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Will M, Hamer M, Müller M, Noury A, Weber P, Bachtold A, Gorbachev RV, Stampfer C, Güttinger J. High Quality Factor Graphene-Based Two-Dimensional Heterostructure Mechanical Resonator. Nano Lett 2017; 17:5950-5955. [PMID: 28906119 DOI: 10.1021/acs.nanolett.7b01845] [Citation(s) in RCA: 30] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
Abstract
Ultralight mechanical resonators based on low-dimensional materials are well suited as exceptional transducers of minuscule forces or mass changes. However, the low dimensionality also provides a challenge to minimize resistive losses and heating. Here, we report on a novel approach that aims to combine different two-dimensional (2D) materials to tackle this challenge. We fabricated a heterostructure mechanical resonator consisting of few layers of niobium diselenide (NbSe2) encapsulated by two graphene sheets. The hybrid membrane shows high quality factors up to 245,000 at low temperatures, comparable to the best few-layer graphene mechanical resonators. In contrast to few-layer graphene resonators, the device shows reduced electrical losses attributed to the lower resistivity of the NbSe2 layer. The peculiar low-temperature dependence of the intrinsic quality factor points to dissipation over two-level systems which in turn relax over the electronic system. Our high sensitivity readout is enabled by coupling the membrane to a superconducting cavity which allows for the integration of the hybrid mechanical resonator as a sensitive and low loss transducer in future quantum circuits.
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Affiliation(s)
- M Will
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University , 52074 Aachen, Germany
| | - M Hamer
- School of Physics and Astronomy and Manchester Centre for Mesoscience and Nanotechnology, University of Manchester , Oxford Road, Manchester M13 9PL, United Kingdom
| | - M Müller
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University , 52074 Aachen, Germany
| | - A Noury
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology , 08860 Castelldefels, Barcelona, Spain
| | - P Weber
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology , 08860 Castelldefels, Barcelona, Spain
| | - A Bachtold
- ICFO-Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology , 08860 Castelldefels, Barcelona, Spain
| | - R V Gorbachev
- School of Physics and Astronomy and Manchester Centre for Mesoscience and Nanotechnology, University of Manchester , Oxford Road, Manchester M13 9PL, United Kingdom
| | - C Stampfer
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University , 52074 Aachen, Germany
- Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich , 52425 Jülich, Germany
| | - J Güttinger
- JARA-FIT and 2nd Institute of Physics, RWTH Aachen University , 52074 Aachen, Germany
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Zhang Y, Moser J, Güttinger J, Bachtold A, Dykman MI. Interplay of driving and frequency noise in the spectra of vibrational systems. Phys Rev Lett 2014; 113:255502. [PMID: 25554894 DOI: 10.1103/physrevlett.113.255502] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2014] [Indexed: 05/22/2023]
Abstract
We study the spectral effect of the fluctuations of the vibration frequency. Such fluctuations play a major role in nanomechanical and other mesoscopic vibrational systems. We find that, for periodically driven systems, the interplay of the driving and frequency fluctuations results in specific spectral features. We present measurements on a carbon nanotube resonator and show that our theory allows not only the characterization of the frequency fluctuations but also the quantification of the decay rate without ring-down measurements. The results bear on identifying the decoherence of mesoscopic oscillators and on the general problem of resonance fluorescence and light scattering by oscillators.
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Affiliation(s)
- Yaxing Zhang
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - J Moser
- ICFO, Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain
| | - J Güttinger
- ICFO, Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain
| | - A Bachtold
- ICFO, Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain
| | - M I Dykman
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
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Moser J, Eichler A, Güttinger J, Dykman MI, Bachtold A. Nanotube mechanical resonators with quality factors of up to 5 million. Nat Nanotechnol 2014; 9:1007-11. [PMID: 25344688 DOI: 10.1038/nnano.2014.234] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/17/2014] [Accepted: 09/13/2014] [Indexed: 05/05/2023]
Abstract
Carbon nanotube mechanical resonators have attracted considerable interest because of their small mass, the high quality of their surfaces, and the pristine electronic states they host. However, their small dimensions result in fragile vibrational states that are difficult to measure. Here, we observe quality factors Q as high as 5 × 10(6) in ultra-clean nanotube resonators at a cryostat temperature of 30 mK, where we define Q as the ratio of the resonant frequency over the linewidth. Measuring such high quality factors requires the use of an ultra-low-noise method to rapidly detect minuscule vibrations, as well as careful reduction of the noise of the electrostatic environment. We observe that the measured quality factors fluctuate because of fluctuations of the resonant frequency. We measure record-high quality factors, which are comparable to the highest Q values reported in mechanical resonators of much larger size, a remarkable result considering that reducing the size of resonators is usually concomitant with decreasing quality factors. The combination of ultra-low mass and very large Q offers new opportunities for ultra-sensitive detection schemes and quantum optomechanical experiments.
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Affiliation(s)
- J Moser
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - A Eichler
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - J Güttinger
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
| | - M I Dykman
- Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824, USA
| | - A Bachtold
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels (Barcelona), Spain
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Weber P, Güttinger J, Tsioutsios I, Chang DE, Bachtold A. Coupling graphene mechanical resonators to superconducting microwave cavities. Nano Lett 2014; 14:2854-60. [PMID: 24745803 DOI: 10.1021/nl500879k] [Citation(s) in RCA: 60] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
Graphene is an attractive material for nanomechanical devices because it allows for exceptional properties, such as high frequencies, quality factors, and low mass. An outstanding challenge, however, has been to obtain large coupling between the motion and external systems for efficient readout and manipulation. Here, we report on a novel approach, in which we capacitively couple a high-Q graphene mechanical resonator (Q ≈ 10(5)) to a superconducting microwave cavity. The initial devices exhibit a large single-photon coupling of ∼10 Hz. Remarkably, we can electrostatically change the graphene equilibrium position and thereby tune the single photon coupling, the mechanical resonance frequency, and the sign and magnitude of the observed Duffing nonlinearity. The strong tunability opens up new possibilities, such as the tuning of the optomechanical coupling strength on a time scale faster than the inverse of the cavity line width. With realistic improvements, it should be possible to enter the regime of quantum optomechanics.
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Affiliation(s)
- P Weber
- ICFO-Institut de Ciencies Fotoniques , Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain
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Moser J, Güttinger J, Eichler A, Esplandiu MJ, Liu DE, Dykman MI, Bachtold A. Ultrasensitive force detection with a nanotube mechanical resonator. Nat Nanotechnol 2013; 8:493-6. [PMID: 23748195 DOI: 10.1038/nnano.2013.97] [Citation(s) in RCA: 107] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/22/2013] [Accepted: 04/25/2013] [Indexed: 05/05/2023]
Abstract
Since the advent of atomic force microscopy, mechanical resonators have been used to study a wide variety of phenomena, including the dynamics of individual electron spins, persistent currents in normal metal rings and the Casimir force. Key to these experiments is the ability to measure weak forces. Here, we report on force sensing experiments with a sensitivity of 12 zN Hz(-1/2) at a temperature of 1.2 K using a resonator made of a carbon nanotube. An ultrasensitive method based on cross-correlated electrical noise measurements, in combination with parametric downconversion, is used to detect the low-amplitude vibrations of the nanotube induced by weak forces. The force sensitivity is quantified by applying a known capacitive force. This detection method also allows us to measure the Brownian vibrations of the nanotube down to cryogenic temperatures. Force sensing with nanotube resonators offers new opportunities for detecting and manipulating individual nuclear spins as well as for magnetometry measurements.
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Affiliation(s)
- J Moser
- ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain
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Güttinger J, Molitor F, Stampfer C, Schnez S, Jacobsen A, Dröscher S, Ihn T, Ensslin K. Transport through graphene quantum dots. Rep Prog Phys 2012; 75:126502. [PMID: 23144122 DOI: 10.1088/0034-4885/75/12/126502] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
We review transport experiments on graphene quantum dots and narrow graphene constrictions. In a quantum dot, electrons are confined in all lateral dimensions, offering the possibility for detailed investigation and controlled manipulation of individual quantum systems. The recently isolated two-dimensional carbon allotrope graphene is an interesting host to study quantum phenomena, due to its novel electronic properties and the expected weak interaction of the electron spin with the material. Graphene quantum dots are fabricated by etching mono-layer flakes into small islands (diameter 60-350 nm) with narrow connections to contacts (width 20-75 nm), serving as tunneling barriers for transport spectroscopy. Electron confinement in graphene quantum dots is observed by measuring Coulomb blockade and transport through excited states, a manifestation of quantum confinement. Measurements in a magnetic field perpendicular to the sample plane allowed to identify the regime with only a few charge carriers in the dot (electron-hole transition), and the crossover to the formation of the graphene specific zero-energy Landau level at high fields. After rotation of the sample into parallel magnetic field orientation, Zeeman spin splitting with a g-factor of g ≈ 2 is measured. The filling sequence of subsequent spin states is similar to what was found in GaAs and related to the non-negligible influence of exchange interactions among the electrons.
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Affiliation(s)
- J Güttinger
- Solid State Physics Laboratory, ETH Zurich, 8092 Zurich, Switzerland.
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Abstract
In this review, recent developments in the fabrication and understanding of the electronic properties of graphene nanostructures are discussed. After a brief overview of the structure of graphene and the two-dimensional transport properties, the focus is put on graphene constrictions, quantum dots and double quantum dots. For constrictions with a width below 100 nm, the current through the constriction is strongly suppressed for a certain back gate voltage range, related to the so-called transport gap. This transport gap is due to the formation of localized puddles in the constriction, and its size depends strongly on the constriction width. Such constrictions can be used to confine charge carriers in quantum dots, leading to Coulomb blockade effects.
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Affiliation(s)
- F Molitor
- Solid State Physics Laboratory, ETH Zurich, Zurich, Switzerland
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Roulleau P, Baer S, Choi T, Molitor F, Güttinger J, Müller T, Dröscher S, Ensslin K, Ihn T. Coherent electron–phonon coupling in tailored quantum systems. Nat Commun 2011; 2:239. [DOI: 10.1038/ncomms1241] [Citation(s) in RCA: 40] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2010] [Accepted: 02/16/2011] [Indexed: 11/09/2022] Open
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Abstract
We investigate ground and excited state transport through small (d≈70 nm) graphene quantum dots. The successive spin filling of orbital states is detected by measuring the difference between ground-state energies as a function of a magnetic field. For a magnetic field in-plane of the quantum dot the Zeeman splitting of spin states is measured. The results are compatible with a g factor of 2, and we detect a spin-filling sequence for a series of states which is reasonable given the strength of exchange interaction effects expected by comparing Coulomb interaction energy and kinetic energy of charge carriers in graphene.
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Affiliation(s)
- J Güttinger
- Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland.
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Güttinger J, Stampfer C, Libisch F, Frey T, Burgdörfer J, Ihn T, Ensslin K. Electron-hole crossover in graphene quantum dots. Phys Rev Lett 2009; 103:046810. [PMID: 19659388 DOI: 10.1103/physrevlett.103.046810] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/22/2009] [Indexed: 05/28/2023]
Abstract
We investigate the addition spectrum of a graphene quantum-dot in the vicinity of the electron-hole crossover as a function of perpendicular magnetic field. Coulomb-blockade resonances of the 50 nm wide dot are visible at all gate voltages across the transport gap ranging from hole to electron transport. The magnetic field dependence of more than 50 states displays the unique complex evolution of the diamagnetic spectrum of a graphene dot from the low-field regime to the Landau regime with the n=0 Landau level situated in the center of the transport gap marking the electron-hole crossover. The average peak spacing in the energy region around the crossover decreases with increasing magnetic field. In the vicinity of the charge neutrality point we observe a well resolved and rich excited state spectrum.
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Affiliation(s)
- J Güttinger
- Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
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Stampfer C, Güttinger J, Hellmüller S, Molitor F, Ensslin K, Ihn T. Energy gaps in etched graphene nanoribbons. Phys Rev Lett 2009; 102:056403. [PMID: 19257529 DOI: 10.1103/physrevlett.102.056403] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/05/2008] [Indexed: 05/13/2023]
Abstract
Transport measurements on an etched graphene nanoribbon are presented. It is shown that two distinct voltage scales can be experimentally extracted that characterize the parameter region of suppressed conductance at low charge density in the ribbon. One of them is related to the charging energy of localized states, the other to the strength of the disorder potential. The lever arms of gates vary by up to 30% for different localized states which must therefore be spread in position along the ribbon. A single-electron transistor is used to prove the addition of individual electrons to the localized states. In our sample the characteristic charging energy is of the order of 10 meV, the characteristic strength of the disorder potential of the order of 100 meV.
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Affiliation(s)
- C Stampfer
- Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
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Stampfer C, Schurtenberger E, Molitor F, Güttinger J, Ihn T, Ensslin K. Tunable graphene single electron transistor. Nano Lett 2008; 8:2378-2383. [PMID: 18642958 DOI: 10.1021/nl801225h] [Citation(s) in RCA: 67] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/26/2023]
Abstract
We report electronic transport experiments on a graphene single electron transistor. The device consists of a graphene island connected to source and drain electrodes via two narrow graphene constrictions. It is electrostatically tunable by three lateral graphene gates and an additional back gate. The tunneling coupling is a strongly nonmonotonic function of gate voltage indicating the presence of localized states in the barriers. We investigate energy scales for the tunneling gap, the resonances in the constrictions, and for the Coulomb blockade resonances. From Coulomb diamond measurements in different device configurations (i.e., barrier configurations) we extract a charging energy of approximately 3.4 meV and estimate a characteristic energy scale for the constriction resonances of approximately 10 meV.
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Affiliation(s)
- C Stampfer
- Solid State Physics Laboratory, ETH Zurich, Zurich, Switzerland.
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Stampfer C, Güttinger J, Roman C, Jungen A, Helbling T, Hierold C. Electron shuttle instability for nano electromechanical mass sensing. Nano Lett 2007; 7:2747-52. [PMID: 17718586 DOI: 10.1021/nl0712419] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
We discuss the potential use of the electromechanical shuttle instability in suspended nanostructures (e.g., nanotubes or nanowires) for nanomechanical sensing. The tunneling-assisted (shuttle-like) electron transport mechanism is addressed from a mechanical and electromechanical point of view, showing strong dependencies on the fundamental frequency, the mechanical restoring and damping force, and the electromechanical charging of the suspended nanostructure. We propose to use these nonlinear dependencies to sense minute mass (and tension) changes. Therefore, we introduce a conceptual sensing device and investigate its operation in the frame of a simple model system. Finally, we discuss different measurement techniques and report on high sensitivities (e.g., 1 nA/zeptogram (zg), or 1 mV/zg depending on the measurement technique) and potential resolutions in the range of 10 zg (10(-23) kg).
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Affiliation(s)
- C Stampfer
- Micro and Nanosystems, ETH Zurich, 8092 Zurich, Switzerland.
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