## Locally Probing Quantum Hall Samples

Measuring the **Hall resistance on a two-dimensional charge carrier system** at low magnetic fields allows determining the charge carrier concentration and the type of charge carrier (electron or hole). However at high magnetic field values (and low temperature), magnetic field intervals appear where the measured value is constant and well described by **| R_{H}|= h/ie^{2}** (

*h*Planck constant,

*e*elementary charge,

*i*={1,2,3 …}), independently of any sample or material properties. In parallel, the longitudinal resistance – measured by the voltage drop along the edge of the two-dimensional charge carrier system – is zero. The effect is nowadays denoted integer

**quantum Hall effect**, discovered in 1980 by

**Klaus von Klitzing**(Noble Prize 1985). The ratio

*R*

_{K}

*=h*/

*e*

^{2}is called von-Klitzing constant. With begin of 1990, the effect has been used in metrology as electrical

**resistance standard**representing the exact-defined resistance value

*R*

_{K-90}= 25812.807 Ω. Recently the quantum Hall effect has played a key role for the

**new definition of the SI units**. With this new definition, the values of elementary physical constants

*c, e, h, k*

_{B}have been fixed, and therefore the von Klitzing constant

*R*

_{K}=

*h*/

*e*

^{2}too. It has now an infinite number of digits:

*R*

_{K}=

*h*/

*e*

^{2}=25812.80745... Ω (NIST reference on Constants, Units, and Uncertainty).

In literature, various models for the quantum Hall effect exist, assuming even different paths the externally bias current flows through the sample. To develop a microscopic picture for the quantum Hall effect on a solid base, in the middle of the 1990’s we started to build up a **scanning force microscope** operated **at 1.4 Kelvin** to look into the Hall potential distribution of quantum Hall samples. In addition, **metallic single-electron transistors** (SETs) have been deposited on top of two-dimensional electron systems and used **as sensitive local electrometers** to monitor electrostatic potential variations inside quantum Hall samples at temperatures below 0.1 Kelvin. In 2014 we have established a **low-temperature scanning probe microscope** in the **Precision Lab** of the Institute working in a top-loading ^{3}He–^{4}He dilution refrigerator **below 50 mK**. As probe an array of about eight single-electron transistors (SETs) is used, made in our cleanroom facility, which act as independent electrometers probing quantum Hall samples at a distance of few tens of nanometers with a resolution below 0.1 µm. Since 2016 Hall potential profiles of 2DES in **fractional quantum Hall plateaus** have been measured. [more]

## Publications on Locally Probing Quantum Hall Samples

**Hall Potential and Current Distribution in Quantum Hall Samples Probed by Scanning Force Microscopy at 1.4 Kelvin**

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