SGM

Spectral analysis of inter-channel scattering in the quantum Hall regime by scanning gate microscopy

Transport phenomena in quantum Hall (QH) systems are explained by chiral edge channels occurring at the sample edge, as pointed out by Halperin [1]. However, in some experiments the inner structure of the edge itself seems to play a role, as shown in Refs. [2-4] in which the charge transfer between co-propagating edge channels was studied in the limit of high imbalance. The inter-channel equilibration is a complex process that takes place along the whole length d over which the two parallel edges are in interaction. In all the experiments performed to date the device geometry univocally fixes the value of d. We demonstrate for the first time how a scanning gate microscope (SGM) can be used to realize devices in which d is tuned continuously. This level of control is crucial to shed light on the microscopic details of edge-edge interaction. In the present work we focus in particular on the spectral analysis of the equilibration in the non-linear regime.

Figure 1: Sketch of the experimental setup

Devices were realized starting from a high-mobility AlGaAs/GaAs heterostructure. A 6um-long 1D channel of two Schottky-gates with a constriction gap of 1 um was patterned on the sample. Measurements were performed at 300 mK and bulk 2DES filling factor v=4 (two spin-degenerate edge channels). Figure 1 schematically illustrates our experiment: inner (i) and outer (o) cyclotron-split edge channels originate from two distinct voltage contacts at potential V and 0, respectively. The inner and outer edge channels meet at the entrance of the 1D channel and travel in close proximity for a distance d [5] before they are separated by the action of the SGM tip [6] and guided to two detector contacts IA and IB. For fixed values of the interaction distance d we can measure the I-V characteristics of the inter-channel charge transfer. In Fig. 2 we show such I-V curves for several values of d. All curves show a linear behavior for small bias and a saturation at the full equilibration conductance value e2/h for V<-Vth. In previous works [2,4] the threshold voltage Vth was found to be a few mV smaller than the cyclotron gap. The origin of this reduction is still under debate [4]. The degree of freedom given by the mobile tip allows us to follow both the change in the zero-bias slope [5] and the position of the threshold voltage as a function of d on the same device. The latter measurement evidences for the first time a monotonic reduction of Vth with increasing d (inset of Fig. 2). We discuss these data on the basis of a simple model for the transfer of carriers between the co-propagating edges, by taking into account the influence of the electron heating due to carrier injection between two highly imbalanced channels.

Figure 2: I-V characteristics of the inter-channel equilibration. In the inset the threshold energy reduction as a function of d is shown.

References

B. I. Halperin, Phys. Rev. B 25, 2185 (1982).
A. Wuertz et al., Phys. Rev. B 65, 075303 (2002).
T. Nakajima et al., Phys. Rev. B 81, 085322 (2010).
K. Ikushima et al., Physica E. 42, 1034 (2010).
N. Paradiso, S. Heun, et al., Phys. Rev. B 83, 155305 (2011).
N. Paradiso, S. Heun, et al., Physica E. 42, 1038 (2010).

Presented at

N. Paradiso, S. Heun, S. Roddaro, G. Biasiol, L. Sorba, and F. Beltram: Spectral analysis of inter-channel scattering in the QH regime, 4th International Workshop on Emergent Phenomena in Quantum Hall Systems, Beijing, China, 23 - 26 June 2011. [Abstract] [Lightening Talk] [Poster]
N. Paradiso: Quantum Hall circuits with variable geometry: study of the inter-channel equilibration by Scanning Gate Microscopy, Oral seminar at the Columbia University (invited by Prof. A. Pinczuk), 21 July 2011. [Talk]
N. Paradiso: Quantum Hall circuits with variable geometry: study of the inter-channel equilibration by Scanning Gate Microscopy, Oral seminar at the Center for Functional Nanomaterials of the Brookhaven National Laboratory (invited by Prof. P. Sutter), 22 July 2011. [Talk]
N. Paradiso, S. Heun, S. Roddaro, G. Biasiol, L. Sorba, and F. Beltram: Spectral analysis of inter-channel scattering in the quantum Hall regime by scanning gate microscopy, 19th international conference on Electronic Properties of Two-Dimensional Systems (EP2DS19), Tallahassee, Florida, USA, July 25 - 29, 2011. [Abstract] [Poster]
N. Paradiso: Quantum Hall circuits with variable geometry: study of the inter-channel equilibration by Scanning Gate Microscopy, Oral seminar at the National High Magnetic Field Laboratory, Tallahassee, FL, (invited by Prof. L. Engel), 29 July 2011. [Talk]
N. Paradiso: Quantum Hall circuits with variable geometry: study of the inter-channel equilibration by Scanning Gate Microscopy, Oral seminar at the Stony Brook University, NY, (invited by Prof. X. Du), 1 August 2011. [Talk]
N. Paradiso: Quantum Hall circuits with variable geometry: study of the inter-channel equilibration by Scanning Gate Microscopy, Oral seminar at the Princeton University, NJ, (invited by Prof. A. Yazdani), 2 August 2011. [Talk]
N. Paradiso: Quantum Hall circuits with variable geometry: study of the inter-channel equilibration by Scanning Gate Microscopy, Oral seminar at the Harvard University, MA, (invited by Prof. R. Westervelt), 4 August 2011. [Talk]
S. Heun: Edge channel interferometry in the quantum Hall regime, The 13th International Conference - School on Advanced Materials and Technologies, Palanga, Lithuania, 27 - 31 August 2011. [Abstract] [Talk]
N. Paradiso, S. Heun, S. Roddaro, D. Venturelli, F. Taddei, V. Giovannetti, R. Fazio, G. Biasiol, L. Sorba, and F. Beltram: Spatially resolved analysis of edge-channel equilibration in quantum Hall circuits, Workshop on entanglement in solid state systems, Lecce, Italy, 20 - 22 September 2011 (oral). [Abstract] [Talk]