We study the effects of a truncated band structure on the linear and nonlinear optical response of crystals using four methods. These are constructed by (i) choosing either length or velocity gauge for the perturbation and (ii) computing the current density either directly or via the time-derivative of the polarization density. In the infinite band limit, the results of all four methods are identical, but basis truncation breaks their equivalence. In particular, certain response functions vanish identically and unphysical low-frequency divergences are observed for few-band models in the velocity gauge. Using hexagonal boron nitride (hBN) monolayer as a case study, we analyze the problems associated with all methods and identify the optimal one. Our results show that the length gauge calculations provide the fastest convergence rates as well as the most accurate spectra for any basis size and, moreover, that low-frequency divergences are eliminated.

The dc photoelectrical currents can be generated purely as a non-linear effect in uniform media lacking inversion symmetry without the need for a material junction or bias voltages to drive it, in what is termed photogalvanic effect. These currents are strongly dependent on the polarization state of the radiation, as well as on topological properties of the underlying Fermi surface such as its Berry curvature. In order to study the intrinsic photogalvanic response of gapped graphene, biased bilayer graphene (BBG), and hexagonal boron nitride (hBN), we compute the non-linear current using a perturbative expansion of the density matrix. This allows a microscopic description of the quadratic response to an electromagnetic field in these materials, which we analyze as a function of temperature and electron density. We find that the intrinsic response is robust across these systems and allows for currents in the range of pA cm/W to nA cm/W. At the independent-particle level, the response of hBN-based structures is significant only in the ultra-violet due to their sizable band-gap. However, when Coulomb interactions are accounted for by explicit solution of the Bethe-Salpeter equation, we find that the photoconductivity is strongly modified by transitions involving exciton levels in the gap region, whose spectral weight dominates in the overall frequency range. Biased bilayers and gapped monolayers of graphene have a strong photoconductivity in the visible and infrared window, allowing for photocurrent densities of several nA cm/W. We further show that the richer electronic dispersion of BBG at low energies and the ability to change its band-gap on demand allows a higher tunability of the photocurrent, including not only its magnitude but also, and significantly, its polarity.

Valley polarization (VP), an induced imbalance in the populations of a multi-valley electronic system, allows emission of second harmonic (SH) light even in centrosymmetric crystals such as graphene. Whereas in systems such as MoS 2 or BN this adds to their intrinsic quadratic response, SH generation in a multi-valley inversion-symmetric crystal can provide a direct measure of valley polarization. By computing the nonlinear response and characterizing theoretically the respective SH as a function of polarization, temperature, electron density, and degree of VP, we demonstrate the possibility of disentangling and individually quantifying the intrinsic and valley contributions to the SH. A specific experimental setup is proposed to obtain direct quantitative information about the degree of VP and allow its remote mapping. This approach could prove useful for direct, contactless, real-space monitoring of valley injection and other applications of valley transport and valleytronics.

The optical conductivity of graphene nanoribbons is analytical and exactly derived. It is shown that the absence of translational invariance along the transverse direction allows considerable intraband absorption in a narrow frequency window that varies with the ribbon width, and lies in the THz range domain for ribbons 10-100 nm wide. In this spectral region the absorption anisotropy can be as high as two orders of magnitude, which renders the medium strongly dichroic, and allows for a very high degree of polarization (up to ∼ 85%) with just a single layer of graphene. Using a cavity for impedance enhancement, or a stack of few layer nanoribbons, these values can reach almost 100%. This opens a potential prospect of employing graphene ribbon structures as efficient polarizers in the far IR and THz frequencies.

We compute the nonlinear optical response of doped mono-and bilayer graphene using the full dispersion based on tight-binding models. The response is derived with the density matrix formalism using the length gauge and is valid for any periodic system, with arbitrary doping. By collecting terms that define effective nonlinear response tensors, we identify all nonlinear Drude-like terms (up to third-order) and show that all additional spurious divergences present in the induced current vanish. The nonlinear response of graphene comprises a large Drude-like divergence and three resonances that are tightly connected with transitions occurring in the vicinity of the Fermi level. The analytic solution derived using the Dirac approximation captures accurately the firstand third-order responses in graphene, even at very high doping levels. The quadratic response of gapped graphene is also strongly enhanced by doping, even for systems with small gaps such as commensurate structures of graphene on SiC. The nonlinear response of bilayer graphene is significantly richer, combining the resonances that stem from doping with its intrinsic strong low-energy resonances.

We present a calculation of third harmonic generation (THG) for two-band systems using the length gauge that avoids unphysical divergences otherwise present in the evaluation of the third-order current density response. The calculation is applied to bulk and monolayer black phosphorus (bP) using a nonorthogonal tight-binding model. Results show that the low-energy response is dominated by mixed inter-intraband processes and estimates of the magnitude of THG susceptibility are comparable to recent experimental reports for bulk bP samples.

The uptake of electric vehicles (EVs) may pose a challenge to power distribution networks (PDNs). While smart charging can be deployed to relieve stress on the grid, user-centric smart charging strategies could also exacerbate peak power demand due to synchronization when optimizing charging with regard to different objectives, such as charging costs. In this paper, we assess the charging demand emerging from a large fleet of EVs, with models for the decision to charge and distribution of the steady-state state-of-charge (SoC). These are applied to the municipality of Frederiksberg, Denmark, using data from the Danish national travel survey. Home and workplace charging are mapped to the urban 10 kV medium voltage PDN of Frederiksberg considering different charging behaviors and degrees of synchronization. Results indicate that the likelihood of severe congestion in the power distribution network is low and that it can be attributed to rare scenarios in which high synchronization is observed, particularly when maintaining the normal steady-state demand. Despite the low likelihood, preventive measures should be devised to mitigate such scenarios, especially if additional high-power consumers are connected.

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