J. Weis

A quantum dot in the limit of strong coupling to reservoirs

Abstract We study quantum dots which are defined in a two-dimensional electron system (2DES) via split gates and concentrate on the case where the dots are strongly coupled to reservoirs. At zero drain-source voltage we find maxima in the differential conductance over one whole Coulomb-blockade regime and study the splitting of these maxima under the influence of an external magnetic field, as well as their temperature dependence. The results agree qualitatively with predictions of the Anderson model. Resonances close to – but not at – zero drain-source voltage are also observed that are still lacking a good explanation.

Hall potential profiles in the quantum Hall regime measured by a scanning force microscope

A low-temperature scanning force microscope sensitive to electrostatics is used to investigate the potential distribution of a two-dimensional electron system (2DES) under quantum Hall conditions at a temperature T = 1.4 K. We mapped out the Hall potential profiles for the Landau level filling factor range 1 < v < 14 with submicron resolution. At integer filling factors, the potential drop is rather nonlinear, but depends strongly on the scan position. Obviously inhomogeneities of the sample strongly affect the Hall potential profile if the bulk of the 2DES is nonconductive and cannot screen. At filling factors slightly above an even integer value, the Hall potential drops at prominent positions at both edges which are associated with the positions of the incompressible strips as confirmed by comparison with theoretical predictions. With these broad incompressible strips electrically decoupling the edge region from the compressible bulk region, a nearly vanishing Hall potential drop is observed in the compressible bulk region, suggesting that most of the current is flowing close to the edges. In addition, potential profiles near the current injecting contacts reveal the well known hot spot region in the direct vicinity of the contact, but recover to the described shape within a distance of only 6 μm.

Hall potential distribution in the quantum Hall regime in the vicinity of a potential probe contact

Abstract Scanning force microscope measurements of the Hall potential distribution of a two-dimensional electron system (2DES) in the quantum Hall regime reveal the presence of a partial depletion along the border between the 2DES and the good ohmic metal contact: incompressible strips are formed in high magnetic fields along this border, decoupling the bulk region of the 2DES from the contact. This finding clarifies the role of potential probe contacts in Hall bar devices and might affect the interpretation of conductance measurements on Corbino devices.

Single-electron transistor as an electrometer measuring chemical potential variations

The magnetic field dependence of the chemical potential of an electron system can be measured using a metallic single-electron transistor (SET). To demonstrate the method, a SET made of aluminum was fabricated on top of a GaAs/AlGaAs heterostructure containing a two-dimensional electron system (2DES). A change in the chemical potential of the 2DES causes a change in the contact voltage between the SET leads and the 2DES below the SET island which affects the current flow through the SET island. Tuning a voltage which is externally applied in series to the contact voltage, the change in the intrinsic contact voltage can be compensated to keep the SET current constant. With this tuning voltage, the change of the chemical potential by the magnetic field is directly measured. The method described here is applicable to other materials and other parameters affecting the intrinsic contact voltages.

Hall-potential investigations under quantum Hall conditions using scanning force microscopy

Abstract Hall-potential profiles of a two-dimensional electron system (2DES) under quantum Hall (QH) conditions have been investigated at T =1.4 K with submicron resolution using a scanning force microscope sensitive to electrostatics. At an even integer Landau level filling factor a rather nonlinear Hall-potential profile across the Hall-bar is observed. But at reduced magnetic field values corresponding to filling factors slightly above this even integer value almost no Hall-potential drop across the bulk region is found. Instead, the potential clearly drops across prominent areas associated with the positions of incompressible strips that just had emerged at that filling factor at both edges. This shows that the dominant incompressible strips of locally even integer filling factor can decouple the bulk from the edge, thus demonstrating the importance of the edge region for the Hall-field distribution even at non-integer filling factors.

Metrology and microscopic picture of the integer quantum Hall effect

Since 1990, the integer quantum Hall effect has provided the electrical resistance standard, and there has been a firm belief that the measured quantum Hall resistances are described only by fundamental physical constants—the elementary charge e and the Planck constant h. The metrological application seems not to rely on detailed knowledge of the microscopic picture of the quantum Hall effect; however, technical guidelines are recommended to confirm the quality of the sample to confirm the exactness of the measured resistance value. In this paper, we give our present understanding of the microscopic picture, derived from systematic scanning force microscopy investigations on GaAs/(AlGa)As quantum Hall samples, and relate these to the technical guidelines.

Experimental evidence for spinless Kondo effect in two electrostatically coupled quantum dot systems

Abstract The Kondo effect was originally observed in metals doped with magnetic impurities. Recent experiments demonstrated Kondo resonances in the electrical transport through quantum dot systems. They were predicted from the Anderson impurity model by replacing the magnetic impurity by a spin-degenerate state in the quantum dot. Studies of the Kondo effect in such quantum dot systems benefit from enhanced tunability of the relevant parameters present in the Anderson impurity model. Here we demonstrate an experimental realization of the Anderson model showing a spinless Kondo resonance due to an electrostatic degeneracy: two electrostatically coupled quantum dots with separate leads.

Correlated Electron Tunneling through Two Separate Quantum Dot Systems with Strong Capacitive Interdot Coupling

A system consisting of two independently contacted quantum dots with a strong electrostatic interaction shows an interdot Coulomb blockade when the dots are weakly tunnel coupled to their leads. How the blockade can be overcome by correlated tunneling when tunnel coupling to the leads increases is studied experimentally. The experimental results are compared with numerical renormalization group calculations using predefined (measured) parameters. Combining our experimental and theoretical results we identify transport through Kondo correlations due to the electrostatic interaction between the two dots.

Two laterally arranged quantum dot systems with strong capacitive interdot coupling

A method has been developed to form two quantum dot systems in lateral arrangement in a two-dimensional electron system of a GaAs–AlGaAs heterostructure with strong capacitive interdot coupling. In the authors’ design, the interdot capacitance can reach more than one-third of the single-dot capacitance while tunneling between the dots is excluded. This has been achieved by a floating metallic electrode covering both quantum dots, a method already used in split-gate designs before. Here, however, they have reduced the capacitive coupling of this floating gate to other electrodes in the surroundings by an etching technique to obtain a large interdot coupling.

A low-temperature scanning force microscope for investigating buried two-dimensional electron systems under quantum Hall conditions

A low-temperature scanning force microscope sensitive to electrostatics has been constructed for investigating a two-dimensional electron system (2DES) under quantum Hall conditions. In order to cope with the highly resistive properties of the 2DES under these conditions, a low-frequency measurement technique is presented, based on the shift of the cantilevers resonance frequency induced by a small ac current modulation within the 2DES. Since the 2DES is buried in a GaAs/AlGaAs heterostructure, a special calibration technique has to be applied, which allows to map Hall-potential profiles with clearly submicron resolution.