We consider a new quantum gate mechanism based on electron spins in coupled semiconductor quantum dots. Such gates provide a general source of spin entanglement and can be used for quantum computers. We determine the exchange coupling J in the effective Heisenberg model as a function of magnetic (B) and electric fields, and of the inter-dot distance (a) within the Heitler-London approximation of molecular physics. This result is refined by using sp-hybridization, and by the Hund-Mulliken molecular-orbit approach which leads to an extended Hubbard description for the two-dot system that shows a remarkable dependence on B and a due to the long-range Coulomb interaction. We find that the exchange J changes sign at a finite field (leading to a pronounced jump in the magnetization) and then decays exponentially. The magnetization and the spin susceptibilities of the coupled dots are calculated. We show that the dephasing due to nuclear spins in GaAs can be strongly suppressed by dynamical nuclear spin polarization and/or by magnetic fields.Comment: 10 pages, 4 figures. v2: minor corrections, appendix added. to be published in Phys.Rev.

The electronic spin degrees of freedom in semiconductors typically have decoherence times that are several orders of magnitude longer than other relevant timescales. A solid-state quantum computer based on localized electron spins as qubits is therefore of potential interest. Here, a scheme that realizes controlled interactions between two distant quantum dot spins is proposed. The effective long-range interaction is mediated by the vacuum field of a high finesse microcavity. By using conduction-band-hole Raman transitions induced by classical laser fields and the cavity-mode, parallel controlled-not operations and arbitrary single qubit rotations can be realized. Optical techniques can also be used to measure the spin-state of each quantum dot. 03.67.Lx, 42.50.Dv, 03.65.Bz Within the last few years, quantum computation (QC) has developed into a truly interdisciplinary field involving the contributions of physicists, engineers, and computer scientists [1]. The seminal discoveries of Shor and others, both in developing quantum algorithms for important problems like prime factorization [2], and in developing protocols for quantum error correction (QEC) [3] and fault-tolerant quantum computation [4], have indicated the desirability and the ultimate feasibility of the experimental realization of QC in various quantum systems.The elementary unit in most QC schemes is a twostate system referred to as a quantum bit (qubit). Since QEC can only work if the decoherence rate is small, it is crucial to identify schemes where the qubits are well isolated from their environment. Ingenious schemes based on Raman-coupled low-energy states of trapped ions [5] and nuclear spins in chemical solutions [6] satisfy this criterion, in addition to providing methods of fast quantum manipulation of qubits that do not introduce significant decoherence. Even though these schemes are likely to provide the first examples of quantum information processing at 5-10 qubit level, they do not appear to be scalable to larger systems containing more than 100 qubits.Here, we propose a new scheme for quantum information processing based on quantum dot (QD) electron spins coupled through a microcavity mode. The motivation for this scheme is threefold: (1) a QC scheme based on semiconductor quantum dot arrays should be scalable to ≥ 100 coupled qubits; (2) recent experiments demonstrated very long spin decoherence times for conduction band electrons in III-V and II-VI semiconductors [7], making electron spin a likely candidate for a qubit; and (3) cavity-QED techniques can provide longdistance, fast interactions between qubits [8]. The QC scheme detailed below relies on the use of a single cavity mode and laser fields to mediate coherent interactions between distant QD spins. As we will show shortly, the proposed scheme does not require that QDs be identical and can be used to carry out parallel quantum logic operations [9].We note that a QC scheme based on electron spins in QDs have been previously proposed [10]: this scheme is based on local exchan...

Various physical implementations of quantum computers are being investigated, although the requirements that must be met to make such devices a reality in the laboratory at present involve capabilities well beyond the state of the art. Recent solid-state approaches have used quantum dots, donor-atom nuclear spins or electron spins; in these architectures, the basic two-qubit quantum gate is generated by a tunable exchange interaction between spins (a Heisenberg interaction), whereas the one-qubit gates require control over a local magnetic field. Compared to the Heisenberg operation, the one-qubit operations are significantly slower, requiring substantially greater materials and device complexity--potentially contributing to a detrimental increase in the decoherence rate. Here we introduced an explicit scheme in which the Heisenberg interaction alone suffices to implement exactly any quantum computer circuit. This capability comes at a price of a factor of three in additional qubits, and about a factor of ten in additional two-qubit operations. Even at this cost, the ability to eliminate the complexity of one-qubit operations should accelerate progress towards solid-state implementations of quantum computation.

We propose how to form spin qubits in graphene. A crucial requirement to achieve this goal is to find quantum dot states where the usual valley degeneracy in bulk graphene is lifted. We show that this problem can be avoided in quantum dots based on ribbons of graphene with semiconducting armchair boundaries. For such a setup, we find the energies and the exact wave functions of bound states, which are required for localized qubits. Additionally, we show that spin qubits in graphene can not only be coupled between nearest neighbor quantum dots via Heisenberg exchange interaction but also over long distances. This remarkable feature is a direct consequence of the quasi-relativistic spectrum of graphene.Comment: 10 pages, 9 figure

We present k· p Hamiltonians parametrised by ab initio density functional theory calculations to describe the dispersion of the valence and conduction bands at their extrema (the K, Q, Γ, and M points of the hexagonal Brillouin zone) in atomic crystals of semiconducting monolayer transition metal dichalcogenides. We discuss the parametrisation of the essential parts of the k· p Hamiltonians for MoS 2 , MoSe 2 , MoTe 2 , WS 2 , WSe 2 , and WTe 2 , including the spin-splitting and spin-polarisation of the bands, and we briefly review the vibrational properties of these materials. We then use k· p theory to analyse optical transitions in two-dimensional transition metal dichalcogenides over a broad spectral range that covers the Van Hove singularities in the band structure (the M points). We also discuss the visualisation of scanning tunnelling microscopy maps. PACS numbers:Contents 1 Introduction 2 2 Lattice parameters, band-structure calculations and vibrational properties 43 Band-edge energy differences and spin-splittings 7 4 Valence band width D vb 9 arXiv:1410.6666v3 [cond-mat.mes-hall] 6 Apr 2015 k · p theory for 2D TMDCs to be studied without constructing slabs in three-dimensionally periodic cells and the resulting electronic spectra are free of plane-wave continua. All our fleur calculations were carried out with a cut-off k max of 10.6 eV −1 for the plane-wave basis set and 144 k points corresponding to a 12 × 12 × 1 Monkhorst-Pack grid in the irreducible wedge of the BZ. Muffin-tin radii of 1.0, 1.21, 1.27, 1.27, and 1.27Å were used for S, Se, Te, Mo, and W, respectively. We note that considering local orbitals for Mo (s, p), Se (s, p, d), and W (s, p, f ) to improve the linearised augmented plane-wave basis proved to be crucial for a correct description of the excited states. We used the Perdew-Burke-Ernzerhof (PBE) generalised gradient approximation [83] to the exchange-correlation potential. The structures were relaxed (with the effects of SOC included) until the forces were less than 0.0005 eV/Å. The calculated values of a 0 and d S−S for monolayer TMDCs are shown in Table 1 and compared to measured values for the corresponding bulk materials. The lattice parameters obtained from the first of the DFT approaches described above are shown in the rows labelled by "(HSE)", the ones from the second approach are in the rows labelled by "(PBE)". "(Exp)" indicates experimental results found in the literature. Although there is some scatter in the experimental data, Table 1 suggests that using the HSE06 functional to relax the monolayer crystal structure leads to a good agreement with the room-temperature empirical bulk a 0 values. On the other hand, the PBE functional seems to slightly overestimates a 0 . However, the situation is less clear in the case of d X−X . We note that both the HSE06 and the PBE results are in good agreement with Reference [84].Recent experiments show that the energy of the photoluminescence peak is quite sensitive to the temperature [5,85,86], which can be understood in terms of th...