Session Q15: Focus Session: Semiconductor Qubit Approaches I

Spin Dependent Transport in Si/SiGe Few-Electron Quantum Dots

Si/SiGe quantum dots are of interest for quantum information processing due in large part to the existence of spin zero isotopes of both Si and Ge. We present the results of transport measurements and integrated charge sensing in silicon double and single quantum dots.[1,2] We observe two effects arising from spin dependent transport in a double quantum dot. First, and as expected, for one direction of current flow we observe spin blockade -- the canonical example of spin-to-charge conversion in transport. In addition, when current flow is reversed, we observe a second effect: strong tails of current extend from the sharp triangular regions in which current conventionally is observed. The presence of these tails is explained by a combination of long spin relaxation times and preferential loading of an excited spin state. We also present charge-sensing measurements of single and double quantum dots using an integrated quantum point contact. The charge sensor signal from single electron tunneling is well correlated with conventional transport through the system. When the tunnel barriers are large and transport through the dot is not measurable, charge sensing remains a viable means to track charge transitions and is used to confirm individual-electron occupation in a single quantum dot. Work performed in collaboration with Nakul Shaji, Madhu Thalakulam, Levente J. Klein, H. Luo, Hua Qin, R. H. Blick, D. E. Savage, M. G. Lagally, A. J. Rimberg, R. Joynt, M. Friesen, S. N. Coppersmith, M. A. Eriksson. Work supported by ARO, LPS, NSF and DOE. (1) Shaji, N. \textit{et al}. e-print arXiv:0708.0794 (2) Simmons, C. B\textit{. et al}. Appl. Phys. Lett. \textbf{91}, 213103 (2007).   

Coulomb Blockade in Double Top Gated Si MOS Nano-Structures

Recent demonstrations of Pauli blockaded transport in Si-based double quantum dots [1,2] have demonstrated that the basic processes involved in spin-to-charge conversion are observable in gated quantum dots in Si. In this work, we will present results on the fabrication and electrical transport properties of novel double top gated Si MOS nano-structures. Potential advantages include: variable 2DEG density, CMOS compatible processes, and relatively small vertical length scales. A silicon foundry was used for initial processing steps and produced MOS structures with a peak mobility of 12000 cm sq/V-s at electron densities of 1e12/cm\^{}2. Resulting structures, demonstrate Coulomb blockade, and we will discuss the effect of different geometries (vertical top gate spacing, and single and double dot designs) on Coulomb blockade in these Si MOS structures. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. (1) Nakul Shaji et. al. arXiv:0708.0794v1 (2) H. W. Liu et. al. arXiv:0707.3513v1   

Dephasing of exchange coupled spin qubits by electron-phonon coupling in Silicon

Silicon is regarded as one of the most promising host materials for solid state spin-based quantum information processing because of small spin-orbit interaction and the prospect of removing nuclear spins through isotopic purification. However, in a coupled spin system, charge and orbital fluctuations are as harmful to the spin qubits as in other semiconducting materials. Here we explore pure dephasing between the two-electron singlet and triplet states for two exchange-coupled spin qubits in a double quantum dot, with particular attention paid to the multi-valley nature of the silicon conduction band.   

Decoherence and Relaxation in Two-electron Si Quantum Dots

We study the relaxation process for a doubly-occupied silicon quantum dot from an excited (triplet) state to the ground (singlet) state. The dominant mechanism available in absence of an external magnetic field is the hyperfine coupling with nuclei via a virtual state. Since a direct transition is forbidden by energy conservation, (the energy associated with a nuclear spin is three orders of magnitude smaller than that of the electron spin), the change in energy of the electron spin has to be compensated by a lattice vibration, or emission of a phonon. On the other hand, in absence of time reversal symmetry, spin-orbit (S0) admistures different spin states through the \emph{Rashba} SO coupling. This leads to a non-vanishing matrix element for the phonon-assisted transition between a singlet and a triplet state, where the phonon provides only energy conservation, potentially increasing the relaxation rate, $\Gamma_{\mathrm{ST}}$. We find relaxation times $T_{\mathrm{ST}}$ of a few seconds for a 40$\times$40$\times$15nm$^3$ Si quantum dot in a magnetic field of 1T.   

Spin singlet-triplet relaxation times in Si double quantum dots

Recent observation of spin-sensitive transport in semiconductor quantum dots presents a new way of spin manipulation in nanoscale devices. Spin-flip processes are essential for understanding the potential of these systems. Following experiments by A.~C.~Johnson {\it et.al.} Phys.Rev.B {\bf 72}, 165308 (2005) and N.~Shaji {\it et.al.} [cond-mat/0708.0794] we calculate the relaxation times of different spin configurations in double quantum dots. For two-electron states, we evaluate the effects of leads on the spin-flip transitions, compare these effects with relevant spin-orbit and nuclear spin relaxation mechanisms, and calculate the electric current profile, including structure of the peaks and temperature dependence of the transport in the suppressed (`valley') region.   

Spin resonance of 2D electrons in silicon MOS structures

Metal-oxide-silicon (MOS) heterostructures are a well developed technology, but not much is known about the electron spin properties of this system. However the promise of utilizing electron spins in MOS structures as qubits for quantum information processing calls for detailed study of these properties. We have previously reported an ESR signal at g = 1.9999(1) originating from 2D electrons in a MOSFET. The signal arises from mobile 2D electrons at gate voltages above threshold and weakly confined electrons below threshold. The signal intensity for confined electrons follows the expected Curie-like 1/T temperature dependence characteristic of isolated, independent spins. At high electron densities, where the Fermi energy is large compared to the microwave frequency, one might expect a simple Pauli susceptibility temperature dependence. In particular, electron spin susceptibility is expected to become constant at low temperatures. Perhaps surprisingly, we find that below about 4 K, the spin susceptibility decreases as the temperature is lowered. At electron densities from $3 \times 10^{11}$ to $10 \times 10^{11}$ cm$^{-2}$, the signal intensity falls by a factor of 5, as the temperature is reduced from 4 to 2 K. A more sophisticated analysis is required to explain the temperature dependence of the mobile 2D electron ESR signal.   

Valley Splitting in Electrostatically Confined Structures at the Si/SiO$_2$ Interface

Silicon is a promising material for qubits that use the spin degree of freedom for their encoding because of the anticipated long spin decoherence times. Electrostatic confinement of electrons at a Si(100)/dielectric interface splits the 6 fold conduction band degeneracy. However, 2DEGs are found to have a relatively small valley splitting between the two lowest levels, which is smaller than predicted for ideal interfaces. Small valley splitting is undesirable as it may detrimentally impact the spin decoherence time. Recent theory suggests that interface properties (e.g., miscut and disorder) can significantly change the valley splitting. Large splitting of the valley states has recently been observed in nanostructures formed in Si/SiGe heterostructures for which it is believed the electrons sampled a small number of atomic terraces [1]. In this talk, we will discuss valley splitting at a Si/SiO$_2$ interface in both conventional MOSFETs, MOS- nanostructures and their dependence on effects such as interface roughness, fixed charge, trap density and strain. The valley splitting is characterized via activation energy measurements in the quantum Hall regime. [1] S. Goswami et al., Nature Physics 3, 41 (2007). Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States DOE under contract DE-AC04- 94AL85000.   

Substrate orientation dependence of valley-splitting in Silicon nanostructures

Si nanostructures are being actively perceived for Quantum Computing (QC) devices where valley-splitting (VS) is an important device design parameter. Si is desirable for QC due to its long spin decoherence times, scaling potential and integratability within the present microelectronic infrastructure. Six-fold degenerate valleys in Si interact with each other in the presence of confinements provided by physical dimensions of the nanostructures, and applied electric and magnetic fields. These interactions can result in very-different splittings depending on substrate orientations and inherently present disorders in nanostructures. Surface morphology of Si is highly dependent on substrate orientations and so is the VS. Such surface irregularities are automatically included in supercell tight-binding calculations due to atomistic nature of the Hamiltonian. VS calculations in the Si nanostructures grown on (100), (110), (111) and high index vicinal surfaces will be presented.   

Why the Long-term Charge Offset Drift in Si SET Transistors is Much Better than Metal-Based Ones: TLF Stability

The charge offset drift is a long-standing problem in metal-based single-electron tunneling (SET) devices, manifesting as a time-dependent instability. Through a compendium of drift measurements on SET transistors fabricated in five different laboratories, we can show that the drift is endemic in metal- based devices, but is absent in Si-based devices. Given that it is well-known that two-level fluctuators (TLF's) exist in Si devices, the question naturally arises: why is the long-term drift so much better in the Si-based devices? Our answer: the TLF's in Si devices are stable over time, thermal cycling, etc., whereas the TLF's in the metal-based devices are unstable, and exist in interacting glass-like state. Following these observations, we have developed a model based on the theory of heat evolution in glasses that quantitatively agrees with the rate of charge offset drift in metal-based devices. Finally, we suggest some particular directions for future fabrication that may eliminate this problem.   

Vertically coupled Al and Si SETs for characterization of MOS structures at low temperature

Due to impurities and interface states, a silicon metal-oxide-semiconductor field-effect transistor (MOSFET) channel is usually imperfect. A single electron transistor (SET) close to the channel provides a useful probe of these imperfections at low temperatures, the regime where Si devices may be used for quantum information processing. We incorporate an Al-AlO$_{x}$-Al SET as the gate of a narrow MOSFET to induce a self-aligned and vertically coupled Si SET at the Si/SiO$_{2}$ interface [1]. We use this SET sandwich architecture to probe and identify sources of defect charge motion in MOS structures via a cross-correlation measurement between the two SETs. In particular, we will present preliminary data from these devices to study a single charge defect at the Si/SiO$_{2}$ interface. [1] L. Sun, K. R. Brown, and B. E. Kane, Appl. Phys. Lett. \textbf{91}, 142117 (2007).   

Gate control of single-electron spins: a multi-scale numerical simulation approach

Among recent proposals for next-generation, non-charge-based logic is the notion that a single electron can be trapped and its spin manipulated through the application of gate voltages (Rev. Mod. Phys. 79, 1217 (2007)). In this talk we present numerical simulations of such Spin Single Electron Transistors (SSET) in support of experimental work at the University at Albany, State University of New York aimed at the practical development of post-CMOS concepts and devices. We use a multi-scale simulation strategy to self-consistently solve the Schroedinger-Poisson equations (with and without exchange-correlation effects) to obtain realistic confining and gating potentials for realistic device geometries. We discuss scaling of the equations in the various sub domains of a finite-element discretization to span the dimensions from the micron scale of the gate structures down the single-electron level. We will discuss the calculation of the gate-tuned ``g-factor" for electrons and holes (Phys. Rev. B 68, 155330 (2003)) in electro-statically- and lithographically-defined quantum dots including the Rashba and Dresselhaus spin-orbit interactions computed numerically from realistic wave functions. This work is supported through funding from the DARPA/NRI INDEX center.   

Negative-result evolution from continuous noisy measurement of a double-dot spin qubit

We consider evolution of a double quantum dot (DQD) two-electron spin qubit that is continuously measured with a linear charge detector (quantum point contact). We identify the regime where a non-unitary negative-result evolution of the qubit emerges due to the fact that the system remains in the (1,1) charge state (each dot is occupied by one electron). In this case, the $|T_0(1,1)\rangle$ triplet spin state is spin-blocked, and the transition between $|S(1,1)\rangle$ and $|S(0,2)\rangle$ states is suppressed by the continuous measurement, due to the quantum Zeno effect. Moreover, unitary evolution between $|T_0(1,1)\rangle$ and $|S(1,1)\rangle$ states is induced by the negative-result measurement due to presence of $|S(0,2)\rangle$ state. We demonstrate that these effects exist for both strong and weak coupling between the detector and the DQD system. They can be observed with present-day technologies and can be used for coherent qubit manipulations complimentary to existing methods.   

Atomistic calculation of electronic and optical properties of a single InAs quantum dots

We present an atomistic tight-binding (TB) theory of electronic structure and optical properties of a single self-assembled InAs quantum dot (SAD). In previous work an effective-bond-orbital model (EBOM) was used to calculate electron and hole states of the SAD. The strain distribution was calculated using the continuum elasticity theory and EBOM was coupled to the strain via the Bir-Pikus Hamiltonian. However, the properties of these multimillion-atom systems are influenced by the presence of crystal facets and the symmetry of underlying zinc-blende lattice. In current work we present a fully atomistic TB model, accounting for the atomistic symmetry, and extended to include d-orbitals for proper treatment of interband/intervalley couplings. Strain is included in the Hamiltonian via Slater-Koster rules and a generalized Harrison law, with the equilibrium positions of atoms calculated using the valence force field method. Coulomb matrix elements are found using the TB functions, and electronic properties of N confined excitons (N=1-6) are determined in the CI approach. Emission spectra of multiexcitons are also obtained. Comparison with the previous approach and the experimental results is presented.