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

Abstract

Anisotropic magnetoresistances and intrinsic adiabatic transport features are generated on quantum Hall samples based on an ͑Al,Ga͒As/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 ͑2DES͒. 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.Few cryogenic scanning force microscopy ͑SFM͒ measurements exist on probing the electrostatic potential distribution in two-dimensional electron systems ͑2DES͒ realized in ͑Al,Ga͒As/GaAs heterostructures under quantum Hall conditions. 1,2 Those results measured over the whole 2DES demonstrated the important role of compressible and incompressible strips 3,4 for the current distribution in quantum Hall samples. Despite of these experimental findings, the edgestate picture 5 remains the widely used model to describe the magnetotransport in quantum Hall devices, also in the context of topological insulators. 6 Its success has been partly legitimated by its ability to include contact effects 7 and to explain adiabatic magnetotransport features 8 -such as the disappearance of peaks in the Shubnikov-de Haas ͑SdH͒ oscillations, the extension of quantum Hall plateaus to lower magnetic fields, and the existence of nonlocal resistances. 9 In this Rapid Communication, we manage a comparison between magnetotransport and scanning force microscopy investigations on Hall bar samples showing adiabatic transport features without the use of gates. The SFM measurements present potential distributions from which we conclude that the incompressible strip in front of alloyed contacts possesses different insulating properties depending of the orientation relatively to the crystal axes of the underlying heterostructure. This result shows how to include contacts and interpret adiabatic features in terms of compressible/incompressible strips and what is the microscopic origin of anisotropy in magnetoresistances.The samples used here are based on an ͑Al,Ga͒As/GaAs heterostructure containing the 2DES at the heterojunction interface 60 nm below the surface. The electron density and mobility at 1.3 K are 3.6ϫ 10 15 m −2 and 160 m 2 ͑V s͒ −1 , respectively. Such conditions lead to high electron mobility samples with an electron mean-free path l Ϸ 13 m, which is three times larger than in Ref. 2. Our Hall bars as depicted in Fig. 1 are defined by optical lithography and wet etching. Au/Ge/Ni film is alloyed to achieve low resistive contacts to the 2DES by following our standard recipe. 10 After annealing, the remaining 2DES has a size of about 10 m w...

Metrology and microscopic picture of the integer quantum Hall effect

“…In this case, the contacts play a crucial role in equilibrating the compressible edge strips. Detailed comparisons between adiabatic transport features and scanning force microscopy investigations can be found in Dahlem et al [32,33]. Because of the scenarios given in figure 8g-l, a perfect quantum Hall plateau can be expected in case (h), where an equilibration happens within the rather narrow depletion region in front of the contact.…”

“…In the following, we will present an outline of the main results, and focus on the role of contacts, the possible constraints for metrological applications. Details of the measurements can be found in earlier studies [25][26][27][28][29][30][31][32][33]. Figure 2 shows the Hall potential profile for different magnetic field values around a bulk Landau level filling factor of n = 2.…”

“…In the easy direction (borderline perpendicular to [011]), the specific contact resistivity value r c = R c w is around 250 Umm, corresponding to R c = 2.5 U for w = 100 mm, and this value r c is almost constant for all borderline lengths w ranging from 100 down to 1 mm. On the other hand, contacts defined in the hard (borderline perpendicular to [011]) direction show approximately a factor of 2 higher r c value for a shallow-lying 2DES (about 60 nm depth) [33]; however, r c increases for heterostructues with a deep-lying 2DES, although the amount of AuGeNi for alloying has been scaled up [40]. In addition, in the hard direction, these r c values show a large spread and the portion of working contacts drastically decreases as the borderline becomes shorter.…”

“…In recent systematic investigations [33]-combining scanning probe imaging with magneto-transport measurements-we demonstrated that the depletion width in front of the alloyed contacts depends-consistent with the specific contact resistivity-on the borderline orientation. Two Hall bars of the same geometry, just turned in their orientation by 90 • on the same piece of heterostructure, show quantum Hall plateaus in different ranges of magnetic field.…”

Low contact resistance in epitaxial graphene devices for quantum metrology

“…Similar on-device variations have been reported for GaAs, with their origin attributed to the disorder introduced by annealed contacts, which leads to inhomogeneous doping profiles around the metallic contacts. 13 As for graphene-based QHR standards, the problem of contact resistance variability has yet to be reported.…”