Probing techniques with spatial resolution have the potential to lead to a better understanding of the microscopic physical processes and to novel routes for manipulating nanostructures.We present scanning-gate images of a graphene quantum dot which is coupled to source and drain via two constrictions. We image and locate conductance resonances of the quantum dot in the Coulomb-blockade regime as well as resonances of localized states in the constrictions in real space.Graphene has sparked intense research among theorists and experimentalists 1,2 alike since its first successful fabrication in 2004. 3 This is mainly due to graphene's extraordinary band structure, a linear relationship between energy and momentum without a band gap. The gapless band structure, however, prohibits confining charge carriers by using electrostatic gates. Hence, lateral confinement in graphene relies on etched structures and the appearance of a transport gap in graphene * To whom correspondence should be addressed † constrictions. [4][5][6] Nevertheless, already the first experiment on graphene nanoribbons by Han et al. 7 showed a discrepancy between the measured transport gap and a simple confinement-induced band gap. Theoretical models explain the observed gap by Coulomb blockade, edge scattering, and/orAnderson-type localization due to edge disorder. [8][9][10][11] On the experimental side, there is increasing evidence for Coulomb-blockade effects in nanoribbons. 6,[12][13][14][15] Transport through graphene quantum dots in the Coulomb blockade regime is typically modulated by resonances arising from the constrictions. 16 However, for both, nanoribbons and quantum dots, the microscopic origin of the transport gap and the resonances in the constrictions needs to be understood in more detail. Atomic-force micrographs of the sample after etching under ambient conditions (a) and of the completed device at T ≈ 2.6 K (b) are shown in Fig. 1. If not stated otherwise, the temperature of all measurements shown in this paper is T = 2.6 K. Fabrication details are given in the supporting information. 24 We first show a backgate sweep in Fig A symmetric bias of V bias = 300 µV was applied across source and drain and the tip was scanned at a constant height of ∆z ≈ 120 nm above the sample. Coulomb resonances of the quantum dot show up as concentric rings denoted by arrow (QD). The center of the Coulomb resonances are offset from the topographic center of the dot by ca. 240 nm. Such a behavior, known from previous scanning-gate experiments, is understood and of minor importance here. 28 The outline of the quantum dot and its connection to source and drain via the two constrictions, depicted with dashed, black lines, is corrected for the offset, assuming that the Coulomb resonances are centered in the quantum dot (see also supporting information 24 ). Most striking, however, is the appearance of two more sets of concentric rings which are highlighted by arrows (A) and (B) and which are centered around points in the constrictions. Th...

We investigate the magnetoresistance of a side-gated ring structure etched out of single-layer graphene. We observe Aharonov-Bohm oscillations with about 5% visibility. We are able to change the relative phases of the wave functions in the interfering paths and induce phase jumps of π in the Aharonov-Bohm oscillations by changing the voltage applied to the side gate or the back gate. The observed data can be interpreted within existing models for 'dirty metals' giving a phase coherence length of the order of 1 µm at a temperature of 500 mK.

We present a comprehensive study of the conductance behavior of atomic-size contacts made of ferromagneti c metals (Co) or noble metals (Au) with ferromagneti c electrodes (Co). In order to separate the influence of the large electrodes fro m the influence of the contacts themse lves, we used different sampl e geometri es. T hese include combinati ons of nonmagnetic electrodes connected to magneti c bridges and vice versa as well as di fferent orientati ons of the mag netic fi eld. The magnetores istance (MR) curves show very rich behavi or with strong MR rati os (MRR). In all geometries the MRR va lu es are of comparabl e size, reaching up to a few thousand percent in the tunneli ng regime. We study the poss ibl e influence of the mi cromag neti c order of the domain s in the vic inity of the contac t as well as balli sti c MR, giant MR, tun nel MR , atomically enh anced ani sotropi c MR (AAMR), and magnetostri cti on. We co nclude that AAMR is the most important origin for the MR at hi gh magnet ic fie lds (iBI > 2 T) , while magnetostri ct ion, tunnel MR , and giant MR govern the low-fie ld reg ime (IBI < 2 T).

We experimentally investigate the conductance of a singlelayer graphene ring. The Aharonov-Bohm oscillation amplitude of the four-terminal resistance is very high with a visibility up to 10%. Additionally, we investigate the amplitude and the period of the Aharonov-Bohm effect over a magnetic field range of AE5 T. We find that, while the period remains constant, the amplitude rises by a factor of 2.

The metallic tip of a scanning force microscope operated at 300 mK is used to locally induce a potential in an fully controllable double quantum dot defined via local anodic oxidation in a GaAs/AlGaAs heterostructure. Using scanning gate techniques we record spatial images of the current through the sample for different numbers of electrons on the quantum dots, i.e. for different quantum states. Owing to the spatial resolution of current maps, we are able to determine the spatial position of the individual quantum dots, and investigate their apparent relative shifts due to the voltage applied to a single gate.