scanning gate microscopy
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.
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.
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
Publications
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
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].
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].
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].
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].
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:
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