Magnetic-field-induced instabilities in localized two-dimensional electron systems

We report density dependent instabilities in the localized regime of mesoscopic two-dimensional electron systems (2DESs) with intermediate strength of background disorder. They are manifested by strong resistance oscillations induced by high perpendicular magnetic fields $B_{\perp }$. While the amplitude of the oscillations is strongly enhanced with increasing $B_{\perp }$, their position in density remains unaffected. The observation is accompanied by an unusual behavior of the temperature dependence of resistance and activation energies. We suggest the interplay between a strongly interacting electron phase and the background disorder as a possible explanation.

Figure 1

(Color online) (a) Schematic of two localized states in the minima of the self-consistent electrostatic potential at $B_{\perp }=0$ (red/gray line) and at a finite field with additional magnetic confinement (blue/dark gray line). The corresponding wave functions and their overlap are also indicated. (b) Microscope picture of a typical device with Hall bar mesa and top gate. Current and voltage probes for four-probe measurements are indicated. [(c)–(f)] Overview of magnetic field induced resistance oscillation for devices from four different wafers. At $B=0$ $\rho$ increases mostly monotonically with decreasing $n_s$ (thick black lines), but a perpendicular magnetic field induces strong oscillations. (c) $B_{\perp }=0–3\text{T}$, $\Delta B_{\perp }=0.05\text{T}$. (d) $B_{\perp }=0–4\text{T}$, $\Delta B_{\perp }=0.05\text{T}$. (e) $B_{\perp }=0$, $0.92–6.7\text{T}$, $\Delta B_{\perp }=0.08\text{T}$. (f) $B_{\perp }=0–9.6\text{T}$, $\Delta B_{\perp }=0.3\text{T}$.

Figure 2

(Color online) $T$ dependence of resistance oscillations. [(a)–(c)] C67, $B_{\perp }=0.5\text{T}$. The high $T$ part is qualitatively the same at peaks and troughs in resistance and the activation energy [slopes of $\rho \left(T\right)={\rho }_0\text{exp}\left(E_0/k_{B}T\right)$ fits (solid lines)] is virtually unchanged between adjacent peaks and troughs. By contrast, the low $T$ behavior changes qualitatively with the oscillations. At the peaks the behavior remains weakly insulating, but the troughs show a metal-like $T$ dependence. [(d)–(f)] A78a, $B_{\perp }=2\text{T}$. The high $T$ behavior is similar to [(a)–(c)], but at low $T$ no metal-like behavior is observed in the troughs. However, a difference persists, with the saturation at the troughs being stronger and starting at higher $T$ than at peaks.

Figure 3

(Color online) Activation energies at various magnetic fields obtained from the high temperature activated behavior as a function of electron density in comparison to the magnetically induced resistance oscillations (A78a). On an overall decrease with increasing $n_s$, clear plateaus are formed, starting approximately at the position of a trough and ending at the next peak.

Figure 4

(Color online) (a) $\rho$ vs $V_g$ of device A78b at stepwise increasing $B_{\perp }=0–2.75\text{T}$ $\left(\Delta B_{\perp }=0.1\text{T}\right)$, after a bad (fast) cooldown. [(b) and (c)] Histograms of the separation between adjacent peaks in terms of $n_s$ and $r_s$. The data include 10 devices from various wafers and of varying dimensions.