Coupling of spin and orbital motion of electrons in carbon nanotubes

Emerging Spintronic Materials and Functionalities

The explosive growth of the information era has put forward urgent requirements for ultrahigh-speed and extremely efficient computations. In direct contrary to charge-based computations, spintronics aims to use spins as information carriers for data storage, transmission, and decoding, to help fully realize electronic device miniaturization and high integration for next-generation computing technologies. Currently, many novel spintronic materials have been developed with unique properties and multifunctionalities, including organic semiconductors (OSCs), organic-inorganic hybrid perovskites (OIHPs), and 2D materials (2DMs). These materials are useful to fulfill the demand for developing diverse and advanced spintronic devices. Herein, these promising materials are systematically reviewed for advanced spintronic applications. Due to the distinct chemical and physical structures of OSCs, OIHPs, and 2DMs, their spintronic properties (spin transport and spin manipulation) are discussed separately. In addition, some multifunctionalities due to photoelectric and chiral-induced spin selectivity (CISS) are overviewed, including the spin-filter effect, spin-photovoltaics, spin-light emitting devices, and spin-transistor functions. Subsequently, challenges and future perspectives of using these multifunctional materials for the development of advanced spintronics are presented.

Chirality-induced spin selectivity in functionalized carbon nanotube networks: The role of spin-orbit coupling

Spin-orbit coupling in a chiral medium is generally assumed to be a necessary ingredient for the observation of the chirality-induced spin selectivity (CISS) effect. However, some recent studies have suggested that CISS may manifest even when the chiral medium has zero spin-orbit coupling. In such systems, CISS may arise due to an orbital polarization effect, which generates an electromagnetochiral anisotropy in two-terminal conductance. Here, we examine these concepts using a chirally functionalized carbon nanotube network as the chiral medium. A transverse measurement geometry is used, which nullifies any electromagnetochiral contribution but still exhibits the tell-tale signs of the CISS effect. This suggests that CISS may not be explained solely by electromagnetochiral effects. The role of nanotube spin-orbit coupling on the observed pure CISS signal is studied by systematically varying nanotube diameter. We find that the magnitude of the CISS signal scales proportionately with the spin-orbit coupling strength of the nanotubes. We also find that nanotube diameter dictates the supramolecular chirality of the medium, which in turn determines the sign of the CISS signal.

Spintronics in double stranded magnetic helix: role of non-uniform disorder

The spin dependent transport phenomena are investigated in a double stranded (ds) magnetic helix (MH) structure. Two different helical systems, short-range hopping helix and long range hopping (LRH) helix, are taken into account. We explore the role of these two kinds of geometries on spin dependent transport phenomena. Using Green's function formalism within a tight-binding framework we compute transport quantities which include spin dependent transmission probabilities, junction currents and spin polarization (SP) coefficient. High degree of SP is obtained for the LRH MH. The SP can be tuned by changing the inter-strand hopping and the direction of magnetic moments at different lattice sites. We find atypical features when we include impurities in one strand of the MH, keeping the other strand free. Unlike uniform disordered systems, SP gets increased with impurity strength beyond a critical value. The effect of temperature on SP and experimental possibilities of our proposed quantum system are also discussed, to make the present communication a self-contained one. Our analysis may provide a new route to explore interesting spintronic properties using similar kind of fascinating helical geometries, possessing higher order electron hopping and subjected to non-uniform disorder.

Nanomaterials for Quantum Information Science and Engineering

Quantum information science and engineering (QISE)-which entails the use of quantum mechanical states for information processing, communications, and sensing-and the area of nanoscience and nanotechnology have dominated condensed matter physics and materials science research in the 21st century. Solid-state devices for QISE have, to this point, predominantly been designed with bulk materials as their constituents. This review considers how nanomaterials (i.e., materials with intrinsic quantum confinement) may offer inherent advantages over conventional materials for QISE. The materials challenges for specific types of qubits, along with how emerging nanomaterials may overcome these challenges, are identified. Challenges for and progress toward nanomaterials-based quantum devices are condidered. The overall aim of the review is to help close the gap between the nanotechnology and quantum information communities and inspire research that will lead to next-generation quantum devices for scalable and practical quantum applications.

Effects of Parity and Symmetry on the Aharonov-Bohm Phase of a Quantum Ring

We experimentally investigate the properties of one-dimensional quantum rings that form near the surface of nanowire quantum dots. In agreement with theoretical predictions, we observe the appearance of forbidden gaps in the evolution of states in a magnetic field as the symmetry of a quantum ring is reduced. For a twofold symmetry, our experiments confirm that orbital states are grouped pairwise. Here, a π-phase shift can be introduced in the Aharonov-Bohm relation by controlling the relative orbital parity using an electric field. Studying rings with higher symmetry, we note exceptionally large orbital contributions to the effective g-factor (up to 300), which are many times higher than those previously reported. These findings show that the properties of a phase-coherent system can be significantly altered by the nanostructure symmetry and its interplay with wave function parity.

Supercurrent and Phase Slips in a Ballistic Carbon Nanotube Bundle Embedded into a van der Waals Heterostructure

We demonstrate long-range superconducting correlations in a several-micrometers-long carbon nanotube bundle encapsulated in a van der Waals stack between hBN and NbSe₂. We show that a substantial supercurrent flows through the nanotube section beneath the NbSe₂ crystal as well as through the 2 μm long section not in contact with it. The large in-plane critical magnetic field of this supercurrent is an indication that even inside the carbon nanotube Cooper pairs enjoy a degree of paramagnetic protection typical of the parent Ising superconductor. As expected for superconductors of nanoscopic cross section, the current-induced breakdown of superconductivity is characterized by resistance steps due to the nucleation of phase slip centers. All elements of our hybrid device are active building blocks of several recently proposed setups for realization of Majorana fermions in carbon nanotubes.

Kondo effect and spin-orbit coupling in graphene quantum dots

The Kondo effect is a cornerstone in the study of strongly correlated fermions. The coherent exchange coupling of conduction electrons to local magnetic moments gives rise to a Kondo cloud that screens the impurity spin. Here we report on the interplay between spin-orbit interaction and the Kondo effect, that can lead to a underscreened Kondo effects in quantum dots in bilayer graphene. More generally, we introduce a different experimental platform for studying Kondo physics. In contrast to carbon nanotubes, where nanotube chirality determines spin-orbit coupling breaking the SU(4) symmetry of the electronic states relevant for the Kondo effect, we study a planar carbon material where a small spin-orbit coupling of nominally flat graphene is enhanced by zero-point out-of-plane phonons. The resulting two-electron triplet ground state in bilayer graphene dots provides a route to exploring the Kondo effect with a small spin-orbit interaction.

Spin-valley coupling in single-electron bilayer graphene quantum dots

Understanding how the electron spin is coupled to orbital degrees of freedom, such as a valley degree of freedom in solid-state systems, is central to applications in spin-based electronics and quantum computation. Recent developments in the preparation of electrostatically-confined quantum dots in gapped bilayer graphene (BLG) enable to study the low-energy single-electron spectra in BLG quantum dots, which is crucial for potential spin and spin-valley qubit operations. Here, we present the observation of the spin-valley coupling in bilayer graphene quantum dots in the single-electron regime. By making use of highly-tunable double quantum dot devices we achieve an energy resolution allowing us to resolve the lifting of the fourfold spin and valley degeneracy by a Kane-Mele type spin-orbit coupling of ≈ 60 μeV. Furthermore, we find an upper limit of a potentially disorder-induced mixing of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K$$\end{document}K and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K^{\prime}$$\end{document}K′ states below 20 μeV.

Understanding the interaction between spin and valley degrees of freedom in graphene-based quantum dots underpins their applications in electronics and quantum information. Here, the authors study the low-energy spectrum and resolve the spin-valley coupling in single-electron quantum dots in bilayer graphene.

Quantum Interferences in Ultraclean Carbon Nanotubes

Electronic analogs of optical interferences are powerful tools to investigate quantum phenomena in condensed matter. In carbon nanotubes (CNTs), it is well established that an electronic Fabry-Perot interferometer can be realized. Other types of quantum interferences should also arise in CNTs, but have proven challenging to realize. In particular, CNTs have been identified as a system to realize the electronic analog of a Sagnac interferometer-the most sensitive optical interferometer. To realize this Sagnac effect, interference between nonidentical transmission channels in a single CNT must be observed. Here, we use suspended, ultraclean CNTs of known chiral index to study both Fabry-Perot and Sagnac electron interferences. We verify theoretical predictions for the behavior of Sagnac oscillations and the persistence of the Sagnac oscillations at high temperatures. As suggested by existing theoretical studies, our results show that these quantum interferences may be used for electronic structure characterization of carbon nanotubes and the study of many-body effects in these model one-dimensional systems.

Spin Dependent Transport through Driven Magnetic System with Aubry-Andre-Harper Modulation

In this work, we put forward a prescription of achieving spin selective electron transfer by means of light irradiation through a tight-binding (TB) magnetic chain whose site energies are modulated in the form of well known Aubry–Andre–Harper (AAH) model. The interaction of itinerant electrons with local magnetic moments in the magnetic system provides a misalignment between up and down spin channels which leads to a finite spin polarization (SP) upon locating the Fermi energy in a suitable energy zone. Both the energy channels are significantly affected by the irradiation which is directly reflected in degree of spin polarization as well as in its phase. We include the irradiation effect through Floquet ansatz and compute spin polarization coefficient by evaluating transmission probabilities using Green’s function prescription. Our analysis can be utilized to investigate spin dependent transport phenomena in any driven magnetic system with quasiperiodic modulations.

Kondo effects in small-bandgap carbon nanotube quantum dots

We study the magnetoconductance of small-bandgap carbon nanotube quantum dots in the presence of spin-orbit coupling in the strong-correlations regime. A finite-U slave-boson mean-field approach is used to study many-body effects. Different degeneracies are restored in a magnetic field and Kondo effects of different symmetries arise, including SU(3) effects of different types. Full spin-orbital degeneracy might be recovered at zero field and, correspondingly, the SU(4) Kondo effect sets in. We point out the possibility of the occurrence of electron-hole Kondo effects in slanting magnetic fields, which we predict to occur in magnetic fields with an orientation close to perpendicular. When the field approaches a transverse orientation a crossover from SU(2) or SU(3) symmetry into SU(4) is observed.

sp3-Functionalization of Single-Walled Carbon Nanotubes Creates Localized Spins

Chemical functionalization-introduced sp³ quantum defects in single-walled carbon nanotubes (SWCNTs) have shown compelling optical properties for their potential applications in quantum information science and bioimaging. Here, we utilize temperature- and power-dependent electron spin resonance measurements to study the fundamental spin properties of SWCNTs functionalized with well-controlled densities of sp³ quantum defects. Signatures of isolated spins that are highly localized at the sp³ defect sites are observed, which we further confirm with density functional theory calculations. Applying temperature-dependent line width analysis and power-saturation measurements, we estimate the spin-lattice relaxation time T₁ and spin dephasing time T₂ to be around 9 μs and 40 ns, respectively. These findings of the localized spin states that are associated with the sp³ quantum defects not only deepen our understanding of the molecular structures of the quantum defects but could also have strong implications for their applications in quantum information science.

Influence of Electronic Structure Modeling and Junction Structure on First-Principles Chiral Induced Spin Selectivity

We have carried out a comprehensive study of the influence of electronic structure modeling and junction structure description on the first-principles calculation of the spin polarization in molecular junctions caused by the chiral induced spin selectivity (CISS) effect. We explore the limits and the sensitivity to modeling decisions of a Landauer/Green's function/two-component density functional theory approach to CISS. We find that although the CISS effect is entirely attributed in the literature to molecular spin filtering, spin-orbit coupling being partially inherited from the metal electrodes plays an important role in our calculations on ideal carbon helices, even though this effect cannot explain the experimental conductance results. Its magnitude depends considerably on the shape, size, and material of the metal clusters modeling the electrodes. Also, a pronounced dependence on the specific description of exchange interaction and spin-orbit coupling is manifest in our approach. This is important because the interplay between exchange effects and spin-orbit coupling may play an important role in the description of the junction magnetic response. Our calculations are relevant for the whole field of spin-polarized electron transport and electron transfer, because there is still an open discussion in the literature about the detailed underlying mechanism and the magnitude of physical parameters that need to be included to achieve a consistent description of the CISS effect: seemingly good quantitative agreement between simulation and the experiment can be caused by error compensation, because spin polarization as contained in a Landauer/Green's function/two-component density functional theory approach depends strongly on computational and structural parameters.

Chirality effects on an electron transport in single-walled carbon nanotube

In our work, we investigate characteristics of conductivity for single-walled carbon nanotubes caused by spin–orbit interaction. In the case study of chirality indexes, we especially research on the three types of single-walled carbon nanotubes which are the zigzag, the chiral, and the armchair. The mathematical analysis employed for our works is the Green-Kubo Method. For the theoretical results of our work, we discover that the chirality of single-walled carbon nanotubes impacts the interaction leading to the spin polarization of conductivity. We acknowledge such asymmetry characteristics by calculating the longitudinal current–current correlation function difference between a positive and negative wave vector in which there is the typical chiral-dependent. We also find out that the temperature and the frequency of electrons affect the function producing the different characteristics of the conductivity. From particular simulations, we obtain that the correlation decrease when the temperature increase for a low frequency of electrons. For high frequency, the correlation is nonmonotonic temperature dependence. The results of the phenomena investigated from our study express different degrees of spin polarization in each chiral of single-walled carbon nanotube and significant effects on temperature-dependent charge transport according to carrier backscattering. By chiral-induced spin selectivity that produces different spin polarization, our work could be applied for intriguing optimization charge transport.

Electron-Hole Crossover in Gate-Controlled Bilayer Graphene Quantum Dots

Electron and hole Bloch states in bilayer graphene exhibit topological orbital magnetic moments with opposite signs, which allows for tunable valley-polarization in an out-of-plane magnetic field. This property makes electron and hole quantum dots (QDs) in bilayer graphene interesting for valley and spin-valley qubits. Here, we show measurements of the electron-hole crossover in a bilayer graphene QD, demonstrating opposite signs of the magnetic moments associated with the Berry curvature. Using three layers of top gates, we independently control the tunneling barriers while tuning the occupation from the few-hole regime to the few-electron regime, crossing the displacement-field-controlled band gap. The band gap is around 25 meV, while the charging energies of the electron and hole dots are between 3 and 5 meV. The extracted valley g-factor is around 17 and leads to opposite valley polarization for electrons and holes at moderate B-fields. Our measurements agree well with tight-binding calculations for our device.

Topologically Protected Correlated End Spin Formation in Carbon Nanotubes

For most chiralities, semiconducting nanotubes display topologically protected end states of multiple degeneracies. We demonstrate using density matrix renormalization group based quantum chemistry tools that the presence of Coulomb interactions induces the formation of robust end spins. These are the close analogs of ferromagnetic edge states emerging in graphene nanoribbons. The interaction between the two ends is sensitive to the length of the nanotube, its dielectric constant, and the size of the end spins: for S=1/2 end spins, their interaction is antiferromagnetic, while for S>1/2, it changes from antiferromagnetic to ferromagnetic as the nanotube length increases. The interaction between end spins can be controlled by changing the dielectric constant of the environment, thereby providing a possible platform for two-spin quantum manipulations.

Analytic Model of Chiral-Induced Spin Selectivity

Organic materials are known to feature long spin-diffusion times, originating in a generally small spin-orbit coupling observed in these systems. From that perspective, chiral molecules acting as efficient spin selectors pose a puzzle that attracted a lot of attention in recent years. Here, we revisit the physical origins of chiral-induced spin selectivity (CISS) and propose a simple analytic minimal model to describe it. The model treats a chiral molecule as an anisotropic wire with molecular dipole moments aligned arbitrarily with respect to the wire's axes and is therefore quite general. Importantly, it shows that the helical structure of the molecule is not necessary to observe CISS and other chiral nonhelical molecules can also be considered as potential candidates for the CISS effect. We also show that the suggested simple model captures the main characteristics of CISS observed in the experiment, without the need for additional constraints employed in the previous studies. The results pave the way for understanding other related physical phenomena where the CISS effect plays an essential role.

Atomic-like charge qubit in a carbon nanotube enabling electric and magnetic field nano-sensing

Quantum sensing techniques have been successful in pushing the sensitivity limits in numerous fields, and hold promise for scanning probes that study nano-scale devices and materials. However, forming a nano-scale qubit that is simple and robust enough to be placed on a scanning tip, and sensitive enough to detect various physical observables, is still a great challenge. Here, we demonstrate, in a carbon nanotube, an implementation of a charge qubit that achieves these requirements. Our qubit’s basis states are formed from the natural electronic wavefunctions in a single quantum dot. Different magnetic moments and charge distributions of these wavefunctions make it sensitive to magnetic and electric fields, while difference in their electrical transport allows a simple transport-based readout mechanism. We demonstrate electric field sensitivity better than that of a single electron transistor, and DC magnetic field sensitivity comparable to that of NV centers. Due to its simplicity, this qubit can be fabricated using conventional techniques. These features make this atomic-like qubit a powerful tool, enabling a variety of imaging experiments.

Among the recent developments in quantum technologies, the use of qubits for quantum sensing has led to significant improvements in resolution and sensitivity at the nanoscale. Here, the authors present a carbon nanotube charge qubit that can act as a highly sensitive scanning probe of electric and magnetic fields.

Hidden Fine Structure of Quantum Defects Revealed by Single Carbon Nanotube Magneto-Photoluminescence

Organic color-center quantum defects in semiconducting carbon nanotube hosts are rapidly emerging as promising candidates for solid-state quantum information technologies. However, it is unclear whether these defect color-centers could support the spin or pseudospin-dependent excitonic fine structure required for spin manipulation and readout. Here we conducted magneto-photoluminescence spectroscopy on individual organic color-centers and observed the emergence of fine structure states under an 8.5 T magnetic field applied parallel to the nanotube axis. One to five fine structure states emerge depending on the chirality of the nanotube host, nature of chemical functional group, and chemical binding configuration, presenting an exciting opportunity toward developing chemical control of magnetic brightening. We attribute these hidden excitonic fine structure states to field-induced mixing of singlet excitons trapped at sp³ defects and delocalized band-edge triplet excitons. These findings provide opportunities for using organic color-centers for spintronics, spin-based quantum computing, and quantum sensing.

Spin-momentum locked modes on anti-phase boundaries in photonic crystals

An anti-phase boundary is formed by shifting a portion of photonic crystal lattice along the direction of periodicity. A spinning magnetic dipole is applied to excite edge modes on the anti-phase boundary. We show the unidirectional propagation of the edge modes which is also known as spin-momentum locking. Band inversion of the edge modes is discovered when we sweep the geometrical parameters, which leads to a change in the propagation direction. Also, an optimized source is applied to excite the unidirectional edge mode with high directivity.

Electrical control of spins and giant g-factors in ring-like coupled quantum dots

Emerging theoretical concepts for quantum technologies have driven a continuous search for structures where a quantum state, such as spin, can be manipulated efficiently. Central to many concepts is the ability to control a system by electric and magnetic fields, relying on strong spin-orbit interaction and a large g-factor. Here, we present a mechanism for spin and orbital manipulation using small electric and magnetic fields. By hybridizing specific quantum dot states at two points inside InAs nanowires, nearly perfect quantum rings form. Large and highly anisotropic effective g-factors are observed, explained by a strong orbital contribution. Importantly, we find that the orbital contributions can be efficiently quenched by simply detuning the individual quantum dot levels with an electric field. In this way, we demonstrate not only control of the effective g-factor from 80 to almost 0 for the same charge state, but also electrostatic change of the ground state spin.

Probing Trions at Chemically Tailored Trapping Defects

Trions, charged excitons that are reminiscent of hydrogen and positronium ions, have been intensively studied for energy harvesting, light-emitting diodes, lasing, and quantum computing applications because of their inherent connection with electron spin and dark excitons. However, these quasi-particles are typically present as a minority species at room temperature making it difficult for quantitative experimental measurements. Here, we show that by chemically engineering the well depth of sp3 quantum defects through a series of alkyl functional groups covalently attached to semiconducting carbon nanotube hosts, trions can be efficiently generated and localized at the trapping chemical defects. The exciton-electron binding energy of the trapped trion approaches 119 meV, which more than doubles that of "free" trions in the same host material (54 meV) and other nanoscale systems (2-45 meV). Magnetoluminescence spectroscopy suggests the absence of dark states in the energetic vicinity of trapped trions. Unexpectedly, the trapped trions are approximately 7.3-fold brighter than the brightest previously reported and 16 times as bright as native nanotube excitons, with a photoluminescence lifetime that is more than 100 times larger than that of free trions. These intriguing observations are understood by an efficient conversion of dark excitons to bright trions at the defect sites. This work makes trions synthetically accessible and uncovers the rich photophysics of these tricarrier quasi-particles, which may find broad implications in bioimaging, chemical sensing, energy harvesting, and light emitting in the short-wave infrared.

Excited States in Bilayer Graphene Quantum Dots

We report ground- and excited-state transport through an electrostatically defined few-hole quantum dot in bilayer graphene in both parallel and perpendicular applied magnetic fields. A remarkably clear level scheme for the two-particle spectra is found by analyzing finite bias spectroscopy data within a two-particle model including spin and valley degrees of freedom. We identify the two-hole ground state to be a spin-triplet and valley-singlet state. This spin alignment can be seen as Hund's rule for a valley-degenerate system, which is fundamentally different from quantum dots in carbon nanotubes, where the two-particle ground state is a spin-singlet state. The spin-singlet excited states are found to be valley-triplet states by tilting the magnetic field with respect to the sample plane. We quantify the exchange energy to be 0.35 meV and measure a valley and spin g factor of 36 and 2, respectively.

Shaping Electron Wave Functions in a Carbon Nanotube with a Parallel Magnetic Field

A magnetic field, through its vector potential, usually causes measurable changes in the electron wave function only in the direction transverse to the field. Here, we demonstrate experimentally and theoretically that, in carbon nanotube quantum dots combining cylindrical topology and bipartite hexagonal lattice, a magnetic field along the nanotube axis impacts also the longitudinal profile of the electronic states. With the high (up to 17 T) magnetic fields in our experiment, the wave functions can be tuned all the way from a "half-wave resonator" shape with nodes at both ends to a "quarter-wave resonator" shape with an antinode at one end. This in turn causes a distinct dependence of the conductance on the magnetic field. Our results demonstrate a new strategy for the control of wave functions using magnetic fields in quantum systems with a nontrivial lattice and topology.

Coherent population trapping by dark state formation in a carbon nanotube quantum dot

Illumination of atoms by resonant lasers can pump electrons into a coherent superposition of hyperfine levels which can no longer absorb the light. Such superposition is known as a dark state, because fluorescent light emission is then suppressed. Here we report an all-electric analogue of this destructive interference effect in a carbon nanotube quantum dot. The dark states are a coherent superposition of valley (angular momentum) states which are decoupled from either the drain or the source leads. Their emergence is visible in asymmetric current−voltage characteristics, with missing current steps and current suppression which depend on the polarity of the applied source-drain bias. Our results demonstrate coherent-population trapping by all-electric means in an artificial atom.

Transport in quantum systems is complex and can be suppressed by coherent superposition of the involved states. Here, the authors find all-electronic suppression of transport in a carbon nanotube originating from coherent population trapping and give criteria for the presence of such a dark state.

Observation of giant spin–orbit interaction in graphene and heavy metal heterostructures

Graphene is a promising material demonstrating some interesting phenomena such as the spin Hall effect, bipolar transistor effect, and non-trivial topological states. However, graphene has an intrinsically small spin–orbit interaction (SOI), making it difficult to apply in spintronic devices. The electronic band structure of graphene makes it possible to develop a systematic method to enhance SOI extrinsically. In this study, we designed a graphene field-effect transistor with a Pb layer intercalated between graphene (Gr) and Au layers and studied the effect on the strength of the SOI. The SOI in our system was significantly increased to 80 meV, which led to a giant non-local signal (∼180 Ω) at room temperature due to the spin Hall effect. Further, we extract key parameters of spin transport from the length and width dependence of non-local measurement. To support these findings, we also measured the temperature and gate-dependent weak localization (WL) effect. We obtained the magnitude of the SOI and spin relaxation time of Gr via quantitative analysis of WL. The SOI magnitudes estimated from the non-local signal and the WL effect are close in value. The enhancement of the SOI of Gr at room temperature is a potential simple manipulation method to explore the use of this material for spin-based applications.

We used Pb as an intercalated layer between the graphene and Au and measured the spin–orbit interaction in local and non-local measurement configurations.

Manipulation of the magnetoresistance effect in a double-helix DNA

Magnetoresistance (R _m) of a double-stranded (G:C) _N DNA sandwiched between ferromagnetic electrodes has been studied using the transfer matrix method of the tight-binding model. A R _m magnitude up to 72.5% for DNA in its natural structure is observed when the spin-orbit coupling with the helix spring geometry and a possible dephasing effect are taken into account. It can be greatly manipulated by stress or torque applied to the DNA with respect to its axis. In addition, the external voltage bias can also be used to efficiently control R _m. The dependence of R _m on the DNA length in a decaying oscillation form is observed.

Curvature induced quantum phase transitions in an electron-hole system

In this work, we study the effect of introducing a periodic curvature on nanostructures, and demonstrate that the curvature can lead to a transition from a topologically trivial state to a non-trivial state. We first present the Hamiltonian for an arbitrarily curved nanostructure, and introduce a numerical scheme for calculating the bandstructure of a periodically curved nanostructure. Using this scheme, we calculate the bandstructure for a sinusoidally curved two-dimensional electron gas. We show that the curvature can lead to a partner switching reminiscent of a topological phase transition at the time reversal invariant momenta. We then study the Bernevig-Hughes-Zhang (BHZ) Hamiltonian for a two-dimensional quantum well. We show that introducing a curvature can lead to the emergence of topological surface states.

Interaction-Driven Giant Orbital Magnetic Moments in Carbon Nanotubes

Carbon nanotubes continue to be model systems for studies of confinement and interactions. This is particularly true in the case of so-called "ultraclean" carbon nanotube devices offering the study of quantum dots with extremely low disorder. The quality of such systems, however, has increasingly revealed glaring discrepancies between experiment and theory. Here, we address the outstanding anomaly of exceptionally large orbital magnetic moments in carbon nanotube quantum dots. We perform low temperature magnetotransport measurements of the orbital magnetic moment and find it is up to 7 times larger than expected from the conventional semiclassical model. Moreover, the magnitude of the magnetic moment monotonically drops with the addition of each electron to the quantum dot directly contradicting the widely accepted shell filling picture of single-particle levels. We carry out quasiparticle calculations, both from first principles and within the effective-mass approximation, and find the giant magnetic moments can only be captured by considering a self-energy correction to the electronic band structure due to electron-electron interactions.

Nanomechanical Characterization of the Kondo Charge Dynamics in a Carbon Nanotube

Using the transversal vibration resonance of a suspended carbon nanotube as a charge detector for its embedded quantum dot, we investigate the case of strong Kondo correlations between a quantum dot and its leads. We demonstrate that even when large Kondo conductance is carried at odd electron number, the charging behavior remains similar between odd and even quantum dot occupations. While the Kondo conductance is caused by higher order processes, a sequential tunneling only model can describe the time-averaged charge. The gate potentials of the maximum current and fastest charge increase display a characteristic relative shift, which is suppressed at increased temperature. These observations agree very well with models for Kondo-correlated quantum dots.

Carbon nanotubes as excitonic insulators

Fifty years ago Walter Kohn speculated that a zero-gap semiconductor might be unstable against the spontaneous generation of excitons–electron–hole pairs bound together by Coulomb attraction. The reconstructed ground state would then open a gap breaking the symmetry of the underlying lattice, a genuine consequence of electronic correlations. Here we show that this excitonic insulator is realized in zero-gap carbon nanotubes by performing first-principles calculations through many-body perturbation theory as well as quantum Monte Carlo. The excitonic order modulates the charge between the two carbon sublattices opening an experimentally observable gap, which scales as the inverse of the tube radius and weakly depends on the axial magnetic field. Our findings call into question the Luttinger liquid paradigm for nanotubes and provide tests to experimentally discriminate between excitonic and Mott insulators.

It has long been anticipated theoretically that semiconductors with small band gaps may form a correlated exciton insulator phase, but it has been difficult to find material realisations. Here, the authors predict numerically that zero-gap armchair carbon nanotubes could be exciton insulators.

Spin-Charge Separation in Finite Length Metallic Carbon Nanotubes

Using time-dependent density functional theory, we study the optical excitations in finite length carbon nanotubes. Evidence of spin-charge separation is given in the spacetime domain. We demonstrate that the charge density wave is due to collective excitations of electron singlets, while the accompanying spin density wave is due to those of electron triplets. The Tomonaga-Luttinger liquid parameter and density-density interaction are extrapolated from the first-principles excitation energies. We show that the density-density interaction increases with the length of the nanotube. The singlet and triplet excitation energies, on the other hand, decrease for increasing length of the nanotube. Their ratio is used to establish a first-principles approach for deriving the Tomonaga-Luttinger parameter (in excellent agreement with experimental data). Time evolution analysis of the charge and spin line densities evidences that the charge and spin density waves are elementary excitations of metallic carbon nanotubes. Their dynamics show no dependence on each other.

Topological Transitions and Fractional Charges Induced by Strain and a Magnetic Field in Carbon Nanotubes

We show that carbon nanotubes (CNT) can be driven through a topological phase transition using either strain or a magnetic field. This can naturally lead to Jackiw-Rebbi soliton states carrying fractionalized charges, similar to those found in a domain wall in the Su-Schrieffer-Heeger model, in a setup with a spatially inhomogeneous strain and an axial field. Two types of fractionalized states can be formed at the interface between regions with different strain: a spin-charge separated state with integer charge and spin zero (or zero charge and spin ±ℏ/2), and a state with charge ±e/2 and spin ±ℏ/4. The latter state requires spin-orbit coupling in the CNT. We show that in our setup, the precise quantization of the fractionalized interface charges is a consequence of the symmetry of the CNT under a combination of a spatial rotation by π and time reversal.

Orbital Contributions to the Electron g Factor in Semiconductor Nanowires

Recent experiments on Majorana fermions in semiconductor nanowires [S. M. Albrecht, A. P. Higginbotham, M. Madsen, F. Kuemmeth, T. S. Jespersen, J. Nygård, P. Krogstrup, and C. M. Marcus, Nature (London) 531, 206 (2016)NATUAS0028-083610.1038/nature17162] revealed a surprisingly large electronic Landé g factor, several times larger than the bulk value-contrary to the expectation that confinement reduces the g factor. Here we assess the role of orbital contributions to the electron g factor in nanowires and quantum dots. We show that an L·S coupling in higher subbands leads to an enhancement of the g factor of an order of magnitude or more for small effective mass semiconductors. We validate our theoretical finding with simulations of InAs and InSb, showing that the effect persists even if cylindrical symmetry is broken. A huge anisotropy of the enhanced g factors under magnetic field rotation allows for a straightforward experimental test of this theory.

Spin-valley dynamics of electrically driven ambipolar carbon-nanotube quantum dots

An ambipolar n-p double quantum dot defined by potential variation along a semiconducting carbon-nanotube is considered. We focus on the (1e,1h) charge configuration with a single excess electron of the conduction band confined in the n-type dot and a single missing electron in the valence band state of the p-type dot for which lifting of the Pauli blockade of the current was observed in the electric-dipole spin resonance (Laird et al 2013 Nat. Nanotechnol. 8 565). The dynamics of the system driven by periodic electric field is studied with the Floquet theory and the time-dependent configuration interaction method with the single-electron spin-valley-orbitals determined for atomistic tight-binding Hamiltonian. We find that the transitions lifting the Pauli blockade are strongly influenced by coupling to a vacuum state with an empty n dot and a fully filled p dot. The coupling shifts the transition energies and strongly modifies the effective g factors for axial magnetic field. The coupling is modulated by the bias between the dots but it appears effective for surprisingly large energy splitting between the (1e,1h) ground state and the vacuum (0e, 0h) state. Multiphoton transitions and high harmonic generation effects are also discussed.

Giant electron-hole transport asymmetry in ultra-short quantum transistors

Making use of bipolar transport in single-wall carbon nanotube quantum transistors would permit a single device to operate as both a quantum dot and a ballistic conductor or as two quantum dots with different charging energies. Here we report ultra-clean 10 to 100 nm scale suspended nanotube transistors with a large electron-hole transport asymmetry. The devices consist of naked nanotube channels contacted with sections of tube under annealed gold. The annealed gold acts as an n-doping top gate, allowing coherent quantum transport, and can create nanometre-sharp barriers. These tunnel barriers define a single quantum dot whose charging energies to add an electron or a hole are vastly different (e−h charging energy asymmetry). We parameterize the e−h transport asymmetry by the ratio of the hole and electron charging energies η_e−h. This asymmetry is maximized for short channels and small band gap tubes. In a small band gap device, we demonstrate the fabrication of a dual functionality quantum device acting as a quantum dot for holes and a much longer quantum bus for electrons. In a 14 nm-long channel, η_e−h reaches up to 2.6 for a device with a band gap of 270 meV. The charging energies in this device exceed 100 meV.

By utilizing electron-hole asymmetry in ultra-short single-walled carbon nanotube (SWCNT) transistors, McRae et al., develop ‘two-in-one' SWCNT quantum devices that can switch from behaving as quantum-dot transistors for holes to quantum buses for electrons by changing the transistor's gate voltage

Room-temperature Magnetism in Carbon Dots and Enhanced Ferromagnetism in Carbon Dots-Polyaniline Nanocomposite

Room temperature magnetic ordering is reported for very small carbon dots (CDs), mat-like polyaniline nanofibers (Mat-PANI) and a composite of CDs@Mat-PANI containing 0.315 wt% CDs. We have found saturation magnetization (M S ) of CDs, Mat-PANI and CDs@Mat-PANI at 5 (20/300) K equals to 0.0079 (0.0048/0.0019), 0.0116 (0.0065/0.0055) and 0.0349 (0.0085/0.0077) emu/g, respectively. The M S enhancement in CDs@Mat-PANI (200% and 40% at 5 K and 300 K, respectively) is attributed to electron transfer from Mat-PANI imine N-atoms to the encapsulated CDs. Changes in M S values reveal that 0.81 (0.08) electron/CD is transferred at 5 (300) K, which is supported by observation of CDs photoluminescence (PL) redshift while in CDs@Mat-PANI. Band-bending and bandgap-renormalization calculations are used to predict a redshift of 117 meV at 300 K as a result of the electron transfer, in excellent agreement with the PL data (110 meV). Raman, X-ray diffraction and X-ray photoelectron spectroscopy data are used to confirm the electron transfer process as well as the strong interaction of CDs with PANI within CDs@Mat-PANI, which increases the crystalline domain size of Mat-PANI from about 4.8 nm to 9.2 nm while reducing the tensile strain from about 6.2% to 1.8%.

Hyperfine and Spin-Orbit Coupling Effects on Decay of Spin-Valley States in a Carbon Nanotube

The decay of spin-valley states is studied in a suspended carbon nanotube double quantum dot via the leakage current in Pauli blockade and via dephasing and decoherence of a qubit. From the magnetic field dependence of the leakage current, hyperfine and spin-orbit contributions to relaxation from blocked to unblocked states are identified and explained quantitatively by means of a simple model. The observed qubit dephasing rate is consistent with the hyperfine coupling strength extracted from this model and inconsistent with dephasing from charge noise. However, the qubit coherence time, although longer than previously achieved, is probably still limited by charge noise in the device.

Thermoelectric unipolar spin battery in a suspended carbon nanotube

A quantum dot formed in a suspended carbon nanotube exposed to an external magnetic field is predicted to act as a thermoelectric unipolar spin battery which generates pure spin current. The built-in spin flip mechanism is a consequence of the spin-vibration interaction resulting from the interplay between the intrinsic spin-orbit coupling and the vibrational modes of the suspended carbon nanotube. On the other hand, utilizing thermoelectric effect, the temperature difference between the electron and the thermal bath to which the vibrational modes are coupled provides the driving force. We find that both magnitude and direction of the generated pure spin current are dependent on the strength of spin-vibration interaction, the sublevel configuration in dot, the temperatures of electron and thermal bath, and the tunneling rate between the dot and the pole. Moreover, in the linear response regime, the kinetic coefficient is non-monotonic in the temperature T and it reaches its maximum when [Formula: see text] is about one phonon energy. The existence of a strong intradot Coulomb interaction is irrelevant for our spin battery, provided that high-order cotunneling processes are suppressed.

Spin-polarized transport in helical membranes due to spin-orbit coupling

Spin-dependent electron transmission through a helical membrane, taking account of linear spin-orbit interaction, has been investigated by numerically solving the Schrödinger equation in cylindrical coordinates. It is shown that the spin precession is affected by the magnitude of geometric parameters and chirality of the membrane. This effect is also explained analytically using perturbation theory in the weak coupling regime. In the strong coupling regime, the current spin polarization is evident when the number of the open modes in leads is larger than that of the open channels in the membrane. Moreover, we find that the chirality of the helical membrane can determine the orientation of current spin polarization. Therefore, one may get totally opposite spin currents from helical membranes rolled in different directions.

Spin–orbit coupling in nearly metallic chiral carbon nanotubes: a density-functional based study

An accurate implementation of spin–orbit interactions in a density-functional theory framework is presented, including both core and valence orbital contributions, thus encompassing the full system potential.

Strong enhancement of spin–orbit splitting induced by σ–π coupling in Pb-decorated silicene

Electronic properties and spin–orbit (SO) splitting of silicene adsorbed with Cu, Ag, Au and Pb atoms at different coverages are investigated by means of first-principles calculations.

Noncollinear Spin-Orbit Magnetic Fields in a Carbon Nanotube Double Quantum Dot

We demonstrate experimentally that noncollinear intrinsic spin-orbit magnetic fields can be realized in a curved carbon nanotube two-segment device. Each segment, analyzed in the quantum dot regime, shows near fourfold degenerate shell structure allowing for identification of the spin-orbit coupling and the angle between the two segments. Furthermore, we determine the four unique spin directions of the quantum states for specific shells and magnetic fields. This class of quantum dot systems is particularly interesting when combined with induced superconducting correlations as it may facilitate unconventional superconductivity and detection of Cooper pair entanglement. Our device comprises the necessary elements.

Pressure effect on the spin-dependent electronic structure of Au intercalated h-BN/graphene/h-BN

The spin-dependent electronic structures of Au intercalated hexagonal-BN/graphene/hexagonal-BN under pressure or electric field are examined on the basis of density-functional theory. Two kinds of doping concentrations are considered: one-monolayer Au doping and 1/4-monolayer Au doping. In one-monolayer Au doped structure, the large band gap of graphene is mainly induced by the B-C interaction, while the large spin-orbit effect is from the C-Au interaction. Both the band gap and the spin-orbit splitting can be modulated by pressure. In the 1/4-monolayer Au doped structure, the conduction band around the [Formula: see text] point is in the band gap of graphene with a Rashba constant of 0.12 eVÅ/[Formula: see text]. The Rashba effect can also be modulated by pressure and electric field. Our study provides a possible method to manipulate the spin-dependent electronic structure of graphene by proximity effect and extract the large spin-orbit effect of Au atoms.