One-dimensional Electronic States Research Articles

Synthesis of Quantum-Confined Borophene Nanoribbons.

Borophene nanoribbons (BNRs) are one-dimensional strips of atomically thin boron expected to exhibit quantum-confined electronic properties that are not present in extended two-dimensional borophene. While the parent material borophene has been experimentally shown to possess anisotropic metallicity and diverse polymorphic structures, the atomically precise synthesis of nanometer-wide BNRs has not yet been achieved. Here, we demonstrate the synthesis of multiple BNR polymorphs with well-defined edge configurations within the nanometer-scale terraces of vicinal Ag(977). Through atomic-scale imaging, spectroscopy, and first-principles calculations, the synthesized BNR polymorphs are characterized and found to possess distinct edge structures and electronic properties. For single-phase BNRs, v1/6-BNRs and v1/5-BNRs adopt reconstructed armchair edges and sawtooth edges, respectively. In addition, the electronic properties of single-phase v1/6-BNRs and v1/5-BNRs are dominated by Friedel oscillations and striped moiré patterns, respectively. On the other hand, mixed-phase BNRs possess quantum-confined states with increasing nodes in the electronic density of states at elevated biases. Overall, the high degree of polymorphism and diverse edge topologies in borophene nanoribbons provide a rich quantum platform for studying one-dimensional electronic states.

Photoemission Study of One-Dimensional Electronic States of (6,5), (6,6), and (7,4) Single-Walled Carbon Nanotubes

We have investigated the one-dimensional electronic states of single-walled carbon nanotubes (SWCNTs) with diameters ranging from 0.8–1.4 nm by optical absorption, photoemission, and inverse photoemission measurements. In the photoemission spectra of (6,5) SWCNTs and (6,6)- and (7,4)-enriched SWCNTs, spike structures caused by Van Hove singularities (VHSs) are clearly observed. The observed VHS positions are compared with the positions calculated using the tight-binding model and density functional theory. A large curvature affects the electronic states of metallic SWCNTs with small diameters.

One-dimensional electronic states in a natural misfit structure

Misfit compounds are thermodynamically stable stacks of two-dimensional materials, forming a three-dimensional structure that remains incommensurate in one direction parallel to the layers. As a consequence, no true bonding is expected between the layers, with their interaction being dominated by charge transfer. In contrast to this well-established picture, we show that interlayer coupling can strongly influence the electronic properties of one type of layer in a misfit structure, in a similar way to the creation of modified band structures in an artificial moir\'e structure between two-dimensional materials. Using angle-resolved photoemission spectroscopy with a micron-scale light focus, we selectively probe the electronic properties of hexagonal ${\mathrm{NbSe}}_{2}$ and square BiSe layers that terminate the surface of the $({\mathrm{BiSe})}_{1+\ensuremath{\delta}}{\mathrm{NbSe}}_{2}$ misfit compound. We show that the band structure in the BiSe layers is strongly affected by the presence of the hexagonal ${\mathrm{NbSe}}_{2}$ layers, leading to quasi-one-dimensional electronic features. The electronic structure of the ${\mathrm{NbSe}}_{2}$ layers, on the other hand, is hardly influenced by the presence of the BiSe. Using density functional theory calculations of the unfolded band structures, we argue that the preferred modification of one type of band is mainly due to the atomic and orbital character of the states involved, opening a promising way to design electronic states that exploit the partially incommensurate character of the misfit compounds.

Realizing One-Dimensional Electronic States in Graphene via Coupled Zeroth Pseudo-Landau Levels.

Strain-induced pseudomagnetic fields can mimic real magnetic fields to generate a zero-magnetic-field analog of the Landau levels (LLs), i.e., the pseudo-Landau levels (PLLs), in graphene. The distinct nature of the PLLs enables one to realize novel electronic states beyond what is feasible with real LLs. Here, we show that it is possible to realize exotic electronic states through the coupling of zeroth PLLs in strained graphene. In our experiment, nanoscale strained structures embedded with PLLs are generated along a one-dimensional (1D) channel of suspended graphene monolayer. Our results demonstrate that the zeroth PLLs of the strained structures are coupled together, exhibiting a serpentine pattern that snakes back and forth along the 1D suspended graphene monolayer. These results are verified theoretically by large-scale tight-binding calculations of the strained samples. Our result provides a new approach to realizing novel quantum states and to engineering the electronic properties of graphene by using localized PLLs as building blocks.

One-dimensional spin-polarized electron channel in the two-dimensional PbBi compound on silicon

Quantum phenomena at the ultimate atomic-scale two-dimensional limit attract increasing interest due to the emergence of exotic physics and potential applications in prospective electronic devices. In this work, we carried out a theoretical and experimental study of the atomic, electronic, and spin structures of the single-atomic-layer PbBi compounds grown on silicon surface. We found that adsorption of half-monolayer of Bi and half-monolayer of Pb onto Si(111) surface leads to the formation of an atomic layer consisting of rhombuslike motifs. The rhombuslike motifs are arranged into the $2\sqrt{3}\ifmmode\times\else\texttimes\fi{}2\sqrt{3}$ and $2\ifmmode\times\else\texttimes\fi{}2$ periodical structures. In the $2\sqrt{3}\ifmmode\times\else\texttimes\fi{}2\sqrt{3}$-PbBi phase, the motifs are oriented according to the ${C}_{3}$ symmetry and this phase is characterized as a trivial insulating spin-split system. In the $2\ifmmode\times\else\texttimes\fi{}2$-PbBi phase, the motifs are oriented along a single direction giving rise to a one-dimensional metallic spin-polarized electron channel, which is of great relevance for spintronic-based applications. We traced the origin of the one-dimensional electronic states in the two-dimensional PbBi compound and discussed the interplay of these one-dimensional states with the geometry of the phase.

One dimensional electronic states in mirror twin boundaries of Bi (1 1 1)

One-dimensional electronic states at mirror twin boundaries of Bi (1 1 1) were revealed by scanning tunneling microscopy/spectroscopy. Two different boundary structures were observed owing to the highly buckled lattice of Bi (1 1 1) and both of them have the one-dimensional boundary states. The boundary states only appear on zigzag boundaries. The dissipationless kink states were predicted in such highly symmetric domain wall of silicon, bilayer graphene or even some sonic crystals. The behavior of the boundary states in Bi (1 1 1) is consistent with the theory predictions of kink states. The strong spin-orbit coupling and anisotropic valleys in Bi (1 1 1) make the mirror twin boundaries an ideal platform to study the spin-valley coupling in the interacting one-dimensional electron systems.

Observation of Topological Edge States at the Step Edges on the Surface of Type-II Weyl Semimetal TaIrTe4.

Topological materials harbor topologically protected boundary states. Recently, TaIrTe4, a ternary transition-metal dichalcogenide, was identified as a type-II Weyl semimetal with the minimal nonzero number of Weyl points allowed for a time-reversal invariant Weyl semimetal. Monolayer TaIrTe4 was proposed to host topological edge states, which, however, lacks of experimental evidence. Here, we report on the topological edge states localized at the monolayer step edges of the type-II Weyl semimetal TaIrTe4 using scanning tunneling microscopy. One-dimensional electronic states that show substantial robustness against the edge irregularity are observed at the step edges. Theoretical calculations substantiate the topologically nontrivial nature of the edge states and their robustness against the edge termination and layer stacking. The observation of topological edge states at the step edges of TaIrTe4 surfaces suggests that monolayer TaIrTe4 is a two-dimensional topological insulator, providing TaIrTe4 as a promising material for topological physics and devices.

Wide-wavelength-range control of photoluminescence polarization in closely stacked InAs/GaAs quantum dots

We developed a method of growing closely stacked InAs/GaAs quantum dots (QDs) to control the photoluminescence (PL) polarization characteristics in a wide wavelength range. The emission wavelength of the closely stacked QDs redshifted with decreasing substrate temperature during stacking growth, while the PL polarization characteristic was controlled by the GaAs spacer layer thickness and the number of QD layers. A unified rule for the optimum GaAs spacer layer thickness that both enhances the transverse magnetic (TM)-polarized component and achieves a high PL intensity for all growth temperatures was revealed. 30-layer stacked QDs with the optimum spacer layer thickness grown at substrate temperatures from 430 to 480 °C exhibited TM-enhanced polarization characteristics in the 1.15–1.3 μm band. Moreover, we studied the one-dimensional electronic states in the closely stacked QDs with the optimized GaAs spacer layer thickness by time-resolved PL.

Interfacial Landau levels in bent graphene racetracks

One-dimensional electronic states are critical to many fascinating phenomena in low dimensions. We show that a series of interfacial states can be induced by applying an in-plane bending to a graphene racetrack geometry, an effective superlattice consisting of multiple graphene and hexagonal boron nitride ($h\mathrm{BN}$) domains. These local states, robust against the detailed atomic configuration along interfaces, display a unique coupling of their energies and their spatial locations. This way, it is possible to identify such a state with certain energy by merely referring to its location, mimicking well the transverse magnetic focusing. Further, these local states are ballistically conducting with different group velocities, indicating that each interfacial transport channel has a unique electric conduction. These findings may have implications for the design of nanoelectronics with heterostructures.

A Novel One-Dimensional Electronic State at IrTe2 Surface

Highly one-dimensional (1D) Fermi sheets are realized at the surface of a layered Ir telluride IrTe2 which exhibits a stripe-type charge and orbital order below ∼280 K. The 1D Fermi sheets appear in the low temperature range where the stripe order is well established. The 1D Fermi sheets are truncated by the bulk Fermi surfaces, and the spectral weight suppression at the Fermi level deviates from the typical Tomonaga–Luttinger behavior. The 1D band runs along the stripe and is accompanied by several branches which can be derived from the quantization in the perpendicular direction.

Spin-polarized quasi-one-dimensional state with finite band gap on the Bi/InSb(001) surface

One-dimensional (1D) electronic states were discovered on 1D surface atomic structure of Bi fabricated on semiconductor InSb(001) substrates by angle-resolved photoelectron spectroscopy (ARPES). The 1D state showed steep, Dirac-cone-like dispersion along the 1D atomic structure with a finite direct bandgap opening as large as 150 meV. Moreover, spin-resolved ARPES revealed the spin polarization of the 1D unoccupied states as well as that of the occupied states, the orientation of which inverted depending on the wave vector direction parallel to the 1D array on the surface. These results reveal that a spin-polarized quasi-1D carrier was realized on the surface of 1D Bi with highly efficient backscattering suppression, showing promise for use in future spintronic and energy-saving devices.

Observation of topological states residing at step edges of WTe2

Topological states emerge at the boundary of solids as a consequence of the nontrivial topology of the bulk. Recently, theory predicts a topological edge state on single layer transition metal dichalcogenides with 1T’ structure. However, its existence still lacks experimental proof. Here, we report the direct observations of the topological states at the step edge of WTe2 by spectroscopic-imaging scanning tunneling microscopy. A one-dimensional electronic state residing at the step edge of WTe2 is observed, which exhibits remarkable robustness against edge imperfections. First principles calculations rigorously verify the edge state has a topological origin, and its topological nature is unaffected by the presence of the substrate. Our study supports the existence of topological edge states in 1T’-WTe2, which may envision in-depth study of its topological physics and device applications.

Nature of the Insulating Ground State of the 5d Postperovskite CaIrO3.

The insulating ground state of the 5d transition metal oxide CaIrO3 has been classified as a Mott-type insulator. Based on a systematic density functional theory (DFT) study with local, semilocal, and hybrid exchange-correlation functionals, we reveal that the Ir t(2g) states exhibit large splittings and one-dimensional electronic states along the c axis due to a tetragonal crystal field. Our hybrid DFT calculation adequately describes the antiferromagnetic (AFM) order along the c direction via a superexchange interaction between Ir^{4+} spins. Furthermore, the spin-orbit coupling (SOC) hybridizes the t(2g) states to open an insulating gap. These results indicate that CaIrO_{3} can be represented as a spin-orbit Slater insulator, driven by the interplay between a long-range AFM order and the SOC. Such a Slater mechanism for the gap formation is also demonstrated by the DFT + dynamical mean field theory calculation, where the metal-insulator transition and the paramagnetic to AFM phase transition are concomitant with each other.

Effect of electron-phonon interaction on the formation of one-dimensional electronic states in coupled Cl vacancies

The formation of extended electron states in one-dimensional nanostructures is of key importance for the function of molecular electronics devices. Here we study the effects of strong electron-phonon interaction on the formation of extended electronic states in intentionally created Cl vacancy pairs and chains in a NaCl bilayer on Cu(111). The interaction between the vacancies was tailored by fabricating vacancy pairs and chains of different orientation and separation with atomic precision using vertical manipulation. Small separation of divacancies led to the formation of symmetric and antisymmetric vacancy states and localized interface-states. By scanning tunneling spectroscopy (STS) we measured their energy splitting and broadening as a function of the inter-vacancy separation. Unexpectedly, the energy splitting between the vacancy states is enlarged by level repulsion resulting from phonon dressing of the electronic states, as evidenced by theory. Already for a few coupled vacancies we observe an emerging band structure of the defect band.

Formation of One-Dimensional Electronic States along the Step Edges of CeO2(111)

Scanning tunneling microscopy (STM) combined with density functional theory (DFT) are used to analyze the structural and electronic properties of step edges on the surface of CeO(2)(111) films grown on Ru(0001). Depending on the preparation conditions, 211 or 110-oriented steps develop on the surface, which results in the formation of ceria ad-islands with hexagonal or triangular shapes. STM conductance spectroscopy reveals pronounced differences in the electronic properties of the step edges, as reflected in different onset positions of the ceria conduction band. The band shifts are related to the development of distinct edge electronic states that split-off from the ceria conduction band, as shown with DFT calculations. The separation of the edge states from the main band is governed by the atom-coordination and local charge-distribution along the edge, the latter giving rise to the development of electrostatic dipoles. We expect that the observed edge morphologies determine not only the electronic properties but also the adsorption behavior of step edges on the CeO(2)(111) surface.

Peierls-like phase transitions in domain walls

In this paper, we give an example how domain walls (DW) within an adsorbed monolayer form one-dimensional localized electronic states. We investigated in detail the Ag3×3 phase on Si (111), a prototype system for a low dimensional electron gas, by means of scanning tunneling microscopy. The doubling of the periodicity along the DW-direction at low temperatures (80K) suggests a metal–insulator transition of Peierls type. The superimposed intensity modulation in the direction across the DW can be interpreted in terms of lateral quantum well states. However, the simultaneous vanishing of both features at room temperature indicates more complicated changes in band structure and/or wave functions during the transition than described by the simple Peierls model.

Electronic states of Ag thin films with a laterally periodic insertion of stacking faults

Electronic states of Ag thin films containing stacking faults periodically in a direction parallel to the surface are studied theoretically. Such Ag stacking-fault superlattice thin films were recently fabricated on the $\text{Si}(111)4\ifmmode\times\else\texttimes\fi{}1\text{-In}$ surface, and the formation mechanism of the one-dimensional electronic states observed in photoemission experiments has not been clarified. These systems are suitable for studying stacking faults on nanometer scales in well-defined conditions. Main results obtained in the present study are threefold. One is that the double stacking-fault model proposed in this paper reproduces better the observed dispersions than the originally proposed model. In addition the fact that the stacking-fault thin films have the (111) surface is the origin of the strong deformation near the bottom of the quantized subbands. Second is that the tilt of the stacking-fault plane with respect to the normal of the surface causes mixing of states in different subbands, which is an important factor to form the flat band structures observed. Third is the discussion on the mechanism of the anomalous perfect transmission through the bulk stacking faults of noble metals. In contrast to usual potential scattering, stacking faults change only the phase of orbitals. The condition for perfect transmission is that the effects of scattering are canceled out by renormalization using single phase factor, which is excellently satisfied in the case of noble metals. In addition the symmetry in atomic positions between regular and stacking-fault structures with respect to an axis is the origin of the directional dependence of transmission property.

One-Dimensional Molecular Chains with Dispersive Electronic States

One-dimensional molecular chains comprising self-assembled double-layer sexithiophene (6T) molecules on Ag(111) are studied with low-temperature scanning tunneling microscopy. Despite the molecular chains being stabilized by van der Waals interactions and isolated from the metal substrate, dispersive electronic states are observed. The measurements of differential conductance and dI/dV maps along the chains reveal the end states forming at the ends of chains. Density functional theory calculations indicate the splitting and hybridization of unoccupied pi molecular orbitals between neighboring layers of 6T molecules resulting in the formation of delocalized one-dimensional electronic states.

The quantum states of high- Tc materials – States of topological resonances

The nature of the electronic states of the CuO 2 planes in high- T c materials is elaborated, being proven as a crucial revision of previous assumptions. One important aspect is the general existence of electronic pair states in two manifestations, which determine superconducting or non-superconducting properties. The decisive basis of the theory developed in this paper is derived from the various broken symmetries of the electronic states and the formation of one-dimensional electronic subspaces. The non-superconducting state is already characterized by a two-dimensional ordering of one-dimensional electronic states in space ( stiffness in space), whereas the superconducting state is represented by a two-dimensional highly correlated electronic state in space and time ( stiffness in space and time). Under the inclusion of lattice dynamics, the electronic ground state is reached by a topological superposition of symmetry-broken sub-states, quantized and determined in time ( Topological Resonance (TR)). This forms the basis for inherent times ( eigentime) of the electronic quantum states, an important but unusual characteristic of these quantum states. Under hole doping, the general nature of the electronic state of the CuO 2 plane can be characterized as a coherent quantum fluid consisting of two partial fluids (b-holes, f-holes). The characteristics of this quantum fluid state are predominantly determined by the strongly correlated b-hole fluid, whereas the f-hole fluid possesses higher internal degrees of freedom. The existence of a b-hole fluid is an indispensable precondition for the existence of a superconducting state in high- T c materials.

Laser-operated chiral molecular switch: quantum simulations for the controlled transformation between achiral and chiral atropisomers

We report quantum dynamical simulations for the laser controlled isomerization of 1-(2-cis-fluoroethenyl)-2-fluorobenzene based on one-dimensional electronic ground and excited state potentials obtained from (TD)DFT calculations. 1-(2-cis-fluoroethenyl)-2-fluorobenzene supports two chiral and one achiral atropisomers, the latter being the most stable isomer at room temperature. Using a linearly polarized IR laser pulse the molecule is excited to an internal rotation around its chiral axis, i.e. around the C-C single bond between phenyl ring and ethenyl group, changing the molecular chirality. A second linearly polarized laser pulse stops the torsion to prepare the desired enantiomeric form of the molecule. This laser control allows the selective switching between the achiral and either the left- or right-handed form of the molecule. Once the chirality is "switched on" linearly polarized UV laser pulses allow the selective change of the chirality using the electronic excited state as intermediate state.