Jamil Tahir-Kheli

Silicon nanowires as efficient thermoelectric materials

Thermoelectric materials interconvert thermal gradients and electric fields for power generation or for refrigeration. Thermoelectrics currently find only niche applications because of their limited efficiency, which is measured by the dimensionless parameter ZT—a function of the Seebeck coefficient or thermoelectric power, and of the electrical and thermal conductivities. Maximizing ZT is challenging because optimizing one physical parameter often adversely affects another. Several groups have achieved significant improvements in ZT through multi-component nanostructured thermoelectrics, such as Bi2Te3/Sb2Te3 thin-film superlattices, or embedded PbSeTe quantum dot superlattices. Here we report efficient thermoelectric performance from the single-component system of silicon nanowires for cross-sectional areas of 10 nm × 20 nm and 20 nm × 20 nm. By varying the nanowire size and impurity doping levels, ZT values representing an approximately 100-fold improvement over bulk Si are achieved over a broad temperature range, including ZT ≈ 1 at 200 K. Independent measurements of the Seebeck coefficient, the electrical conductivity and the thermal conductivity, combined with theory, indicate that the improved efficiency originates from phonon effects. These results are expected to apply to other classes of semiconductor nanomaterials.

Antiferromagnetic band structure ofLa2CuO4: Becke-3–Lee-Yang-Parr calculations

Using the Becke-3-LYP functional, we have performed band structure calculations on the high temperature superconductor parent compound, La2CuO4. Under the restricted spin formalism (ρ↑ = ρ↓), the R-B3LYP band structure agrees well with the standard LDA band structure. It is metallic with a single Cu x − y/O pσ band crossing the Fermi level. Under the unrestricted spin formalism (ρ↑ 6= ρ↓), the U-B3LYP band structure has a spin polarized antiferromagnetic solution with a band gap of 2.0 eV, agreeing well with experiment. This state is 1.0 eV (per formula unit) lower than that calculated from the R-B3LYP. The apparent high energy of the spin restricted state is attributed to an overestimate of on-site Coulomb repulsion which is corrected in the unrestricted spin calculations. The stabilization of the total energy with spin polarization arises primarily from the stabilization of the x − y band, such that the character of the eigenstates at the top of the valence band in the antiferromagnetic state becomes a strong mixture of Cu x − y/O pσ and Cu z /O pz. Since the Hohenberg-Kohn theorem requires the spin restricted and spin unrestricted calculations to give identical ground state energies and total spatial densities for the exact functionals, this large disparity in energy reflects the inadequacy of current functionals for describing the cuprates. This calls into question the use of band structures based on current restricted spin density functionals (including LDA) as a basis for single band theories of superconductivity in these materials.

Dynamic admittance of carbon nanotube-based molecular electronic devices and their equivalent electric circuit

We use first-principles quantum mechanics to simulate the transient electrical response through carbon nanotube-based conductors under time-dependent bias voltages. The dynamic admittance and time-dependent charge distribution are reported and analyzed. We find that the electrical response of these two-terminal molecular devices can be mapped onto an equivalent classical electric circuit and that the switching time of these end-on carbon nanotube devices is only a few femtoseconds. This result is confirmed by studying the electric response of a simple two-site model device and is thus generalized to other two-terminal molecular electronic devices.

Resolution of the Band Gap Prediction Problem for Materials Design

An important property with any new material is the band gap. Standard density functional theory methods grossly underestimate band gaps. This is known as the band gap problem. Here, we show that the hybrid B3PW91 density functional returns band gaps with a mean absolute deviation (MAD) from experiment of 0.22 eV over 64 insulators with gaps spanning a factor of 500 from 0.014 to 7 eV. The MAD is 0.28 eV over 70 compounds with gaps up to 14.2 eV, with a mean error of -0.03 eV. To benchmark the quality of the hybrid method, we compared the hybrid method to the rigorous GW many-body perturbation theory method. Surprisingly, the MAD for B3PW91 is about 1.5 times smaller than the MAD for GW. Furthermore, B3PW91 is 3-4 orders of magnitude faster computationally. Hence, B3PW91 is a practical tool for predicting band gaps of materials before they are synthesized and represents a solution to the band gap prediction problem.

Ab initio evidence for the formation of impurity d3z2-r2 holes in doped La2-xSrxCuO4

Using the spin unrestricted Becke-3-Lee-Yang-Parr density functional, we computed the electronic structure of explicitly doped La2-xSrxCuO4 (x=0.125, 0.25, and 0.5). At each doping level, an impurity hole band is formed within the undoped insulating gap. This band is well localized to CuO6 octahedra adjacent to the Sr impurities. The nature of the impurity hole is A1g in symmetry, formed primarily from the z2 orbital on the Cu and pz orbitals on the apical O’s. There is a strong triplet coupling of this hole with the intrinsic B1g Cu x2-y2/O1 pσ hole on the same site. Optimization of the c coordinate of the apical O’s in the doped CuO6 octahedron leads to an asymmetric anti-Jahn-Teller distortion of the O_2 atoms toward the central Cu. In particular, the O_2 atom between the Cu and Sr is displaced 0.26 A while the O_2 atom between the Cu and La is displaced 0.10 A. Contrary to expectations, investigation of a 0.1 A enhanced Jahn-Teller distortion of this octahedron does not force formation of an x^2 - y^2 hole, but instead leads to migration of the z^2 hole to the four other CuO_6 octahedra surrounding the Sr impurity. This latter observation offers a simple explanation for the bifurcation of the Sr-O_2 distance revealed in x-ray absorption fine structure data.

Accurate Ab Initio Quantum Mechanics Simulations of Bi2Se3 and Bi2Te3 Topological Insulator Surfaces

It has been established experimentally that Bi2Te3 and Bi2Se3 are topological insulators, with zero band gap surface states exhibiting linear dispersion at the Fermi energy. Standard density functional theory (DFT) methods such as PBE lead to large errors in the band gaps for such strongly correlated systems, while more accurate GW methods are too expensive computationally to apply to the thin films studied experimentally. We show here that the hybrid B3PW91 density functional yields GW-quality results for these systems at a computational cost comparable to PBE. The efficiency of our approach stems from the use of Gaussian basis functions instead of plane waves or augmented plane waves. This remarkable success without empirical corrections of any kind opens the door to computational studies of real chemistry involving the topological surface state, and our approach is expected to be applicable to other semiconductors with strong spin-orbit coupling.

Chiral plaquette polaron theory of cuprate superconductivity

Ab initio density functional calculations on explicitly doped La2−xSrxCuO4 find that doping creates localized holes in out-of-plane orbitals. A model for cuprate superconductivity is developed based on the assumption that doping leads to the formation of holes on a four-site Cu plaquette composed of the out-of-plane A1 orbitals apical O pz, planar Cu d3z2−r2, and planar O psigma. This is in contrast to the assumption of hole doping into planar Cu dx^2−y^2 and O psigma orbitals as in the t-J model. Allowing these holes to interact with the d^9 spin background leads to chiral polarons with either a clockwise or anticlockwise charge current. When the polaron plaquettes percolate through the crystal at x[approximate]0.05 for La2−xSrxCuO4, a Cu dx^2−y^2 and planar O psigma band is formed. The computed percolation doping of x[approximate]0.05 equals the observed transition to the “metallic” and superconducting phase for La2−xSrxCuO4. Spin exchange Coulomb repulsion with chiral polarons leads to d-wave superconducting pairing. The equivalent of the Debye energy in phonon superconductivity is the maximum energy separation between a chiral polaron and its time-reversed partner. This energy separation is on the order of the antiferromagnetic spin coupling energy, Jdd~0.1 eV, suggesting a higher critical temperature. An additive skew-scattering contribution to the Hall effect is induced by chiral polarons and leads to a temperature dependent Hall effect that fits the measured values for La2−xSrxCuO4. The integrated imaginary susceptibility, observed by neutron spin scattering, satisfies omega/T scaling due to chirality and spin-flip scattering of polarons along with a uniform distribution of polaron energy splittings. The derived functional form is compatible with experiments. The static spin structure factor for chiral spin coupling of the polarons to the undoped antiferromagnetic Cu d^9 spins is computed for classical spins on large two-dimensional lattices and is found to be incommensurate with a separation distance from (pi/a,pi/a) given by deltaQ[approximate](2pi/a)x, where x is the doping. When the perturbed x^2−y^2 band energy in mean field is included, incommensurability along the Cu-O bond direction is favored. A resistivity ~T^(µ+1) arises when the polaron energy separation density is of the form ~Deltaµ due to Coulomb scattering of the x^2−y^2 band with polarons. A uniform density leads to linear resistivity. The coupling of the x^2−y^2 band to the undoped Cu d^9 spins leads to the angle-resolved photoemission pseudogap and its qualitative doping and temperature dependence. The chiral plaquette polaron leads to an explanation of the evolution of the bilayer splitting in Bi-2212.

Numerical resistivity calculations for disordered three-dimensional metal models using tight-binding Hamiltonians

We calculate the zero-temperature resistivity of model 3-dimensional disordered metals described by tight-binding Hamiltonians. Two different mechanisms of disorder are considered: diagonal and off-diagonal. The non-equilibrium Green function formalism provides a Landauer-type formula for the conductance of arbitrary mesoscopic systems. We use this formula to calculate the resistance of finite-size disordered samples of different lengths. The resistance averaged over disorder configurations is linear in sample length and resistivity is found from the coefficient of proportionality. Two structures are considered: (1) a simple cubic lattice with one s-orbital per site, (2) a simple cubic lattice with two d-orbitals. For small values of the disorder strength, our results agree with those obtained from the Boltzmann equation. Large off-diagonal disorder causes the resistivity to saturate, whereas increasing diagonal disorder causes the resistivity to increase faster than the Boltzmann result. The crossover toward localization starts when the Boltzmann mean free path relative to the lattice constant has a value between 0.5 and 2.0 and is strongly model dependent.