Scanning gate microscopy as a new tool to investigate ballistic transport – SGM-Bal

The experimental tools employed by the Zurich group include existing low-temperature scanning gate setups reaching temperatures of 300 mK ( 3 He system) and 100 mK (dilution refrigerator) and allowing the application of magnetic fields up to 10 T normal to the plane of a two-dimensional electron gas. Furthermore we have world-class state-of-the-art Ga[Al]As heterostructure material available for sample fabrication, which is provided by the group of Prof. Wegscheider at ETH Zurich. The low-temperature mobilities of electrons in this material exceed those of most previous experiments.
The theoretical tools and concepts used by the Strasbourg group include analytical (semiclassical expansions) and numerical (recursive Green function algorithm, sums over classical trajectories, and self-consistent) approaches.

The group at the ETH Zürich has produced samples where the strength of the confining potential can be changed by gate voltages and shown that the interpretation of the SGM response in terms of local electron flow works without confinement, but not for strong confinement. For a circular cavity the conclusion is similar. The Strasbourg team found conditions under which the local density of states can be extracted from the SGM response.
The SGM response of a circular cavity was measured in Zürich for different values of tip strength. The conductance through the cavity has a surprising non-monotonic dependence on tip strength when the tip is in the centre of the cavity. The Strasbourg group performed a numerical quantum transport simulation and evaluated the semiclassical conductance through the cavity, confirming the non-monotonic tip-strength dependence. The semiclassical analysis of the conductance, based on the classical trajectories transmitted through the cavity, reproduces the conductance oscillations, proving that the effect is of classical origin. Only particular classes of short trajectories are responsible for the effect. The dominant trajectories alternate with tip strength between transmitted and reflected ones, thereby providing a simple explanation for the observed phenomenon.
To approach the regime of weakly invasive SGM, the Zürich team considered a QPC facing a circular cavity gate. The SGM response showed an enhanced SGM sensitivity and measurable signals for weak tip strength. A simulation by the Strasbourg group confirms that the reflecting gate enhances the SGM response. It was also found that the disorder plays an important role and cannot be ignored. The confrontation between experiment and theory is made for the length scale of the fluctuations in the SGM response. Experiment (Zürich) and simulations (Strasbourg) agree, and an understanding of the length scale at weak tip strength is provided by the perturbation theory of the Strasbourg team.

The joint publication “Classical origin of conductance oscillations in an integrable cavity” by C. Pöltl, A. Kozikov, K. Ensslin, T. Ihn, R.A. Jalabert, C. Reichl, W. Wegscheider, and D. Weinmann, Phys. Rev. B 94 , 195304 (2016) explains a non-trivial and counter-intuitive experimental observation of quantum transport (non-monotonic variation of quantum conductance with the size of an obstacle) by a remarkably simple mechanism based on short classical trajectories. The paper has been selected by the editors of Phys. Rev. B as an Editor’s Suggestion.
Present work aims at a better understanding of the branches that appear in the SGM response close to QPCs.

Joint publications:

- Electron backscattering in a cavity: ballistic and coherent effects, A.A. Kozikov, D. Weinmann, C. Rössler, T. Ihn, K. Ensslin, C. Reichl, W. Wegscheider, Phys. Rev. B 94, 195428 (2016)
- Classical origin of conductance oscillations in an integrable cavity, C. Pöltl, A. Kozikov, K. Ensslin, T. Ihn, R.A. Jalabert, C. Reichl, W. Wegscheider, D. Weinmann, Phys. Rev. B 94, 195304 (2016); Editor's Suggestion
- Scanning gate experiments: from strongly to weakly invasive probes, R. Steinacher, C. Pöltl, T. Krähenmann, A. Hofmann, C. Reichl, W. Zwerger, W. Wegscheider, R.A. Jalabert, K. Ensslin, D. Weinmann, T. Ihn, submitted to New J. Phys., arXiv:1709.08559

Single-partner publications:

- Scattering approach to scanning gate microscopy, R.A. Jalabert, D. Weinmann, Physica E 74, 637 (2015)
- Partial local density of states from scanning gate microscopy, O. Ly, R.A. Jalabert, S. Tomsovic, D. Weinmann, Phys. Rev. B 96, 125439 (2017)
- Scanning-gate-induced effects and spatial mapping of a cavity, R.
Steinacher, A.A. Kozikov, C. Rössler, C. Reichl, W. Wegscheider, T. Ihn, and K. Ensslin, New J. Phys. 17, 043043 (2015).
- Mode Specific Backscattering in a Quantum Point Contact, A.A.
Kozikov, R. Steinacher, C. Rössler, T. Ihn, K. Ensslin, C. Reichl, and W. Wegscheider , Nano Letters 15, 7994 (2015).
- Investigating energy scales of fractional quantum Hall states using scanning gate microscopy, BA Braem, T Krähenmann, S Hennel, C Reichl, W Wegscheider, K. Ensslin, and T. Ihn, Phys. Rev. B 93, 115442 (2016).
- Scanning gate imaging in confined geometries, R. Steinacher, A.A. Kozikov, C. Rössler, C. Reichl, W. Wegscheider, K. Ensslin, and T. Ihn, Phys. Rev. B 93, 085303 (2016).