Dirac Semimetals in Two Dimensions

Graphene is famous for being a host of 2D Dirac fermions. However, spin-orbit coupling introduces a small gap, so that graphene is formally a quantum spin hall insulator. Here we present symmetry-protected 2D Dirac semimetals, which feature Dirac cones at high-symmetry points that are emph{not} gapped by spin-orbit interactions, and exhibit behavior distinct from both graphene and 3D Dirac semimetals. Using a two-site tight-binding model, we construct representatives of three possible distinct Dirac semimetal phases, and show that single symmetry-protected Dirac points are impossible in two dimensions. An essential role is played by the presence of non-symmorphic space group symmetries. We argue that these symmetries tune the system to the boundary between a 2D topological and trivial insulator. By breaking the symmetries we are able to access trivial and topological insulators as well as Weyl semimetal phases.

Bulk photovoltaic effect enhancement via electrostatic control in layered ferroelectrics

The correlation between the shift current mechanism for the bulk photovoltaic effect (BPVE) and the structural and electronic properties of ferroelectric perovskite oxides is not well understood. Here, we study and engineer the shift current photovoltaic effect using a visible-light-absorbing ferroelectric Pb(Ni$_{x}$Ti$_{1-x}$)O$_{3-x}$ solid solution from first principles. We show that the covalent orbital character dicates the direction, magnitude, and onset energy of shift current in a predictable fashion. In particular, we find that the shift current response can be enhanced via electrostatic control in layered ferroelectrics, as bound charges face a stronger impetus to screen the electric field in a thicker material, delocalizing electron densities. This heterogeneous layered structure with alternative photocurrent generating and insulating layers is ideal for BPVE applications.

First-Principles Calculation of the Bulk Photovoltaic Effect in the Polar Compounds LiAsS$_text{2}$, LiAsSe$_text{2}$, and NaAsSe$_text{2}$

We calculate the shift current response, which has been identified as the dominant mechanism for the bulk photovoltaic effect, for the polar compounds LiAsS$_text{2}$, LiAsSe$_text{2}$, and NaAsSe$_text{2}$. We find that the magnitudes of the photovoltaic responses in the visible range for these compounds exceed the maximum response obtained for BiFeO$_text{3}$ by 10 - 20 times. We correlate the high shift current response with the existence of $p$ states at both the valence and conduction band edges, as well as the dispersion of these bands, while also showing that high polarization is not a requirement. With low experimental band gaps of less than 2 eV and high shift current response, these materials have potential for use as bulk photovoltaics.

Bulk Dirac points in distorted spinels

We report on a Dirac-like Fermi surface in three-dimensional bulk materials in a distorted spinel structure on the basis of density functional theory (DFT) as well as tight-binding theory. The four examples we provide in this paper are BiZnSiO4, BiCaSiO4, BiMgSiO4, and BiAlInO4. A necessary characteristic of these structures is that they contain a Bi lattice which forms a hierarchy of chain-like substructures, with consequences for both fundamental understanding and materials design.

First principles calculations of the Shift Current Bulk Photovoltaic Effect in Ferroelectrics

We calculate the bulk photovoltaic response of the ferroelectrics BaTiO$_3$ and PbTiO$_3$ from first principles by applying shift current theory to the electronic structure from density functional theory. The first principles results for BaTiO$_3$ reproduce eperimental photocurrent direction and magnitude as a function of light frequency, as well as the dependence of current on light polarization, demonstrating that shift current is the dominant mechanism of the bulk photovoltaic effect in BaTiO$_3$. Additionally, we analyze the relationship between response and material properties in detail. The photocurrent does not depend simply or strongly on the magnitude of material polarization, as has been previously assumed; instead, electronic states with delocalized, covalent bonding that is highly asymmetric along the current direction are required for strong shift current enhancements. The complexity of the response dependence on both external and material parameters suggests applications not only in solar energy conversion, but to photocatalysis and sensor and switch type devices as well.

Theoretical investigation of the evolution of the topological phase of Bi$_{2}$Se$_{3}$ under mechanical strain

The topological insulating phase results from inversion of the band gap due to spin-orbit coupling at an odd number of time-reversal symmetric points. In Bi$_2$Se$_3$, this inversion occurs at the $Gamma$ point. For bulk Bi$_2$Se$_3$, we have analyzed the effect of arbitrary strain on the $Gamma$ point band gap using Density Functional Theory. By computing the band structure both with and without spin-orbit interactions, we consider the effects of strain on the gap via Coulombic interaction and spin-orbit interaction separately. While compressive strain acts to decrease the Coulombic gap, it also increases the strength of the spin-orbit interaction, increasing the inverted gap. Comparison with Bi$_2$Te$_3$ supports the conclusion that effects on both Coulombic and spin-orbit interactions are critical to understanding the behavior of topological insulators under strain, and we propose that the topological insulating phase can be effectively manipulated by inducing strain through chemical substitution.