Second harmonic spectroscopy to optically detect valley polarization in 2D materials

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$\mathrm{_2}$ 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.Comment: Updating with published version, including typesetting corrections to eqs 3 and 4; 7 pages, 5 figure

Designing electronic properties of two-dimensional crystals through optimization of deformations

One of the enticing features common to most of the two-dimensional electronic systems that are currently at the forefront of materials science research is the ability to easily introduce a combination of planar deformations and bending in the system. Since the electronic properties are ultimately determined by the details of atomic orbital overlap, such mechanical manipulations translate into modified electronic properties. Here, we present a general-purpose optimization framework for tailoring physical properties of two-dimensional electronic systems by manipulating the state of local strain, allowing a one-step route from their design to experimental implementation. A definite example, chosen for its relevance in light of current experiments in graphene nanostructures, is the optimization of the experimental parameters that generate a prescribed spatial profile of pseudomagnetic fields in graphene. But the method is general enough to accommodate a multitude of possible experimental parameters and conditions whereby deformations can be imparted to the graphene lattice, and complies, by design, with graphene's elastic equilibrium and elastic compatibility constraints. As a result, it efficiently answers the inverse problem of determining the optimal values of a set of external or control parameters that result in a graphene deformation whose associated pseudomagnetic field profile best matches a prescribed target. The ability to address this inverse problem in an expedited way is one key step for practical implementations of the concept of two-dimensional systems with electronic properties strain-engineered to order. The general-purpose nature of this calculation strategy means that it can be easily applied to the optimization of other relevant physical quantities which directly depend on the local strain field, not just in graphene but in other two-dimensional electronic membranes.Comment: 37 pages, 9 figures. This submission contains low-resolution bitmap images; high-resolution images can be found in version 1, which is ~13.5 M

Nonlinear photocurrents in two-dimensional systems based on graphene and boron nitride

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 (GG), 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 sizeable 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.Comment: Updating with published version and respective references; 14 pages, 11 figure

Boron and nitrogen doping in graphene antidot lattices

Bottom-up fabrication of graphene antidot lattices (GALs) has previously yielded atomically precise structures with sub-nanometer periodicity. Focusing on this type of experimentally realized GAL, we perform density functional theory calculations on the pristine structure as well as GALs with edge carbon atoms substituted with boron or nitrogen. We show that p- and n-type doping levels emerge with activation energies that depend on the level of hydrogenation at the impurity. Furthermore, a tight-binding parameterization together with a Green's function method are used to describe more dilute doping.Comment: 8 pages, 7 figure

Polarization Charge Distribution in Gapped Graphene

We study the distribution of vacuum polarization charge induced by a Coulomb impurity in massive graphene. By analytically computing the polarization function, we show that the charge density is distributed in space in a non-trivial fashion, and on a characteristic length-scale set by the effective Compton wavelength. The density crosses over from a logarithmic behavior below this scale, to a power law variation above it. Our results in the continuum limit are confirmed by explicit diagonalization of the corresponding tight-binding model on a finite-size lattice. Electron-electron interaction effects are also discussed.Comment: 6 pages, 4 figures; expanded versio