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Register a new userPrecision comparison of the quantum Hall effect in graphene and gallium arsenide
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Jan-Theodoor Janssen Dr
Publication date
2012
fields
Physics
and research's language is
English
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The half-integer quantum Hall effect in epitaxial graphene is compared with high precision to the well known integer effect in a GaAs/AlGaAs heterostructure. We find no difference between the quantised resistance values within the relative standard uncertainty of our measurement of $8.7times 10^{-11}$. The result places new tighter limits on any possible correction terms to the simple relation $R_{rm K}=h/e^2$, and also demonstrates that epitaxial graphene samples are suitable for application as electrical resistance standards of the highest metrological quality. We discuss the characterisation of the graphene sample used in this experiment and present the details of the cryogenic current comparator bridge and associated uncertainty budget.
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Electronic devices are extremely sensitive to defects in their constituent semiconductors, but locating electronic point defects in bulk semiconductors has previously been impossible. Here we apply scanning transmission electron microscopy (STEM) electron beam-induced current (EBIC) imaging to map electronic defects in a GaAs nanowire Schottky diode. Imaging with a non-damaging 80 or 200 kV STEM acceleration potential reveals a minority-carrier diffusion length that decreases near the surface of the hexagonal nanowire, thereby demonstrating that the devices charge collection efficiency (CCE) is limited by surface defects. Imaging with a 300 keV STEM beam introduces vacancy-interstitial (VI, or Frenkel) defects in the GaAs that increase carrier recombination and reduce the CCE of the diode. We create, locate, and characterize a single insertion event, determining that a defect inserted 7 nm from the Schottky interface broadly reduces the CCE by 10% across the entire nanowire device. Variable-energy STEM EBIC imaging thus allows both benign mapping and pinpoint modification of a devices e-h recombination landscape, enabling controlled experiments that illuminate the impact of both extended (1D and 2D) and point (0D) defects on semiconductor device performance.
Graphene consists of single or few layers of crystalline ordered carbon atoms. Its visibility on oxidized silicon (Si/SiO_2) enabled its discovery and spawned numerous studies of its unique electronic properties. The combination of graphene with the equally unique electronic material gallium arsenide (GaAs) has up to now lacked such easy visibility. Here we demonstrate that a deliberately tailored GaAs/AlAs (aluminum arsenide) multi-layer structure makes graphene just as visible on GaAs as on Si/SiO_2. We show that standard microscope images of exfoliated graphite on GaAs/AlAs suffice to identify mono-, bi-, and multi-layers of graphene. Raman data confirm our results.
When electrons are confined in two dimensions and subjected to strong magnetic fields, the Coulomb interactions between them become dominant and can lead to novel states of matter such as fractional quantum Hall liquids. In these liquids electrons linked to magnetic flux quanta form complex composite quasipartices, which are manifested in the quantization of the Hall conductivity as rational fractions of the conductance quantum. The recent experimental discovery of an anomalous integer quantum Hall effect in graphene has opened up a new avenue in the study of correlated 2D electronic systems, in which the interacting electron wavefunctions are those of massless chiral fermions. However, due to the prevailing disorder, graphene has thus far exhibited only weak signatures of correlated electron phenomena, despite concerted experimental efforts and intense theoretical interest. Here, we report the observation of the fractional quantum Hall effect in ultraclean suspended graphene, supporting the existence of strongly correlated electron states in the presence of a magnetic field. In addition, at low carrier density graphene becomes an insulator with an energy gap tunable by magnetic field. These newly discovered quantum states offer the opportunity to study a new state of matter of strongly correlated Dirac fermions in the presence of large magnetic fields.
We numerically study the quantum Hall effect (QHE) in bilayer graphene based on tight-binding model in the presence of disorder. Two distinct QHE regimes are identified in the full energy band separated by a critical region with non-quantized Hall Effect. The Hall conductivity around the band center (Dirac point) shows an anomalous quantization proportional to the valley degeneracy, but the $ u=0$ plateau is markedly absent, which is in agreement with experimental observation. In the presence of disorder, the Hall plateaus can be destroyed through the float-up of extended levels toward the band center and higher plateaus disappear first. The central two plateaus around the band center are most robust against disorder scattering, which is separated by a small critical region in between near the Dirac point. The longitudinal conductance around the Dirac point is shown to be nearly a constant in a range of disorder strength, till the last two QHE plateaus completely collapse.
The observation of the anomalous quantum Hall effect in exfoliated graphene flakes triggered an explosion of interest in graphene. It was however not observed in high quality epitaxial graphene multilayers grown on silicon carbide substrates. The quantum Hall effect is shown on epitaxial graphene monolayers that were deliberately grown over substrate steps and subjected to harsh processing procedures, demonstrating the robustness of the epitaxial graphene monolayers and the immunity of their transport properties to temperature, contamination and substrate imperfections. The mobility of the monolayer C-face sample is 19,000 cm^2/Vs. This is an important step towards the realization of epitaxial graphene based electronics.
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