Semiconductor quantum ring as a solid-state spin qubit

The implementation of a spin qubit in a quantum ring occupied by one or a few electrons is proposed. Quantum bit involves the Zeeman sublevels of the highest occupied orbital. Such a qubit can be initialized, addressed, manipulated, read out and coherently coupled to other quantum rings. An extensive discussion of relaxation and decoherence is presented. By analogy with quantum dots, the spin relaxation times due to spin-orbit interaction for experimentally accessible quantum ring architectures are calculated. The conditions are formulated under which qubits build on quantum rings can have long relaxation times of the order of seconds. Rapidly improving nanofabrication technology have made such ring devices experimentally feasible and thus promising for quantum state engineering.Comment: 16 pages, 3 figure 3 table

A learning by confusion approach to characterize phase transitions

Recently, the learning by confusion (LBC) approach has been proposed as a machine learning tool to determine the critical temperature Tc of phase transitions without any prior knowledge of its even approximate value. However, the effectiveness of the method has been demonstrated only for continuous phase transitions, where confusion can result only from a deliberate incorrect labeling of the data and not from the coexistence of different phases. To verify whether the confusion scheme can also be used for discontinuous phase transitions, in this work, we apply the LBC method to three microscopic models, the Blume-Capel, the q-state Potts, and the Falicov-Kimball models, which undergo continuous or discontinuous phase transitions depending on model parameters. With the help of a simple model, we predict that the phase coexistence present in discontinuous phase transitions can make the neural network more confused and thus decrease its performance. However, numerical calculations performed for the models mentioned above indicate that other aspects of this kind of phase transition are more important and can render the LBC method less effective. Nevertheless, we demonstrate that in some cases the same aspects allow us to use the LBC method to identify the order of a phase transitio

Spin–orbit coupling in buckled monolayer nitrogene

Buckled monolayer nitrogene has been recently predicted to be stable above the room temperature. The low atomic number of nitrogen atom suggests, that spin–orbit coupling in nitrogene is weak, similar to graphene or silicene. We employ first principles calculations and perform a systematic study of the intrinsic and extrinsic spin–orbit coupling in this material. We calculate the spin mixing parameter b 2 , reflecting the strength of the intrinsic spin–orbit coupling and find, that b 2 is relatively small, on the order of 10 −6 . It also displays a weak anisotropy, opposite for electrons and holes. To study extrinsic effects of spin–orbit coupling we apply a transverse electric field enabling spin–orbit fields . We find, that are on the order of a single μ eV in the valence band, and tens to a hundred of μ eV in the conduction band, depending on the applied electric field. Similar to b 2 , is also anisotropic, in particular for the conduction electrons

Spin-orbit coupling in elemental two-dimensional materials

The fundamental spin-orbit coupling and spin mixing in graphene and rippled honeycomb lattice materials silicene, germanene, stanene, blue phosphorene, arsenene, antimonene, and bismuthene is investigated from first principles. The intrinsic spin-orbit coupling in graphene is revisited using multi-band $k\cdot p$ theory, showing the presence of non-zero spin mixing in graphene despite the mirror symmetry. However, the spin mixing itself does not lead to the the Elliott-Yafet spin relaxation mechanism, unless the mirror symmetry is broken by external factors. For other aforementioned elemental materials we present the spin-orbit splittings at relevant symmetry points, as well as the spin admixture $b^2$ as a function of energy close to the band extrema or Fermi levels. We find that spin-orbit coupling scales as the square of the atomic number Z, as expected for valence electrons in atoms. For isolated bands, it is found that $b^2\sim Z^4$. The spin-mixing parameter also exhibits giant anisotropy which, to a large extent, can be controlled by tuning the Fermi level. Our results for $b^2$ can be directly transferred to spin relaxation time due to the Elliott-Yafet mechanism, and therefore provide an estimate of the upper limit for spin lifetimes in materials with space inversion center.Comment: 10 pages, 8 figure

k.p theory for phosphorene: Effective g-factors, Landau levels, and excitons

Phosphorene, a single layer of black phosphorus, is a direct band gap two-dimensional semiconductor with promising charge and spin transport properties. The electronic band structure of phosphorene is strongly affected by the structural anisotropy of the underlying crystal lattice. We describe the relevant conduction and valence bands close to the Gamma-point by four-and six-band (with spin) k . p models, including the previously overlooked interband spin-orbit coupling which is essential for studying anisotropic crystals. All the k . p parameters are obtained by a robust fit to ab initio data, by taking into account the nominal band structure and the k-dependence of the effective mass close to the Gamma-point. The inclusion of interband spin-orbit coupling allows us to determine dipole transitions along both armchair and zigzag directions. The interband coupling is also key to determine the effective g-factors and Zeeman splittings of the Landau levels. We predict the electron and hole g-factor correction of approximate to 0.03 due to the intrinsic contributions in phosphorene, which lies within the existing range of experimental data. Furthermore, we investigate excitonic effects using the k . p models and find exciton binding energy (0.81 eV) and exciton diameters consistent with experiments and ab initio based calculations. The proposed k . p Hamiltonians should be useful for investigating magnetic, spin, transport, and optical properties and many-body effects in phosphorene

Proximity-induced spin-orbit coupling in phosphorene on WSe2_2 monolayer

We investigate, using first-principles methods and effective-model simulations, the spin-orbit coupling proximity effects in a bilayer heterostructure comprising phosphorene and WSe$_2$ monolayers. We specifically analyze holes in phosphorene around the $\Gamma$ point, at which we find a significant increase of the spin-orbit coupling that can be attributed to the strong hybridization of phosphorene with the WSe$_2$ bands. We also propose an effective spin-orbit model based on the ${\bf C}_{1{\rm v}}$ symmetry of the studied heterostructure. The corresponding spin-orbit field can be divided into two parts: the in-plane field, present due to the broken nonsymmorphic horizontal glide mirror plane symmetry, and the dominant out-of-plane field triggered by breaking the out-of-plane rotational symmetry of the phosphorene monolayer. Furthermore, we also demonstrate that a heterostructure with 60$^\circ$ twist angle exhibits an opposite out-of-plane spin-orbit field, indicating that the coupling can effectively be tuned by twisting. The studied phosphorene/WSe$_2$ bilayer is a prototypical low common-symmetry heterostructure in which the proximity effect can be used to engineer the spin texture of the desired material.Comment: 7 pages, 3 figure

Spin-orbit coupling and spin relaxation in phosphorene: Intrinsic versus extrinsic effects

First-principles calculations of the essential spin-orbit and spin relaxation properties of phosphorene are performed. Intrinsic spin-orbit coupling induces spin mixing with the probability of b(2) approximate to 10(-4), exhibiting a large anisotropy, following the anisotropic crystalline structure of phosphorene. For realistic values of the momentum relaxation times, the intrinsic (Elliott-Yafet) spin relaxation times are hundreds of picoseconds to nanoseconds. Applying a transverse electric field ( simulating gating and substrates) generates extrinsic C-2v symmetric spin-orbit fields in phosphorene, which activate the D'yakonov-Perel' mechanism for spin relaxation. It is shown that this extrinsic spin relaxation also has a strong anisotropy and can dominate over the Elliott-Yafet one for strong enough electric fields. Phosphorene on substrates can thus exhibit an interesting interplay of both spin-relaxation mechanisms, whose individual roles could be deciphered using our results