Quantum Hall based Aharonov-Bohm spectroscopy: electron-electron interaction in non-linear magnetotransport

• Applicant: Privatdozent Dr. Stefan Ludwig
• Subject Area: Experimental Condensed Matter Physics
• Term: from 2012 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 218453298

Final Report Abstract

The integer quantum Hall effect (QHE) is one of the most fundamental and at the same time most astonishing phenomena in condensed matter physics. As Klaus von Klitzing discovered in 1980, the Hall resistance is quantized in fractions of the fundamental constant h/e, with the Planck constant h and the elementary charge e, having precisely defined values since the revision of the International System of Units (SI) in May 2019. Despite its importance for metrology as a sample-independent standard of resistance, our microscopic understanding of the QHE is not yet complete. The simplifying concept of the well-known Landauer-Büttiker picture that in the region of the quantized Hall resistance the current flows in chiral one-dimensional edge channels has been challenged both theoretically and experimentally. The screening theory is based on first principle calculations taking into account the Coulomb interaction of the free charge carriers. It predicts that the current flows in so-called incompressible strips (ICS), which form due to a combination of the Coulomb interaction between the charge carriers and the local formation of a Landau energy gap. The latter leads to scattering free current inside the ICSs. The calculations also suggest that with increasing magnetic field along a quantized plateau of the Hall resistance the ICSs move gradually from the edges of a two-dimensional conductive sample towards its center, thereby becoming significantly wider, until finally a single ICS occupies almost the entire conductive region. In the present project, we tested and confirmed the screening theory in several experiments. In particular, using tiny ohmic contacts within the sample, we were able to demonstrate how the ICSs broaden from the edge to the interior of the sample. We also found that for the plateaus of quantized Hall resistance the current is always chiral, flowing in opposite directions on opposite sides of the Hall bar, even in the case of a bulk ICS. The combination of our experimental results and model calculations significantly deepened our understanding of the microscopic electrostatics and carrier dynamics in the regime of the QHE.

Publications

• Anomalous resistance overshoot in the integer quantum Hall effect. Scientific Reports, 3(1).
  Kendirlik, E. M.; Sirt, S.; Kalkan, S. B.; Dietsche, W.; Wegscheider, W.; Ludwig, S. & Siddiki, A.
  
• Mesoscopic Field-Effect-Induced Devices in Depleted Two-Dimensional Electron Systems. Physical Review Applied, 8(6).
  Bachsoliani, N.; Platonov, S.; Wieck, A. D. & Ludwig, S.
  
• The topological in-equivalence of Hall bar and Corbino geometries in coordinate space: Screening theory and direct transport experiments. Physica E: Low-dimensional Systems and Nanostructures, 153(2023, 9), 115780.
  Sırt, Serkan; İren, Emre; Ekşi, Deniz; Tunalı, Aylin Yıldız; Güvenilir, Eren; Kendirlik, Enver M.; Ofek, Nissim; Umansky, Vladimir; Ludwig, Stefan & Siddiki, Afif
  
• Current distribution and chirality in the regime of the quantized Hall effect. arXiv:2407.01277 (2024)
  Sirt, S.; Kamm, M.; Umansky, V. Y. & Ludwig, S.
  
• Direct measurement of bulk currents in the quantized Hall regime. arXiv:2405.05138 (2024)
  Sirt, S.; Umansky, V. Y.; Siddiki, A. & Ludwig, S.