Infrared probe of the anomalous magnetotransport of highly oriented pyrolytic graphite in the extreme quantum limit

We present a systematic investigation of the magnetoreflectance $R(\omega ,B)$ of highly oriented pyrolytic graphite in magnetic field $B$ up to $18\mathrm{T}$. From these measurements, we report the determination of lifetimes $\tau$ associated with the lowest Landau levels in the quantum limit. We find a linear field dependence for inverse lifetime $1∕\tau \left(B\right)$ of the lowest Landau levels, which is consistent with the hypothesis of a three-dimensional (3D) to 1D crossover in an anisotropic 3D metal in the quantum limit. This enigmatic result uncovers the origin of the anomalous linear in-plane magnetoresistance observed both in bulk graphite and recently in mesoscopic graphite samples.

Figure 1

(Color online) Zero field $ab$-plane reflectance $R\left(\omega \right)$ (top panel) and real part of the optical conductivity ${\sigma }_1\left(\omega \right)$ (bottom panel) of graphite. The thin dashed lines in the bottom panel are Drude fits of the ${\sigma }_1\left(\omega \right)$ spectra in the low frequency region. The bottom inset displays the absorption peak of ${\sigma }_1\left(\omega \right)$ in the mid-IR region, which shifts to high energy with increasing temperature.

Figure 2

(Color online) Schematics of the band structure of graphite at $K$ and $H$ points of the Brillouin zone at 10 and $292\mathrm{K}$. The arrows indicate the interband transtions observed in the bottom inset of Fig. 1.

Figure 3

(Color online) The $\omega ∕B$ scaled plot of the $ab$-plane reflectance spectra $R(\omega ,B)$ in several magnetic fields. At each field $B$, the zero field reflectance spectrum $R(\omega ,B=0)$ is also scaled by the corresponding factor $B$ for comparison. Every set of spectra is offset by 30% for clarity. The model spectra are obtained from the analysis detailed in the text.

Figure 4

(Color online) Top panel: ${\sigma }_1\left(\omega \right)$ at zero field and model spectra ${\sigma }_{1+}\left(\omega \right)$ and ${\sigma }_{1-}\left(\omega \right)$ at $16\mathrm{T}$ obtained from the analysis detailed in the text$.$ The black square on the left axis represents the dc conductivity ${\sigma }_{\mathrm{d}\mathrm{c}}$ at $0\mathrm{T}$. The green (light gray) curve is the high frequency field-independent absorption in both ${\sigma }_{1-}\left(\omega \right)$ and ${\sigma }_{1+}\left(\omega \right)$. Bottom panel: experimental $R\left(\omega \right)$ spectra at 0 and $16\mathrm{T}$ and model spectra $R\left(\omega \right)$ at $16\mathrm{T}$. The arrows indicate the resonance features in $R\left(\omega \right)$ and ${\sigma }_{1-}\left(\omega \right)$ due to the (LL-1)-(LL0) transition.

Figure 5

(Color online) Resonance frequency (left panel) and linewidth (middle panel) of the (LL-1)-(LL0) transition in magnetic field. The dashed curves in these two panels are linear fits to the data. The dotted curves in the left panel are $\omega \sim \sqrt{B}$ fits. Right panel: a schematic of the LL-1 and LL0 Landau levels in the quantum limit (adapted from Ref. 25).