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Using the effective mass model for an electron and the dielectric continuum model, analytical solutions of the self-consistent Schrödinger-Poisson system of equations are obtained. Quantum mechanical theory of electronic stationary states, the oscillator strengths of quantum transitions and a method of potential profile calculation is developed for the experimentally constructed three-well resonance-tunneling structure — a separate cascade of quantum cascade detector. For the proposed method, a comparison with the results of other methods and with the results of the experiment was carried out. A good agreement between the calculated value of the detected energy and its experimental value has been obtained, the difference being no more than 2.5%.

The study of physical processes associated with acoustic phonons in nitride-based nanosystems is of great importance for the effective operation of modern nanoscale devices. In this paper, a consistent theory of acoustic phonons arising in multilayer nitride-based semiconductor resonant tunneling structures, that can function as a separate cascade of a quantum cascade laser or detector is proposed. Using the physical and geometric parameters of a typical nanostructure, the spectrum of various types of acoustic phonons and the corresponding normalized components of the elastic displacement vector are calculated. It has been established that the spectrum of acoustic phonons of a multilayer nanostructure consists of two groups of the shear phonons dependencies and three groups of dependencies for a mixed spectrum of flexural and dilatational phonons. The dependencies of the acoustic phonons spectrum of the nanostructure and the components of the elastic displacement vector on its geometric parameters are studied. It has been established that for the components of the displacement vector u2 for shear phonons have a decrease in the absolute values of their maxima with increasing of energy level number. The components u1 and u3 of flexural and dilatational phonons behave respectively as symmetric and antisymmetric functions relatively the center of an separate selected layer of the nanostructure. The proposed theory can be further applied to study the interaction of electrons with acoustic phonons in multilayer resonant tunneling structures.

In approximations of the effective mass and rectangular potential wells and potentials for the electron, by using solutions of the complete Schrödinger equation, was developed the theory of active dynamic conductivity of three barrier resonant tunnel structure in a weak electromagnetic field, taking into account the contribution of detector one- and two-photon electronic transitions with different frequencies. It is shown that the value of the contribution of two-photon transitions in the formation of the total amount of active dynamic conductivity in detector transitions is not less 35 %.

The interaction of nuclei with nonzero spin with electron spins creates small electronic energy. With a scanning tunneling microscope tip, Willke et al. measured these hyperfine interactions for iron and titanium atoms that were manipulated on a magnesium oxide surface. The tip was also used to measure electron paramagnetic resonance spectra. The hyperfine structure of single atoms was sensitive to the binding site of the atom as well as its position relative to other magnetic atoms. Science , this issue p. 336 Atom manipulation and spin sensing with scanning tunneling microscopy reveal details underlying hyperfine interactions. Taking advantage of nuclear spins for electronic structure analysis, magnetic resonance imaging, and quantum devices hinges on knowledge and control of the surrounding atomic-scale environment. We measured and manipulated the hyperfine interaction of individual iron and titanium atoms placed on a magnesium oxide surface by using spin-polarized scanning tunneling microscopy in combination with single-atom electron spin resonance. Using atom manipulation to move single atoms, we found that the hyperfine interaction strongly depended on the binding configuration of the atom. We could extract atom- and position-dependent information about the electronic ground state, the state mixing with neighboring atoms, and properties of the nuclear spin. Thus, the hyperfine spectrum becomes a powerful probe of the chemical environment of individual atoms and nanostructures.

Electron spin resonance (ESR) spectroscopy is a crucial tool, through spin labelling, in investigations of the chemical structure of materials and of the electronic structure of materials associated with unpaired spins. ESR spectra measured in molecular systems, however, are established on large ensembles of spins and usually require a complicated structural analysis. Recently, the combination of scanning tunnelling microscopy with ESR has proved to be a powerful tool to image and coherently control individual atomic spins on surfaces. Here we extend this technique to single coordination complexes—iron phthalocyanines (FePc)—and investigate the magnetic interactions between their molecular spin with either another molecular spin (in FePc–FePc dimers) or an atomic spin (in FePc–Ti pairs). We show that the molecular spin density of FePc is both localized at the central Fe atom and also distributed to the ligands (Pc), which yields a strongly molecular-geometry-dependent exchange coupling. Electron spin resonance spectroscopy has traditionally been used to study large ensembles of spins, but its combination with scanning tunnelling microscopy recently enabled measurements on single adatoms. Now, individual iron phthalocyanine complexes adsorbed on a surface have been probed. Their spin distribution partially extends on the phthalocyanine, leading to a strong geometry-dependent exchange coupling interaction.

Imaging of biomolecules guides our understanding of their diverse structures and functions 1 , 2 . Real-space imaging at sub-nanometre resolution using cryo-electron microscopy has provided key insights into proteins and their assemblies 3 , 4 . Direct molecular imaging of glycans—the predominant biopolymers on Earth, with a plethora of structural and biological functions 5 —has not been possible so far 6 . The inherent glycan complexity and backbone flexibility require single-molecule approaches for real-space imaging. At present, glycan characterization often relies on a combination of mass spectrometry and nuclear magnetic resonance imaging to provide insights into size, sequence, branching and connectivity, and therefore requires structure reconstruction from indirect information 7 – 9 . Here we show direct imaging of single glycan molecules that are isolated by mass-selective, soft-landing electrospray ion beam deposition and imaged by low-temperature scanning tunnelling microscopy 10 . The sub-nanometre resolution of the technique enables the visualization of glycan connectivity and discrimination between regioisomers. Direct glycan imaging is an important step towards a better understanding of the structure of carbohydrates. An imaging method combining soft-landing electrospray ion beam deposition and low-temperature scanning tunnelling microscopy resolves the structures of glycans at sub-nanometre resolution, revealing the connectivity of glycan chains and the types of linkages.

The design and control of atomic-scale spin structures constitute major challenges for spin-based quantum technology platforms, including quantum dots, color centers, and molecular spins. Here, we showcase a strategy for designing the quantum properties of molecular spin qubits by combining tip-assisted on-surface assembly with electron spin resonance scanning tunneling microscopy (ESR-STM): We fabricate magnetic dimer complexes that consist of an iron phthalocyanine (FePc) molecule and an organometallic half-sandwich complex formed by the FePc ligand and an attached iron atom, Fe(C 6 H 6 ). The total complex forms a mixed-spin (1/2,1) quantum ferrimagnet with a well-separated correlated ground state doublet, which we utilize for coherent control. As a result of the correlation, the quantum ferrimagnet shows an improved spin lifetime ( > 1.5 μs) as it is partially protected against inelastic electron scattering. Lastly, the ferrimagnet units also enable intermolecular coupling, that can be used to realize both ferromagnetic or antiferromagnetic structures. Thus, quantum ferrimagnets provide a versatile platform to improve coherent control in general and to study complex magnetic interactions.

Biological electron-transfer (ET) reactions are typically described in the framework of coherent two-state electron tunneling or multistep hopping. However, these ET reactions may involve multiple redox cofactors in van der Waals contact with each other and with vibronic broadenings on the same scale as the energy gaps among the species. In this regime, fluctuations of the molecular structures and of the medium can produce transient energy level matching among multiple electronic states. This transient degeneracy, or flickering electronic resonance among states, is found to support coherent (ballistic) charge transfer. Importantly, ET rates arising from a flickering resonance (FR) mechanism will decay exponentially with distance because the probability of energy matching multiple states is multiplicative. The distance dependence of FR transport thus mimics the exponential decay that is usually associated with electron tunneling, although FR transport involves real carrier population on the bridge and is not a tunneling phenomenon. Likely candidates for FR transport are macromolecules with ET groups in van der Waals contact: DNA, bacterial nanowires, multiheme proteins, strongly coupled porphyrin arrays, and proteins with closely packed redox-active residues. The theory developed here is used to analyze DNA charge-transfer kinetics, and we find that charge-transfer distances up to three to four bases may be accounted for with this mechanism. Thus, the observed rapid (exponential) distance dependence of DNA ET rates over distances of ≲15 Å does not necessarily prove a tunneling mechanism.

Two gold nanostructures with controllable subnanometre separation are used to follow the evolution of plasmonic modes; the distance at which quantum tunnelling sets in is determined, and a quantum limit for plasmonic field confinement is estimated. Subnanometre plasmonic interactions Confining and enhancing light at nanometre length scales using plasmonic effects has become a widely used tool for applications including imaging, sensing, transformation optics and photovoltaics. To exploit plasmonics at even smaller, subnanometre length scales, it becomes essential to include quantum effects for a full description. Here, Jeremy Baumberg and colleagues. use two gold nanostructures with controllable subnanometre separation and carefully follow the evolution of the plasmonic modes. They can pinpoint at what distance quantum tunnelling sets in, and establish a quantum limit for plasmonic-field enhancement. The findings are relevant to future nanoplasmonic approaches and nanometer-scale photochemistry. When two metal nanostructures are placed nanometres apart, their optically driven free electrons couple electrically across the gap. The resulting plasmons have enhanced optical fields of a specific colour tightly confined inside the gap. Many emerging nanophotonic technologies depend on the careful control of this plasmonic coupling, including optical nanoantennas for high-sensitivity chemical and biological sensors 1 , nanoscale control of active devices 2 , 3 , 4 , and improved photovoltaic devices 5 . But for subnanometre gaps, coherent quantum tunnelling becomes possible and the system enters a regime of extreme non-locality in which previous classical treatments 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 fail. Electron correlations across the gap that are driven by quantum tunnelling require a new description of non-local transport, which is crucial in nanoscale optoelectronics and single-molecule electronics. Here, by simultaneously measuring both the electrical and optical properties of two gold nanostructures with controllable subnanometre separation, we reveal the quantum regime of tunnelling plasmonics in unprecedented detail. All observed phenomena are in good agreement with recent quantum-based models of plasmonic systems 15 , which eliminate the singularities predicted by classical theories. These findings imply that tunnelling establishes a quantum limit for plasmonic field confinement of about 10 −8 λ 3 for visible light (of wavelength λ ). Our work thus prompts new theoretical and experimental investigations into quantum-domain plasmonic systems, and will affect the future of nanoplasmonic device engineering and nanoscale photochemistry.

Single atomic adsorbates on ultrathin insulating films provide a promising route towards building bottom-up quantum architectures based on atomically identical yet individually addressable spin qubits on solid surfaces. A key challenge in engineering quantum-coherent spin nanostructures lies in understanding and controlling the spin state of individual adsorbates. In this work, we investigate single titanium (Ti) atoms adsorbed on MgO/Ag(100) surfaces using a combined scanning tunneling microscopy and electron spin resonance. Our measurements reveal two distinct spin states, S  = 1/2 and S  = 1, depending on the local adsorption site and the thickness of the MgO film. Density functional theory calculations suggest a Ti + configuration for the Ti adsorbates with approximately 3 electrons in the 4 s and 3 d valence shells. Using multi-orbital magnetic multiplet calculations the site dependence of the spin can be rationalized as a charge redistribution between spin-polarizing and depolarizing orbitals. These findings underscore the potential of surface-supported single atoms as spin qubits with tunable spin and charge states, enabling atom-by-atom control in the realization of a versatile quantum platform on surfaces. The study shows that the spin state of a single titanium atom on an insulating surface can be reversibly switched by its local environment, without chemical changes (no hydrogenation), using advanced microscopy, spectroscopy, and theory.