Geometric symmetries cause orbital degeneracies in a molecule's spectrum. In a single-molecule junction, these degeneracies are lifted by various symmetry-breaking effects. We study quantum transport through such nanostructures with an almost degenerate spectrum. We show that the master equation for the reduced density matrix must be derived within the singular-coupling limit as opposed to the conventional weak-coupling limit. This results in signatures of the density matrix's off-diagonal elements in the transport characteristics.
We consider electronic transport through a single-molecule junction where the molecule has a degenerate spectrum. Unlike previous transport models, and theories a rate-equations description is no longer possible, and the quantum coherences between degenerate states have to be taken into account. We present the derivation and application of a master equation that describes the system in the weak-coupling limit and give an in-depth discussion of the parameter regimes and the new phenomena due to coherent on-site dynamics.
Circulating orbital currents, originating from the spin-orbit interaction, are calculated for semiconductor nanostructures in the shape of spheres, disks, spherical shells and rings for the electron ground state with spin oriented along a symmetry axis. The currents and resulting orbital and spin magnetic moments, which combine to yield the effective electron g factor, are calculated using a recently introduced formalism that allows the relative contributions of different regions of the nanostructure to be identified. For all these spherically or cylindrically symmetric hollow or solid nanostr…
We use the concept of resonant tunneling to calculate the thermopower of molecular nanosystems. It turns out that the sign of the thermovoltage under resonant tunneling conditions depends sensitively on the participating molecular orbital, and one finds a sign change when the transport channel switches from the highest occupied molecular orbital to the lowest unoccupied molecular orbital. Comparing our results to recent experimental data obtained for a BDT molecule contacted with an STM tip, we observe good agreement.
We present a simple way to describe the lowest unoccupied diffuse states in carbon nanostructures in density functional theory (DFT) calculations using a minimal LCAO (linear combination of atomic orbitals) basis set. By comparing plane wave basis calculations, we show how these states can be captured by adding long-range orbitals to the standard LCAO basis sets for the extreme cases of planar <it>sp2</it> (graphene) and curved carbon (C60). In particular, using Bessel functions with a long range as additional basis functions retain a minimal basis size. This provides a smaller and simpler ato…
We describe magnetotransport experiments performed on Hall crosses made from quantum wires at LaAlO3/SrTiO3 interfaces. Shubnikov-de Haas oscillations measured in a 14-nm wide structure exhibit modulations that are consistent with spin-orbit coupling or valley degeneracies. Hall measurements performed on the 6 nm-wide Hall cross reveal dissipative coupling to magnetic phases. Hall plateaus are observed that deviate significantly from two-dimensional quantum Hall counterparts. Non-monotonic dips in the Hall resistance are attributed to one-dimensional confinement and spin-orbit coupling.
Circulating orbital currents produced by the spin-orbit interaction for a single electron spin in a quantum dot are explicitly evaluated at zero magnetic field, along with their effect on the total magnetic moment (spin and orbital) of the electron spin. The currents are dominated by coherent superpositions of the conduction and valence envelope functions of the electronic state, are smoothly varying within the quantum dot, and are peaked roughly halfway between the dot center and edge. Thus the spatial structure of the spin contribution to the magnetic moment (which is peaked at the dot cente…
Atomically precise placement of dopants in Si permits creating substitutional P nanowires by design. High-resolution images show that these wires are few atoms wide with some positioning disorder with respect to the substitutional Si structure sites. Disorder is expected to lead to electronic localization in one-dimensional (1D) - like structures. Experiments, however, report good transport properties in quasi-1D P nanoribbons. We investigate theoretically their electronic properties using an effective single-particle approach based on a linear combination of donor orbitals (LCDO), with a basi…
We report on a general theory for analyzing quantum transport through devices in the Metal-QD-Metal configuration where QD is a quantum dot or the device scattering region which contains Rashba spin-orbital and electron-electron interactions. The metal leads may or may not be ferromagnetic, they are assumed to weakly couple to the QD region. Our theory is formulated by second quantizing the Rashba spin-orbital interaction in spectral space (instead of real space), and quantum transport is then analyzed within the Keldysh nonequilibrium Green's function formalism. The Rashba interaction causes …
We consider the orbital magnetic properties of non-interacting charge carriers in graphene-based nanostructures in the low-energy regime. The magnetic response of such systems results both, frombulk contributions and from confinement effects that can be particularly strong in ballistic quantum dots. First we provide a comprehensive study of the magnetic susceptibility $χ$ of bulk graphene in a magnetic field for the different regimes arising from the relative magnitudes of the energy scales involved, i.e. temperature, Landau level spacing and chemical potential. We show that for finite tempera…
We present a first-principles study of the surface magnetism induced by Cr, Mn, Fe and Co adatoms on the (111) surfaces of Rh, Pd, Ag, Ir, Pt and Au. We first describe how the different contributions to the surface magnetism enter the magnetic stray field, with special attention paid to the induced orbital moments. Then we present results for the spin and orbital magnetic moments of the adatoms, and for the induced surface spin and orbital magnetic moments, the latter being further divided into atomic and inter-atomic contributions. We investigate how the surface magnetism is determined by the…
An important challenge in silicon quantum electronics in the few electron regime is the potentially small energy gap between the ground and excited orbital states in 3D quantum confined nanostructures due to the multiple valley degeneracies of the conduction band present in silicon. Understanding the "valley-orbit" (VO) gap is essential for silicon qubits, as a large VO gap prevents leakage of the qubit states into a higher dimensional Hilbert space. The VO gap varies considerably depending on quantum confinement, and can be engineered by external electric fields. In this work we investigate V…
We investigate theoretically the linear and nonlinear conductance through a nanostructure with two-fold degenerate single levels, corresponding to the transport through nanostructures such as a carbon nanotube, or double dot systems with capacitive interaction. It is shown that the presence of the interaction asymmetry between orbits/dots affects significantly the profile of the linear conductance at finite temperature, and, of the nonlinear conductance, particularly around half-filling, where the two-particle Kondo effect occurs. Within the range of experimentally feasible parameters, the SU(…
Transport properties of the two-orbital Kondo effect involving both spin and orbital (pseudospin) degrees of freedom were examined in a parallel double quantum dot with a sufficient interdot Coulomb interaction and negligibly small interdot tunneling. The Kondo effect was observed at the interdot Coulomb blockade region with degeneracies of both spin and orbital degrees of freedom. When the orbital degeneracy is lifted by applying a finite detuning, the Kondo resonance exhibits a triple-peak structure, indicating that both spin and orbital contributions are involved.
A theoretical model of a single molecule coupled to many vibronic modes is presented. At low energies, transport is dominated by electron-vibron processes where transfer of an electron through the dot is accompanied by the excitation/emission of quanta (vibrons). Because the frequency of the $n$th mode is taken as an $n$th multiple of the frequency of the fundamental mode, several energetically degenerate or quasi-degenerate vibronic configurations can contribute to transport. We investigate the consequences of strong electron-vibron coupling in a fully \emph{symmetric} set-up. Several strikin…
A theoretical model of a single molecule coupled to many vibronic modes is presented. At low energies, transport is dominated by electron-vibron processes where transfer of an electron through the dot is accompanied by the excitation/emission of quanta (vibrons). Because the frequency of the $n$th mode is taken as an $n$th multiple of the frequency of the fundamental mode, several energetically degenerate or quasi-degenerate vibronic configurations can contribute to transport. We investigate the consequences of strong electron-vibron coupling in a fully \emph{symmetric} set-up. Several strikin…
We theoretically investigate the effect of inhomogeneous light beams with (twisted light) and without (plane-wave light) orbital angular momentum on semiconductor-based nanostructures, when the symmetry axes of the beam and the nanostructure are displaced parallel to each other. Exact analytical results are obtained by expanding the off-centered light field in terms of the appropriate light modes centered around the nanostructure. We demonstrate how electronic transitions involving the transfer of different amounts of orbital angular momentum are switched on and off as a function of the separa…
Polyalanine molecules (PA) with an α-helix conformation gathered recently a lot of interest as the propagation of electrons through the chiral backbone structure comes along with spin polarization of the transmitted electrons. By means of scanning tunneling microscopy and spectroscopy at ambient conditions, PA molecules adsorbed on surfaces of epitaxial magnetic Al2O3/Pt/Au/Co/Au nanostructures with perpendicular anisotropy were studied. Thereby, a correlation between the PA molecules ordering at the surface with the electron tunneling across this hybrid system as a function of the substrate m…
Organic and carbon-based materials are attractive for spintronics because their small spin-orbit coupling and low hyperfine interaction is expected to give rise to large spin-relaxation times. However, the corresponding spin-relaxation length is not necessarily large when transport is via weakly interacting molecular orbitals. Here we use graphite as a model system and study spin transport in the direction perpendicular to the weakly bonded graphene sheets. We achieve injection of highly (75%) spin-polarized electrons into graphite nanostructures of 300-500 nm across and up to 17 nm thick, and…
A first-principles approach is introduced to calculate electron field emission characteristics of nanostructures, based on the nonequilibrium Green function technique combined with the density functional theory. The method employs atomic-like basis orbitals with large confinement radii and lithium anode to describe the electron density in the vacuum between the nanostructure tip and the anode, so takes the presence of emitted current into account. The simulation results on a capped single-walled carbon nanotube reproduce the experimental trend closely, in particular, the current saturation and…
Spin and angular momenta of light are important degrees of freedom in nanophotonics which control light propagation, optical forces and information encoding. Typically, optical angular momentum is generated using q-plates or spatial light modulators. Here, we show that graphene-supported plasmonic nanostructures with broken rotational symmetry provide a surprising spin to orbital angular momentum conversion, which can be continuously controlled by changing the electrochemical potential of graphene. Upon resonant illumination by a circularly polarized plane wave, a polygonal array of indium-tin…
We investigate strongly asymmetric self-assembled nanostructures with one of dimensions reaching hundreds of nanometers. Close to the nanowire-like type of confinement, such objects are sometimes assigned as one-dimensional in nature. Here, we directly observe the spectrum of exciton excited states corresponding to longitudinal quantization. This is based on probing the optical transitions via polarization-resolved microphotoluminescence excitation ($μ$PLE) measurement performed on single nanostructures combined with theoretical calculation of neutral and charged exciton optical properties. We…
In modeling low-dimensional electronic nanostructures, the evaluation of the electron-electron interaction is a challenging task. Here we present an accurate and practical density-functional approach to the two-dimensional many-electron problem. In particular, we show that spin-density functionals in the class of meta-generalized-gradient approximations can be greatly simplified by reducing the explicit dependence on the Kohn-Sham orbitals to the dependence on the electron spin density and its spatial derivatives. Tests on various quantum-dot systems show that the overall accuracy is well pres…
We extend the time-dependent Gutzwiller variational approach, recently introduced by Schirò and Fabrizio, Phys. Rev. Lett. 105 076401 (2010), to impurity problems. Furthermore, we derive a consistent theory for the steady state, and show its equivalence with the previously introduced nonequilibrium steady-state extension of the Gutzwiller approach. The method is shown to be able to capture dissipation in the leads, so that a steady state is reached after a sufficiently long relaxation time. The time-dependent method is applied to the single orbital Anderson impurity model at half-filling, mode…
Motivated by recent experiments, in which the Kondo effect has been observed for the first time in a double quantum-dot structure, we study electron transport through a system consisting of two ultrasmall, capacitively-coupled dots with large level spacing and charging energy. Due to strong interdot Coulomb correlations, the Kondo effect has two possible sources, the spin and orbital degeneracies, and it is maximized when both occur simultaneously. The large number of tunable parameters allows a range of manipulations of the Kondo physics -- in particular, the Kondo effect in each dot is sensi…
The propagation of electrons in an orbital multiplet dispersing on a lattice can support anomalous transport phenomena deriving from an orbitally-induced Berry curvature. In striking contrast to the related situation in graphene, we find that anomalous transport for an $L=1$ multiplet on the primitive 2D triangular lattice is activated by easily implemented on-site and optically-tunable potentials. We demonstrate this for dynamics in a Bloch band where point degeneracies carrying opposite winding numbers are generically offset in energy, allowing both an anomalous charge Hall conductance with …
The idea of quantum computation is the most promising recent developments in the high-tech domain, while experimental realization of a quantum computer poses a formidable challenge. Among the proposed models especially attractive are semiconductor based nuclear spin quantum computer's (S-NSQC), where nuclear spins are used as quantum bistable elements, ''qubits'', coupled to the electron spin and orbital dynamics. We propose here a scheme for implementation of basic elements for S-NSQC's which are realizable within achievements of the modern nanotechnology. These elements are expected to be ba…
We demonstrate an experimental method for measuring quantum state degeneracies in bound state energy spectra. The technique is based on the general principle of detailed balance, and the ability to perform precise and efficient measurements of energy-dependent tunnelling-in and -out rates from a reservoir. The method is realized using a GaAs/AlGaAs quantum dot allowing for the detection of time-resolved single-electron tunnelling with a precision enhanced by a feedback-control. It is thoroughly tested by tuning orbital and spin-degeneracies with electric and magnetic fields. The technique also…
Electrons in atoms possess both spin and orbital degrees of freedom. In non-relativistic quantum mechanics, these are independent, resulting in large degeneracies in atomic spectra. However, relativistic effects couple the spin and orbital motion leading to the well-known fine structure in their spectra. The electronic states in defect-free carbon nanotubes (NTs) are widely believed to be four-fold degenerate, due to independent spin and orbital symmetries, and to also possess electron-hole symmetry. Here we report measurements demonstrating that in clean NTs the spin and orbital motion of ele…
We discuss out-of-equilibrium population imbalances between different orbital states due to applied thermal gradients. This purely thermoelectric orbital effect appears quite generically in nanostructures with a pseudospin degree of freedom. We establish an orbital Seebeck coefficient that characterizes the induced orbital bias in response to a temperature difference between reservoirs coupled to a quantum conductor. We analyze a two-terminal strongly interacting quantum dot with two orbital states and find that the orbital thermopower acts as an excellent tool to describe the transition betwe…
Lanthanide atoms and molecules are promising candidates for atomic data storage and quantum logic due to the long magnetic lifetime of their electron quantum states. Accessing these states through electrical transport requires the engineering of their electronic configuration down to the level of individual atomic orbitals. Here, we address the magnetism of surface-supported lanthanide atoms, clusters, and films with orbital selectivity using X-ray absorption spectroscopy and magnetic circular dichroism. We exploit the selection rules of electric dipole transitions to reveal the occupation and…
We study bistability in the electron transport through a ring of N coupled quantum dots with two orbitals in each dot. One orbital is localized (called b orbital) and coupling of the b orbitals in any two dots is negligible; the other is delocalized in the plane of the ring (called d orbital), due to coupling of the d orbitals in the neighboring dots, as described by a tight-binding model. The d orbitals thereby form a band with finite width. The b and d orbitals are connected to the source and drain electrodes with a voltage bias V, allowing the electron tunnelling. Tunnelling current is calc…
The electrostatic confinement of massless charge carriers is hampered by Klein tunneling. Circumventing this problem in graphene mainly relies on carving out nanostructures or applying electric displacement fields to open a band gap in bilayer graphene. So far, these approaches suffer from edge disorder or insufficiently controlled localization of electrons. Here we realize an alternative strategy in monolayer graphene, by combining a homogeneous magnetic field and electrostatic confinement. Using the tip of a scanning tunneling microscope, we induce a confining potential in the Landau gaps of…
Conventional understanding implies that the ground state of a nonmagnetic quantum mechanical system should be nodeless. While this notion also provides a valuable guidance in understanding the ordering of energy levels in semiconductor nanostructures, there are reports that $\textit{nodal}$ ground states for holes are possible. However, the existence of such nodal states has been debated and even viewed merely as an artifact of a $\boldsymbol{k{\cdot}p}$ model. Using complementary approaches of both $\boldsymbol{k{\cdot}p}$ and tight-binding models, further supported by an effective Hamiltonia…
Carbon nanostructures are ideal substrates for functionalization with molecules, since they consist of a single atomic layer giving rise to an extraordinary sensitivity to changes in their surrounding. The functionalization opens a new research field of hybrid nanostructures with tailored properties. Here, we present a microscopic view on the substrate-molecule interaction in the exemplary hybrid material consisting of graphene functionalized with perylene molecules. First experiments on similar systems have been recently realized illustrating an extremely efficient transfer of excitation ener…
Quantum spin-orbital liquids are elusive strongly correlated states of matter that emerge from quantum frustration between spin and orbital degrees of freedom. A promising route towards the observation of those states is the creation of artificial Mott insulators where antiferromagnetic correlations between spins and orbitals can be designed. We show that Coulomb impurity lattices on the surface of gapped honeycomb substrates, such as graphene on SiC, can be used to simulate SU(4) symmetric spin-orbital lattice models. We exploit the property that massive Dirac fermions form mid-gap bound stat…
We present a plane wave/pseudopotential implementation of the method to calculate electron transport properties of nanostructures. The conductance is calculated via the Landauer formula within formalism of Green's functions. Nonorthogonal Wannier-type atomic orbitals are obtained by the sequential unitary rotations of virtual and occupied Kohn-Sham orbitals, which is followed by two-step variational localization. We use these non-orthogonal Wannier type atomic orbitals to partition the Kohn-Sham Hamiltonian into electrode-contact-electrode submatrices. The electrode parts of the system are mod…
The tuneability and control of quantum nanostructures in two-dimensional materials offer promising perspectives for their use in future electronics. It is hence necessary to analyze quantum transport in such nanostructures. Material properties such as a complex dispersion, topology, and charge carriers with multiple degrees of freedom, are appealing for novel device functionalities but complicate their theoretical description. Here, we study quantum tunnelling transport across a few-electron bilayer graphene quantum dot. We demonstrate how to uniquely identify single- and two-electron dot stat…
Progress in the fabrication of nanometer-scale electronic devices is opening new opportunities to uncover the deepest aspects of the Kondo effect, one of the paradigmatic phenomena in the physics of strongly correlated electrons. Artificial single-impurity Kondo systems have been realized in various nanostructures, including semiconductor quantum dots, carbon nanotubes and individual molecules. The Kondo effect is usually regarded as a spin-related phenomenon, namely the coherent exchange of the spin between a localized state and a Fermi sea of electrons. In principle, however, the role of the…
The exchange coupling of the spins of two electrons in double well potentials in a semiconductor background is calculated within the Heitler-London (HL) approximation. Atomic and quantum dot types of confining potentials are considered, and a systematic analysis for the source of inaccuracies in the HL approach is presented. For the strongly confining coulombic atomic potentials in the H2 molecule, the most dramatic failure occurs at very large interatomic distances, where HL predicts a triplet ground state, both in 3D and in 2D, coming from the absence of electron-electron correlation effects…
We explore theoretically the spin transport in nanostructures consisting of a gold quantum dot bridging nonmagnetic electrodes and two Mn12-Ph single molecule magnets (SMMs) that are thiol-bonded to the dot but are not in direct contact with the electrodes. We find that reversal of the magnetic moment of either SMM by the application of a magnetic field leads to a large change in the resistance of the dot, i.e., a strong spin valve effect. We show that this phenomenon arises from a novel physical principle: The spin-dependent molecular orbitals that extend over the dot and both SMMs change dra…
A multiband empirical tight-binding model for group-III-nitride semiconductors with a wurtzite structure has been developed and applied to both bulk systems and embedded quantum dots. As a minimal basis set we assume one s-orbital and three p-orbitals, localized in the unit cell of the hexagonal Bravais lattice, from which one conduction band and three valence bands are formed. Non-vanishing matrix elements up to second nearest neighbors are taken into account. These matrix elements are determined so that the resulting tight-binding band structure reproduces the known Gamma-point parameters, w…
We derive an effective continuum model for describing the propagation of electrons in ballistic one-dimensional curved nanostructure which are marked by a strong interplay of spin-orbital degrees of freedom due to local electronic states with $d-$orbital symmetry, atomic spin-orbit and orbital Rashba couplings. We demonstrate how a planar inhomogeneous spatial curvature of the nanochannel can generate both spin and orbital textures represented through loops on the corresponding Bloch spheres. In particular, we employ the paradigmatic case of an elliptically shaped quantum ring to investigate t…
Quantum theory of surface plasmons is very important for studying the interactions between light and different metal nanostructures in nanoplasmonics. In this work, using the canonical quantization method, the SPPs on nanowires and their orbital and spin angular momentum are investigated. The results show that the SPPs on nanowire carry both orbital and spin momentum during propagation. Later, the result is applied on the plasmonic nanowire waveguide to show the agreement of the theory. The study is helpful for the nano wire based plasmonic interactions and the quantum information based optica…
The coupled nonlinear coordinate and spin dynamics of an electron in a double quantum dot with spin-orbit interaction is studied semiclassically. The system is driven by an electric field with the frequency matching the orbital or the Zeeman resonance in magnetic field. Calculated evolution of the spin state is crucially sensitive to the irregularities in the spatial motion and the geometry of the host nanostructure. The resulting spin-flip Rabi frequency has an unusual dependence on the field amplitude, demonstrating approach to the chaotic spin motion. In turn, the orbital dynamics depends s…
The nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The unique combination of spin, valley, and orbital degeneracies in bilayer graphene is predicted to produce novel and tunable FQH ground states. Here we present local electronic compressibility measurements of the FQH effect in the lowest Landau level of bilayer graphene. We observe incompressible FQH states at filling factors v = 2p + 2/3 with hints of additional states appearing at v = 2p + 3/5, where p = -2,-1, 0, and 1. This sequence of states…
Metalated phthalocyanines (Pc's) are robust and versatile molecular complexes, whose properties can be tuned by changing their functional groups and central metal atom. The electronic structure of magnesium Pc (MgPc) - structurally and electronically similar to chlorophyll - adsorbed on the Ag(100) surface is investigated by low-temperature scanning tunneling microscopy (STM) and spectroscopy (STS), non-contact atomic force microscopy (ncAFM) and density functional theory (DFT). Single, isolated MgPc's exhibit a flat, four-fold rotationally symmetric morphology, with doubly degenerate, partial…
Understanding the interaction between cavity photons and electronic nanocircuits is crucial for the development of Mesoscopic Quantum Electrodynamics (QED). One has to combine ingredients from atomic Cavity QED, like orbital degrees of freedom, with tunneling physics and strong cavity field inhomogeneities, specific to superconducting circuit QED. It is therefore necessary to introduce a formalism which bridges between these two domains. We develop a general method based on a photonic pseudo-potential to describe the electric coupling between electrons in a nanocircuit and cavity photons. In t…
A scale for magnetic field resilience of a superconductor is set by the paramagnetic limit. Comparing the condensation energy of the Bardeen-Cooper-Schrieffer (BCS) singlet ground state with the paramagnetically polarised state suggests that for an applied field ${μ_0}H > 1.8~T_c$ (in SI), singlet pairing is not energetically favourable. Materials exceeding or approaching this limit are interesting from fundamental and technological perspectives. This may be a potential indicator of triplet superconductivity, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing and other mechanisms involving topolo…
