Corrugated single layer templates for molecules: From h-BN nanomesh to graphene based quantum dot arrays

Functional nano-templates enable self-assembly of otherwise impossible arrangements of molecules. A particular class of such templates is that of sp ² hybridized single layers of hexagonal boron nitride or carbon (graphene) on metal supports. If the substrate and the single layer have a lattice mismatch, superstructures are formed. On substrates like rhodium or ruthenium these superstructures have unit cells with ∼3-nm lattice constant. They are corrugated and contain sub-units, which behave like traps for molecules or quantum dots, which are small enough to become operational at room temperature. For graphene on Rh(111) we emphasize a new structural element of small extra hills within the corrugation landscape. For the case of molecules like water it is shown that new phases assemble on such templates, and that they can be used as “nano-laboratories” where many individual processes are studied in parallel. Furthermore, it is shown that the h-BN/Rh(111) nanomesh displays a strong scanning tunneling microscopy-induced luminescence contrast within the 3 nm unit cell which is a way to address trapped molecules and/or quantum dots.     

Corrugated single layer templates for molecules: From h-BN nanomesh to graphene based quantum dot arrays

Functional nano-templates enable self-assembly of otherwise impossible arrangements of molecules. A particular class of such templates is that of sp² hybridized single layers of hexagonal boron nitride or carbon (graphene) on metal supports. If the substrate and the single layer have a lattice mismatch, superstructures are formed. On substrates like rhodium or ruthenium these superstructures have unit cells with ~3-nm lattice constant. They are corrugated and contain sub-units, which behave like traps for molecules or quantum dots, which are small enough to become operational at room temperature. For graphene on Rh(111) we emphasize a new structural element of small extra hills within the corrugation landscape. For the case of molecules like water it is shown that new phases assemble on such templates, and that they can be used as “nano-laboratories” where many individual processes are studied in parallel. Furthermore, it is shown that the h-BN/Rh(111) nanomesh displays a strong scanning tunneling microscopy-induced luminescence contrast within the 3 nm unit cell which is a way to address trapped molecules and/or quantum dots.     

Formation of a monolayer <Emphasis Type="Italic">h</Emphasis>-BN nanomesh on Rh (111) studied using <Emphasis Type="Italic">in-situ</Emphasis> STM

As a member of the 2D family of materials, h-BN is an intrinsic insulator and could be employed as a dielectric or insulating inter-layer in ultra-thin devices. Monolayer h-BN can be synthesized on Rh (111) surfaces using borazine as a precursor. Using in-situ variable-temperature scanning tunneling microscopy (STM), we directly observed the formation of h in real-time. By analyzing the deposition under variable substrate temperatures and the filling rate of the h-BN overlayer vacant hollows during growth, we studied the growth kinetics of how the borazine molecules construct the h-BN overlayer grown on the Rh surface.     

Generation of dislocation loops in strained quantum dots embedded in a heterolayer

The generation of prismatic dislocation loops in strained quantum dots is investigated. The quantum dots are embedded in a film-substrate heterostructure with mechanical stresses caused by the difference between the lattice parameters of the film (heterolayer) and the substrate. The intrinsic plastic strain ?_m of a quantum dot arises from the misfit between the lattice parameters of the materials of the quantum dot and the surrounding matrix. The interface between the heterolayer and the substrate is characterized by a misfit parameter f. The critical radius of a quantum dot R _c at which the generation of a dislocation loop in the quantum dot becomes energetically favorable is analyzed as a function of the intrinsic plastic strain ?_m and the misfit parameter f.     

Coulomb oscillations of the current through spin-nondegenerate <Emphasis Type="Italic">p</Emphasis> states of InAs quantum dots

The electron transport is studied in split-gate structures fabricated on the basis of a modulation-doped heterostructure that contains a single quantum well and self-assembled InAs quantum dots near the 2D electron gas regions. The current passing through the channel with a denumerable set of InAs quantum dots is found to exhibit Coulomb oscillations as a function of the gate voltage. The oscillations are associated with the excited p states of InAs quantum dots, which are characterized by opposite spins and caused by lifting of the spin degeneracy of the p state due to the Coulomb interaction. The Coulomb oscillations of the current are observed up to a temperature of ～20 K. The Coulomb energy is found to be ΔE_c = 12.5 meV, which agrees well with the theoretical estimates for the p states of quantum dots in the structures under study.     

Effects of nonstoichiometry and ordering on the basic lattice constant of vanadium carbide VC<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript>

The effect of nonstoichiometry and ordering on the lattice constant a _B1 of the basic lattice of vanadium carbide VC _y (0.65 < y < 0.875) is studied. A change in the lattice constant of disordered carbide VC _y at the reduction of the carbon content is considered using the direction of static displacements of atoms near a vacancy. A model for the calculation of the basic lattice constant a _B1 of vanadium carbide is proposed taking into account nonstoichiometry and ordering. It is shown that the ordering of vanadium carbide VC _y with the formation of V₆C₅ and V₈C₇ superstructures results in an increase in the basic lattice constant as compared to disordered carbide.     

Mechanisms of low-temperature high-frequency conductivity in systems with a dense array of Ge<Subscript>0.7</Subscript>Si<Subscript>0.3</Subscript> quantum dots in silicon

High-frequency (HF) conductivity in systems with a dense (with a density of n = 3 × 10¹¹ cm^?2) array of self-organized Ge_0.7Si_0.3 quantum dots in silicon with different boron concentrations n_B is determined by acoustic methods. The measurements of the absorption coefficient and the velocity of surface acoustic waves (SAWs) with frequencies of 30–300 MHz that interact with holes localized in quantum dots are carried out in magnetic fields of up to 18 T in the temperature interval from 1 to 20 K. Using one of the samples (n_B = 8.2 × 10¹¹ cm^?2), it is shown that, at temperatures T ≤ 4 K, the HF conductivity is realized by the hopping of holes between the states localized in different quantum dots and can be explained within a two-site model in the case of

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, where ω is the SAW frequency and τ₀ is the relaxation time of the populations of the sites (quantum dots). For T > 7 K, the HF conductivity has an activation character associated with the diffusion over the states at the mobility threshold. In the interval 4 K < T < 7 K, the HF conductivity is determined by a combination of the hopping and activation mechanisms. The contributions of these mechanisms are distinguished; it is found that the temperature dependence of the hopping HF conductivity approaches saturation at T* ≈ 4.5 K, which points to a τ₀ ≤ 1. A value of τ₀(T*) ≈ 5 × 10^?9 s is determined from the condition ωτ₀(T*) ≈ 1.

     

Partial pseudospin polarization,latticetronics and Fano resonances in quantum dots based in graphene ribbons: a conductance spectroscopy

In this work we study, as a function of the height V and width L _b of the potentialbarriers, the transport of Dirac quasi-particles through quantum dots in graphene ribbons.We observed, as we increase V, a partial polarization (PP) of the pseudospin due to the participation of the hyperbolic bands. This generates polarizations in the sub-lattices A or B outside the dot regions for single, coupled, and open dots. Thus for energies around the Dirac point, the conductance G at both sides of the dot shows a latticetronics of conductances G _A and G _B as a function ofV and L _b . This fact can be used as a PPspectroscopy which associates hole-type waves with the latticetronics. A periodic enhancement of PP is obtained with the increase of V in dots formed bybarriers that completely occupy the nanoribbon width. For this case, a direct correspondence between G(V) and PP(V) exists. On the other hand, for the open dots, the PP(V) and the G(V) show a complex behavior that exhibit higher intensities when compared to the previous case. In the Dirac limit we have no backscattering signs, however when we move slightly away from this limit the firstsigns of confinement appear in the PP(V) (it freezes in a given sub-lattice). In the last case the backscattering fingerprints are obtained directly fromthe conductance (splittings). The open quantum dots are very sensible to their opening w _d and this generatesFano line-shapes of difficult interpretation around the Dirac point. The PP spectroscopy used here allows us to understand the influence of w _d in the relativistic analogues and to associate electron-type waves with the observed Fano line-shapes.     

Effect of nonstoichiometry on the lattice constant of cubic vanadium carbide VC<Subscript><Emphasis Type="Italic">y</Emphasis></Subscript>

The effect of nonstoichiometry on the lattice constant of cubic vanadium carbide VC _y (0.65 < y < 0.875) is studied. It is found that the ordering of vanadium carbide VC _y with the formation of superstructures V₆C₅ and V₈C₇ leads to an increase in the base lattice constant in comparison with disordered carbide. Taking into account the change in the lattice constant, the direction of the static displacements of atoms near the vacancy is discussed.     

1/<Emphasis Type="Italic">Q</Emphasis> expansion for the energy spectrum of quantum dots

A new method is proposed for calculating the energy spectrum and the wave functions of N-electron quantum dots with an arbitrary confining potential. The method consists in expansion with respect to a dimensionless quantum parameter 1/Q, which is expressed in terms of the ratio of the characteristic Coulomb energy of electron-electron interaction to the characteristic energy of one-particle transition in a confining potential. Two-electron quantum dots with a parabolic confining potential in an external magnetic field are considered. Strongly correlated states of the system and the spin rearrangement in a strong magnetic field are analyzed. Analytic expressions are obtained for the energy and the wave functions of the system. It is shown that restriction of the analysis only to the first three terms in the quantum-parameter expansion gives an accuracy of one percent when calculating the energy even for values of Q on the order of unity, i.e., for the presently implementable GaAs quantum dots. The expressions for energy obtained are in a good agreement with the experimental data for quantum dots in a perpendicular magnetic field.     

Electronic transport through a Majorana bound state coupled to a T-shaped quantum-dot system with Coulomb interaction

Using the Green’s function technique, we respectively investigate the electron transport properties of two spin components through the system of a T-shaped double quantum dot structure coupled to a Majorana bound state, in which only one quantum dot is connected with two metallic leads. We explore the interplay between the Fano effect and the MBSs for different dot-MBS coupling strength λ, dot-dot coupling strength t, and MBS-MBS coupling strength ε_M in the noninteracting case. Then the Coulomb interaction and magnetic field effect on the conductance spectra are investigated. Our results indicate that G_↓(ω) is not affected by the Majorana bound states, but a “0.5” conductance signature occurs in the vicinities of Fermi level of G_↑(ω). This robust property persists for a wide range of dot-dot coupling strength and dot-MBS coupling strength, but it can be destroyed by Coulomb interaction in quantum dots. By adjusting the size and direction of magnetic field around the quantum dots, the “0.5” conductance signature damaged by U can be restored. At last, the spin magnetic moments of two dots by applying external magnetic field are also predicted.     

Adsorption configurations of carbon monoxide on gold monolayer supported by graphene or monolayer hexagonal boron nitride: a first-principles study

Using density functional theory with a semiempirical van der Waals approach proposed by Grimme, the adsorption behavior of carbon monoxide on a gold monolayer supported by graphene or monolayer hexagonal boron nitride has been investigated. Based on the changes in the Dirac cone of graphene and a Bader charge analysis, we observe that the Au(111) monolayer gains a small charge from graphene and monolayer h-BN. The adsorbed CO molecule adopts similar adsorption configurations on Au(111)/graphene and Au(111)/h-BN with Au-C distance 2.17?2.50 Å and Au-C-O angle of 123.9°–139.6°. Moreover, we found that for low CO coverages, bonding to the gold surface is surprisingly energy-favorable. Yet the CO adsorption binding energy diminishes at high coverage due to the repulsive van der Waals interactions between CO molecules.     

Coulomb Problem for <Emphasis Type="Italic">Z</Emphasis> &gt; Z<Subscript>cr</Subscript> in Doped Graphene

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Z_cr(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z < Z_cr (J, n = 0), the energy of a level is presented as a function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z>Z_cr (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions ε₀ and widths γ of quasistationary states as a function of supercriticality. The values of ε₀* and width γ* are pointed out for which quasidiscrete levels may show up as Breit–Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z_cr. In this single-particle approximation, there is no spontaneous creation of electron–hole pairs, and the impurity charge cannot be screened by this mechanism.     

Intuitionistic Quantum Logic of an <Emphasis Type="Italic">n</Emphasis>-level System

A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum mechanics, which meanwhile has been extended by Döring and Isham so as to provide a new mathematical foundation for all of physics. Last year, three of the present authors redeveloped and refined these ideas by combining the C*-algebraic approach to quantum theory with the so-called internal language of topos theory (Heunen et al. in arXiv:0709.4364). The goal of the present paper is to illustrate our abstract setup through the concrete example of the C*-algebra M _n (?) of complex n×n matrices. This leads to an explicit expression for the pointfree quantum phase space Σ _n and the associated logical structure and Gelfand transform of an n-level system. We also determine the pertinent non-probabilisitic state-proposition pairing (or valuation) and give a very natural topos-theoretic reformulation of the Kochen–Specker Theorem.In our approach, the nondistributive lattice ?(M _n (?)) of projections in M _n (?) (which forms the basis of the traditional quantum logic of Birkhoff and von Neumann) is replaced by a specific distributive lattice \(\mathcal{O}(\Sigma_{n})\) of functions from the poset \(\mathcal{C}(M_{n}(\mathbb{C}))\) of all unital commutative C*-subalgebras C of M _n (?) to ?(M _n (?)). The lattice \(\mathcal{O}(\Sigma_{n})\) is essentially the (pointfree) topology of the quantum phase space Σ _n , and as such defines a Heyting algebra. Each element of \(\mathcal{O}(\Sigma_{n})\) corresponds to a “Bohrified” proposition, in the sense that to each classical context \(C\in\mathcal{C}(M_{n}(\mathbb{C}))\) it associates a yes-no question (i.e. an element of the Boolean lattice ?(C) of projections in C), rather than being a single projection as in standard quantum logic. Distributivity is recovered at the expense of the law of the excluded middle (Tertium Non Datur), whose demise is in our opinion to be welcomed, not just in intuitionistic logic in the spirit of Brouwer, but also in quantum logic in the spirit of von Neumann.     

Index Theory of One Dimensional Quantum Walks and Cellular Automata

If a one-dimensional quantum lattice system is subject to one step of a reversible discrete-time dynamics, it is intuitive that as much “quantum information” as moves into any given block of cells from the left, has to exit that block to the right. For two types of such systems — namely quantum walks and cellular automata — we make this intuition precise by defining an index, a quantity that measures the “net flow of quantum information” through the system. The index supplies a complete characterization of two properties of the discrete dynamics. First, two systems S ₁, S ₂ can be “pieced together”, in the sense that there is a system S which acts like S ₁ in one region and like S ₂ in some other region, if and only if S ₁ and S ₂ have the same index. Second, the index labels connected components of such systems: equality of the index is necessary and sufficient for the existence of a continuous deformation of S ₁ into S ₂. In the case of quantum walks, the index is integer-valued, whereas for cellular automata, it takes values in the group of positive rationals. In both cases, the map \({S \mapsto {\rm ind} S}\) is a group homomorphism if composition of the discrete dynamics is taken as the group law of the quantum systems. Systems with trivial index are precisely those which can be realized by partitioned unitaries, and the prototypes of systems with non-trivial index are shifts.     

Phononless hopping conduction in two-dimensional layers of quantum dots

Regularities are studied in charge transport due to the hopping conduction of holes along two-dimensional layers of Ge quantum dots in Si. It is shown that the temperature dependence of the conductivity obeys the Efros-Shklovskii law. It is found that the effective localization radius of charge carriers in quantum dots varies nonmonotonically upon filling quantum dots with holes, which is explained by the successive filling of electron shells. The preexponential factor of the hopping conductivity ceases to depend on temperature at low temperatures (T<10 K) and oscillates as the degree of filling quantum dots with holes varies, assuming values divisible by the conductance quantum e²/h. The results obtained indicate that a transition from phonon-assisted hopping conduction to phononless charge transfer occurs as the temperature decreases. The Coulomb interaction of localized charge carriers has a dominant role in these phononless processes.     

Cluster-Type Structure of Amorphous Smooth Hydrocarbon CD<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> Films (<Emphasis Type="Italic">x</Emphasis> ~ 0.5) from T-10 Tokamak

Structure of smooth hydrocarbon CD _x films with a high deuterium ratio x ~ 0.5 redeposited from T-10 tokamak D-plasma discharges (NRC Kurchatov Institute, Moscow) has been studied. For the first time, small and wide angle X-ray scattering technique using synchrotron radiation and neutron diffraction have been employed. A fractal structure of CD _x films is found to consist of mass-fractals with rough border, surface fractals (with rough surface), plane scatterers and linear chains forming a branched and highly cross-linked 3D carbon network. The found fractals, including sp² clusters, are of typical size ~1.60 nm. They include a C₁₃ fragment consisting of three interconnected aromatic rings forming a minimal fractal sp² aggregate 9 × C₁₃. These graphene-like sp² clusters are interconnected and form a 3D lattice which can be alternatively interpreted as a highly defective graphene layer with a large concentration of vacancies. The unsaturated chemical bonds are filled with D, H atoms, linear sp² C=C, C=O, and sp³ structural elements like C-C, C-H(D), C-D_2,3, C-O, O-H, COOH, C _x D(H) _y found earlier from the infrared spectra of CD _x films, which are binding linear elements of a carbon network. The amorphous structure of CD _x films has been confirmed by the results of earlier fractal structure modeling, as well as by researches with X-ray photoelectron spectroscopy which allow finding a definite similarity with the electron structure of their model analogues — polymeric a-C:H and a-C:D films with a disordered carbon network consisting of atoms in sp³ + sp² states.     

Spatially inhomogeneous states of charge carriers in graphene

The interaction of two-dimensional quasiparticles characterized by a linear dispersion E = ±u|p| (graphene) with impurity potentials is studied. It is shown that discrete levels corresponding to localized states are present in a one-dimensional potential well (quantum wire), whereas such states are absent in a two-dimensional well (quantum dot). The cross section for the scattering of electrons (holes) of graphene by an axially symmetric potential well is determined. It is shown that the cross section tends to a constant value in the limit of infinite particle energy. The effective Hamiltonian is derived for a curved quantum wire of graphene.     

Superposition of M<Subscript>5</Subscript>X<Subscript>5</Subscript> superstructures and X-ray diffraction in TiO<Subscript>1.0</Subscript> titanium monoxide

The interpretation of diffraction spectra of ordered high-temperature phases of solid solutions and strongly nonstoichiometric compounds is discussed. It has been shown that variations of the intensities of superstructure reflections, which cannot be explained within simple ordering models, can be due to the superposition of superstructures with different symmetries in the matrix of the basis crystal structure. Using an example of atom–vacancy ordering in TiO_1.0 titanium monoxide, a model of the order–order transition state formed by the superposition of low-temperature monoclinic (space group A2/m (C2/m)) and high-temperature cubic (space group Pm3?m) M₅X₅ superstructures has been proposed. It has been shown that the transition state is thermodynamically equilibrium and should be implemented instead of the M₅X₅ cubic superstructure. The transition state model can be considered as an M_(5–i)X_(5–i) superstructure (i = 1, 14/18, 11/18) with the monoclinic symmetry (space group P1m1).     

g-Factor Calculation in Small Quantum Dots

It is shown that the effective Lande splitting factor or g-factor of electrons localized on heterostructures such as small quantum dots is always formed as a difference of two values. The first of themrelates to thematerial of the dot itself and critically depends on its sizes and shape; the second one relates to the barriermaterial (surrounding matrix); therewith, the dependence on the latter does not disappear at any dot sizes. The known (k, p) Kane theory defining the renormalization of electron mass and g-factor in bulk semiconductors, is modified for small quantum dots with “incomplete” band structure. Specific calculations of the electron ground state energy and g-factor are performed for the covariant InAs/AlSb heterostructure not localizing holes and, hence, capable of forming pure one-electron states (prototypes of solid-state qubits).