Non-equilibrium Transport in Density Modulated Phases of the Second Landau Level

Abstract

We investigate non-equilibrium transport in the reentrant integer quantum Hall phases of the second Landau level. At high currents, we observe a transition from the reentrant integer quantum Hall phases to isotropic conduction. Surprisingly, this transition is markedly different for the hole- and electron sides of each spin-branch of the second Landau level. While the hole bubble phases exhibit a sharp transition to an isotropic compressible phase, the transition for the electron side occurs gradually via an intermediate phase. This behavior might be understood in terms of a current-driven two-dimensional melting transition, either taking place as a first order phase transition or as two continuous transitions involving an intermediate phase. The breaking of the particle-hole symmetry might have consequences for the physics at $\nu$ = 5/2 and other fractional quantum Hall states in the second Landau level.

Results shown in the following chapter have been partially published in the article [1]: Nonequilibrium transport in density modulated phases of the second Landau level.

Appendix

1.1 Dependence on Magnetic Field Direction

Changing the magnetic field direction does not change the qualitative behavior of the RIQH phases (see Fig. 15.9). However, details of the transition to the isotropic background may change.

Fig. 15.9

Differential Hall resistance measured in two different magnetic field directions. (Sample D110726B-3D)

1.2 Hysteresis of Current Sweeps

Figure 15.10 demonstrates that no strong hysteresis is observed for the transition from RIQH phases to the isotropic compressible phase. Here, three consecutive sweeps of the DC current ($I_\mathrm {DC}$ was changed from –57.5 nA $\rightarrow$ 57.5 nA $\rightarrow$ –57.5 nA $\rightarrow$ 57.5 nA) are shown for the RIQH states R2B, R3B and R4B.

Fig. 15.10

Differential Hall resistance versus the DC current for RIQH states R2B, R3B and R4B. For each magnetic field, three consecutive sweeps of the current are shown ($I_\mathrm {DC}$: –57.5 nA $\rightarrow$ 57.5 nA $\rightarrow$ –57.5 nA $\rightarrow$ 57.5 nA). All curves lie nearly perfectly on top of each other. (Sample D110726B-3D)

1.3 Negative Differential Resistance from DC Measurement

To exclude a measurement problem owing for example to unexpected frequency dependencies in an AC measurement, the longitudinal voltage drop $V_{xx}$ has been measured in a pure DC measurement as a function of the magnetic field and the DC current. From this, the differential longitudinal resistance has been obtained by numerically deriving $V_{xx}$ with respect to the current. The result is shown in Fig. 15.11. Apart from the increased noise level, this measurement perfectly agrees with the AC measurement of Fig. 15.1, excluding a problem with the AC measurement technique employed by us. Also here, pronounced regions of negative differential resistance are found (turquoise areas in Fig. 15.11). It should be noted that the ordinary resistance always remains positive.

Fig. 15.11

Differential longitudinal resistance $\partial V_{xx,\mathrm {DC}}/\partial I_\mathrm {DC}$ versus the magnetic field and the DC current. $\partial V_{xx,\mathrm {DC}}/\partial I_\mathrm {DC}$ has been obtained by numerically deriving $V_{xx,\mathrm {DC}}$ with respect to the applied DC current. The measurement agrees with Fig. 15.1, excluding a measurement problem as reason for the regions of negative differential resistance. (Sample D120427C-1C)

1.4 Bias Dependence of the Longitudinal Resistance

The bias dependence of the longitudinal resistance is shown in more detail in Fig. 15.12. At zero DC bias, $R_{xx}$ shows a minimum at the B-field corresponding to the center of the RIQH phase, which is neighbored by two resistance maxima. When $I_\mathrm {DC}$ is increased, the minimum in $R_{xx}$ is lifted and the magnetic field spacing between the side-peaks begins to shrink. At large biases, the side-peaks join to a single peak in $R_{xx}$, which then shrinks with subsequent increase of $I_\mathrm {DC}$. This behavior is qualitatively similar to what is obtained when the temperature is increased [18, 52]. When the temperature is increased, the side-peaks move together until only a single peak is observed. The resistance peak shrinks as the temperature is further increased. This behavior is in sharp contrast to the activated behavior of FQH states.

Fig. 15.12

DC current dependence of the RIQH minima in $R_{xx}$. At zero DC bias, $R_{xx}$ shows a minimum at the B-field corresponding to the center of the RIQH phase, which is neighbored by two resistance maxima. When $I_\mathrm {DC}$ is increased, the minimum in $R_{xx}$ is lifted and the magnetic field spacing between the side-peaks begins to shrink. At large biases, the side-peaks join to a single peak in $R_{xx}$, which then shrinks with subsequent increase of $I_\mathrm {DC}$. (Sample D120427C-1C)