Belita Koiller

Exchange in silicon-based quantum computer architecture.

The silicon-based quantum computer proposal has been one of the actively pursued ideas during the past three years. Here we calculate the donor electron exchange in silicon and germanium, and demonstrate an atomic-scale challenge for quantum computing in Si (and Ge), as the six (four) conduction-band minima in Si (Ge) lead to intervalley electronic interference, generating strong oscillations in the exchange splitting of two-donor two-electron states. Donor positioning with atomic-scale precision within the unit cell thus becomes a decisive factor in determining the strength of the exchange coupling-a fundamental ingredient for two-qubit operations in a silicon-based quantum computer.

Tight-binding study of the influence of the strain on the electronic properties of InAs 'GaAs quantum dots

We present an atomistic investigation of the influence of strain on the electronic properties of quantum dots (QDs) within the empirical sp 3 stight-binding (ETB) model with interactions up to 2nd nearest neighbors and spin-orbit coupling. Results for the model system of capped pyramid-shaped InAs QDs in GaAs, with supercells containing ∼ 10 5 atoms are presented and compared with previous empirical pseudopotential results. The good agreement shows that ETB is a reliable alternative for an atomistic treatment. The strain is incorporated through the atomistic valence force field model. The ETB treatment allows for the effects of bond length and bond angle deviations from the ideal InAs and GaAs zincblende structure to be selectively removed from the electronic-structure calculation, giving quantitative information on the importance of strain effects on the bound state energies and on the physical origin of the spatial elongation of the wave functions. Effects of dot-dot coupling have also been examined to determine the relative weight of both strain field and wave function overlap.

Local density of states in a disordered chain: A renormalization group approach

Abstract We apply renormalization group techiques to evaluate the local density of phonon states for the isotopically (randomly) disordered linear chain. The method is based on a systematic decimation of atoms in the chain. Numerical studies reveal a richly structured spectrum, in reasonable agreement both with numerical simulations and with exact moments results. This is the first analytic alloy approximation which takes into account potential fluctuations of arbitrary range.

Electromechanical Effects in Carbon Nanotubes

We perform ab initio calculations of charged graphene and single-wall carbon nanotubes (CNTs). A wealth of electromechanical behaviors is obtained. (1) Both nanotubes and graphene expand upon electron injection. (2) Upon hole injection, metallic nanotubes and graphene display a nonmonotonic behavior. Upon increasing hole densities, the lattice constant initially contracts, reaches a minimum, and then starts to expand. The hole densities at minimum lattice constants are 0.3 ‖e‖/atom for graphene and between 0.1 and 0.3‖e‖/atom for the metallic nanotubes studied. (3) Semiconducting CNTs with small diameters (d<∼20 A) always expand upon hole injection. (4) Semiconducting CNTs with large diameters (d<∼20 A) display a behavior intermediate between those of metallic and large-gap CNTs. (5) The strain versus extra charge displays a linear plus power-law behavior, with characteristic exponents for graphene, metallic, and semiconducting CNTs. All these features are physically understood within a simple tight-binding total-energy model.

Spin quantum computation in silicon nanostructures

Abstract Proposed silicon-based quantum-computer architectures have attracted attention because of their promise for scalability and their potential for synergetically utilizing the available resources associated with the existing Si technology infrastructure. Electronic and nuclear spins of shallow donors (e.g. phosphorus) in Si are ideal candidates for qubits in such proposals because of their long spin coherence times due to their limited interactions with their environments. For these spin qubits, shallow donor exchange gates are frequently invoked to perform two-qubit operations. We discuss in this review a particularly important spin decoherence channel, and bandstructure effects on the exchange gate control. Specifically, we review our work on donor electron spin spectral diffusion due to background nuclear spin flip–flops, and how isotopic purification of silicon can significantly enhance the electron spin dephasing time. We then review our calculation of donor electron exchange coupling in the presence of degenerate silicon conduction band valleys. We show that valley interference leads to orders of magnitude variations in electron exchange coupling when donor configurations are changed on an atomic scale. These studies illustrate the substantial potential that donor electron/nuclear spins in silicon have as candidates for qubits and simultaneously the considerable challenges they pose. In particular, our work on spin decoherence through spectral diffusion points to the possible importance of isotopic purification in the fabrication of scalable solid state quantum computer architectures. We also provide a critical comparison between the two main proposed spin-based solid state quantum computer architectures, namely, shallow donor bound states in Si and localized quantum dot states in GaAs.

Quantum control of donor electrons at the Si-SiO2 interface.

Prospects for the quantum control of electrons in the silicon quantum computer architecture are considered theoretically. In particular, we investigate the feasibility of shuttling donor-bound electrons between the impurity in the bulk and the Si-SiO2 interface by tuning an external electric field. We calculate the shuttling time to range from subpicoseconds to nanoseconds depending on the distance (approximately 10-50 nm) of the donor from the interface. Our results establish that quantum control in such nanostructure architectures could, in principle, be achieved.

Electric-field control and adiabatic evolution of shallow donor impurities in silicon

We present a tight-binding study of donor impurities in Si, demonstrating the adequacy of this approach for this problem by comparison with Kohn-Luttinger effective mass theory and experimental results. We consider the response of the system to an applied electric field: donors near a barrier material and in the presence of a uniform electric field may undergo two different ionization regimes according to the distance of the impurity to the Si/barrier interface. We show that for impurities ∼5 nm below the barrier, adiabatic ionization is possible within switching times of the order of one picosecond, while for impurities ∼ 10 nm or more below the barrier, no adiabatic ionization may be carried out by an external uniform electric field. Our results are discussed in connection with proposed Si:P quantum computer architectures.

Electronic structure of the transition-metal monoxides

A model for the electronic structure of the transition-metal monoxides is presented. It consists of: (a) A criterion based on 4s bandwidths and spectroscopic term values to decide on the metallic versus insulating character; (b) A quantitative description for the insulating oxides which includes itinerant metal 4s and oxygen 2p states and correlated localized ionic levels arising from the 3d electrons. Optical properties are studied in detail; comparison with experiment is reasonably good.

Physical mechanisms of interface-mediated intervalley coupling in Si

The conduction band degeneracy in Si is detrimental to quantum computing based on spin qubits, for which a nondegenerate ground orbital state is desirable. This degeneracy is lifted at an interface with an insulator as the spatially abrupt change in the conduction band minimum leads to intervalley scattering. We present a theoretical study of the interface-induced valley splitting in Si that provides simple criteria for optimal fabrication parameters to maximize this splitting. Our work emphasizes the relevance of different interface-related properties to the valley splitting.

Valley-based noise-resistant quantum computation using Si quantum dots.

We devise a platform for noise-resistant quantum computing using the valley degree of freedom of Si quantum dots. The qubit is encoded in two polarized (1,1) spin-triplet states with different valley compositions in a double quantum dot, with a Zeeman field enabling unambiguous initialization. A top gate gives a difference in the valley splitting between the dots, allowing controllable interdot tunneling between opposite valley eigenstates, which enables one-qubit rotations. Two-qubit operations rely on a stripline resonator, and readout on charge sensing. Sensitivity to charge and spin fluctuations is determined by intervalley processes and is greatly reduced as compared to conventional spin and charge qubits. We describe a valley echo for further noise suppression.