suspended CVD graphene
Our groups has been pioneering shot-noise measurements in nanodevices.1 We have studied noise in various geometries, in the single-electron tunneling device,2 in diffusive wires,3,4 in metallic S-N devices,5 in ballistic cavities6 and in quantum Hall devices where we could demonstrate the antibunching of fermions.7,8 These studies were all done at modest detection frequencies in the 10-100kHz range. In recent years, we have developed a noise measurements scheme that works in the GHz window where we can benefit from low-noise cryogenic HEMT amplifiers.9 Due to the 50W transmission lines, we had to develop impedance matching circuits to efficiently interface high impedance quantum devices,10 such as QDs. We are currently studying shot-noise in clean QDs where we can resolve a detailed map of Fano factors in different gate- and bias voltage regions where different processes involving the QD ground and excited states are relevant.
- C. Beenakker and CS, Phys. Today 56 (5), 37-42 (2003).
- H. Birk, M. J. M. Dejong and CS, Phys. Rev. Lett. 75 (8), 1610-1613 (1995).
- M. Henny, H. Birk, R. Huber, C. Strunk, A. Bachtold, M. Kruger and CS, Appl. Phys. Lett. 71 (6), 773-775 (1997).
- M. Henny, S. Oberholzer, C. Strunk and CS, Phys. Rev. B 59 (4), 2871-2880 (1999).
- T. Hoss, C. Strunk, T. Nussbaumer, R. Huber, U. Staufer and CS, Phys. Rev. B 62 (6), 4079-4085 (2000).
- S. Oberholzer, E. V. Sukhorukov and CS, Nature 415 (6873), 765-767 (2002).
- M. Henny, S. Oberholzer, C. Strunk, T. Heinzel, K. Ensslin, M. Holland and CS, Science 284 (5412), 296 (1999).
- S. Oberholzer, M. Henny, C. Strunk, C. Schonenberger, T. Heinzel, K. Ensslin and M. Holland, Physica E 6 (1-4), 314-317 (2000).
- T. Hasler, M. Jung, V. Ranjan, G. Puebla-Hellmann, A. Wallraff and CS, Phys. Rev. Appl. 4 (5), 054002 (2015).
Funding: ERC-QUEST, SNF, NCCR-QSIT
Relevant papers (keyword: NOISE):
- Measuring a Quantum Dot with an Impedance-Matching On-Chip Superconducting LC Resonator at Gigahertz Frequencies
M. -C. Harabula, T. Hasler, G. Fülöp, M. Jung, V. Ranjan, and C. Schönenberger.
Phys. Rev. Appl., 8:54006, nov 2017. arXiv:1707.09061
We report on the realization of a bonded-bridge on-chip superconducting coil and its use in impedance matching a highly ohmic quantum dot (QD) to a 3-GHz measurement setup. The coil, modeled as a lumped-element LC resonator, is more compact and has a wider bandwidth than resonators based on coplanar transmission lines (e.g., λ/4 impedance transformers and stub tuners), at potentially better signal-to-noise ratios. Specifically, for measurements of radiation emitted by the device, such as shot noise, the 50 × larger bandwidth reduces the time to acquire the spectral density. The resonance frequency, close to 3.25 GHz, is 3 times higher than that of the one previously reported, a wire-bonded coil. As a proof of principle, we fabricate an LC circuit that achieves impedance matching to an approximately 15 kOhm load and validate it with a load defined by a carbon nanotube QD, whose shot noise we measure in the Coulomb-blockade regime.
- Shot Noise of a Quantum Dot Measured with Gigahertz Impedance Matching
T. Hasler, M. Jung, V. Ranjan, G. Puebla-Hellmann, A. Wallraff, and C. Schönenberger.
Physical Review Applied, 4(5):54002, nov 2015. arXiv:1507.04884.pdf
The demand for a fast high-frequency read-out of high-impedance devices, such as quantum dots, necessitates impedance matching. Here we use a resonant impedance-matching circuit (a stub tuner) realized by on-chip superconducting transmission lines to measure the electronic shot noise of a carbonnanotube quantum dot at a frequency close to 3 GHz in an efficient way. As compared to wideband detection without impedance matching, the signal-to-noise ratio can be enhanced by as much as a factor of 800 for a device with an impedance of 100 kOmega. The advantage of the stub resonator concept is the ease with which the response of the circuit can be predicted, designed, and fabricated. We further demonstrate that all relevant matching circuit parameters can reliably be deduced from power-reflectance measurements and then used to predict the power-transmission function from the device through the circuit. The shot noise of the carbon-nanotube quantum dot in the Coulomb blockade regime shows an oscillating suppression below the Schottky value of 2eI, as well as an enhancement in specific regions
- Positive cross-correlations in a normal-conducting fermionic beam-splitter
S. Oberholzer, E. Bieri, C. Schönenberger, M. Giovannini, and J. Faist.
Phys. Rev. Lett., 96:46804, feb 2006. arXiv:0510240
We investigate a beam-splitter experiment implemented in a normal-conducting fermionic electron gas in the quantum Hall regime. The cross correlations between the current fluctuations in the two exit leads of the three terminal device are found to be negative, zero, or even positive, depending on the scattering mechanism within the device. Reversal of the cross correlation sign occurs due to interaction between different edge states and does not reflect the statistics of the fermionic particles which “antibunch.”
- Quantum Shot Noise
C. Beenakker and C. Schönenberger.
Physics Today, 56(5):37-42, May 2003. arXiv:0605025
Fluctuations in the flow of electrons can signal the transition from particlelike to wavelike behavior and signify the nature of charge transport in mesoscopic systems.
- Shot noise of series quantum point contacts intercalating chaotic cavities
S. Oberholzer, E. V. Sukhorukov, C. Strunk, and C. Schönenberger.
Phys. Rev. B, 66:233304, dec 2002. arXiv:0105403
Shot noise of series quantum point contacts forming a sequence of cavities in a two-dimensional electron gas are studied theoretically and experimentally. Noise in such a structure originates from local scattering at the point contacts as well as from chaotic motion of the electrons in the cavities. We found that the measured shot noise is in reasonable agreement with our theoretical prediction taking the cavity noise into account
- Crossover between classical and quantum shot noise in chaotic cavities
S. Oberholzer, E. V. Sukhorukov, and C. Schönenberger.
Nature, 415:765-767, feb 2002.
The discreteness of charge in units of e led Schottky in 1918 to predict that the electrical current in a vacuum tube fluctuates even if all spurious noise sources are eliminated carefully1. This phenomenon is now widely known as shot noise. In recent years, shot noise in mesoscopic conductors, where charge motion is quantum-coherent over distances comparable to the system size, has been studied extensively2, 3, 4, 5. In those experiments, charge does not propagate as an isolated entity through free space, as for vacuum tubes, but is part of a degenerate and quantum-coherent Fermi sea of charges. It has been predicted that shot noise in mesoscopic conductors can disappear altogether when the system is tuned to a regime where electron motion becomes classically chaotic6. Here we experimentally verify this prediction by using chaotic cavities where the time that electrons dwell inside can be tuned7. Shot noise is present for large dwell times, where the electron motion through the cavity is ‘smeared’ by quantum scattering, and it disappears for short dwell times, when the motion becomes classically deterministic
- Shot Noise in Schottky’s Vacuum Tube is Classical
C. Schönenberger, S. Oberholzer, E. V. Sukhorukov, and H. Grabert.
cond-mat/0112504, pages 1-5, dec 2001. arXiv:0112504
In these notes we discuss the origin of shot noise (‘Schroteffekt’) of vacuum tubes in detail. It will be shown that shot noise observed in vacuum tubes and first described by W. Schottky in 1918 is a purely classical phenomenon. This is in pronounced contrast to shot noise investigated in mesoscopic conductors which is due to quantum mechanical diffraction of electron waves.
- Shot Noise by Quantum Scattering in Chaotic Cavities
S.~Oberholzer, E.~V.~Sukhorukov, C.~Strunk, C.~Schönenberger, T.~Heinzel, and M.~Holland.
Phys. Rev. Lett., 86(10):2114-2117, mar 2001. arXiv:0009087
We have experimentally studied shot noise of chaotic cavities defined by two quantum point contacts in series. The cavity noise is determined as (1/4)2e/I/ in agreement with theory and can be well distinguished from other contributions to noise generated at the contacts. Subsequently, we have found that cavity noise decreases if one of the contacts is further opened and reaches nearly zero for a highly asymmetric cavity. Heating inside the cavity due to electron-electron interaction can slightly enhance the noise of large cavities and is also discussed quantitatively.
- The Hanbury Brown and Twiss experiment with fermions
S. Oberholzer, M. Henny, C. Strunk, C. Schönenberger, T. Heinzel, K. Ensslin, and M. Holland.
Physica E, 6:314-317, feb 2000.
We realized an equivalent Hanbury Brown and Twiss experiment for a beam of electrons in a two-dimensional electron gas in the quantum Hall regime. A metallic split gate serves as a tunable beam splitter which is used to partition the incident beam into transmitted and reflected partial beams. The current fluctuations in the reflected and transmitted beam are fully anticorrelated demonstrating that fermions tend to exclude each other (anti-bunching). If the occupation probability of the incident beam is lowered by an additional gate, the anticorrelation is reduced and disappears in the classical limit of a highly diluted beam.
- 1/3-shot-noise suppression in diffusive nanowires
M. Henny, S. Oberholzer, C. Strunk, and C. Schönenberger.
Phys. Rev. B., 59:2871-2880, jan 1999.
We report low-temperature shot noise measurements of short diffusive Au wires attached to electron reservoirs of varying sizes. The measured noise suppression factor compared to the classical noise value 2e|I| strongly depends on the electric heat conductance of the reservoirs. For small reservoirs injection of hot electrons increases the measured noise and hence the suppression factor. The universal 1/3-suppression factor can only asymptotically be reached for macroscopically large and thick electron reservoirs. A heating model based on the Wiedemann-Franz law is used to explain this effect.
- The Fermionic Hanbury-Brown & Twiss Experiment
M. Henny, S. Oberholzer, C. Strunk, T. Heinzel, K. Ensslin, M. Holland, and C. Schönenberger.
Science, 284:296, 1999.
A Hanbury Brown and Twiss experiment for a beam of electrons has been realized in a two-dimensional electron gas in the quantum Hall regime. A metallic split gate serves as a tunable beam splitter to partition the incident beam into transmitted and reflected partial beams. In the nonequilibrium case the fluctuations in the partial beams are shown to be fully anticorrelated, demonstrating that fermions exclude each other. In equilibrium, the cross-correlation of current fluctuations at two different contacts is also found to be negative and nonzero, provided that a direct transmission exists between the contacts.
- Size Dependent Thermopower in Mesoscopic AuFe Wires
C. Strunk, M. Henny, C. Schönenberger, G. Neuttiens, and Van C. Haesendonck.
Phys. Rev. Lett., 81:2982-2985, oct 1998.
We have combined electron heating experiments and noise thermometry to perform quantitative measurements of the thermopower in mesoscopic samples. This new measuring technique allows us to detect finite size effects in the thermopower of narrow AuFe wires with an Fe concentration ranging from 50 to 3000 ppm. The size effects emerge when reducing the width of the wires below ~300 nm and may be related to a spin-orbit induced magnetic anisotropy close to the wire surface.
- Electron heating effects in diffusive metal wires
M. Henny, H. Birk, R. Huber, C. Strunk, A. Bachtold, M. Krüger, and C. Schönenberger.
Appl. Phys. Lett., 71:773-775, jun 1997.
We have investigated the electron heating in metallic diffusive wires of varying length at liquid-helium temperature by measuring the electric noise. The local increase of the electron temperature can be essential already for small currents and is well described by a heat-diffusion equation for the electrons. Depending on the electron thermal conductance and the electron–phonon coupling in the wire, different length regimes are identified. The quantitative knowledge of the electron temperature is important for analysis of nonequilibrium effects involving current heating in mesoscopic wires.
- Preamplifier for electric current noise measurements at low temperatures
H. Birk, K. Oostveen, and C. Schönenberger.
Rev. Sci. Instr., 67:2977-2980, apr 1996.
We have developed a current preamplifier that operates in a liquid-helium bath cryostat. It has been optimized for the measurement of dynamical electric-current fluctuations (noise) of high-impedance sources R>100 MΩ. A bandwidth of up to 400 kHz has been achieved by effectively minimizing the capacitance of the input transistor with a dynamical feedback. The amplifier measures current noise in a scanning tunneling microscope (STM). It enables the measurement of shot noise for currents as low as 30 pA (sampling rate 5 s) for a high-impedance source with a resistance of R>1 GΩ, a value typical for tunneling resistances in STM.
- Shot-Noise Suppression in the Single-Electron Tunneling Regime
H. Birk, M. J. M. de Jong, and C. Schönenberger.
Phys. Rev. Lett., 75:1610-1613, aug 1995.
Electrical current fluctuations through tunnel junctions are studied with a scanning-tunneling microscope. For single-tunnel junctions classical Poisson shot noise is observed, indicative for uncorrelated tunneling of electrons. For double-barrier tunnel junctions, formed by a nanoparticle between tip and surface, the shot noise is observed to be suppressed below the Poisson value. For strongly asymmetric junctions, where a Coulomb staircase is observed in the current-voltage characteristic, the shot-noise suppression is periodic in the applied voltage. This originates from correlations in the transfer of electrons imposed by single-electron charging effects.