Thema der Dissertation:
Signatures of Coulomb Screening in the Quantum Hall Effect
Signatures of Coulomb Screening in the Quantum Hall Effect
Abstract: The quantum Hall effect (QHE) is a manifestation of Landau quantization in two-dimensional conductors under a strong perpendicular magnetic field. Based on its quantized Hall resistance, which depends only on the elementary charge and the Planck constant but not the material, it is used as the resistance standard of the SI unit system. Despite this important application, the microscopic mechanisms underlying the QHE remain a subject of ongoing debate.
The QHE is often explained using the widely accepted Landauer-Büttiker picture, which correctly predicts the quantized values of the Hall resistance. It assumes that the bulk of the Hall bar is insulating, while all current flows without scattering within one-dimensional edge channels.
However, as the Landauer-Büttiker picture completely neglects the Coulomb interaction of the charge carriers, it fails to correctly describe the microscopic properties of the QHE. In contrast, the screening theory incorporates Coulomb interactions. It predicts that the Hall bar partitions into compressible and incompressible strips (ICSs) with geometries depending on the magnetic field. The compressible regions form where there is a finite density of states (DOS) at the chemical potential, such that carriers can scatter and screen local electric fields. ICSs form because of a local energy gap between Landau levels, where the DOS vanishes at the chemical potential. Here, all Landau levels are either completely full or empty, such that scattering is suppressed by the Landau gap and the electric field cannot be screened. This implies that the current flows inside the ICSs.
The screening theory predicts that ICSs form edge channels at the low magnetic field ends of each plateau of a quantized resistance, while they more and more extend through the bulk of the Hall bar as the magnetic field is increased along the plateau. In my first experiment, I verified this behavior by measuring the current that flows through the ICSs into a tiny ohmic contact in the center of the Hall bar. In my next experiment, I performed multiterminal current measurements and compared them with model calculations. I found that on quantized Hall plateaus the current flow is chiral, while between plateaus my results agree with the Drude model, which predicts unidirectional diffusive current flow. For the third experiment, I fabricated a sample in which a Hall bar can be defined by means of two metal gates. A global top gate was used to fully deplete the two-dimensional electron system (2DES) almost everywhere beneath it. A second gate (screen gate) in the shape of the Hall bar is placed between the top gate and the 2DES such that it screens the electric field of the top gate in the plane of the 2DES. This way, a Hall bar can be defined beneath the screen gate while the gate voltages can be used to control its carrier density and confinement potential. I used this tunability to demonstrate how the quantized Hall plateaus can be tuned by adjusting the confinement potential.
All these results agree with the screening theory but cannot be explained within the Landauer-Büttiker picture. They improve our understanding of the integer QHE and its topological relatives, and pave the way for future applications in quantum electronics and metrology.
The QHE is often explained using the widely accepted Landauer-Büttiker picture, which correctly predicts the quantized values of the Hall resistance. It assumes that the bulk of the Hall bar is insulating, while all current flows without scattering within one-dimensional edge channels.
However, as the Landauer-Büttiker picture completely neglects the Coulomb interaction of the charge carriers, it fails to correctly describe the microscopic properties of the QHE. In contrast, the screening theory incorporates Coulomb interactions. It predicts that the Hall bar partitions into compressible and incompressible strips (ICSs) with geometries depending on the magnetic field. The compressible regions form where there is a finite density of states (DOS) at the chemical potential, such that carriers can scatter and screen local electric fields. ICSs form because of a local energy gap between Landau levels, where the DOS vanishes at the chemical potential. Here, all Landau levels are either completely full or empty, such that scattering is suppressed by the Landau gap and the electric field cannot be screened. This implies that the current flows inside the ICSs.
The screening theory predicts that ICSs form edge channels at the low magnetic field ends of each plateau of a quantized resistance, while they more and more extend through the bulk of the Hall bar as the magnetic field is increased along the plateau. In my first experiment, I verified this behavior by measuring the current that flows through the ICSs into a tiny ohmic contact in the center of the Hall bar. In my next experiment, I performed multiterminal current measurements and compared them with model calculations. I found that on quantized Hall plateaus the current flow is chiral, while between plateaus my results agree with the Drude model, which predicts unidirectional diffusive current flow. For the third experiment, I fabricated a sample in which a Hall bar can be defined by means of two metal gates. A global top gate was used to fully deplete the two-dimensional electron system (2DES) almost everywhere beneath it. A second gate (screen gate) in the shape of the Hall bar is placed between the top gate and the 2DES such that it screens the electric field of the top gate in the plane of the 2DES. This way, a Hall bar can be defined beneath the screen gate while the gate voltages can be used to control its carrier density and confinement potential. I used this tunability to demonstrate how the quantized Hall plateaus can be tuned by adjusting the confinement potential.
All these results agree with the screening theory but cannot be explained within the Landauer-Büttiker picture. They improve our understanding of the integer QHE and its topological relatives, and pave the way for future applications in quantum electronics and metrology.
Time & Location
Sep 11, 2025 | 01:00 PM
Hörsaal B (0.1.01)
(Fachbereich Physik, Arnimallee 14, 14195 Berlin)