνT = 1, as evidenced by the dis- appearance of its Josephson-like tunneling with temperature [12]. Here, we consider how Corbino counterflow measurements evolve as temperature is increased. Through comparisons with parallel Corbino conductance data, we will show how exciton trans- port fades with temperature.
We first show a set of Corbino counterflow data in figure 6.16a. Here we plot the temperature dependence of differential conductance for Corbino counterflow at d/` = 1.49 and θ = 28◦. For this set of traces, the shunt between the two layers is a single, floating ohmic contact. At low temperature (for example, T = 25 mK), the two-terminal conductance is strongly dependent on bias, reflecting the nonohmic series resistance. At zero bias and 25 mK, the conductance obtains the minimum value
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of 2µS. If excitons were dissipationless, this suggests that each arm would contribute 125 kΩ of series resistance under these conditions. Independent measurements of series resistance will bolster this assumption. As a finite bias is applied, the resistance per arm first rapidly declines to 36 kΩ and then slowly increases again. A hint of the coherent tunneling peak can also be seen, manifested as a small bump in the conductance at zero interlayer bias.
As the temperature rises, the nonlinearity in conductance goes away and is absent above 100 mK. But at high bias (|V| > 100 µV), the Corbino counterflow conduc- tance monotonically declines with temperature. This is consistent with the thermal disruption of interlayer correlations required by exciton transport. Counterflow cur- rents then begin to be carried by charged excitations instead, which are deflected by the strong perpendicular magnetic field.
For example, consider the Corbino counterflow trace obtained at T = 274 mK. In figure 6.17, we plot the observed counterflow current along with the expected charge transport trace, derived using equation (6.3). The two traces are practically identical, indicating that at this high temperature exciton transport is nearly absent and the two layers act independently of each other.
In a second set of Corbino counterflow traces (figure 6.18), the shunt is an exterior shunt resistor with one end grounded by a current preamp. Consequently, counterflow current (as detected by the current preamp recording I1) falls to zero becauseσxx|| is becoming finite and is permitting the current preamp recordingI2 to essentially short out the other current preamp. For comparison, we show parallel Corbino conductance for multiple temperatures at d/`= 1.49 in figure 6.19. The rapid drop in counterflow current in figure 6.18 between T = 48 and 94 mK is coincident with a sharp rise in parallel Corbino conductance during that same temperature range.
To better illustrate how signatures of exciton transport disappear at elevated temperature, we calculate the difference between the observed Corbino counterflow current ICF(V) and the expected charge transport Icharge(V) for a given bias V. We will focus on the case where the shunt is left floated and effective interlayer separation d/` = 1.49. We limit ourselves to θ = 28◦ so that we can ignore tunneling. The
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Figure 6.16: Corbino counterflow (a) conductance and (b) DC current at d/`= 1.49 and θ = 28◦. As depicted in the inset of (a), the shunt resistance is provided by a single, floating ohmic contact.
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Figure 6.17: Solid black trace: Corbino counterflow I−V for d/` = 1.49, T = 274 mK, andθ= 28◦. The dotted blue trace is the expectedI−V for charged excitations, as determined from a parallel Corbino measurement under the same conditions using equation (6.3.
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Figure 6.18: Corbino counterflow (a) conductance and (b) DC current at d/`= 1.49 andθ = 28◦. Here, the shunt resistance is provided by an exterior 50 kΩ resistor that is grounded at one end by a current preamp.
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Figure 6.19: (a) Parallel Corbino conductance and (b) Parallel Corbino current versus applied DC bias at d/`= 1.49, θ = 28◦, and multiple temperatures.
Icharge. We plot the difference ∆I(V) ≡ ICF(V)−Icharge(V) versus V for various temperatures in figure 6.20. Note that ∆I is positive even at moderate temperature, when charge current is not fully suppressed. It becomes negative at T = 274 mK likely because the series resistance during the counterflow measurement is somewhat larger than in the parallel flow measurement from which Icharge(V) is calculated. In the counterflow measurement, an interlayer voltage is present due to the applied bias.
Because of the capacitive coupling between the two layers, this interlayer voltage will induce a transfer of charge density from one layer to another. The layer with reduced density will experience an increase in resistivity while the other layer will generally have a nearly unchanged resistance. The total resistance for current traveling through the bilayer system will ultimately increase. This effect is not present in the parallel flow measurement.
We close our discussion of finite temperature effects on exciton transport by com- menting on interlayer tunneling at θ = 28◦. In figure 6.21 we plot the tunneling conductance versus interlayer bias for T = 25 to 274 mK. Interestingly, the height of the zero bias tunneling peak declines with temperature at approximately the same rate as ∆I. It is difficult to interpret the meaning of this similarity because the pre- cise origin of the tunneling peak while at large B|| is not known. Nonetheless, the persistence of the νT = 1 tunneling peak suggests that stationary, long-range phase coherence is not completely destroyed by the sizableB||or thermal fluctuations. This might also be reflected in the gradual decline of ∆I with temperature.