SGM 3

Quantum Hall Interferometry

The interest in the development of solid state quantum devices goes well beyond fundamental research on many-body systems. An example is the quantum mechanics concept of entanglement. In the last decade entanglement has become synonymous with quantum computing. A number of physical systems were already proposed as possible candidates as quantum computing hardware. In this context, the peculiar properties of quantum Hall (QH) systems can be very useful. First of all, since these are implemented within solid state devices, they can be easily miniaturized and integrated on chip by means of well-established semiconductor-technology fabrication methods. More importantly, QH circuits operate with electrons: due to their fermionic statistics, it is much easier to obtain a single-electron rather than a single-photon source. Moreover, in QH systems, the Lorentz force compels electrons to move along counter-propagating chiral channels at sample edges. When Landau levels (LLs) in the bulk are fully occupied, backscattering between counter-propagating edge states is drastically suppressed. When several LLs are populated, edge channels consist of a series of dissipationless edge states that can be easily separated and independently contacted much like a computer bus. Edge channels in the fractional QH regime are even more interesting, since their excitations are expected to display anyonic statistics.

A two-particle entangler can in principle be obtained in a two-channel conductor, for example employing two edge channels in the integer QH regime. Coherent mixing between two counter-propagating edge states was achieved by means of quantum point contacts and employed to realize an all-electronic Mach-Zehnder interferometer. Such devices have nevertheless several drawbacks caused by their non-simply connected topology. It is not obvious how to concatenate many devices in series, i.e. how to achieve scalability. On the contrary, Giovannetti and coworkers recently theoretically showed that if a coherent mixer between co-propagating edges is realized, scalable simply-connected interferometers can be build. Such devices could in principle work with many modes, if implemented in QH systems with filling factor v > 2. This advantage, along with the scalability, could be pivotal to practically access the potential of quantum circuits as electron entanglers and open the way to an innovative class of quantum computing devices.

The application of this scheme to the quantum computation of anyonic qubits crucially depends on the ability to determine (i) how parallel edge channels can be mixed, and whether this mixing is coherent or not, and (ii) the inner structure of edges, and in particular to determine possible fractional components that could be used as a bus of anyonic quasi-particles. Our work is aimed at experimentally addressing these challenging questions. To this end, we combine transport measurements and a scanning probe microscopy technique to directly manipulate edge channels.

To explore the inner (fractional) structure of (integer) edges, we used the scanning gate microscopy (SGM) technique. Our SGM maps provided the first images of the fractional features (corresponding to filling factors 1/3, 2/5, 3/5, and 2/3) that form the inner edge structure. SGM maps showed that the edge consists of a series of alternating compressible and incompressible stripes (see Fig. 1). The high resolution of the SGM technique allowed us to directly measure stripe widths and compare them with the predictions of the edge-reconstruction theory. The experimental demonstration of fractional structures within integer edge channels represents the conclusive answer to long-time debated issues: the stripe structure explains how edge channels behave at the interface between an integer and a fractional QH phase. In this case, an integer edge is partitioned into its fractional components, so that there is continuity between the fractional incompressible stripe and the corresponding macroscopic fractional phase.

FQHE
Figure 1: (a) SGM scan at the center of a QPC in a quantum Hall system at integer filling factor 1. The map shows the transmitted differential conductance as a function of the tip position, together with contour lines at constant differential conductance. On the right, a zoom of the 50 x 200 nm region corresponding to the dashed rectangle is displayed. (b) Profile of the differential conductance along the light blue line in (a), together with its derivative. (c) Scheme of the SGM experimental setup.

Our results open the way to the realization of simply-connected Mach-Zehnder interferometers based on co-propagating edge channels. Our SGM work on the fractional sub-structure of edge channels furthermore indicates how to operate the interferometer with individual fractional stripes instead of single integer-edge channels. The impact of such a result can be vast since it may represent a valid step forward towards the achievement of an interferometer operating with exotic quasi-particles, like the non-abelian excitations of the v = 5/2 QH phase. Such an advance would in perspective lead to the implementation of fault-tolerant quantum computers, because of the nonlocal encoding of the quasiparticle states, which makes them immune to errors caused by local perturbations.

Publications:

  1. N. Paradiso, S. Heun, S. Roddaro, L. Sorba, F. Beltram, G. Biasiol, L. N. Pfeiffer, and K. W. West: Imaging fractional incompressible stripes in integer quantum Hall systems, arXiv:1205.0367 [cond-mat.mes-hall].
  2. N. Paradiso, S. Heun, S. Roddaro, L. Sorba, F. Beltram, G. Biasiol, L. N. Pfeiffer, and K. W. West: Imaging fractional incompressible stripes in integer quantum Hall systems, Phys. Rev. Lett. 108, 246801 (2012).
  3. S. Heun: Charge down and heat up, Nat. Phys. 8, 640 (2012).
  4. N. Paradiso, S. Heun, S. Roddaro, G. Biasiol, L. Sorba, D. Venturelli, F. Taddei, V. Giovannetti, and F. Beltram: Imaging backscattering through impurity-induced antidots in quantum Hall constrictions, arXiv:1209.2438 [cond-mat.mes-hall].
  5. N. Paradiso, S. Heun, S. Roddaro, G. Biasiol, L. Sorba, D. Venturelli, F. Taddei, V. Giovannetti, and F. Beltram: Imaging backscattering through impurity-induced antidots in quantum Hall constrictions, Phys. Rev. B 86, 085326 (2012).
  6. N. Paradiso: Tomography and manipulation of quantum Hall edge channels, PhD thesis, Scuola Normale Superiore, Pisa, Italy (2012). [thesis]
  7. Selected Application in the Attocube Product Catalog 2012 – 2013 (page 122).
  8. Selected Application in the Attocube Product Catalog 2013 – 2014 (page 158).
  9. N. Paradiso, S. Heun, S. Roddaro, L. Sorba, F. Beltram, G. Biasiol, L. N. Pfeiffer, and K. W. West: Imaging fractional incompressible stripes in integer quantum Hall systems using the attoAFM III, Attocube Application Note M39 (2014).
  10. S. Mukhopaghyay, B. A. Piot, S. Pezzini, V. Bellani, A. Iagallo, S. Heun, L. Sorba, G. Biasiol: Multi-terminal probing of the IQHE across a QPC, Annual Report 2013, Laboratoire National des Champs Magnetiques Intenses, Grenoble (France).
  11. F. Taddei and S. Heun: Quantum Hall Interferometry, Scientific Report 2012 – 2013, CNR Nano.
  12. Quantum Hall Interferometry – Scanning Gate Microscopy, NEST Activity Report 2008-2013.
  13. Selected Application in the Attocube Product Catalog 2015 – 2016 (page 127).
  14. Selected Application in the Attocube Product Catalog 2016 – 2017 (page 109).
  15. Selected Application in the Attocube Product Catalog 2017 – 2018 (page 117).
  16. M. Carrega, L. Chirolli, S. Heun, and L. Sorba: Anyons in quantum Hall interferometry, arXiv:2109.13427 [cond-mat.mes-hall].
  17. M. Carrega, L. Chirolli, S. Heun, and L. Sorba: Anyons in quantum Hall interferometry, Nat. Rev. Phys. 3 (2021) 698 – 711.
  18. M. Carrega and S. Heun: To measure a magnon population, Nat. Phys. 18 (2022) 3 – 4. [Link]

Presented at:

  1. N. Paradiso: Tomography and manipulation of quantum Hall edge channels by Scanning Gate Microscopy, PhD thesis, Scuola Normale Superiore, Pisa, Italy (2012). [defense talk]
  2. N. Paradiso, S. Heun, S. Roddaro, G. Biasiol, L. Sorba, L. N. Pfeiffer, K. W. West, and F. Beltram: Scanning gate microscopy imaging of fractional incompressible stripes in integer quantum Hall channels, 7th International Workshop on Nano-scale Spectroscopy and Nanotechnology, Zurich, Switzerland, 2 – 6 July 2012 (oral). [Abstract] [Talk]
  3. N. Paradiso, S. Heun, S. Roddaro, G. Biasiol, L. Sorba, L. N. Pfeiffer, K. W. West, and F. Beltram: Imaging fractional incompressible stripes in integer quantum Hall systems, 31st International Conference on the Physics of Semiconductors, Zurich, Switzerland, 29 July – 3 August 2012 (oral). [Abstract] [Talk]
  4. S. Heun, N. Paradiso, S. Roddaro, G. Biasiol, L. Sorba, L. N. Pfeiffer, K. W. West, and F Beltram: Imaging fractional incompressible stripes in integer quantum Hall systems, 24th Conference of the EPS Condensed Matter Division (CMD-24), Edinburgh, UK, 3 – 7 September 2012 (oral). [Abstract] [Talk]
  5. S. Heun: Tomography and manipulation of Quantum Hall edge channels by Scanning Gate Microscopy, IBM Rueschlikon, Switzerland (Dr. Gerhard Meyer), 17 October 2012. [Abstract] [Talk]
  6. Nicola Paradiso, Stefan Heun, Stefano Roddaro, Lucia Sorba, Giorgio Biasiol, L. N. Pfeiffer, K. W. West, and Fabio Beltram: Imaging Fractional Incompressible Stripes in Integer Quantum Hall Systems, IXth Rencontres du Vietnam, Quy-Nhon, Vietnam, 4 – 10 August 2013 (oral). [Abstract] [Talk]
  7. S. Heun: Imaging fractional incompressible stripes in integer quantum Hall systems, CNRS GDR Physique Quantique Mésoscopique, Aussois, France, 9 – 12 December 2013. [Abstract] [Talk]
  8. S. Heun: Nanomaterials characterization by low-temperature Scanning Probe Microscopy, International School on “New frontiers in down-scaled materials and devices: realization and investigation by advanced methods”, Otranto, Italy, 15 – 20 September 2014. [Talk]
  9. S. Heun: Topologically protected edge states in the quantum Hall regime, CnrNano Quantum Technology workshop,Florence, Italy, 21 February 2017. [Talk]