Cryogenic scanning force microscopy of quantum Hall samples: Adiabatic transport originating in anisotropic depletion at contact interfaces

Anisotropic magnetoresistances and intrinsic adiabatic transport features are generated on quantum Hall samples based on an (Al,Ga)As/GaAs heterostructure with alloyed Au/Ge/Ni contacts. We succeed to probe the microscopic origin of these transport features with a cryogenic scanning force microscope by measuring the local potential distribution within the two-dimensional electron system (2DES). These local measurements reveal the presence of an incompressible strip in front of contacts with insulating properties depending on the orientation of the contact/2DES interface line relatively to the crystal axes of the heterostructure. Such an observation gives another microscopic meaning to the term “nonideal contact” used in context with the Landauer-Büttiker formalism applied to the quantum Hall effect.

Figure 1

(Color) Magnetoresistances $R_{ij,kl}$ measured on a four-terminal Hall-bar geometry shown in the inset: (a) Hall plateaus in $R_{14,14}^{\left[01\overline{1}\right]}$ (red curve) are shifted to lower magnetic field values, Shubnikov-de Haas peaks in the longitudinal resistance $R_{14,23}^{\left[01\overline{1}\right]}$ (blue curve) are missing between $\nu =2-3$, 4–6, and a nonlocal resistance $R_{12,34}^{\left[01\overline{1}\right]}$ (green curve) is observed at negative magnetic field $\left(T=1.3\text{K}\right)$. (b) Comparison of $R_{14,14}$ and $R_{23,23}$ measured on Hall bars oriented either along [011] or $\left[01\overline{1}\right]$ direction $\left(T=26\text{mK}\right)$.

Figure 2

(Color) (a) Hall potential profiles at negative magnetic fields measured with a cryogenic scanning force microscope. The local potential is recorded along the $10\mu \text{m}$ width in the center of the mesa for measurement configurations $R_{23,kl}^{\left[01\overline{1}\right]}$ (left) and $R_{14,kl}^{\left[01\overline{1}\right]}$ (right). (b) and (c) Sketch of the (incompressible) compressible regions [in (white) color] and potential landscape for $\nu =2.5$ and $\nu =3$, respectively. Further incompressible strips at the edges—if anyhow existing—are suppressed.

Figure 3

(Color) (a) Local potential distribution probed for the measurement configuration $R_{12,kl}^{\left[01\overline{1}\right]}$. The potential profiles are different in switching the magnetic field orientation. At negative magnetic field in between $2<\nu <3$, a high potential (red) followed by a low potential (blue) is present at one edge. In contrary, the potential stays at low value (blue) for positive magnetic field. (b) Sketch of the (incompressible) compressible regions and potential landscape for $\nu =3$.

Figure 4

(Color) (a) Sketch of Hall bar showing our (incompressible) compressible strip model in $R_{13,kl}^{\left[01\overline{1}\right]}$ configuration. (b) Corresponding potential distribution for various negative magnetic fields probed on a scan line located at a distance of $1.5\mu \text{m}$ from the voltage probing contact 4. (c) $x\text{−}y$ potential mapping measured 200 nm away from the contact 4 at $\nu =2.2$ and $\nu =2$. At $\nu =2.2$ the potential remains high (red) along the mesa border whereas the inside has low potential (blue).