Circular polarization dependent cyclotron resonance in large-area graphene in ultrahigh magnetic fields

Abstract

Using ultrahigh magnetic fields up to 170 T and polarized midinfrared radiation with tunable wavelengths from 9.22 to 10.67 μm, we studied cyclotron resonance in large-area graphene grown by chemical vapor deposition. Circular polarization dependent studies reveal strong p-type doping for as-grown graphene, and the dependence of the cyclotron resonance on radiation wavelength allows for a determination of the Fermi energy. Thermal annealing shifts the Fermi energy to near the Dirac point, resulting in the simultaneous appearance of hole and electron cyclotron resonance in the magnetic quantum limit, even though the sample is still p-type, due to graphene's linear dispersion and unique Landau level structure. These high-field studies therefore allow for a clear identification of cyclotron resonance features in large-area, low-mobility graphene samples. The band structure of graphene exhibits a zero-gap linear dispersion relation near each of the Dirac points, which results in a variety of exotic properties of two-dimensional (2D) Dirac fermions. [1][2][3] While a number of electronic transport studies have revealed novel phenomena in the presence of a high magnetic field, including half-integer quantum Hall states observed at room temperature, 1,2,4 magneto-optical properties are expected to be equally unusual, 5-15 especially in the magnetic quantum limit 12 where the Fermi level resides in the lowest Landau level (LL). Even in conventional 2D electron systems such as found in GaAs quantum wells, studies of cyclotron resonance (CR) in the magnetic quantum limit have shown many-body effects, [16][17][18][19] such as spin splitting in the fractional quantum Hall regime, even though CR is not expected to be sensitive to electron-electron interactions due to Kohn's theorem. 20 The linear dispersions of graphene automatically evade this basic requirement for Kohn's theorem, motivating CR studies of graphene in ultrahigh magnetic fields.An applied magnetic field (B) creates LLs for charge carriers both in the conduction and valence bands, and CR measures resonant optical transitions between adjacent LLs ( n = ±1, where n is the Landau level index). 21 CR is a well-established and powerful technique to determine many fundamental parameters of a sample, such as carrier effective masses, densities, mobilities, and scattering rates. When performed with circularly polarized radiation, the sign of the charge carriers can also be determined. Furthermore, owing to graphene's nonparabolic (i.e., linear) dispersion, LL energies are not equally spaced; rather, they follow E n,± = ±c * √ 2ehBn, where n 0 and c * ≈ 1.0 × 10 6 m/s corresponds to the slope of the linear dispersions. Thus, different inter-Landau level (LL) transitions occur at different energies or magnetic fields. Hence, the absence or presence of a certain resonance can determine the Fermi energy. This is in marked contrast to conventional materials with parabolic dispersions, which form equally spaced LLs in a magnetic field [E n = (n + 1/2)ehB/m * , where m * is ...

Classical to quantum crossover of the cyclotron resonance in graphene: a study of the strength of intraband absorption

“…However, at the same time, it first shows clear indications of the approaching quantum regime, in which CR absorption corresponds to transitions between well-defined adjacent LLs. A number of CR studies of graphene in this regime have already been performed; see, e.g., [19][20][21][22][23][24][25][26][27]. A typical response in the quantum regime closely reflects the properties of the LL spectrum:…”

“…Formally, the Drude approach follows from the commonly used random phase approximation (RPA) [14], which indeed grants equation (1), but, with the velocity parameter fixed at its bare value [15] v F,0 = 0.85 × 10 6 m s −1 -the value of v F,0 can be accurately estimated, for example, from calculations based on density-functional theory at the local density approximation (LDA) level [16][17][18]. Markedly, v F,0 is smaller than the apparent (renormalized) Fermi velocity, v F = (1.0-1.1) × 10 6 m s −1 , which is derived from most of the spectroscopy studies on graphene-based systems [19][20][21][22][23][24][25][26][27] (and from beyond-LDA theoretical approaches).…”

Infrared magnetospectroscopy of graphite in tilted fields

“…A simple model, invoking inter-Landau-level (LL) excitations between highly degenerated Landau levels (LLs) of massless Dirac fermions, implies a magneto-optical response that is linear in √ B (see, e.g., Refs. [19][20][21][22][23][24][25][26] and is capable of accounting for a significant part of the magneto-optical data acquired on graphite. Importantly, these data come not only from recent magnetotransmission studies of thin specimens 8,10,11 but also from original measurements carried out in the late seventies, 27 in which √ B-scaled spectral features have been observed using magnetoreflection techniques.…”

Terahertz science and technology of carbon nanomaterials

“…Also, two groups have used microscopy techniques to map out dynamic conductivity non-uniformity in the GHz [209] and THz [210] range and many successful dynamic conductivity measurements in magnetic fields (cyclotron resonance) exist [211][212][213][214][215][216][217][218][219][220][221][222].…”