scanning gate microscopy

Equilibration of integer quantum Hall edge channels

The concept of one-dimensional (1D) edge channels can be successfully applied to the description of transport phenomena in two-dimensional electron systems (2DES) in the quantum Hall (QH) regime [1]. QH resistance is not sensitive to inter-channel scattering, but there is renewed interest in interactions between copropagating edge channels [2] mostly in view of possible applications in quantum information technology [3]. Inter-channel transport was studied in the past by several authors (for a review, see [1]), but only in devices with fixed channel interaction length d. We demonstrate for the first time the use of scanning gate microscopy (SGM) to realize devices in which d can be tuned continuously. This level of control is crucial to pinpoint the exact mechanism of edge-edge interaction.

ICPS-Fig1

Figure 1: Sketch of the experimental setup

Figure 1 schematically illustrates our experiment: inner (i) and outer (o) edge channels originate from two distinct voltage contacts at potential V1 and V2, respectively. They propagate together for a distance d and are then separated and guided to two current contacts IA and IB, respectively. In what follows we set V1 = V and V2 = 0. If we assume that there is no equilibration between the two (spin-degenerate) edge channels, then IA = 2 e2/h V and IB = 0. On the other hand, if we assume that the two edge channels equilibrate their voltage imbalance completely, then IA = IB = e2/h V. In a model of spatially-uniform interaction one expects differential conductance to scale as GB = G0(1-exp(-2d/l)) with G0 = e2/h and l the equilibration length [4]. Therefore, a measurement of IA and IB as a function of d and V makes it possible to analyze the equilibration behavior and verify if it is indeed consistent with an exponential decay. Moreover it yields the value of l as a function of V.

ICPS-Fig2

Figure 2: Conductance GB vs. d; from fit: l = 4.5 um

Devices were realized starting from a high-mobility AlGaAs/GaAs heterostructure. A 6 um-long 1D channel of two Schottky-gates with a constriction gap of 1 um was patterned on the sample. Experiments were performed at 300 mK and bulk 2DES filling factor v = 4 (two spin-degenerate edge channels). The selective backscattering of individual edge channels was achieved by the biased tip of a SGM, as described in detail in Ref. [5]. The inner and outer edge channels meet at the entrance of the 1D channel and travel in close proximity for a distance d before they are separated by the action of the SGM tip. Figure 2 shows the resulting differential conductance GB as a function of d for a voltage V = 5 mV. The curve starts for d = 0 at GB = 0, i.e. no equilibration occurs, and nearly reaches GB = e2/h for d = 5 um, i.e. complete equilibration is achieved.

References

  1. E. Deviatov, Physics - Uspekhi 50, 197 (2007).
  2. C. Altimiras, H. le Sueur, U. Gennser, A. Cavanna, D. Mailly, and F. Pierre, Nature Physics 6, 34 (2010).
  3. V. Giovannetti, F. Taddei, D. Frustaglia, and R. Fazio, Phys. Rev. B 77, 155320 (2008).
  4. G. Mueller, D. Weiss, A. V. Khaetskii, K. von Klitzing, S. Koch, et al., Phys. Rev. B 45, 3932 (1992).
  5. N. Paradiso, S. Heun, S. Roddaro, L. N. Pfeiffer, K. W. West, L. Sorba, G. Biasiol, and F. Beltram, Physica E 42, 1038 (2010).

Publications

  1. 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, Phys. Rev. B 83 (2011) 155305.

Presented at

  1. N. Paradiso, S. Heun, S. Roddaro, D. Venturelli, F. Taddei, V. Giovannetti, R. Fazio, G. Biasiol, L. Sorba, and F. Beltram: Equilibration of integer quantum Hall edge channels studied by scanning gate microscopy, 30th International Conference on the Physics of Semiconductors (ICPS-30), COEX, Seoul, Corea, 25 - 30 July 2010 [Abstract] [Poster].

  2. N. Paradiso, S. Heun, S. Roddaro, D. Venturelli, F. Taddei, V. Giovannetti, R. Fazio, G. Biasiol, L. Sorba, and F. Beltram: Quantum Hall circuits with variable geometry: study of the inter-channel equilibration by scanning gate microscopy, The 23rd General Conference of the Condensed Matter Division of the European Physical Society , Warsaw, Poland, 30 August - 03 September 2010 [Abstract] [Talk].

  3. N. Paradiso, S. Heun, S. Roddaro, D. Venturelli, F. Taddei, V. Giovannetti, R. Fazio, G. Biasiol, L. Sorba, and F. Beltram: Equilibration of integer quantum Hall edge channels studied by scanning gate microscopy, First Meeting of the Institute of Nanoscience, Villa Guinigi, Matraia (Capannori, LU), 4 - 5 October 2010 [Poster].

  4. N. Paradiso, S. Heun, S. Roddaro, D. Venturelli, F. Taddei, V. Giovannetti, R. Fazio, G. Biasiol, L. Sorba, and F. Beltram: Equilibration of integer quantum Hall edge channels studied by scanning gate microscopy, The 6th International Workshop on Nano-scale Spectroscopy and Nanotechnology, Kobe, Japan, 25 - 29 October 2010 [Abstract] [Talk].

  5. 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, Dept. of Physics, McGill University, Montreal, Canada (Prof. G. Gervais), 29 April 2011. [Abstract] [Talk]

See also:

Contact

sample

Dr. Stefan Heun
Senior Scientist

NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore
Piazza San Silvestro 12
56127 Pisa, Italy

tel. office +39-050-509 472
SGM lab. +39-050-509 467
STM lab. +39-050-509 461
fax. +39-050-509 417

e-mail: stefan.heun@nano.cnr.it