Quantum Hall effect in lightly hydrogenated graphene

TL;DR

This work investigates how light hydrogenation of graphene affects its quantum Hall response and band structure. By hydrogenating monolayer graphene with a cold-plasma and performing magnetotransport up to 30 T, the authors observe a strong reduction of Landau-level spacings and a linear-in-B dependence of activation gaps, consistent with a shift from linear Dirac dispersion to a quadratic dispersion with an effective mass $m^* \,=\$ $0.24$–$0.40\,m_e$. Band-structure simulations predict band-gap opening and a quadratic near the K point that grows with hydrogen coverage, yielding $m^*$ values matching the transport-derived masses for coverages around 4% and 7%. The results agree with ab initio calculations for hydrogen-decorated graphene and suggest that hydrogenation provides a tunable route to engineer graphene's low-energy bands, with potential relevance for graphene-based beta-decay sensing/substrates in tritium experiments.

Abstract

We have measured the quantum Hall effect in monolayer graphene samples that were exposed to a cold hydrogen plasma leading to a hydrogenation level of a few percent. Compared to pristine graphene, the Landau level distance significantly decreases in the hydrogenated structures, and its field dependence changes from square root type to linear. From this observation we conclude that the band structure in hydrogenated graphene changes from a linear Dirac-Weyl type dispersion to a quadratic one with an effective electron mass $m_e^* = 0.24~m_e$. This is in good agreement with ab-initio band structure calculations of hydrogen decorated graphene monolayer.

Figures (4)

• Figure 1: (a) Cold plasma hydrogenation setup. The graphene sample is located in the top left corner. The plasma is located in the middle. Hydrogen gas flows in from the bottom right. (b) Exfoliated graphene sample. The channel width is 5 $\mu$m. The red contour shows the graphene flake. (c) CVD graphene sample acquired from graphenea graphenea. The graphene flake is visible as the darker blue area. (d) Raman spectra of the CVD graphene sample in consecutive states: pristine, after 30 minutes of hydrogen plasma exposure, and after annealing at 300 $^\circ$C. Peaks correlated to graphene peaks and graphene defect peaks are indicated.
• Figure 2: a. Change of the transfer curve at room temperature as a function of hydrogen plasma exposure, measured on an exfoliated graphene sample. Color coding matches the points in the inset. Inset: room temperature CNP resistance as a function of hydrogen plasma exposure time. b. Temperature dependence of the transfer curve at 0 T for the exfoliated graphene sample shown in Fig. \ref{['fig:transport']}a, exposed to hydrogen plasma for 25 minutes. The temperature is encoded in the color of the lines (right color bar). Inset: temperature dependence of the CNP resistance for a cleaved graphene sample that was exposed to hydrogen plasma for 25 (orange) and 30 minutes (yellow).
• Figure 3: a. Temperature dependence of hydrogenated graphene shown in Fig. \ref{['fig:transport']}b as a function of charge carrier concentration (bottom axis) and filling factor (top axis) at 30 T. The temperature is encoded in the color of the lines (right color bar). Resistance minima are visible at filling factors $\pm$2. b. Fit of the resistance minima for $\nu=-2$ visible in Fig. \ref{['fig:QHE']}a to thermal activation. c. Landau-level activation gaps as a function of magnetic field for two hydrogenation states of the same sample. d. Density of states in magnetic field for pristine and hydrogenated graphene. After hydrogenation the Landau levels broaden and the gaps between them decrease. This figure is not to scale.
• Figure 4: a. Band structure for a graphene sheet consisting of 128 carbon atoms with a single hydrogen atom attached to it. b. Band structure for a graphene sheet consisting of 32 carbon atoms with a single hydrogen atom attached to it. c. Effective electron mass (gray dots) as function of hydrogen coverage, extracted from simulations. The effective electron mass was calculated using the second derivative of the conduction band near the K point. On the right axis, the energy gap is plotted (red triangles). d. Setup of the simulation. A base cell of in this case 32 carbon atoms is used, to which a single hydrogen atom (purple) is added. The hydrogen is bonded to one of the carbon atoms. Forcefield optimisation induces buckling of the graphene sheet reaxFF_CH_2017.