Graphene

Spatial mapping of the Dirac point in monolayer and bilayer graphene
A. Deshpande, W. Bao, Z. Zhao, C.N. Lau, and B.J. LeRoy
We have mapped the Dirac point in exfoliated monolayer and bilayer graphene using spatially resolved scanning tunneling spectroscopy (STS) measurements at low temperature. The Dirac point shifts in energy at different locations in graphene. However, a cross correlation with the topography shows no correlation indicating that topographic features such as ripples are not the primary source of the variation. Rather, we attribute the shift of the Dirac point to random charged impurities located near the graphene. Our findings emphasize the need to advance exfoliated graphene sample preparation to minimize the effect of impurities.
ArXiv:0912.0547.

Mapping the Dirac point in gated bilayer graphene
A. Deshpande, W. Bao, Z. Zhao, C.N. Lau, and B.J. LeRoy
We have performed low temperature scanning tunneling spectroscopy measurements on exfoliated bilayer graphene on SiO2. By varying the back gate voltage we observed a linear shift of the Dirac point and an opening of a band gap due to the perpendicular electric field. In addition to observing a shift in the Dirac point, we also measured its spatial dependence using spatially resolved scanning tunneling spectroscopy. The spatial variation of the Dirac point was not correlated with topographic features and therefore we attribute its shift to random charged impurities.
Applied Physics Letters 95, 243502 (2009).

Lithography-free Fabrication of High Quality Substrate-supported and Suspended Graphene devices
W. Bao, G. Liu, Z. Zhao, H. Zhang, D. Yan, A. Deshpande, B.J. LeRoy, and C.N. Lau
We present a lithography-free technique for fabrication of clean, high quality graphene devices. This technique is based on evaporation through hard Si shadow masks, and eliminates contaminants introduced by lithographical processes. We demonstrate that devices fabricated by this technique have significantly higher mobility values than those by standard electron beam lithography. To obtain ultra-high mobility devices, we extend this technique to fabricate suspended graphene samples with mobility as high as 200,000 cm2/Vs.
Nano Research 3, 98 (2010).

Spatially resolved spectroscopy of monolayer graphene on SiO2
A. Deshpande, W. Bao, F. Miao, C.N. Lau, and B.J. LeRoy
We carried out scanning tunneling spectroscopy measurements on exfoliated monolayer graphene on SiO2 to probe the correlation between its electronic and structural properties. Maps of the local density of states are characterized by electron and hole puddles that arise due to long-range intravalley scattering from intrinsic ripples in graphene and random-charged impurities. At low energy, we observe short-range intervalley scattering which we attribute to lattice defects. Our results demonstrate that the electronic properties of graphene are influenced by intrinsic ripples, defects, and the underlying SiO2 substrate.
Physical Review B 79, 205411 (2009).


Spectroscopy of nanotubes

Simultaneous electrical transport and scanning tunneling spectroscopy of carbon nanotubes
B.J. LeRoy, I. Heller, V.K. Pahilwani, C. Dekker and S.G. Lemay
We performed scanning tunneling spectroscopy measurements on suspended single-walled carbon nanotubes with independently addressable source and drain electrodes in the Coulomb blockade regime. This three-terminal configuration allows the resistance to the source and drain electrodes to be individually measured, which we exploit to demonstrate that electrons were added to spin-degenerate states of the carbon nanotube. Unexpectedly, the Coulomb peaks also showed a strong spatial dependence. By performing simultaneous scanning tunneling spectroscopy and electrical transport measurements we show that the probed states are extended between the source and drain electrodes. This indicates that the observed spatial dependence reflects a modulation of the contact resistance.
Nano Letters 7, 2937 (2007).

Three-terminal scanning tunneling spectroscopy of suspended carbon nanotubes
B.J. LeRoy, J. Kong, V.K. Pahilwani, C. Dekker and S.G. Lemay
We have performed low-temperature scanning tunneling spectroscopy measurements on suspended singlewall carbon nanotubes with a gate electrode allowing three-terminal spectroscopy measurements. These measurements show well-defined Coulomb diamonds as well as side peaks from phonon-assisted tunneling. The side peaks have the same gate voltage dependence as the main Coulomb peaks, directly proving that they are excitations of these states.
Physical Review B 72, 075413 (2005).

Integration of a gate electrode into carbon nanotube devices for scanning tunneling microscopy
J. Kong, B.J. LeRoy, S.G. Lemay and C. Dekker
We have developed a fabrication process for incorporating a gate electrode into suspended single-walled carbon nanotube structures for scanning tunneling spectroscopy studies. The nanotubes are synthesized by chemical vapor deposition directly on a metal surface. The high temperature s800 °Cd involved in the growth process poses challenging issues such as surface roughness and integrity of the structure which are addressed in this work. We demonstrate the effectiveness of the gate on the freestanding part of the nanotubes by performing tunneling spectroscopy that reveals Coulomb blockade diamonds. Our approach enables combined scanning tunneling microscopy and gated electron transport investigations of carbon nanotubes.
Applied Physics Letters 86, 112106 (2005).

Electrical generation and absorption of phonons in carbon nanotubes
B.J. LeRoy, S.G. Lemay, J. Kong and C. Dekker
The interplay between discrete vibrational and electronic degrees of freedom directly influences the chemical and physical properties of molecular systems. This coupling is typically studied through optical methods such as fluorescence, absorption and Raman spectroscopy. Molecular electronic devices provide new opportunities for exploring vibration–electronic interactions at the single molecule level. For example, electrons injected from a scanning tunnelling microscope tip into a metal can excite vibrational excitations of a molecule situated in the gap between tip and metal. Here we show how current directly injected into a freely suspended individual single-wall carbon nanotube can be used to excite, detect and control a specific vibrational mode of the molecule. Electrons tunnelling inelastically into the nanotube cause a non-equilibrium occupation of the radial breathing mode, leading to both stimulated emission and absorption of phonons by successive electron tunnelling events.We exploit this effect to measure a phonon lifetime of the order of 10 ns, corresponding to a quality factor of well over 10,000 for this nanomechanical oscillator.
Nature 432, 371 (2004).

Scanning tunneling spectroscopy of suspended single-wall carbon nanotubes
B.J. LeRoy, S.G. Lemay, J. Kong and C. Dekker
We have performed low-temperature scanning tunneling microscopy measurements on single-wall carbon nanotubes that are freely suspended over a trench. The nanotubes were grown by chemical vapor deposition on a Pt substrate with predefined trenches etched into it. Atomic resolution was obtained on the freestanding portions of the nanotubes. Spatially resolved spectroscopy on the suspended portion of both metallic and semiconducting nanotubes was also achieved, showing a Coulomb-staircase behavior superimposed on the local density of states. The spacing of the Coulomb blockade peaks changed with tip position reflecting a changing tip-tube capacitance.
Applied Physics Letters 84, 4280 (2004).


Imaging electron flow

Imaging electron interferometer
B.J. LeRoy, A.C. Bleszynski, K.E. Aidala, R.M. Westervelt, A. Kalben, E.J. Heller, S.E.J. Shaw,
K.D. Maranowski, and A.C. Gossard
An imaging interferometer was created in a two-dimensional electron gas by reflecting electron waves emitted from a quantum point contact with a circular mirror. Images of electron flow obtained with a scanning probe microscope at liquid He temperatures show interference fringes when the mirror is energized. A quantum phase shifter was created by moving the mirror via its gate voltage, and an interferometric spectrometer can be formed by sweeping the tip over many wavelengths. Experiments and theory demonstrate that the interference signal is robust against thermal averaging.
Physical Review Letters 94, 126801 (2005).
For movies associated with this paper follow this link.

Imaging Coherent Electron Flow Through Semiconductor Nanostructures
B.J. LeRoy
Ph. D. Thesis, Harvard University (2003).

Imaging Coherent Electron Flow
B.J. LeRoy, A.C. Bleszynski, M.A. Topinka, R.M. Westervelt, S.E.J. Shaw, E.J. Heller,
K.D. Maranowski and A.C. Gossard
Images of electron flow through a two-dimensional electron gas from a quantum point contact (QPC) can be obtained at liquid He temperatures using scanning probe microscopy (SPM). A negatively charged SPM tip depletes the electron gas immediately below it and decreases the conductance by backscattering electrons. Images of electron flow are obtained by recording the conductance as the tip is scanned over the sample. These images show angular patterns that are characteristic of electron flow through individual modes of the QPC, as well as well- defined branches at longer distances. The addition of a prism formed by a triangular gate bends electron paths as the electron density is reduced under the prism by an applied gate voltage. Under the conditions of the experiment, electron–electron scattering is the dominant inelastic process. By observing how the amplitude of backscattered electrons in images of electron flow decreases with added electron energy, we are able to determine the average length and time necessary for inelastic scattering. A dc voltage V0 applied across the QPC accelerates electrons so that their energy is greater than the Fermi energy before inelastic scattering occurs. The signal is observed to decrease in amplitude and eventually disappear at distances from the QPC that decrease progressively as V0 is increased.
Proceedings of the International Conference on the Physics of Semiconductors (ICPS), cond-mat/0208194.

Imaging Electron Density in a Two-Dimensional Electron Gas
B.J. LeRoy, M.A. Topinka, R.M. Westervelt, K.D. Maranowski and A.C. Gossard
Spatial profiles of the electron density in a two-dimensional electron gas were obtained from the spacing of interference fringes in coherent electron flow. Images of electron flow from a quantum point contact formed in a GaAs/AlGaAs heterostructure were recorded with a liquid He cooled scanned probe microscope. The images are decorated with interference fringes spaced by half the Fermi wavelength; the fringe spacing measures the electron density below the scanned probe microscope tip. As the density is decreased with a back gate, the fringe spacing increases in agreement with a planar capacitor model.
Applied Physics Letters 80, 4431 (2002).

Coherent Branched Flow in a Two-Dimensional Electron Gas
 M.A. Topinka, B.J. LeRoy, R.M. Westervelt, S.E.J. Shaw, R. Fleischmann, E.J. Heller,
K.D. Maranowski, A.C. Gossard
Semiconductor nanostructures based on two-dimensional electron gases (2DEGs) could form the basis of future devices for sensing, information processing and quantum computation. Although electron transport in 2DEG nanostructures has been well studied, and many remarkable phenomena have already been discovered (for example, weak localization, quantum chaos, universal conductance fluctuations), fundamental aspects of the electron flow through these structures have so far not been clarified. However, it has recently become possible to image current directly through 2DEG devices using scanning probe microscope techniques. Here, we use such a technique to observe electron flow through a narrow constriction in a 2DEG—a quantum point contact. The images show that the electron flow from the point contact forms narrow, branching strands instead of smoothly spreading fans. Our theoretical study of this flow indicates that this branching of current flux is due to focusing of the electron paths by ripples in the background potential. The strands are decorated by interference fringes separated by half the Fermi wavelength, indicating the persistence of quantum mechanical phase coherence in the electron flow. These findings may have important implications for a better understanding of electron transport in 2DEGs and for the design of future nanostructure devices.
Nature 410, 183 (2001).

Imaging Coherent Electron Flow From a Quantum Point Contact
M.A. Topinka, B.J. LeRoy, S.E.J. Shaw, E.J. Heller, R.M. Westervelt, K.D. Maranowski and
A.C. Gossard
Scanning a charged tip above the two-dimensional electron gas inside a gallium arsenide/aluminum gallium arsenide nanostructure allows the coherent electron flow from the lowest quantized modes of a quantum point contact at liquid helium temperatures to be imaged. As the width of the quantum point contact is increased, its electrical conductance increases in quantized steps of 2 e²/h, where e is the electron charge and h is Planck's constant. The angular dependence of the electron flow on each step agrees with theory, and fringes separated by half the electron wavelength are observed. Placing the tip so that it interrupts the flow from particular modes of the quantum point contact causes a reduction in the conductance of those particular conduction channels below 2 e²/h without affecting other channels.
Science 289, 2323 (2000).