We demonstrate experimentally that graphene quantum capacitance $C_{mathrm{q}}$ can have a strong impact on transport spectroscopy through the interplay with nearby charge reservoirs. The effect is elucidated in a field-effect-gated epitaxial graphen
e device, in which interface states serve as charge reservoirs. The Fermi-level dependence of $C_{mathrm{q}}$ is manifested as an unusual parabolic gate voltage ($V_{mathrm{g}}$) dependence of the carrier density, centered on the Dirac point. Consequently, in high magnetic fields $B$, the spectroscopy of longitudinal resistance ($R_{xx}$) vs. $V_{mathrm{g}}$ represents the structure of the unequally spaced relativistic graphene Landau levels (LLs). $R_{xx}$ mapping vs. $V_{mathrm{g}}$ and $B$ thus reveals the vital role of the zero-energy LL on the development of the anomalously wide $ u=2$ quantum Hall state.
To derive a new H$alpha$ luminosity function and to understand the clustering properties of star-forming galaxies at $z approx 0.24$, we have made a narrow-band imaging survey for H$alpha$ emitting galaxies in the HST COSMOS 2 square degree field. We
used the narrow-band filter NB816 ($lambda_c = 8150$ AA, $Delta lambda = 120$ AA) and sampled H$alpha$ emitters with $EW_{rm obs}(rm Halpha + [Ntextsc{ii}]) > 12$ AA in a redshift range between $z=0.233$ and $z=0.251$ corresponding to a depth of 70 Mpc. We obtained 980 H$alpha$ emitting galaxies in a sky area of 5540 arcmin$^2$, corresponding to a survey volume of $3.1 times 10^4 {rm Mpc^3}$. We derive a H$alpha$ luminosity function with a best-fit Schechter function parameter set of $alpha = -1.35^{+0.11}_{-0.13}$, $logphi_* = -2.65^{+0.27}_{-0.38}$, and $log L_* ({rm erg s^{-1}}) = 41.94^{+0.38}_{-0.23}$. The H$alpha$ luminosity density is $2.7^{+0.7}_{-0.6} times 10^{39}$ ergs s$^{-1}$ Mpc$^{-3}$. After subtracting the AGN contribution (15 %) to the H$alpha$ luminosity density, the star formation rate density is evaluated as $1.8^{+0.7}_{-0.4} times 10^{-2}$ $M_{sun}$ yr$^{-1}$ Mpc$^{-3}$. The angular two-point correlation function of H$alpha$ emitting galaxies of $log L({rm Halpha}) > 39.8$ is well fit by a power law form of $w(theta) = 0.013^{+0.002}_{-0.001} theta^{-0.88 pm 0.03}$, corresponding to the correlation function of $xi(r) = (r/1.9{rm Mpc})^{-1.88}$. We also find that the H$alpha$ emitters with higher H$alpha$ luminosity are more strongly clustered than those with lower luminosity.
