We present Raman spectroscopy measurements on single-and few-layer graphene flakes. Using a scanning confocal approach we collect spectral data with spatial resolution, which allows us to directly compare Raman images with scanning force micrographs. Single-layer graphene can be distinguished from double-and few-layer by the width of the D' line: the single peak for single-layer graphene splits into different peaks for the double-layer. These findings are explained using the double-resonant Raman model based on ab-initio calculations of the electronic structure and of the phonon dispersion. We investigate the D line intensity and find no defects within the flake. A finite D line response originating from the edges can be attributed either to defects or to the breakdown of translational symmetry. The interest in graphite has been revived in the last two decades with the advent of fullerenes 1 and carbon nanotubes. 2 However, only recently single-and few-layer graphene could be transferred to a substrate. 3 Transport measurements revealed a highly-tunable two-dimensional electron/hole gas of relativistic Dirac Fermions embedded in a solid-state environment. 4,5 Going to few-layer graphene, however, disturbs this unique system in such a way that the usual parabolic energy dispersion is recovered. The large structural anisotropy makes few-layer graphene therefore a promising candidate to study the rich physics at the crossover from bulk to purely twodimensional systems. Turning on the weak interlayer coupling while stacking a second layer onto a graphene sheet leads to a branching of the electronic bands and the phonon dispersion at the K point. Double-resonant Raman scattering 6 which depends on electronic and vibrational properties turns out to be an ingenious tool to probe the lifting of that specific degeneracy.We report on Raman mapping of single-and few-layer graphene flakes resting on a silicon oxide substrate. Lateral resolution of 400 nm allows to address neighboring sections with various layers of graphene down to a single graphene sheet, previously determined with the scanning force microscope (SFM). We find that the integrated G line signal is directly correlated with the thickness of the graphitic flake and is shifted upward in frequency for double-and single-layer graphene compared to bulk graphite. The mapping of the peak width of the D' line shows a strong contrast between single-and few-layer graphene. Such a pronounced sensitivity to the transition to the very last layer offers an optical and nondestructive method to unambiguously detect single-layer graphene. In addition, we locally resolve the structural quality of the flake by investigating the D band, which is related to elastic backscattering. The map of the integrated D line signal of a graphitic flake with doubleand single-layer sections shows that the inner part of the flake is quasi defect free, whereas edges and steps serves as scatterers. Finally, we explain the splitting of the D' line as a function of the number of graphene layers with...

We have measured the full counting statistics (FCS) of current fluctuations in a semiconductor quantum dot (QD) by real-time detection of single electron tunneling with a quantum point contact (QPC). This method gives direct access to the distribution function of current fluctuations. Suppression of the second moment (related to the shot noise) and the third moment (related to the asymmetry of the distribution) in a tunable semiconductor QD is demonstrated experimentally.With this method we demonstrate the ability to measure very low current and noise levels.

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.PACS numbers: 71.15. Mb, 78.30Na, 81.05.Uw, 63.20.Kr Graphene nanoribbons [1,2,3,4,5] and narrow graphene constrictions [6,7,8] display unique electronic properties based on truly two-dimensional (2D) graphene [9] with potential applications in nanoelectronics [10] and spintronics [11]. Quasi-1D graphene nanoribbons and constrictions are of interest due to the presence of an effective energy gap, overcoming the gap-less band structure of graphene and leading to overall semiconducting behavior, most promising for the fabrication of nanoscale graphene transistors [5], tunnel barriers, and quantum dots [6,7,8]. On the other hand, ideal graphene nanoribbons [12,13] promise interesting quasi-1D physics with strong relations to carbon nanotubes [14]. Zonefolding approximations [13], π-orbital tight-binding models [15,16], and first principle calculations [17,18] predict an energy gap E g scaling as E g = α/W with the nanoribbon width W , where α ranges between 0.2-1.5 eV×nm, depending on the model and the crystallographic orientation of the nanoribbon [4]. However, these theoretical estimates can neither explain the experimentally observed energy gaps of etched nanoribbons of widths beyond 20 nm, which turn out to be larger than predicted, nor do they explain the large number of resonances found inside the gap [1,2,8]. This has led to the suggestion that localized states (and interactions effects) due to edge roughness, bond contractions at the edges [20] and disorder may dominate the transport gap. Several mechanisms have been proposed to describe the observed gap, including re-normalized lateral confinement [2], quasi-1D Anderson localization [21], percolation models [22] and many-body effects (incl. quantum dots) [19], where substantial edge disorder is required. Recently, it has been shown that also moderate amounts of edge roughness can substantially suppress the linear conductance near the charge neutrality point [23], giving rise to localized states relevant for both single particle and many-body descriptions.In this paper we show experimental evidence that the transport gap in an etched graphene nanoribbon (see schematic in Fig. 1a) is primarily formed by local resonances and quantum dots along the ribbon. We employ lateral graphene gates to show that size...

Quantum coherence in solid-state systems has been demonstrated in superconducting circuits [1] and in semiconductor quantum dots [2]. This has paved the way to investigate solid-state systems for quantum information processing with the potential benefit of scalability compared to other systems based on atoms, ions and photons [3]. Coherent coupling of superconducting circuits to microwave photons, circuit quantum electrodynamics (QED) [4], has opened up new research directions [5] and enabled long distance coupling of qubits [6]. Here we demonstrate how the electromagnetic field of a superconducting microwave resonator can be coupled to a semiconductor double quantum dot. The charge stability diagram of the double dot, typically measured by direct current (DC) transport techniques [7], is investigated via dispersive frequency shifts of the coupled resonator. This hybrid all-solid-state approach offers the potential to coherently couple multiple quantum dot and superconducting qubits together on one chip, and offers a method for high resolution spectroscopy of semiconductor quantum structures.Semiconductor quantum dots are highly controllable solid-state quantum systems [8,9]. Charge measurements in the radio frequency (RF) regime have been demonstrated [10][11][12][13] and recently a lumped element RF resonator was used to measure the quantum capacitance of a double dot [14]. A number of schemes have been proposed for the scaling of quantum dot based quantum information processing [15][16][17][18]. In this work we implement a form of circuit QED [4], coupling charge states of a double dot to the field of an on-chip microwave transmission line resonator [15].The sample investigated is shown in Fig. 1a-c along with an electrical circuit schematic (Fig. 1d). The microwave resonator (see Fig. 1a) is realized using a 200 nm thick Aluminum coplanar waveguide on GaAs and is capacitively coupled to an input and output line to probe its transmission spectrum. The double quantum dot (see Fig. 1c), is fabricated at the position of an anti-node of the standing wave field distribution of the resonator. The left and right dots (LD, RD) are arranged in series with respect to the source and drain (S, D) and are realized on an Al x Ga 1−x As heterostructure with the twodimensional electron gas (2DEG) at a depth of about 35 nm below the surface.To enable a strong coupling between the two systems, an additional gate (RG) (Fig. 1c) was implemented, which extends from the resonator to the right quantum dot. This gives a selective capacitive coupling of the resonator to the right quantum dot, confirmed by DC biasing the resonator via an on-chip inductor (Fig. 1a, inset). This results in a strong dipole coupling of the resonator to two charge states in which an electron is on either the left or right quantum dot. In order to accommodate the gate (RG), a design is realized in which the dots are placed at the mesa edge (beyond which the 2DEG is etched away), which is used as part of the confining potential. To complete the formation of ...

(24). Single-crystal films are essential for devices based on superconductor, giant magnetoresistance, thermionic, piezoelectric, and ferroelectric metal oxides because the intrinsic properties of the material, rather than its grain boundaries, can be exploited. The most active crystallographic orientation can also be selected. Our results show that epitaxy can be achieved even for systems with very high lattice mismatch, and they provide a method for producing other nonequilibrium phases that cannot be accessed by traditional thermal processing. Golden, ibid. 258, 1918Golden, ibid. 258, (1992. 3. J. A. Switzer et al., ibid. 264, 1573Switzer et al., ibid. 264, (1994 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 crosscorrelation of current fluctuations at two different contacts is also found to be negative and nonzero, provided that a direct transmission exists between the contacts.

Ring geometries have fascinated experimental and theoretical physicists over many years. Open rings connected to leads allow the observation of the Aharonov-Bohm effect [1], a paradigm of quantum mechanical phase coherence [2,3]. The phase coherence of transport through a quantum dot embedded in one arm of an open ring has been demonstrated [4]. The energy spectrum of closed rings [5] has only recently been analysed by optical experiments [6,7] and is the basis for the prediction of persistent currents [8] and related experiments [9-11]. Here we report magnetotransport experiments on a ring-shaped semiconductor quantum dot in the Coulomb blockade regime [12]. The measurements allow us to extract the discrete energy levels of a realistic ring, which are found to agree well with theoretical expectations. Such an agreement, so far only found for few-electron quantum dots, is here extended to a many-electron system [13]. In a semiclassical language our results indicate that electron motion is governed by regular rather than chaotic motion, an unexplored regime in many-electron quantum dots.

Understanding the influence of vibrational motion of the atoms on electronic transitions in molecules constitutes a cornerstone of quantum physics, as epitomized by the Franck-Condon principle 1,2 of spectroscopy. Recent advances in building molecular-electronics devices 3 and nanoelectromechanical systems 4 open a new arena for studying the interaction between mechanical and electronic degrees of freedom in transport at the single-molecule level. The tunneling of electrons through molecules or suspended quantum dots 5,6 has been shown to excite vibrational modes, or vibrons 7-9,6 . Beyond this effect, theory predicts that strong electron-vibron coupling dramatically suppresses the current flow at low biases, a collective behaviour known as Franck-Condon blockade 10 . Here we show measurements on quantum dots formed in suspended single-wall carbon nanotubes revealing a remarkably large electron-vibron coupling and, due to the high quality and unprecedented tunability of our samples, admit a quantitative analysis of vibronmediated electronic transport in the regime of strong electron-vibron coupling. This allows us to unambiguously demonstrate the Franck-Condon blockade in a suspended nanostructure. The large observed electron-vibron coupling could ultimately be a key ingredient for the detection of quantized mechanical motion 11,12 . It also emphasizes the unique potential for nanoelectromechanical device applications based on suspended graphene sheets and carbon nanotubes. In a polar semiconductor, a conduction electron deforms the surrounding lattice to form a polaron state 13 . The formation of this quasi-particle, by combining an electron and a cloud of lattice vibrations, or phonons, strongly influences the transport properties. The possibility for localization of strongly coupled polarons was suggested by Landau more than 70 years ago 13 . Recently, Koch et al. predicted that a related trapping of heavy polarons can occur in a quantum dot (QD) formed in a mechanically suspended nanostructure 10 . In such a nanoelectromechanical system (NEMS), the vibrational modes of the nanostructure can be strongly affected by the presence of electrons in the QD, as they deform the embedding medium. For strong electron-phonon coupling, the deformation effectively blocks electronic transport, termed Franck-Condon (FC) blockade. By analysing electronic transport through a suspended carbon nanotube (CNT) quantum dot over a wide range of electronic states, we are able to highlight generic features of vibron-assisted electronic transport, and unambiguously confirm the FC blockade scenario.Scanning electron microscope images and a scheme of our suspended CNT quantum dot device are shown in Figs. 1a, 1b and 1c. The CNT is electrically and mechanically connected to both source (S) and drain (D) contacts, while the central electrode acts as a suspended top-gate (TG). A quantum dot in the CNT is formed between defects 14 , which are presumably created during the release process and act as local barriers. The double top-and back-gat...

The strong coupling limit of cavity quantum electrodynamics (QED) implies the capability of a matter-like quantum system to coherently transform an individual excitation into a single photon within a resonant structure. This not only enables essential processes required for quantum information processing but also allows for fundamental studies of matter-light interaction. In this work we demonstrate strong coupling between the charge degree of freedom in a gate-defined GaAs double quantum dot (DQD) and a frequency-tunable high impedance resonator realized using an array of superconducting quantum interference devices (SQUIDs). In the resonant regime, we resolve the vacuum Rabi mode splitting of size 2g/2π = 238 MHz at a resonator linewidth κ/2π = 12 MHz and a DQD charge qubit dephasing rate of γ2/2π = 80 MHz extracted independently from microwave spectroscopy in the dispersive regime. Our measurements indicate a viable path towards using circuit based cavity QED for quantum information processing in semiconductor nano-structures.In the strong coupling limit, cavity QED realizes the coherent exchange of a single quantum of energy between a nonlinear quantum system with two or more energy levels, e.g. a qubit, and a single mode of a high quality cavity capable of storing individual photons [1]. The distinguishing feature of strong coupling is a coherent coupling rate g, determined by the product of the dipole moment of the multi-level system and the vacuum field of the cavity, which exceeds both the cavity mode linewidth κ, determining the photon life time, and the qubit linewidth γ 2 = γ 1 /2 + γ ϕ , set by its energy relaxation and pure dephasing rates, γ 1 and γ ϕ , respectively.The strong coupling limit of Cavity QED has been reached with a multitude of physical systems including alkali atoms [2], Rydberg atoms [3], superconducting circuits [4,5] and optical transitions in semiconductor quantum dots [6,7]. Of particular interest is the use of this concept in quantum information processing with supercondcuting circuits where it is known as circuit QED [4,8,9].Motivated by the ability to suppress the spontaneous emission of qubits beyond the free space limit [10], to perform quantum non-demolition (QND) qubit read-out [11,12], to couple distant qubits through microwave photons coherently [13,14] and to convert quantum information stored in stationary qubits to photons [15,16], research towards reaching the strong coupling limit of cavity QED is pursued for the charge and spin degrees of freedom in semiconductor nano-structures [17][18][19][20][21][22]. Recently, in parallel with the work discussed here, independent efforts to reach this goal have come to fruition with gate defined DQDs in silicon [23] and carbon nanotubes [24].The essence of our approach to reach the strong coupling limit with individual electronic charges in GaAs DQDs is rooted in the enhancement of the electric component of the vacuum fluctuations ∝ √ Z r [25] by increas-ing the resonator impedance Z r beyond the typical 50 Ω of a standard copl...