Tuning the conductance of carbon rings with impurities and electric fields.

We explore two mechanisms to tune the electronic conductance of carbon atom rings, namely, substitutional impurities and in-plane external electric fields. First-principles calculations and a tight-binding approach are used to model the systems. Two bond configurations are studied, cumulenic and polyynic, which can be relevant depending on the number of carbon atoms in the ring. We find that both impurity substitution and electric field mechanisms allow for modifying the electronic spectrum and transport characteristics. Interestingly, cumulenic and polyynic carbon rings present a different response to these perturbations, which can also be a way to elucidate the bond nature of these structures.

Correction: Persistence of symmetry-protected Dirac points at the surface of the topological crystalline insulator SnTe upon impurity doping.

Correction for 'Persistence of symmetry-protected Dirac points at the surface of the topological crystalline insulator SnTe upon impurity doping' by Olga Arroyo-Gascón et al., Nanoscale, 2022, 14, 7151-7162, https://doi.org/10.1039/D1NR07120C.

Transport signatures of few-atom carbon rings.

We study the electronic transport through an all-carbon quantum ring side-coupled to a quantum wire. We employ both first-principles calculations and a tight-binding approach; the latter allows for the derivation of analytical expressions for the conductance and density of states, which facilitates the interpretation of the transport characteristics. Two bond models are employed: either all the hoppings are equal (cumulenic ring) or they have alternating bonds (polyynic ring). Assuming cumulenic bonds, if the number of atoms in the carbon ring is a multiple of four, it produces an antiresonant peak in the conductance at the Fermi level. This effect disappears for the polyynic configuration, i.e., when the hoppings in the carbon rings are alternating. Additionally, a gap opens at the Fermi energy in the polyynic rings, yielding distinct transport signatures for the two bond configurations. Comparison to first-principles calculations shows an excellent agreement on the changes of the conductance due to the carbon ring. We propose such transport measurements as a way to elucidate the character of the bonds in these novel carbon nanostructures.

Topological bands in the PdSe2 pentagonal monolayer.

The electronic structure of monolayer pentagonal palladium diselenide (PdSe2) is analyzed from the topological band theory perspective. Employing first-principles calculations, effective models and symmetry indicators, we find that the low-lying conduction bands are topologically nontrivial, protected by time reversal and crystalline symmetries. Numerical evidence supporting the nontrivial character of the bands is presented. Furthermore, we obtain a relevant physical response from the topological viewpoint, such as the spin Hall conductivity.

Persistence of symmetry-protected Dirac points at the surface of the topological crystalline insulator SnTe upon impurity doping.

We investigate the effect of a non-magnetic donor impurity located at the surface of the SnTe topological crystalline insulator. In particular, the changes on the surface states due to a Sb impurity atom are analyzed by means of ab initio simulations of pristine and impurity-doped SnTe. Both semi-infinite and slab geometries are considered within the first-principles approach. Furthermore, minimal and Green's function continuum models are proposed with the same goal. We find that the Dirac cones are shifted down in energy upon doping; this shift strongly depends on the position of the impurity with respect to the surface. In addition, we observe that the width of the impurity band presents an even-odd behavior by varying the position of the impurity. This behavior is related to the position of the nodes of the wave function with respect to the surface, and hence it is a manifestation of confinement effects. We compare slab and semi-infinite geometries within the ab initio approach, demonstrating that the surface states remain gapless and their spin textures are unaltered in the doped semi-infinite system. In the slab geometry, a gap opens due to hybridization of the states localized at opposite surfaces. Finally, by means of a continuum model, we extrapolate our results to arbitrary positions of the impurity, clearly showing a non-monotonic behavior of the Dirac cone.

Fast response photogating in monolayer MoS2 phototransistors.

Two-dimensional transition metal dichalcogenide (TMD) phototransistors have been the object of intensive research during the last years due to their potential for photodetection. Photoresponse in these devices is typically caused by a combination of two physical mechanisms: the photoconductive effect (PCE) and photogating effect (PGE). In earlier literature for monolayer (1L) MoS2 phototransistors, PGE is generally attributed to charge trapping by polar molecules adsorbed to the semiconductor channel, giving rise to a very slow photoresponse. Thus, the photoresponse of 1L-MoS2 phototransistors at high-frequency light modulation is assigned to PCE alone. Here we investigate the photoresponse of a fully h-BN encapsulated monolayer (1L) MoS2 phototransistor. In contrast with previous understanding, we identify a rapidly-responding PGE mechanism that becomes the dominant contribution to photoresponse under high-frequency light modulation. Using a Hornbeck-Haynes model for the photocarrier dynamics, we fit the illumination power dependence of this PGE and estimate the energy level of the involved traps. The resulting energies are compatible with shallow traps in MoS2 caused by the presence of sulfur vacancies.

Two-dimensional Weyl points and nodal lines in pentagonal materials and their optical response.

Two-dimensional pentagonal structures based on the Cairo tiling are the basis of a family of layered materials with appealing physical properties. In this work we present a theoretical study of the symmetry-based electronic and optical properties of these pentagonal materials. We provide a complete classification of the space groups that support pentagonal structures for binary and ternary systems. By means of first-principles calculations, the electronic band structures and the local spin textures in momentum space are analyzed for four examples of these materials, namely, PdSeTe, PdSeS, InP5 and GeBi2, all of which are dynamically stable. Our results show that pentagonal structures can be realized in chiral and achiral lattices with Weyl nodes pinned at high-symmetry points and nodal lines along the Brillouin zone boundary; these degeneracies are protected by the combined action of crystalline and time-reversal symmetries. Additionally, we computed the linear and nonlinear optical features of the proposed pentagonal materials and discuss some particular features such as the shift current, which shows an enhancement due to the presence of nodal lines and points, and their possible applications.

One-Dimensional Moiré Superlattices and Flat Bands in Collapsed Chiral Carbon Nanotubes.

We demonstrate that one-dimensional moiré patterns, analogous to those found in twisted bilayer graphene, can arise in collapsed chiral carbon nanotubes. Resorting to a combination of approaches, namely, molecular dynamics to obtain the relaxed geometries and tight-binding calculations validated against ab initio modeling, we find that magic angle physics occur in collapsed carbon nanotubes. Velocity reduction, flat bands, and localization in AA regions with diminishing moiré angle are revealed, showing a magic angle close to 1°. From the spatial extension of the AA regions and the width of the flat bands, we estimate that many-body interactions in these systems are stronger than in twisted bilayer graphene. Chiral collapsed carbon nanotubes stand out as promising candidates to explore many-body effects and superconductivity in low dimensions, emerging as the one-dimensional analogues of twisted bilayer graphene.

Flat bands and gaps in twisted double bilayer graphene.

We present electronic structure calculations of twisted double bilayer graphene (TDBG): a tetralayer graphene structure composed of two AB-stacked graphene bilayers with a relative rotation angle between them. Using first-principles calculations, we find that TDBG is semiconducting with a band gap that depends on the twist angle, that can be tuned by an external electric field. The gap is consistent with TDBG symmetry and its magnitude is related to surface effects, driving electron transfer from outer to inner layers. The surface effect competes with an energy upshift of localized states at inner layers, giving rise to the peculiar angle dependence of the band gap, which reduces at low angles. For these low twist angles, the TDBG develops flat bands, in which electrons in the inner layers are localized at the AA regions, as in twisted bilayer graphene.

Symmetry-protected metallic and topological phases in penta-materials.

We analyze the symmetry and topological features of a family of materials closely related to penta-graphene, derived from it by adsorption or substitution of different atoms. Our description is based on a novel approach, called topological quantum chemistry, that allows to characterize the topology of the electronic bands, based on the mapping between real and reciprocal space. In particular, by adsorption of alkaline (Li or Na) atoms we obtain a nodal line metal at room temperature, with a continuum of Dirac points around the perimeter of the Brillouin zone. This behavior is also observed in some substitutional derivatives of penta-graphene, such as penta-PC2. Breaking of time-reversal symmetry can be achieved by the use of magnetic atoms; we study penta-MnC2, which also presents spin-orbit coupling and reveals a Chern insulator phase. We find that for this family of materials, symmetry is the source of protection for metallic and nontrivial topological phases that can be associated to the presence of fractional band filling, spin-orbit coupling and time-reversal symmetry breaking.

Interface effects in hybrid hBN-graphene nanoribbons.

We analyze the electronic properties of a hybrid graphene-BN nanoribbon system, using a Hubbard model Hamiltonian within a mean field approximation. Due to the different electronegativities of the boron and nitrogen atoms, an electric field is induced across the zigzag graphene strip, breaking the spin degeneracy of the electronic band structure. Optimal tight-binding parameters are found from first-principles calculations. Edge potentials are proposed as corrections for the on-site energies, modeling the BN-graphene nanoribbon interfaces. We show that half-metallic responses in the hybrid systems may be driven with the help of an external electric field. We also study the role of defects across the graphene nanoribbon and at the h-BN/graphene interface regions. Modulations on the spin-dependent gaps may be achieved depending on the nature and position of the defect, constituting a way towards spin-gap engineering by means of spatial doping.

Tight-binding model for opto-electronic properties of penta-graphene nanostructures.

We present a tight-binding parametrization for penta-graphene that correctly describes its electronic band structure and linear optical response. The set of parameters is validated by comparing to ab-initio density functional theory calculations for single-layer penta-graphene, showing a very good global agreement. We apply this parameterization to penta-graphene nanoribbons, achieving an adequate description of quantum-size effects. Additionally, a symmetry-based analysis of the energy band structure and the optical transitions involved in the absorption spectra is introduced, allowing for the interpretation of the optoelectronic features of these systems.

Controlling the layer localization of gapless states in bilayer graphene with a gate voltage.

Experiments in gated bilayer graphene with stacking domain walls present topological gapless states protected by no-valley mixing. Here we research these states under gate voltages using atomistic models, which allow us to elucidate their origin. We find that the gate potential controls the layer localization of the two states, which switches non-trivially between layers depending on the applied gate voltage magnitude. We also show how these bilayer gapless states arise from bands of single-layer graphene by analyzing the formation of carbon bonds between layers. Based on this analysis we provide a model Hamiltonian with analytical solutions, which explains the layer localization as a function of the ratio between the applied potential and interlayer hopping. Our results open a route for the manipulation of gapless states in electronic devices, analogous to the proposed writing and reading memories in topological insulators.

Electric control of the bandgap in quantum wells with band-inverted junctions.

In IV-VI semiconductor heterojunctions with band-inversion, such as those made of [Formula: see text] [Formula: see text]Te or [Formula: see text] [Formula: see text]Se, interface states are properly described by a two-band model, predicting the appearance of a Dirac cone in single junctions. However, in quantum wells the interface dispersion is quadratic in momentum and the energy spectrum presents a gap. We show that the interface gap shrinks under an electric field parallel to the growth direction. Therefore, the interface gap can be dynamically tuned in experiments on double-gated quantum wells based on band-inverted compounds.

Tuning the Fermi velocity in Dirac materials with an electric field.

Dirac materials are characterized by energy-momentum relations that resemble those of relativistic massless particles. Commonly denominated Dirac cones, these dispersion relations are considered to be their essential feature. These materials comprise quite diverse examples, such as graphene and topological insulators. Band-engineering techniques should aim to a full control of the parameter that characterizes the Dirac cones: the Fermi velocity. We propose a general mechanism that enables the fine-tuning of the Fermi velocity in Dirac materials in a readily accessible way for experiments. By embedding the sample in a uniform electric field, the Fermi velocity is substantially modified. We first prove this result analytically, for the surface states of a topological insulator/semiconductor interface, and postulate its universality in other Dirac materials. Then we check its correctness in carbon-based Dirac materials, namely graphene nanoribbons and nanotubes, thus showing the validity of our hypothesis in different Dirac systems by means of continuum, tight-binding and ab-initio calculations.

Atomically-resolved edge states on surface-nanotemplated graphene explored at room temperature.

Graphene edges present localized electronic states strongly depending on their shape, size and border configuration. Chiral- or zigzag-ended graphene nanostructures develop spatially and spectrally localized edge states around the Fermi level; however, atomic scale investigations of such graphene terminations and their related electronic states are very challenging and many of their properties remain unexplored. Here we present a combined experimental and theoretical study on graphene stripes showing strong metallic edge states at room temperature. By means of scanning tunneling microscopy, we demonstrate the use of vicinal Pt(111) as a template for the growth of graphene stripes and characterize their electronic structure. We find the formation of a sublattice localized electronic state confined on the free-standing edges of the graphene ribbons at energies close to the Fermi level. These experimental results are reproduced and understood with tight-binding and ab initio calculations. Our results provide a new way of synthesizing wide graphene stripes with zigzag edge termination and open new prospects in the study of valley and spin phenomena at their interfaces.

Enhancement of thermoelectric efficiency by quantum interference effects in trilayer silicene flakes.

In recent years, the enhancement of thermoelectric efficiencies has been accomplished in nanoscale systems by making use of quantum effects. We exploit the presence of quantum interference phenomena such as bound states in the continuum and Fano antiresonances in trilayer silicene flakes to produce sharp changes in the electronic transmission of the system. By applying symmetric gate voltages the thermoelectric properties can be tuned and, for particular flake lengths, a great enhancement of the figure of merit can be achieved. We show that the most favorable configurations are those in which the electronic transmission is dominated by the coupling of bound states to the continuum, tuned by an external gate.

Existence of nontrivial topologically protected states at grain boundaries in bilayer graphene: signatures and electrical switching.

Recent experiments [L. Ju, et al., Nature, 2015, 520, 650] confirm the existence of gapless states at domain walls created in gated bilayer graphene, when the sublattice stacking is changed from AB to BA. These states are significant because they are topologically protected, valley-polarized and give rise to conductance along the domain wall. Current theoretical models predict the appearance of such states only at domain walls, which preserve the sublattice order. Here we show that the appearance of the topologically protected states in stacking domain walls can be much more common in bilayer graphene, since they can also emerge in unexpected geometries, e.g., at grain boundaries with atomic-scale topological defects. We focus on a bilayer system in which one of the layers contains a line of octagon-double pentagon defects that mix graphene sublattices. We demonstrate that gap states are preserved even with pentagonal defects. Remarkably, unlike previous predictions, the number of gap states changes by inverting the gate polarization, yielding an asymmetric conductance along the grain boundary under gate reversal. This effect, linked to defect states, should be detectable in transport measurements and could be exploited in electrical switches.

Symmetries of quantum transport with Rashba spin-orbit: graphene spintronics.

The lack of some spatial symmetries in planar devices with Rashba spin-orbit interactions opens up the possibility of producing spin polarized electrical currents in the absence of external magnetic fields or magnetic impurities. We study how the direction of the spin polarization of the current is related to spatial symmetries of the device. As an example of these relations we study numerically the spin-resolved current in graphene nanoribbons. Different configurations are explored and analyzed to demonstrate that graphene nanoflakes may be used as excellent spintronic devices in an all-electrical setup.

Octagonal defects at carbon nanotube junctions.

We investigate knee-shaped junctions of semiconductor zigzag carbon nanotubes. Two dissimilar octagons appear at such junctions; one of them can reconstruct into a pair of pentagons. The junction with two octagons presents two degenerate localized states at Fermi energy (E(F)). The reconstructed junction has only one state near E(F), indicating that these localized states are related to the octagonal defects. The inclusion of Coulomb interaction splits the localized states in the junction with two octagons, yielding an antiferromagnetic system.