Decrypting the cyclotron effect in graphite using Kerr rotation spectroscopy

We measure the far-infrared magneto-optical Kerr rotation and reflectivity spectra in graphite and achieve a highly accurate unified microscopic description of all data in a broad range of magnetic fields by taking rigorously the c-axis band dispersion and the trigonal warping into account. We find that the second- and the forth-order cyclotron harmonics are optically almost as strong as the fundamental resonance even at high fields. They must play, therefore, a major role in magneto-optical and magneto-plasmonic applications based on Bernal stacked graphite and multilayer graphene.Comment: 4 pages, 3 figures + Supplemental Materia

Magneto-optical Kramers-Kronig analysis

We describe a simple magneto-optical experiment and introduce a magneto-optical Kramers-Kronig analysis (MOKKA) that together allow extracting the complex dielectric function for left- and right-handed circular polarizations in a broad range of frequencies without actually generating circularly polarized light. The experiment consists of measuring reflectivity and Kerr rotation, or alternatively transmission and Faraday rotation, at normal incidence using only standard broadband polarizers without retarders or quarter-wave plates. In a common case, where the magneto-optical rotation is small (below $\sim$ 0.2 rad), a fast measurement protocol can be realized, where the polarizers are fixed at 45$^\circ$ with respect to each other. Apart from the time-effectiveness, the advantage of this protocol is that it can be implemented at ultra-high magnetic fields and in other situations, where an \emph{in-situ} polarizer rotation is difficult. Overall, the proposed technique can be regarded as a magneto-optical generalization of the conventional Kramers-Kronig analysis of reflectivity on bulk samples and the Kramers-Kronig constrained variational analysis of more complex types of spectral data. We demonstrate the application of this method to the textbook semimetals bismuth and graphite and also use it to obtain handedness-resolved magneto-absorption spectra of graphene on SiC.Comment: 11 pages, 4 figur

Magnetoplasmon resonances in polycrystalline bismuth as seen via terahertz spectroscopy

We report the magnetic field-dependent far-infrared reflectivity of polycrystalline bismuth. We observe four distinct absorptions that we attribute to magnetoplasmon resonances, which are collective modes of an electron-hole liquid in magnetic field and become optical and acoustic resonances of the electron-hole system in the small-field limit. The acoustic mode is expected only when the masses of distinct components are very different, which is the case in bismuth. In a polycrystal, where the translational symmetry is broken, a big shift of spectral weight to acoustic plasmon is possible. This enables us to detect an associated plasma edge. Although the polycrystal sample has grains of randomly distributed orientations, our reflectivity results can be explained by invoking only two, clearly distinct, series of resonances. In the limit of zero field, the optical modes of these two series converge onto plasma frequencies measured in monocrystal along the main optical axes.Comment: Accepted in PR

Fabry-Perot enhanced Faraday rotation in graphene

We demonstrate that giant Faraday rotation in graphene in the terahertz range due to the cyclotron resonance is further increased by constructive Fabry-Perot interference in the supporting substrate. Simultaneously, an enhanced total transmission is achieved, making this effect doubly advantageous for graphene-based magneto-optical applications. As an example, we present far-infrared spectra of epitaxial multilayer graphene grown on the C-face of 6H-SiC, where the interference fringes are spectrally resolved and a Faraday rotation up to 0.15 radians (9{\deg}) is attained. Further, we discuss and compare other ways to increase the Faraday rotation using the principle of an optical cavity

Fermi liquid behavior of the in-plane resistivity in the pseudogap state of YBa_2Cu_4O_8

Our knowledge of the ground state of underdoped hole-doped cuprates has evolved considerably over the last few years. There is now compelling evidence that inside the pseudogap phase, charge order breaks translational symmetry leading to a reconstructed Fermi surface made of small pockets. Quantum oscillations, [Doiron-Leyraud N, et al. (2007) Nature 447:564-568], optical conductivity [Mirzaei SI, et al. (2013) Proc Natl Acad Sci USA 110:5774-5778] and the validity of Wiedemann-Franz law [Grissonnache G, et al. (2016) Phys. Rev. B 93:064513] point to a Fermi liquid regime at low temperature in the underdoped regime. However, the observation of a quadratic temperature dependence in the electrical resistivity at low temperatures, the hallmark of a Fermi liquid regime, is still missing. Here, we report magnetoresistance measurements in the magnetic-field-induced normal state of underdoped YBa_2Cu_4O_8 which are consistent with a T^2 resistivity extending down to 1.5 K. The magnitude of the T^2 coefficient, however, is much smaller than expected for a single pocket of the mass and size observed in quantum oscillations, implying that the reconstructed Fermi surface must consist of at least one additional pocket.Comment: Main + SI : published versio

Multi-component magneto-optical conductivity of multilayer graphene on SiC

Far-infrared diagonal and Hall conductivities of multilayer epitaxial graphene on the C-face of SiC were measured using magneto-optical absorption and Faraday rotation in magnetic fields up to 7 T and temperatures between 5 and 300 K. Multiple components are identified in the spectra, which include: (i) a quasi-classical cyclotron resonance (CR), originating from the highly doped graphene layer closest to SiC, (ii) transitions between low-index Landau levels (LLs), which stem from weakly doped layers and (iii) a broad optical absorption background. Electron and hole type LL transitions are optically distinguished and shown to coexist. An electron-hole asymmetry of the Fermi velocity of about 2% was found within one graphene layer, while the Fermi velocity varies by about 10% across the layers. The optical intensity of the LL transitions is several times smaller than what is theoretically expected for isolated graphene monolayers without electron-electron and electron-phonon interactions.Comment: 9 pages, 6 figure

Lifshitz critical point in the cuprate superconductor YBa2Cu3Oy from high-field Hall effect measurements

The Hall coefficient R_H of the cuprate superconductor YBa2Cu3Oy was measured in magnetic fields up to 60 T for a hole concentration p from 0.078 to 0.152, in the underdoped regime. In fields large enough to suppress superconductivity, R_H(T) is seen to go from positive at high temperature to negative at low temperature, for p > 0.08. This change of sign is attributed to the emergence of an electron pocket in the Fermi surface at low temperature. At p < 0.08, the normal-state R_H(T) remains positive at all temperatures, increasing monotonically as T \to 0. We attribute the change of behaviour across p = 0.08 to a Lifshitz transition, namely a change in Fermi-surface topology occurring at a critical concentration p_L = 0.08, where the electron pocket vanishes. The loss of the high-mobility electron pocket across p_L coincides with a ten-fold drop in the conductivity at low temperature, revealed in measurements of the electrical resistivity $\rho$ at high fields, showing that the so-called metal-insulator crossover of cuprates is in fact driven by a Lifshitz transition. It also coincides with a jump in the in-plane anisotropy of $\rho$, showing that without its electron pocket the Fermi surface must have strong two-fold in-plane anisotropy. These findings are consistent with a Fermi-surface reconstruction caused by a unidirectional spin-density wave or stripe order.Comment: 16 pages, 13 figures, see associated Viewpoint: M. Vojta, Physics 4, 12 (2011

de Haas-van Alphen oscillations in the underdoped cuprate YBa2_2Cu3_3O6.5_{6.5}

The de Haas-van Alphen effect was observed in the underdoped cuprate YBa$_2$Cu$_3$O$_{6.5}$ via a torque technique in pulsed magnetic fields up to 59 T. Above an irreversibility field of $\sim$30 T, the magnetization exhibits clear quantum oscillations with a single frequency of 540 T and a cyclotron mass of 1.76 times the free electron mass, in excellent agreement with previously observed Shubnikov-de Haas oscillations. The oscillations obey the standard Lifshitz-Kosevich formula of Fermi-liquid theory. This thermodynamic observation of quantum oscillations confirms the existence of a well-defined, close and coherent, Fermi surface in the pseudogap phase of cuprates.Comment: published versio

Shubnikov-de Haas oscillations in YBa_2Cu_4O_8

We report the observation of Shubnikov-de Haas oscillations in the underdoped cuprate superconductor YBa$_2$Cu$_4$O$_8$ (Y124). For field aligned along the c-axis, the frequency of the oscillations is $660\pm 30$ T, which corresponds to $\sim 2.4$ % of the total area of the first Brillouin zone. The effective mass of the quasiparticles on this orbit is measured to be $2.7\pm0.3$ times the free electron mass. Both the frequency and mass are comparable to those recently observed for ortho-II YBa$_2$Cu$_3$O$_{6.5}$ (Y123-II). We show that although small Fermi surface pockets may be expected from band structure calculations in Y123-II, no such pockets are predicted for Y124. Our results therefore imply that these small pockets are a generic feature of the copper oxide plane in underdoped cuprates.Comment: v2: Version of paper accepted for publication in Physical Review Letters. Only minor changes to the text and reference

Optical Self Energy in Graphene due to Correlations

In highly correlated systems one can define an optical self energy in analogy to its quasiparticle (QP) self energy counterpart. This quantity provides useful information on the nature of the excitations involved in inelastic scattering processes. Here we calculate the self energy of the intraband optical transitions in graphene originating in the electron-electron interaction (EEI) as well as electron-phonon interaction (EPI). Although optics involves an average over all momenta ($k$) of the charge carriers, the structure in the optical self energy is nevertheless found to mirror mainly that of the corresponding quasiparticles for $k$ equal to or near the Fermi momentum $k_F$. Consequently plasmaronic structures which are associated with momenta near the Dirac point at $k=0$ are not important in the intraband optical response. While the structure of the electron-phonon interaction (EPI) reflects the sharp peaks of the phonon density of states, the excitation spectrum associated with the electron-electron interaction is in comparison structureless and flat and extends over an energy range which scales linearly with the value of the chemical potential. Modulations seen on the edge of the interband optical conductivity as it rises towards its universal background value are traced to structure in the quasiparticle self energies around $k_F$ of the lower Dirac cone associated with the occupied states.Comment: 30 pages, 10 figure