Degenerate Conduction Band Research Articles

Spin quantum computation in silicon nanostructures

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.

Dynamical properties of the Anderson impurity model within a diagrammatic pseudoparticle approach

The Anderson model of a twofold spin degenerate impurity level in the limit of infinite Coulomb repulsion, $U\ensuremath{\rightarrow}\ensuremath{\infty}$, coupled to one and two degenerate conduction bands or channels, is considered in pseudo-particle representation. We extend the conserving T-matrix approximation (CTMA), a general diagrammatic approximation scheme based on a fully renormalized computation of two-particle vertex functions in the spin and in the charge channel, to the calculation of thermodynamic and spectral properties. In the single-channel case, the CTMA yields in the Kondo regime a temperature independent Pauli spin susceptibility for temperatures below the Kondo temperature ${T}_{K}$ and down to the lowest temperatures considered, reproducing the exact spin screening in the Fermi liquid state. The impurity spectral density appears to remain non-singular down to the lowest temperatures, in agreement with Fermi liquid behavior. However, the unitarity sum rule, which is crucial for an impurity solver like the CTMA to be applicable within dynamical mean field theories for strongly correlated lattice models, is overestimated at the lowest temperatures. We argue that this shortcoming may be due to numerical imprecision and discuss an appropriate scheme for its correction. In the two-channel case, the spectral density calculated within CTMA exhibits qualitatively the correct non-Fermi liquid behavior at low temperatures, i.e., a power law singularity.

Evolution of electronic states inGaAs1−xNxprobed by resonant Raman spectroscopy

Two distinct maxima ${E}_{W}$ and ${E}_{W}^{\ensuremath{'}}$ are observed in the resonant Raman-scattering profile for the LO phonon asymmetric linewidth broadening in ${\mathrm{GaAs}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$ and are attributed to states arising from a splitting of the quadruply degenerate conduction band near the L point. The data provide further insight into the physics underlying the giant band-gap bowing observed in ${\mathrm{GaAs}}_{1\ensuremath{-}x}{\mathrm{N}}_{x},$ as well as reveal asymmetric linewidth broadening to be a powerful signature for studying strongly localized impurity states in semiconductors.

Electron exchange coupling for single-donor solid-state spin qubits

Inter-valley interference between degenerate conduction band minima has been shown to lead to oscillations in the exchange energy between neighbouring phosphorus donor electron states in silicon \cite{Koiller02,Koiller02A}. These same effects lead to an extreme sensitivity of the exchange energy on the relative orientation of the donor atoms, an issue of crucial importance in the construction silicon-based spin quantum computers. In this article we calculate the donor electron exchange coupling as a function of donor position incorporating the full Bloch structure of the Kohn-Luttinger electron wavefunctions. It is found that due to the rapidly oscillating nature of the terms they produce, the periodic part of the Bloch functions can be safely ignored in the Heitler-London integrals as was done by Koiller et. al. [Phys. Rev. Lett. 88,027903(2002),Phys. Rev. B. 66,115201(2002)], significantly reducing the complexity of calculations. We address issues of fabrication and calculate the expected exchange coupling between neighbouring donors that have been implanted into the silicon substrate using an 15keV ion beam in the so-called 'top down' fabrication scheme for a Kane solid-state quantum computer. In addition we calculate the exchange coupling as a function of the voltage bias on control gates used to manipulate the electron wavefunctions and implement quantum logic operations in the Kane proposal, and find that these gate biases can be used to both increase and decrease the magnitude of the exchange coupling between neighbouring donor electrons. The zero-bias results reconfirm those previously obtained by Koiller.

Origin of the nitrogen-induced optical transitions inGaAs1−xNx

The temperature and concentration dependence of optical transitions in ${\mathrm{GaAs}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$ $(<3.8\mathrm{eV})$ are studied by electromodulated reflectance. These studies suggest that the ${E}_{+}$ transition involves the valence-band maximum at $\ensuremath{\Gamma}$ and a singlet state originating from the splitting of the quadruply degenerate conduction band at L. Such a transition, forbidden in pure GaAs, becomes allowed in ${\mathrm{GaAs}}_{1\ensuremath{-}x}{\mathrm{N}}_{x}$ due to the strong perturbation of nitrogen doping to the band structure. A similar analysis applied to the transition ${E}_{*}$ suggests that it is related either to resonant states evolving from the level created by a single isolated nitrogen impurity in GaAs, or to the splitting of the triplet originating from the L conduction band, induced by a further reduction in symmetry associated with nitrogen pairs.

Gaps and excitations in fullerides with partially filled bands: NMR study ofNa2C60andK4C60

We present an NMR study of Na2C60 and K4C60, two compounds that are related by electron-hole symmetry in the C60 triply degenerate conduction band. In both systems, it is known that NMR spin-lattice relaxation rate (1/T1) measurements detect a gap in the electronic structure, most likely related to singlet-triplet excitations of the Jahn-Teller distorted (JTD) C60^{2-} or C60^{4-}. However, the extended temperature range of the measurements presented here (10 K to 700 K) allows to reveal deviations with respect to this general trend, both at high and low temperatures. Above room temperature, 1/T1 deviates from the activated law that one would expect from the presence of the gap and saturates. In the same temperature range, a lowering of symmetry is detected in Na2C60 by the appearance of quadrupole effects on the 23Na spectra. In K4C60, modifications of the 13C spectra lineshapes also indicate a structural modification. We discuss this high temperature deviation in terms of a coupling between JTD and local symmetry. At low temperatures, 1/T$_1$T tends to a constant value for Na2C60, both for 13C and 23Na NMR. This indicates a residual metallic character, which emphasizes the proximity of metallic and insulting behaviors in alkali fullerides.

Theoretical Study of Electronic Structure of Silicon Nanocrystals

We report on a theoretical study of the electronic structure of silicon nanocrystals with a shape of the regular rhombic dodecahedron, based on a tight-binding method. The energies of the lowest unoccupied state and the highest occupied state have been calculated. We have shown that the six-fold degenerate conduction band minima of the bulk silicon crystal are split into a non-degenerate A1 state, a double-degenerate E state and a triple-degenerate T2 state and that the ordering of the energies of these states depends on the size of the silicon nanocrystal. Thus the lowest unoccupied state of the silicon nanocrystal can have different symmetries at different nanocrystal sizes. However, as the size of the nanocrystal changes, the symmetry of the highest occupied state remains the same; it is T2 symmetric. The wave functions of the lowest unoccupied and highest occupied states have also been calculated. It is shown that these states have very different localization properties. The wave function of the lowest unoccupied A1 state is largely localized on the central atomic site and on its nearest neighbors. In contrast, the wave function of the lowest unoccupied E state has no contribution from the orbitals of the central atom. Furthermore, the wave functions of both the lowest unoccupied and the highest occupied T2 states are distributed more evenly over a large portion of the silicon nanocrystals.

Electronic structure model for n- and p-type silicon quantum dots

We present effective mass, single-particle calculations of the electronic structure of n- and p-type silicon quantum dots. The structures investigated approximate silicon quantum dots fabricated on 〈 001〉-oriented SIMOX wafers. The effects of possible built-in strain are investigated in the framework of deformation potential induced splitting of the six degenerate conduction band valleys and the splitting of the degeneracy at the top of the bulk valence band. We present the energy levels and their degeneracies as functions of the dimensions of simple tetragonal model quantum dots. Our results are relevant for silicon quantum dots that are sufficiently small such as to lead to a predominance of the confinement energy over the Coulomb energy.

Boltzmann-Green functions for nonequilibrium fluctuations in metallic systems.

I describe a method for calculating nonequilibrium fluctuations in degenerate conduction bands. The method uses Green-function propagators to solve the one-particle Boltzmann equation. In the equilibrium limit of the uniform electron gas, I confirm that the Nyquist noise theorem is recovered within this formalism. \textcopyright{} 1996 The American Physical Society.

Design of C60-graphite cointercalation compounds.

We design a ${\mathrm{C}}_{60}$-intercalated all-carbon graphite intercalation compound, a ${\mathrm{C}}_{60}$-graphite cointercalation compound, and a K-doped ${\mathrm{C}}_{60}$-graphite cointercalation compound. Their electronic structure is studied within the density-functional theory. The geometrical structures assumed are the stage-1 cointercalation compound ${\mathrm{C}}_{60}$${\mathrm{C}}_{32}$ with alternating stacking of the ${\mathrm{C}}_{60}$ monolayer and the graphite sheet, and ${\mathrm{K}}_{4}$${\mathrm{C}}_{60}$${\mathrm{C}}_{32}$ where all the interstitial sites of ${\mathrm{C}}_{60}$${\mathrm{C}}_{32}$ are occupied by K atoms. In ${\mathrm{C}}_{60}$${\mathrm{C}}_{32}$, a small but finite charge transfer from the graphite layer to the ${\mathrm{C}}_{60}$ layer, as well as the redistribution of electrons within the graphite layer, is found to take place. This is a consequence of the round shape of ${\mathrm{C}}_{60}$ and the flat graphite sheet. Around the Fermi level, nearly degenerate graphite-layer valence and conduction bands exist as in the case of the graphite crystal. On the other hand, ${\mathrm{K}}_{4}$${\mathrm{C}}_{60}$${\mathrm{C}}_{32}$ is found to have conduction electrons on both ${\mathrm{C}}_{60}$ layers and graphite layers. The system has a high Fermi-level density of states due to the narrow ${\mathrm{C}}_{60}$ ${\mathit{t}}_{1\mathit{u}}$ conduction band but still the screening for Coulomb repulsion between conduction electrons is expected to be effective due to the coexistence of carriers in a wide graphite conduction band. Hence, the K-doped ${\mathrm{C}}_{60}$-graphite cointercalation compound is a promising candidate to exhibit superconductivity. Energetical considerations suggest that undoped as well as metal-doped ${\mathrm{C}}_{60}$-graphite cointercalation compounds should be stable and can be synthesized.

Elastic anomaly of heavy-fermion systems in a crystalline field

An elastic anomaly, observed in the heavy-Fermi liquid state of Ce alloys (for example, CeCu 6 and CeTe), is analyzed by using the infinite- U Anderson lattice model. Four atomic energy levels are assumed for f-electrons. Two of them are mutually degenerate. A small crystalline splitting 2Δ is assumed between two energy levels. Fourfold degenerate conduction bands are also considered. We solve the model using the mean field approximation to slave bosons and the renormalized elastic constant is calculated. The temperature dependence of the constant shows a downward dip. The result is compared with the experimental data of CeTe.

Elastic anomaly of heavy fermion systems in a crystalline field

An elastic anomaly, observed in the heavy Fermi liquid state of Ce alloys (for example, CeCu6 and CeTe), is analysed by using the infinite-U Anderson lattice model. Four atomic energy levels are assumed for f-electrons. Two of them are mutually degenerate. A small crystalline splitting 2 Delta is assumed between two energy levels. The fourfold degenerate conduction bands are also considered in the model. The authors solve the model using the mean-field approximation to slave bosons, changing the Fermi energy in order to keep the total electron number constant. The non-zero value of the mean field of the slave bosons persists over temperatures much higher than the Kondo temperature. This is an effect of the constant electron number. Next, the linear susceptibility with respect to Delta is calculated in order to obtain the renormalized elastic constant. The resulting temperature dependence of the constant shows a downward dip. The authors discuss the relation of their findings to experimental data.

The mobility of electrons in strained silicon

The development of Si and Si 1−xGe x layer growth by molecular beam epitaxy has enabled heterostructures and HEMT devices to be made with Group IV semiconductors. Strain is very important in determining the electronic behaviour of this system and as an initial step towards understanding mobility in SiGe HEMT structures a Monte Carlo technique has been used to simulate electron transport in bulk Si, strained by commensurate growth on a (001) Si 1−yGe y buffer. The in-plane mobility initially increases with increasing strain but then falls at higher strains and fields. Results are presented for both undoped and 10 17 cm −3 n-type Si, fields of 10 2 to 10 4 Vcm −1 and strain levels up to the equivalence of growth on a Si 0.25Ge 0.75 buffer. The results are explained by the splitting of the degenerate conduction band minimum and the transition probability between the two-fold and four-fold split minima.

Theoretical Analysis of a Si/SiGe Hemt Structure

ABSTRACTAn analysis has been made of a Si/SiGe HEMT structure, grown on a (001) oriented substrate, by adapting an existing model for III–V HEMT's. Strain plays a critical role in the behaviour of these SiGe structures by separating the degenerate conduction band minimum into 2- and 4- fold symmetric minima. This effect has been incorporated into a ID solution of Poisson's equation in the device structure. The effects of strain, Schottky barrier height, layer width and doping density on both enhancement and depletion mode HEMT properties are all considered. In addition initial estimates of the effect of strain on electron mobility are presented.

Negative magnetoresistance in magnetic semiconductors with narrow degenerate conduction bands

We propose a model to explain electrical conductivity anomalies in magnetic chalcogenide spinels near the Curie point. The model is based on strong electronelectron correlations between d-electrons in the narrow, orbitally degenerate conduction band. We demonstrate that in this system spin inhomogeneities produce scattering and lead to strong negative magnetoresistance. Experimental data on the electrical conductivity of the CdCr2Se4 compound in a magnetic field is compared to numerical computation. We explain the absence of magnetoresistance anomalies in p-type samples.

Electric subbands in Si/SiGe strained layer superlattices

The subband structure for electrons in Si/SiGe strained layer superlattices along the (100) direction is calculated self-consistently including many-body effects in the local density approximation. The strain induced splitting of the six-fold degenerate conduction band results in different potential wells for different valleys. The charge distribution between the layers and valleys is calculated versus carrier concentration and conduction band offset for different strains. An estimate for the band offsets is obtained by comparison of experimental results with the calculations.

The band structure of tetraza porphin polysiloxane

The band structure of tetraza porphin polysiloxane is studied by means of a semiempirical crystal orbital model. The width of the valence band amounts to 2.00 eV, while the Δε value of the degenerate conduction band is 1.52 eV. The forbidden band gap of the unoxidized polymer is 2.04 eV.

Electron mobility in degenerate tellurium doped In 0.53 Ga 0.47 As LPE layers

Tellurium doped In0.53Ga0.47As epitaxial layers have been grown by LPE in the range n=1018−4×1019 cm−3; the distribution coefficient of tellurium was found to be 0.1. These layers exhibit a two to three times higher mobility than InP or GaAs doped to the same level. Theoretically calculated values of mobility taking account of the degenerate and nonparabolic conduction band conditions are compared with the experimental data.

On the Theory of Photon‐Assisted Zener Tunneling

AbstractZener tunneling assisted by one‐photon absorption is studied theoretically. A general expression for the transition rate is obtained and further evaluated for both a two‐band and a three‐band process, where analytical results are presented in terms of Airy functions. Furthermore, an interband current is produced by photon assisted tunneling which is shown to be proportional to the corresponding transition rate. It can be concluded from these results that photon assisted tunneling noticeably contributes to macroscopically observable quantities like electroabsorption and electric current, especially, if two nearly degenerate valence or conduction bands exist. In the latter case an interband current is produced flowing opposite to the field direction.

Experimental System for Studying Itinerant d-Electron Ferromagnetism

Typical theoretical models of an itinerate electron ferromagnet consist of a single narrow band, but experimental data have been obtained primarily from the ferrous metals whose behavior is more complex because of overlapping broad s bands and narrow d bands. Transition metal sulfides of the cubic pyrite structure appear to have a doubly degenerate conduction band arising from atomic d orbitals of eg symmetry without overlapping s bands.1 The full band would contain four electrons per metal atom. Metallic conductivity is observed, except for the empty FeS2, exactly half-filled NiS2, and filled ZnS2 bands. The electron concentration, n, can be varied from zero to one electron per metal ion in the Fe1−xCoxS2 systems (n=x) and can be extended to higher values by use of the Ni1−yCoyS2 system (n=2−y).2 In these systems the effective moment obtained from paramagnetic susceptibility measurements is that of the isolated cobalt and nickel ions. It appears, therefore, that a model based on strong electron-electron correlation at the metal-ion sites would be applicable to these pyrite compounds. Such a model for a nondegenerate band has been given extensive theoretical treatment by Hubbard.3,4 Solutions for the degenerate case have also been indicated,5 and calculations of the Hubbard model for the two-fold degenerate band are currently being carried out.6 Significant features of the pyrite system which should be qualitatively explained by a theoretical model are: (1) Ferromagnetism exists down to very low electron concentrations. A plot of Curie temperature vs n goes to zero at n≈0.05. For n<0.05 the electrical resistivity vs temperature curves exhibit shallow minima at 20°K indicative of localized states. The loss of ferromagnetism below n≈0.05 may thus be due to loss of itinerancy and not to a critical electron concentration. (2) The ferromagnetic moment, μs, is equal to one Bohr magneton per electron over a wide range of electron concentration 0.15 ≤n≤0.95. Ferromagnetic behavior is observed for 0.05<n<0.15, but the curve of magnetization vs applied field does not saturate, and μs appears to be less than n. (3) In Ni1−yCoyS2 (n>1) the saturation magnetization, Curie temperature, and Weiss constant decrease rapidly with Ni concentration, indicating strong antiferromagnetic Ni–Co interactions. Ferromagnetism disappears for n>1.1. This would be expected if strong correlations at the Ni sites dominate. (4) In Fe1−xCoxS2, μs decreases from 0.95 to 0.89 as n is increased from 0.95 to 1.0, but the effective moment in the paramagnetic state continues to increase linearly with cobalt concentration. Neutron-diffraction studies indicate a collinear spin state.7 A localized moment model which seems to explain much of the magnetic behavior cannot account for this decrease in μs with increasing Co concentration.