Theory of Bilayer Graphene Spectroscopy.

In this thesis, we model theoretically spectra measured for bilayer graphene obtained using the angle-resolved photoemission spectroscopy, magneto-optical absorption spectroscopy and electronic Raman spectroscopy The theories are based on the tight-binding description of the pi bands in the material. In particular, we concentrate on the comparison of the four-band model and its effective low-energy approximation neglecting the split high-energy bands, in the description of specific spectra. We demonstrate that both for monolayer and bilayer graphene, the observed anisotropy of angle-resolved photoelectron spectroscopy spectra reflects the electronic chirality in the system. However, for bilayer graphene, the influence of the nonchiral dimer states not captured within the effective approximation is significant and should not be neglected. We also show that the anisotropy of the constant-energy maps may be used to extract information about the magnitude and sign of interlayer coupling parameters and about symmetry breaking inflicted on a bilayer by the underlying substrate. We then determine selection rules and optical strengths of the inter-Landau-level excitations among any of the pi bands and including the physically most relevant symmetry-breaking parameters. We then present a self-consistent calculation of the interlayer asymmetry caused by an applied electric field in magnetic fields. We show how this asymmetry influences the Landau level spectrum in bilayer graphene and the observable inter-Landau level transitions when they are studied as a function of high magnetic field at fixed filling factor as measured experimentally. We also analyse the magneto-optical spectra of bilayer flakes in the photon-energy range corresponding to transitions between degenerate and split bands of bilayers. Finally, we investigate the contribution of the low-energy electronic excitations toward the Raman spectrum of bilayer graphene for the incoming photon energy Ω " 1eV. Using the four-band model, we de rive an effective scattering amplitude that can be incorporated into the two-band approximation and show that this amplitude is different from the contact interaction amplitude obtained within the two-band model alone. We then calculate the spectral density of the inelastic light scattering accompanied by the excitation of electron-hole pairs in bilayer graphene. In the absence of a magnetic field this contribution is constant and in doped structures has a threshold at twice the Fermi energy. In an external magnetic field, the dominant Raman-active modes are the n- --->n+ inter-Landau-level transitions with crossed polarization of in/out photons. We estimate the quantum efficiency of a single n- ---> n+ transition in the magnetic field of 10 T as In- -> n+ ~ 10. 12

Superconductivity-induced features in electronic Raman spectrum of monolayer graphene

Using the continuum model, we investigate theoretically contribution of the low-energy electronic excitations to the Raman spectrum of superconducting monolayer graphene. We consider superconducting phases characterised by an isotropic order parameter in a single valley and find a Raman peak at a shift set by the size of the superconducting gap. The height of this peak is proportional to the square root of the gap and the third power of the Fermi level, and we estimate its quantum efficiency as $I\sim10^{-14}$.Comment: 7 pages, 2 figure

Strained bilayer graphene: Band structure topology and Landau level spectrum

We show that topology of the low-energy band structure in bilayer graphene critically depends on mechanical deformations of the crystal which may easily develop in suspended graphene flakes. We describe the Lifshitz transition that takes place in strained bilayers upon splitting the parabollic bands at intermediate energies into several Dirac cones at the energy scale of few meV. Then, we show how this affects the electron Landau level spectra and the quantum Hall effect.Comment: slightly over 4 pages, 3 figures, updated discussion and references; almost identical to the published versio

Strain-induced modifications of transport in gated graphene nanoribbons

We investigate the effects of homogeneous and inhomogeneous deformations and edge disorder on the conductance of gated graphene nanoribbons. Under increasing homogeneous strain the conductance of such devices initially decreases before it acquires a resonance structure, and finally becomes completely suppressed at larger strain. Edge disorder induces mode mixing in the contact regions, which can restore the conductance to its ballistic value. The valley-antisymmetric pseudo-magnetic field induced by inhomogeneous deformations leads to the formation of additional resonance states, which either originate from the coupling into Fabry-Perot states that extend through the system, or from the formation of states that are localized near the contacts, where the pseudo-magnetic field is largest. In particular, the n=0 pseudo-Landau level manifests itself via two groups of conductance resonances close to the charge neutrality point.Comment: 10 pages, 6 figure

2T-POT Hawkes model for left- and right-tail conditional quantile forecasts of financial log-returns: out-of-sample comparison of conditional EVT models

Conditional extreme value theory (EVT) methods promise enhanced forecasting of the extreme tail events that often dominate systemic risk. We present an improved two-tailed peaks-over-threshold (2T-POT) Hawkes model that is adapted for conditional quantile forecasting in both the left and right tails of a univariate time series. This is applied to the daily log-returns of six large cap indices. We also take the unique step of fitting the model at multiple exceedance thresholds (from the 1.25% to 25.00% mirrored quantiles). Quantitatively similar asymmetries in Hawkes parameters are found across all six indices, adding further empirical support to a temporal leverage effect in financial price time series in which the impact of losses is not only larger but also more immediate. Out-of-sample backtests find that our 2T-POT Hawkes model is more reliably accurate than the GARCH-EVT model when forecasting (mirrored) value-at-risk and expected shortfall at the 5% coverage level and below. This suggests that asymmetric Hawkes-type arrival dynamics are a better approximation of the true data generating process for extreme daily log-returns than GARCH-type conditional volatility; our 2T-POT Hawkes model therefore presents a better performing alternative for financial risk modelling.Comment: Main paper: 25 pages, 7 figures, 6 tables. Supplementary material: 12 pages, 14 figure

Asymmetric excitation of left- and right-tail extreme events probed using a Hawkes model: Application to financial returns

We construct a two-tailed peak-over-threshold Hawkes model that captures asymmetric self- and cross-excitation in and between left- and right-tail extreme values within a time series. We demonstrate its applicability by investigating extreme gains and losses within the daily log-returns of the S&P 500 equity index. We find that the arrivals of extreme losses and gains are described by a common conditional intensity to which losses contribute twice as much as gains. However, the contribution of the former decays almost five times more quickly than that of the latter. We attribute these asymmetries to the different reactions of market traders to extreme upward and downward movements of asset prices: an example of negativity bias, wherein trauma is more salient than euphoria.Comment: 11 pages. 7 figures and 5 table

Controlled formation of isolated miniband in bilayer graphene on almost commensurate √3 × √3 substrate

We investigate theoretically the interplay between the effects of a perpendicular electric field and incommensurability at the interface on the electronic properties of a heterostructure of bilayer graphene and a semiconducting substrate with a unit cell almost three times larger then that of graphene. It is known that the former introduces an asymmetry in the distribution of the electronic wave function between the layers and opens a band gap in the electronic spectrum. The latter generates a long wavelength periodic moir\'{e} perturbation of graphene electrons which couples states in inequivalent graphene Brillouin zone corners and leads to the formation of minibands. We show that, depending on the details of the moir\'{e} perturbation, the miniband structure can be tuned from that with a single band gap at the neutrality point and over-lapping minibands on the conduction/valence band side to a situation where a single narrow miniband is separated by gaps from the rest of the spectrum.Comment: 7 pages, 3 figure

Using in-plane anisotropy to engineer Janus monolayers of rhenium dichalcogenides

The new class of Janus two-dimensional (2D) transition-metal dichalcogenides with two different interfaces are currently gaining increasing attention due to their distinct properties different from the typical 2D materials. Here, we show that in-plane anisotropy of a 2D atomic crystal, like ReS$_{2}$ or ReSe$_{2}$, allows formation of a large number of inequivalent Janus monolayers. We use first-principles calculations to investigate the structural stability of 29 distinct ReX$_{2-x}$Y$_{x}$ ($\mathrm{X,Y \in \{S,Se\}}$) structures, which can be obtained by selective exchange of exposed chalcogens in a ReX$_{2}$ monolayer. We also examine the electronic properties and work function of the most stable Janus monolayers and show that the large number of inequivalent structures provides a way to engineer spin-orbit splitting of the electronic bands. We find that the breaking of inversion symmetry leads to sizable spin splittings and spontaneous diople moments than are larger than those in other Janus dichalcogenides. Moreover, our caluclations suggest that the work function of the Janus monolayers can be tuned by varying the content of the substituting chalcogen. Our work demonstrates that in-plane anisotropy provides additional flexibility in sub-layer engineering of 2D atomic crystals

Infrared absorption of closely-aligned heterostructures of monolayer and bilayer graphene with hexagonal boron nitride

We model optical absorption of monolayer and bilayer graphene on hexagonal boron nitride for the case of closely-aligned crystal lattices. We show that perturbations with different spatial symmetry can lead to similar absorption spectra. We suggest that a study of the absorption spectra as a function of the doping for almost completely full first miniband is necessary to extract meaningful information about the moire characteristics from optical absorption measurements and to distinguish between various theoretical proposals for the physically realistic interaction. Also, for bilayer graphene, the ability to compare spectra for the opposite signs of electric-field-induced interlayer asymmetry might provide additional information about the moire parameters.Comment: 7 pages, 6 figures, minor changes, version accepted to PR

Moiré miniband features in the angle-resolved photoemission spectra of graphene/hBN heterostructures

We identify features in the angle-resolved photoemission spectra (ARPES) arising from the periodic pattern characteristic for graphene heterostructure with hexagonal boron nitride (hBN). For this, we model ARPES spectra and intensity maps for five microscopic models used previously to describe moire superlattice in graphene/hBN systems. We show that detailed analysis of these features can be used to pin down the microscopic mechanism of the interaction between graphene and hBN. We also analyze how the presence of a moire-periodic strain in graphene or scattering of photoemitted electrons off hBN can be distinguished from the miniband formation.Comment: 8.5 pages and 9 figures; version published in Phys. Rev.