Interaction-Induced Shift of the Cyclotron Resonance of Graphene Using Infrared Spectroscopy

We report a study of the cyclotron resonance (CR) transitions to and from the unusual $n=0$ Landau level (LL) in monolayer graphene. Unexpectedly, we find the CR transition energy exhibits large (up to 10%) and nonmonotonic shifts as a function of the LL filling factor, with the energy being largest at half filling of the $n=0$ level. The magnitude of these shifts, and their magnetic field dependence, suggests that an interaction-enhanced energy gap opens in the $n=0$ level at high magnetic fields. Such interaction effects normally have a limited impact on the CR due to Kohn’s theorem [W. Kohn, Phys. Rev. 123, 1242 (1961)], which does not apply in graphene as a consequence of the underlying linear band structure.

Figure 1

(a) Optical microscope image of sample $A$. (b) Measured Hall ($R_{xy}$) and longitudinal ($R_{xx}$) 4-wire resistances of sample $A$. (c) Calculated Hall (${\sigma }_{xy}$) and longitudinal (${\sigma }_{xx}$) conductivities, showing a Hall plateau forming at $\nu =0$. (d) Schematic of experimental setup showing IR light focused through graphene. The varying bolometer resistance tracks changes in the transmitted light.

Figure 2

(a) The change in transmission, $\Delta T/T$, for CR traces in monolayer graphene at fixed field $B=18\mathrm{T}$ over a range of $\nu$. Traces are offset for clarity. The bottom trace is $\nu =+4\frac{1}{2}$; $\nu$ of successive traces decreases by $\frac{1}{2}$. The dashed line is a guide to the eye, marking the peak energies determined by curve fits. (b) Example of a fit (solid red line) to the CR line shape at $\nu =+1\frac{1}{2}$ using a multilayer IR transmission model. (c) CR peak energies plotted versus $\nu$. The area of the markers represents the relative intensity.

Figure 3

Two CR peaks visible in $\Delta T/T$ traces from sample $B$ at $B=18\mathrm{T}$. The underlying transitions are $n=0\to 1$ and/or $n=-1\to 0$ near 170 meV (short blue arrows), and $n=-1\to +2$ and $n=-2\to +1$ at 440 meV (long red arrows). Traces are offset for clarity. Left inset: LL schematic showing transitions at $\nu =+2$, when $E_F$ lies between the zeroth and first LLs. Right inset: proposed LL schematic at charge neutrality ($\nu =0$), showing a gap in the $n=0$ LL and the corresponding lowest energy CR transitions.

Figure 4

$B$ field dependence of the CR shift, $\Delta E$, between $\nu =+2$ and 0, as a function of $B$ for five samples. Open symbols are from the high mobility [$\mu =17000{\mathrm{cm}}^2/(\mathrm{V}\mathrm{s})$] sample $A$ resonances shown in Fig. 2; filled symbols show lower mobility samples [$\mu \le 10000{\mathrm{cm}}^2/(\mathrm{V}\mathrm{s})$]. The dotted line is the bare Zeeman splitting, $2{\mu }_{B}B$. Error bars are estimated by varying the best fit parameters. Inset: $\nu =0$ and $+2$ CR energies of sample $A$ at two fields, plotted against $\sqrt{B}$. Dashed lines are least-squares linear fits through zero.