1
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Sestoft JE, Marnauza M, Olsteins D, Kanne T, Schlosser RD, Chen IJ, Grove-Rasmussen K, Nygård J. Shadowed versus Etched Superconductor-Semiconductor Junctions in Al/InAs Nanowires. NANO LETTERS 2024; 24:8394-8401. [PMID: 38865258 PMCID: PMC11249013 DOI: 10.1021/acs.nanolett.4c02055] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2024]
Abstract
Hybrid semiconductor-superconductor nanowires have emerged as a cornerstone in modern quantum devices. Integrating such nanowires into hybrid devices typically requires extensive postgrowth processing which may affect device performance unfavorably. Here, we present a technique for in situ shadowing superconductors on nanowires and compare the structural and electronic properties of Al junctions formed by shadowing versus etching. Based on transmission electron microscopy, we find that typical etching procedures lead to atomic-scale surface roughening. This surface perturbation may cause a reduction of the electron mobility as demonstrated in transport measurements. Further, we display advanced shadowing geometries aiding in the pursuit of bringing fabrication of hybrid devices in situ. Finally, we give examples of shadowed junctions exploited in various device geometries that exhibit high-quality quantum transport signatures.
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Affiliation(s)
- Joachim E Sestoft
- Center for Quantum Devices and Nano-science Center, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Mikelis Marnauza
- Center for Quantum Devices and Nano-science Center, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Dags Olsteins
- Center for Quantum Devices and Nano-science Center, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Thomas Kanne
- Center for Quantum Devices and Nano-science Center, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Rasmus D Schlosser
- Center for Quantum Devices and Nano-science Center, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - I-Ju Chen
- Center for Quantum Devices and Nano-science Center, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Kasper Grove-Rasmussen
- Center for Quantum Devices and Nano-science Center, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
| | - Jesper Nygård
- Center for Quantum Devices and Nano-science Center, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark
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2
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Liu L, Wen L, He F, Zhuo R, Pan D, Zhao J. Selective area growth of in-plane InAs nanowires and nanowire networks on Si substrates by molecular-beam epitaxy. NANOTECHNOLOGY 2023; 35:065705. [PMID: 37944189 DOI: 10.1088/1361-6528/ad0b1f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2023] [Accepted: 11/09/2023] [Indexed: 11/12/2023]
Abstract
In-plane InAs nanowires and nanowire networks show great potential to be used as building blocks for electronic, optoelectronic and topological quantum devices, and all these applications are keen to grow the InAs materials directly on Si substrates since it may enable nanowire electronic and quantum devices with seamless integration with Si platform. However, almost all the in-plane InAs nanowires and nanowire networks have been realized on substrates of III-V semiconductors. Here, we demonstrate the selective area epitaxial growth of in-plane InAs nanowires and nanowire networks on Si substrates. We find that the selectivity of InAs growth on Si substrates is mainly dependent on the growth temperature, while the morphology of InAs nanowires is closely related to the V/III flux ratio. We examine the cross-sectional shapes and facets of the InAs nanowires grown along the 〈110〉, 〈100〉 and 〈112〉 orientations. Thanks to the non-polar characteristics of Si substrates, the InAs nanowires and nanowire networks exhibit superior symmetry compared to that grown on III-V substrates. The InAs nanowires and nanowire networks are zinc-blende (ZB) crystals, but there are many defects in the nanowires, such as stacking faults, twins and grain boundaries. The crystal quality of InAs nanowires and nanowire networks can be improved by increasing the growth temperature within the growth temperature window. Our work demonstrates the feasibility of selective area epitaxial growth of in-plane InAs nanowires and nanowire networks on Si substrates.
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Affiliation(s)
- Lei Liu
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, PO Box 912, Beijing 100083, People's Republic of China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Lianjun Wen
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, PO Box 912, Beijing 100083, People's Republic of China
| | - Fengyue He
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, PO Box 912, Beijing 100083, People's Republic of China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Ran Zhuo
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, PO Box 912, Beijing 100083, People's Republic of China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Dong Pan
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, PO Box 912, Beijing 100083, People's Republic of China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
| | - Jianhua Zhao
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, PO Box 912, Beijing 100083, People's Republic of China
- Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, People's Republic of China
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3
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Song MS, Koren T, Załuska-Kotur M, Buczko R, Avraham N, Kacman P, Shtrikman H, Beidenkopf H. Sub-Band Spectrum Engineering via Structural Order in Tapered Nanowires. NANO LETTERS 2021; 21:10215-10221. [PMID: 34882412 PMCID: PMC8704197 DOI: 10.1021/acs.nanolett.1c03071] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/11/2021] [Revised: 11/30/2021] [Indexed: 06/13/2023]
Abstract
The cross-sectional dimensions of nanowires set the quantization conditions for the electronic subbands they host. These can be used as a platform to realize one-dimesional topological superconductivity. Here we develop a protocol that forces such nanowires to kink and change their growth direction. Consequently, a thin rectangular nanoplate is formed, which gradually converges into a very thin square tip. We characterize the resulting tapered nanowires structurally and spectroscopically by scanning and transmission electron microscopy and scanning tunneling microscopy and spectroscopy and model their growth. A unique structure composed of ordered rows of atoms on the (110) facet of the nanoflag is further revealed by atomically resolved topography and modeled by simulations. We discuss possible advantages tapered InAs nanowires offer for Majorana zero-mode realization and manipulation.
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Affiliation(s)
- Man Suk Song
- Department
of Condensed Matter Physics, Weizmann Institute
of Science, Rehovot 7610001, Israel
| | - Tom Koren
- Department
of Condensed Matter Physics, Weizmann Institute
of Science, Rehovot 7610001, Israel
| | - Magdalena Załuska-Kotur
- Institute
of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, Warsaw PL-02-668, Poland
| | - Ryszard Buczko
- Institute
of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, Warsaw PL-02-668, Poland
| | - Nurit Avraham
- Department
of Condensed Matter Physics, Weizmann Institute
of Science, Rehovot 7610001, Israel
| | - Perla Kacman
- Institute
of Physics, Polish Academy of Sciences, Aleja Lotnikow 32/46, Warsaw PL-02-668, Poland
| | - Hadas Shtrikman
- Department
of Condensed Matter Physics, Weizmann Institute
of Science, Rehovot 7610001, Israel
| | - Haim Beidenkopf
- Department
of Condensed Matter Physics, Weizmann Institute
of Science, Rehovot 7610001, Israel
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4
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Carrad DJ, Bjergfelt M, Kanne T, Aagesen M, Krizek F, Fiordaliso EM, Johnson E, Nygård J, Jespersen TS. Shadow Epitaxy for In Situ Growth of Generic Semiconductor/Superconductor Hybrids. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2020; 32:e1908411. [PMID: 32337791 DOI: 10.1002/adma.201908411] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2019] [Revised: 02/27/2020] [Accepted: 03/23/2020] [Indexed: 06/11/2023]
Abstract
Uniform, defect-free crystal interfaces and surfaces are crucial ingredients for realizing high-performance nanoscale devices. A pertinent example is that advances in gate-tunable and topological superconductivity using semiconductor/superconductor electronic devices are currently built on the hard proximity-induced superconducting gap obtained from epitaxial indium arsenide/aluminum heterostructures. Fabrication of devices requires selective etch processes; these exist only for InAs/Al hybrids, precluding the use of other, potentially superior material combinations. This work introduces a crystal growth platform-based on 3D structuring of growth substrates-which enables synthesis of semiconductor nanowire hybrids with in situ patterned superconductor shells. The platform eliminates the need for etching, thereby enabling full freedom in the choice of hybrid constituents. All of the most frequently used superconducting hybrid device architectures are realized and characterized. These devices exhibit increased yield and electrostatic stability compared to etched devices, and evidence of ballistic superconductivity is observed. In addition to aluminum, hybrid structures based on tantalum, niobium, and vanadium are presented.
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Affiliation(s)
- Damon J Carrad
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
| | - Martin Bjergfelt
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
| | - Thomas Kanne
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
| | - Martin Aagesen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
- Danish Defence Research Center, Ballerup, 2750, Denmark
| | - Filip Krizek
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
- Department of Spintronics, Institute of Physics, Czech Academy of Sciences, Praha 6, Prague, 162 00, Czech Republic
| | | | - Erik Johnson
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
- Department of Mechanical Engineering, Technical University of Denmark, Kgs. Lyngby, 2800, Denmark
| | - Jesper Nygård
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
| | - Thomas Sand Jespersen
- Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Copenhagen, 2100, Denmark
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5
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Grivnin A, Bor E, Heiblum M, Oreg Y, Shtrikman H. Concomitant opening of a bulk-gap with an emerging possible Majorana zero mode. Nat Commun 2019; 10:1940. [PMID: 31036841 PMCID: PMC6488617 DOI: 10.1038/s41467-019-09771-0] [Citation(s) in RCA: 44] [Impact Index Per Article: 8.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/06/2018] [Accepted: 03/20/2019] [Indexed: 11/23/2022] Open
Abstract
Majorana quasiparticles are generally detected in a 1D topological superconductor by tunneling electrons into its edge, with an emergent zero-bias conductance peak (ZBCP). However, such a ZBCP can also result from other mechanisms, hence, additional verifications are required. Since the emergence of a Majorana must be accompanied by an opening of a topological gap in the bulk, two simultaneous measurements are performed: one in the bulk and another at the edge of a 1D InAs nanowire coated with epitaxial aluminum. Only under certain experimental parameters, a closing of the superconducting bulk-gap that is followed by its reopening, appears simultaneously with a ZBCP at the edge. Such events suggest the occurrence of a topologically non-trivial phase. Yet, we also find that ZBCPs are observed under different tuning parameters without simultaneous reopening of a bulk-gap. This demonstrates the importance of simultaneous probing of bulk and edge in the identification of Majorana edge-states.
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Affiliation(s)
- Anna Grivnin
- Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot, 76100, Israel
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | - Ella Bor
- Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot, 76100, Israel
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | - Moty Heiblum
- Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot, 76100, Israel.
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel.
| | - Yuval Oreg
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
| | - Hadas Shtrikman
- Braun Center for Submicron Research, Weizmann Institute of Science, Rehovot, 76100, Israel
- Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100, Israel
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6
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Pan D, Wang JY, Zhang W, Zhu L, Su X, Fan F, Fu Y, Huang S, Wei D, Zhang L, Sui M, Yartsev A, Xu H, Zhao J. Dimension Engineering of High-Quality InAs Nanostructures on a Wafer Scale. NANO LETTERS 2019; 19:1632-1642. [PMID: 30779588 DOI: 10.1021/acs.nanolett.8b04561] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Low-dimensional narrow-band-gap III-V semiconductors are key building blocks for the next generation of high-performance nanoelectronics, nanophotonics, and quantum devices. Realizing these various applications requires an efficient methodology that enables the material dimensional control during the synthesis process and the mass production of these materials with perfect crystallinity, reproducibility, low cost, and outstanding electronic and optoelectronic properties. Although advances in one- and two-dimensional narrow-band-gap III-V semiconductors synthesis, the progress toward reliable methods that can satisfy all of these requirements has been limited. Here, we demonstrate an approach that provides a precise control of the dimension of InAs from one-dimensional nanowires to wafer-scale free-standing two-dimensional nanosheets, which have a high degree of crystallinity and outstanding electrical and optical properties, using molecular-beam epitaxy by controlling catalyst alloy segregation. In our approach, two-dimensional InAs nanosheets can be obtained directly from one-dimensional InAs nanowires by silver-indium alloy segregation, which is much easier than the previously reported methods, such as the traditional buffering technique and select-area epitaxial growth. Detailed transmission electron microscopy investigations provide solid evidence that the catalyst alloy segregation is the origination of the InAs dimensional transformation from one-dimensional nanowires to two-dimensional nanosheets and even to three-dimensional complex crosses. Using this method, we find that the wafer-scale free-standing InAs nanosheets can be grown on various substrates including Si, MgO, sapphire, GaAs, etc. The InAs nanosheets grown at high temperature are pure-phase single crystals and have a high electron mobility and a long time-resolved terahertz kinetics lifetime. Our work will open up a conceptually new and general technology route toward the effective controlling of the dimension of the low-dimensional III-V semiconductors. It may also enable the low-cost fabrication of free-standing nanosheet-based devices on an industrial scale.
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Affiliation(s)
- Dong Pan
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors , Chinese Academy of Sciences , P.O. Box 912, Beijing 100083 , China
- Center of Materials Science and Optoelectronics Engineering , University of Chinese Academy of Sciences , Beijing 100190 , China
| | - Ji-Yin Wang
- Beijing Key Laboratory of Quantum Devices, Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics , Peking University , Beijing 100871 , China
| | - Wei Zhang
- NanoLund and Division of Chemical Physics , Lund University , Box 124, 22100 Lund , Sweden
- School of Physics and Electronic Engineering , Guangzhou University , Guangzhou 510006 , China
| | - Lujun Zhu
- Institute of Microstructure and Properties of Advanced Materials , Beijing University of Technology , Beijing 100124 , China
- College of Physics and Information Technology , Shaanxi Normal University , Xi'an 710062 , China
| | - Xiaojun Su
- NanoLund and Division of Chemical Physics , Lund University , Box 124, 22100 Lund , Sweden
| | - Furong Fan
- Beijing Key Laboratory of Quantum Devices, Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics , Peking University , Beijing 100871 , China
| | - Yuhao Fu
- Key Laboratory of Automobile Materials of MOE and School of Materials Science and Engineering , Jilin University , Changchun 130012 , China
| | - Shaoyun Huang
- Beijing Key Laboratory of Quantum Devices, Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics , Peking University , Beijing 100871 , China
| | - Dahai Wei
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors , Chinese Academy of Sciences , P.O. Box 912, Beijing 100083 , China
| | - Lijun Zhang
- Key Laboratory of Automobile Materials of MOE and School of Materials Science and Engineering , Jilin University , Changchun 130012 , China
| | - Manling Sui
- Institute of Microstructure and Properties of Advanced Materials , Beijing University of Technology , Beijing 100124 , China
| | - Arkady Yartsev
- NanoLund and Division of Chemical Physics , Lund University , Box 124, 22100 Lund , Sweden
| | - Hongqi Xu
- Beijing Key Laboratory of Quantum Devices, Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics , Peking University , Beijing 100871 , China
- NanoLund and Division of Solid-State Physics , Lund University , Box 118, S-22100 Lund , Sweden
- Beijing Academy of Quantum Information Sciences , Beijing 100193 , China
| | - Jianhua Zhao
- State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors , Chinese Academy of Sciences , P.O. Box 912, Beijing 100083 , China
- Center of Materials Science and Optoelectronics Engineering , University of Chinese Academy of Sciences , Beijing 100190 , China
- Beijing Academy of Quantum Information Sciences , Beijing 100193 , China
- CAS Center for Excellence in Topological Quantum Computation , University of Chinese Academy of Sciences , Beijing 100190 , China
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7
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Gill ST, Damasco J, Janicek BE, Durkin MS, Humbert V, Gazibegovic S, Car D, Bakkers EPAM, Huang PY, Mason N. Selective-Area Superconductor Epitaxy to Ballistic Semiconductor Nanowires. NANO LETTERS 2018; 18:6121-6128. [PMID: 30200769 DOI: 10.1021/acs.nanolett.8b01534] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Semiconductor nanowires such as InAs and InSb are promising materials for studying Majorana zero modes and demonstrating non-Abelian particle exchange relevant for topological quantum computing. While evidence for Majorana bound states in nanowires has been shown, the majority of these experiments are marked by significant disorder. In particular, the interfacial inhomogeneity between the superconductor and nanowire is strongly believed to be the main culprit for disorder and the resulting "soft superconducting gap" ubiquitous in tunneling studies of hybrid semiconductor-superconductor systems. Additionally, a lack of ballistic transport in nanowire systems can create bound states that mimic Majorana signatures. We resolve these problems through the development of selective-area epitaxy of Al to InSb nanowires, a technique applicable to other nanowires and superconductors. Epitaxial InSb-Al devices generically possess a hard superconducting gap and demonstrate ballistic 1D superconductivity and near-perfect transmission of supercurrents in the single mode regime, requisites for engineering and controlling 1D topological superconductivity. Additionally, we demonstrate that epitaxial InSb-Al superconducting island devices, the building blocks for Majorana-based quantum computing applications, prepared using selective-area epitaxy can achieve micron-scale ballistic 1D transport. Our results pave the way for the development of networks of ballistic superconducting electronics for quantum device applications.
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Affiliation(s)
| | | | | | | | | | - Sasa Gazibegovic
- QuTech and Kavli Institute of NanoScience , Delft University of Technology , 2600 GA Delft , The Netherlands
- Department of Applied Physics , Eindhoven University of Technology , 5600 MB Eindhoven , The Netherlands
| | - Diana Car
- QuTech and Kavli Institute of NanoScience , Delft University of Technology , 2600 GA Delft , The Netherlands
- Department of Applied Physics , Eindhoven University of Technology , 5600 MB Eindhoven , The Netherlands
| | - Erik P A M Bakkers
- QuTech and Kavli Institute of NanoScience , Delft University of Technology , 2600 GA Delft , The Netherlands
- Department of Applied Physics , Eindhoven University of Technology , 5600 MB Eindhoven , The Netherlands
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8
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Kang JH, Krizek F, Zaluska-Kotur M, Krogstrup P, Kacman P, Beidenkopf H, Shtrikman H. Au-Assisted Substrate-Faceting for Inclined Nanowire Growth. NANO LETTERS 2018; 18:4115-4122. [PMID: 29879360 DOI: 10.1021/acs.nanolett.8b00853] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We study the role of gold droplets in the initial stage of nanowire growth via the vapor-liquid-solid method. Apart from serving as a collections center for growth species, the gold droplets carry an additional crucial role that necessarily precedes the nanowire emergence, that is, they assist the nucleation of nanocraters with strongly faceted {111}B side walls. Only once these facets become sufficiently large and regular, the gold droplets start nucleating and guiding the growth of nanowires. We show that this dual role of the gold droplets can be detected and monitored by high-energy electron diffraction during growth. Moreover, gold-induced formation of craters and the onset of nanowires growth on the {111}B facets inside the craters are confirmed by the results of Monte Carlo simulations. The detailed insight into the growth mechanism of inclined nanowires will help to engineer new and complex nanowire-based device architectures.
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Affiliation(s)
- Jung-Hyun Kang
- Department of Condensed Matter Physics, Braun Center for Submicron Research , Weizmann Institute of Science , Rehovot 76100 , Israel
| | - Filip Krizek
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute , University of Copenhagen , 2100 Copenhagen , Denmark
| | - Magdalena Zaluska-Kotur
- Institute of Physics Polish Academy of Science , Al. Lotnikow 32/46 , 02-668 Warsaw , Poland
| | - Peter Krogstrup
- Center for Quantum Devices and Station Q Copenhagen, Niels Bohr Institute , University of Copenhagen , 2100 Copenhagen , Denmark
| | - Perla Kacman
- Institute of Physics Polish Academy of Science , Al. Lotnikow 32/46 , 02-668 Warsaw , Poland
| | - Haim Beidenkopf
- Department of Condensed Matter Physics, Braun Center for Submicron Research , Weizmann Institute of Science , Rehovot 76100 , Israel
| | - Hadas Shtrikman
- Department of Condensed Matter Physics, Braun Center for Submicron Research , Weizmann Institute of Science , Rehovot 76100 , Israel
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