Zigzag Nanoribbons Research Articles

Significant enhancement in thermoelectric performance of S-shaped germanene nanoribbon devices

Due to the advantages including high efficiency and environmental friendliness, the two-dimensional thermoelectric materials have received huge attention. However, the energy conversion efficiency is not high enough for application. In this work, we have theoretically investigated the thermoelectric performance for both zigzag (ZGeNRs) and armchair (AGeNRs) germanene nanoribbons with edge defects by nonequilibrium Green's function method. For perfect germanene nanoribbons (GeNRs), it is shown that with its width increasing, the maximum of ZT values (ZTmax) decreases monotonously while the phononic thermal conductance increases linearly. For both ZGeNRs and AGeNRs, with increasing defect numbers in longitudinal direction, ZTmax increases monotonously while the phononic thermal conductance decreases. In particular, by introducing periodic defects, the ZTmax of both ZGeNRs and AGeNRs has been raised to above 2, which is due to higher Seebeck coefficient and lower thermal conductance. Our findings provide an effective way to enhance thermoelectric performance, which is beneficial for the design of ultra-thin thermoelectric devices.

Magnetic edge states and edge current in honeycomb zigzag nanoribbons by Kane–Mele–Hubbard model

We investigate spin-dependent edge states of honeycomb zigzag nanoribbons with a focus on electron–electron interaction as the origin of the initial edge magnetism which is assumed to be anti-ferromagnetism order as a stable form. We study the effect of intrinsic spin–orbit interaction (SOI) and also applied in-plane transverse electric field on low energy spectrum and edge spin density. Tight-binding method in the framework of the self-consistent Kane–Mele–Hubbard model has been utilized for exploring electronic properties. Edge currents and electric dipole moments are also calculated. Results show electric field and SOI can dramatically affect the edge states and energy gaps. A transition from a magnetic edge state to a non-magnetic one occurs at critical values of SOI and electric field. Furthermore, the system goes into the topological insulator phase at sufficiently large SOI strengths. The results of edge spin density, electric dipole moment, and spin currents indicate that one can reach the favorite spin-dependent transport by manipulating the electric field and SOI in a zigzag nanoribbon. The outcome may pave the way to further control of spin-based transport in future devices.

Role of symmetry in quantum blocking of Andreev reflection in graphene nanoribbons side-terminated by superconductors

Andreev reflection can be forbidden by means of quantum interference when superconductors are attached at the side edges of graphene nanoribbons (GNRs). The blocking is restricted to single-mode nanoribbons having symmetric zigzag edges and is destroyed by the application of a magnetic field. These characteristics are shown to be the effects of the wavefunction parity on the Andreev retro and specular reflections. Not only the mirror symmetry of the GNRs but also symmetric coupling of the superconductors is required for the quantum blocking. The quasi-flat-band states around the Dirac point energy induced for armchair nanoribbons by adding carbon atoms at the nanoribbon edges do not cause the quantum blocking due to the lack of the mirror symmetry. Furthermore, the phase modulation by the superconductors is shown to be able to convert the quasi-flat dispersion for the edge states of zigzag nanoribbons to a quasi-vertical dispersion.

Size Limiting Elemental Ferroelectricity in Bi Nanoribbons: Observation, Mechanism, and Opportunity

Combined with the inherent spin-orbital coupling effect, the elemental ferroelectricity of monolayer Bi (bismuthene) is the critical property that renders this system a 2D ferroelectric topological insulator. Here, using first-principles calculations, we systematically investigate the ferroelectric polarization in bismuthene nanoribbons and discover the width size limiting effect arising from the edge effects. The decreasing width led to the spontaneous transformation of the zigzag (ZZ) and armchair (AC) paired Bi nanoribbons into newly discovered high-symmetric nonpolarized nanoribbons. For ZZ-paired nanoribbons, the driving force of the phase transition is attributed to the depolarization field, similar to the conventional perovskite ferroelectric thin films. Instead, edge stress as a novel mechanism played a major role in the phase transition of AC-paired nanoribbons. Inspired by such a revealed mechanism, the phase transition and related ultrahigh piezoelectricity can be achieved by strain engineering in Bi nanoribbons, which could enable new applications for 2D ferroelectric devices.

Intrinsic Rashba effect and anomalous valley Hall effect in one-dimensional magnetic nanoribbon

Stable one-dimensional (1D) magnetic nanoribbons are superior to the two-dimensional (2D) or bulk materials due to the quantum size effect and edge effect as well as the controllable bandwidth. Through first-principles calculations, Wannier functions and Monte Carlo simulation, it is found that the GdX2 (X = Cl, Br) zigzag nanoribbons (ZNRs) are dynamically stable, with Curie temperature of ferromagnetic ground state significantly higher than that of their 2D counterpart. The results show that inherent transverse dipole moment and perpendicular magnetocrystalline anisotropy energy (PMAE) induce the coexistence of Rashba effect and valley polarization in such 1D magnetic ZNRs. GdBr2 ZNR with four zigzag chains (GdBr2-4ZNR) has larger valley splitting and PMAE than that of GdCl2-4ZNR, demonstrating room temperature ferromagnetic ground state. Through regulating the bandwidth of GdBr2 ZNR, intrinsic anomalous valley Hall (AVH) effect is observed in GdBr2-5ZNR. Importantly, Dirac-cone-like electronic states, PMAE and AVH effect are robust against the increment of nanoribbon bandwidth which is essential for utilization. These results provide important insights and pave an avenue for the potential application of magnetic nanoribbons in spin-dependent and valley-dependent miniature information storage devices.

Double-Heterostructure Resonant Tunneling Transistors of Surface-Functionalized Sb and Bi Monolayer Nanoribbons

Zigzag nanoribbons tailored from chemically surface-modified Sb or Bi monolayers by methyl, amino or hydroxyl are investigated through first-principles electronic-structure calculations to explore their potential applications in topological transport nanoelectronics. It is verified by Dirac-point-like energy dispersion of band-edges near Fermi level that the scattering-forbidden edge-states of these nanoribbons can give a topological conductive channel with extremely high electron mobility. Accordingly, Sb/SbXHn/Sb and Bi/BiXHn/Bi nanoribbon double-heterostructures (SbXHn or BiXHn: XHn = CH3, NH2, OH) are designed as resonant tunneling transistors and modeled by bipolar transport devices with their electron transport characteristics being calculated by nonequilibrium Green’s function combined first-principles schemes. Ballistic equilibrium conduction spectra and current-voltage characteristics prove that quantum conductance currents of these nanoribbon double heterostructures originate from the electron resonant tunneling between the topological edge-states of the two constituent Sb or Bi monolayer nanoribbons through the central barrier of SbXHn or BiXHn nanoribbon segment. This renders a high resonant current peak with strong negative differential conductance, thus being competent for zero-loss and ultrahigh-frequency resonant tunneling nanotransistors.

One-dimensional magnetism and Rashba-like effects in zigzag bismuth nanoribbons

Discoveries of low-dimensional quantum materials have renewed interest in some of the fundamental phenomena, such as magnetism and Rashba-type spin orbit coupling. In particular, exploring these phenomena by themselves and/or in combination within one-dimensional (1D) systems is of interest for fields as disparate as spintronics and biology. For example, a better understanding of Rashba-type spin orbit coupling in 1D systems may be used to explain spin-selective electron transport in long helical molecules. In this paper, using first principle calculations, we show that each edge of a zigzag nanoribbon composed of a bismuth (Bi) bilayer is a truly 1D structure that naturally combines both 1D magnetism and Rashba-type spin orbit coupling in a single system. In particular, we study the combined effects of exchange and spin-orbit coupling in nanoribbons that are: (i) ideal freestanding, (ii) placed on a hexagonal boron nitride substrate, and (iii) decorated with N atoms. The edges of the Bi zigzag NRs can display ferromagnetic, antiferromagnetic, or noncollinear ordering, resulting in a broken quantum spin Hall state. The interplay of Rashba and exchange effects in different magnetic phases can result in different spin-dependent transport regimes.

Wave functions and edge states in rectangular honeycomb lattices revisited: Nanoflakes, armchair and zigzag nanoribbons, and nanotubes

Properties of bulk and boundaries of materials can, in general, be quite different, both for topological and nontopological reasons. One of the simplest boundary problems to pose is the tight-binding problem of noninteracting electrons on a finite honeycomb lattice. Despite its simplicity, the problem is quite rich and directly related to the physics of graphene. We revisit this long-studied problem and present an analytical derivation of the electron spectrum and wave functions for graphene rectangular derivatives. We provide an exact analytical description of extended and localized states, the transition between them, and a special case of a localized state when the wave function is nonzero only at the edge sites. The latter state has zero energy, and we discuss its existence in zigzag nanoribbons, zigzag nanotubes with a number of sites along a zigzag edge divisible by 4, and rectangular graphene nanoflakes with an odd number of sites along both zigzag and armchair edges.

Effects of edge type and reconstruction on the electronic properties and magnetism of 1T′-ReS2 nanoribbons: A study based on DFT calculations

1T′-ReS2 has attracted great attention of scientists due to its unique properties, symmetry, and wide application in electronic devices. Many methods have been developed to tune its electronic and magnetic properties based on the fundamental knowledge on other two-dimensional (2D) materials. In this work, we explored the electronic and magnetic properties of 1T′-ReS2 nanoribbons (1T′-ReS2-NRs) through density functional theory simulations. Our results show that 1T′-ReS2-NRs possess chirality-related electronic and magnetic properties. Armchair nanoribbons exhibit electronic properties ranging from metallic to semiconducting properties, and magnetic properties can also be introduced in certain nanoribbons. The zigzag nanoribbons can be classified into two types, characterized with large (ZZA-) and small (ZZB-) S-Re-S angles, and the one with larger S-Re-S angle is the energetically favourable one. Both types of ZZ-1T′-ReS2-NRs are magnetic, and the magnetism exhibits opposite parity dependence on the number of ReS2 chains. Further results show that edge reconstruction can effectively stabilize the ferromagnetic states in zigzag nanoribbons by forming Re trimmers. This study should provide useful information for tuning the properties of 1T′-ReS2 thin films and facilitate its application in integrated circuits and spintronic devices.

A family of robust Dirac cone materials: two-dimensional hexagonal M3X2 (M = Zn/Cd/Hg, X = Si/Ge).

The fascinating Dirac cone, which has produced some excellent properties in graphene, such as ballistic charge transport, ultra-high carrier mobility and the quantum Hall effect, has motivated researchers to design and study more two dimensional (2D) Dirac materials. In this work, we have designed a family of 2D Dirac cone materials M3X2 (M = Zn/Cd/Hg, X = Si/Ge) and studied their superior properties by first principles calculation. The calculated cohesive energy, phonon dispersion and ab initio molecular dynamics confirmed the energetic, dynamic and thermodynamic stability of Zn3Ge2, Cd3Ge2, Hg3Si2, and Cd3Si2 monolayers. It was found that the intrinsic Dirac cones exist in the electronic structure of the Zn3Ge2, Cd3Ge2, Hg3Si2 and Cd3Si2 monolayers. Their Fermi velocities are from 3.26 × 105 m s-1 to 4.32 × 105 m s-1 (8.2 × 105 m s-1 for graphene). It is noteworthy that the Dirac cone in the M3X2 structure is robust. It is independent of external strain (from -7% to +19%) and can also be preserved as one-dimensional zigzag nanoribbons and multilayers (from two to three-layers). Our work shows that the novel M3X2 Dirac cone materials are an important candidate for high-speed nanoelectronic devices.

Decoupling 1D and 2D features of 2D sp-nanoribbons—the megatom model

The dependence of the electron energy band gap on the width of an sp-nanoribbon is investigated using a generalization of the 1D tight binding model for a chain of atoms. Within the proposed generalization, small linear atomic formations along lines perpendicular to the 2D ribbon axis are modeled as single large atoms called megatoms whose properties depend on the type, the size and the atomic conformation. Replacement of a 1D chain of atoms by that of the megatoms is accompanied by the incorporation of zeroth order 2D features into the 1D model approximation of the nanoribbon. We use this model to investigate the oscillating band gap of an sp-nanoribbon in terms of the ribbon’s width. Results are presented for the width dependence of the energy gap of the zig-zag Si2BN nanoribbons.

Multitude of exceptional points in van der Waals magnets

Several works have recently addressed the emergence of exceptional points (EPs), i.e., degeneracies of non-Hermitian Hamiltonians, in the long-wavelength dynamics of coupled magnetic systems. Here, by focusing on the driven magnetization dynamics of a van der Waals ferromagnetic bilayer, we show that exceptional points can appear over extended portions of the first Brillouin zone as well. Furthermore, we demonstrate that the effective non-Hermitian magnon Hamiltonian, whose eigenvalues are purely real or come in complex conjugate pairs, respects an unusual wavevector-dependent pseudo-Hermiticity. Finally, for both armchair and zigzag nanoribbon geometries, we discuss both the complex and purely real spectra of the topological edge states and their experimental implications.

Topological and Spectral Properties of Wavy Zigzag Nanoribbons

Low-dimensional graphene-based nanomaterials are interesting due to their cutting-edge electronic and magnetic properties. Their large surface area, strong mechanical resistance, and electronic properties have enabled potential pharmaceutical and opto-electronic applications. Graphene nanoribbons (GNRs) are graphene strips of nanometer size possessing zigzag and armchair edge geometries with tunable widths. Despite the recent developments in the characterization, design and synthesis of GNRs, the study of electronic, magnetic and topological properties, GNRs continue to pose a challenge owing to their multidimensionality. In this study, we obtain the topological and electronic properties of a series of wave-like nanoribbons comprising nanographene units with zigzag-shaped edges. The edge partition techniques based on the convex components are employed to compute the mathematical formulae of molecular descriptors for the wave-like zigzag GNRs. We have also obtained the spectral and energetic properties including HOMO-LUMO gaps, bond delocalization energies, resonance energies, 13C NMR and ESR patterns for the GNRs. All of these computations reveal zero to very low HOMO-LUMO gaps that make these nanoribbons potential candidates for topological spintronics.

Band structures and electronic properties of edge-functionalized germanene nanoribbons

Free-standing germanene is a buckled 2D hexagonal semimetal with an intrinsic carrier mobility more than double that of graphene's. The germanene lattice allows for band gap opening via an applied electric field or adsorption of foreign atoms, enabling the creation of germanene based field-effect devices. While the formation of germanene nanoribbons has been shown to have a band gap, little research has been done on the electronic tunability of Ge nanoribbons. In this study, we analyzed the effect of H, C, P, As, S, Se, Te, F, Cl, Br, and I for edge-functionalization on the physical and electronic properties of germanene armchair (AGeNRs) and zigzag (ZGeNRs) nanoribbons. We found that the band gaps of AGeNRs are tunable through width and edge species, and alternate between semiconducting and semi-metallic. Through these methods the band gap can be tuned to any IR spectral band, while ZGeNRs are shown to be nodal semimetals at small atomic widths but transition to metallic behavior at large widths. This work indicates that the functionalized germanene nanoribbons are promising quantum materials with tunable band structures and electronic properties.

Electronic Band Gap Tuning and Calculations of Mechanical Strength and Deformation Potential by Applying Uniaxial Strain on MX2 (M = Cr, Mo, W and X = S, Se) Monolayers and Nanoribbons.

Two-dimensional (2D) transition-metal dichalcogenides (TMDs) are new crystalline materials with exotic electronic, mechanical, and optical properties. Due to their inherent exceptional mechanical strength, these 2D materials provide us the best platform for strain engineering. In this study, we have performed first-principles calculations to study the effect of uniaxial strains on the electronic, magnetic, and mechanical properties of transition-metal dichalcogenides (TMDs) MX2 (where M = Cr, Mo, W and X = S, Se), monolayers (2D), and armchair and zigzag nanoribbons (1D). For the mechanical strength, we determined the tensile strength (σ) and Young's modulus (Y) and observed that σ and Y are higher in monolayers (most in WS2ML) as compared to nanoribbons where monolayers resist tension up to 25-28% strain while nanoribbons (armchair and zigzag) can be only up to 5-10%. Deformation potential (Δ p ) in the linear regime near the equilibrium position(ϵ < 2%) has also been calculated, and its effect on monolayers is observed less as compared to nanoribbons. In addition, unstrained nonmagnetic monolayers are direct band gap semiconductors (D) which changed to indirect band gap semiconductors (I) with the application of strain. Ferromagnetic states of metallic zigzag nanoribbons (including up spin channel of 7-CrS2NR and 7-CrSe2NR) are greatly affected by strain and show half-metal-like behavior in different strain range. The magnetic moment (μ) that is predominantly observed in zigzag nanoribbons is 2 times higher than that of other nanoribbons. This magnetism in nanoribbons is mostly caused by transition-metal atoms (M = Cr, Mo, W). Thus, our study suggests that strain engineering is the best approach to modify or control the structural, electronic, magnetic, and mechanical properties of the TMD monolayer and nanoribbons which, therefore, open their potential applications in spintronics, photovoltaic cells, and tunneling field-effect transistors.

High performance piezotronic thermoelectric devices based on zigzag MoS2 nanoribbon

Piezotronic and piezophototronic devices have high performance due to the coupling of piezoelectric and semiconductor properties. Strain-induced polarization can effectively modulate the energy band structure and electrical conductivity in low-dimensional structures. In this study, piezotronic effect on the thermoelectric properties of MoS2 zigzag nanoribbons is theoretically investigated. The thermoelectric efficiency (ZT) and Seebeck coefficient of piezotronic thermoelectric devices can be increased by 44 times and 6 times, respectively. This work not only investigates piezotronic effect on thermoelectric properties, but also paves a new way to design high-performance thermoelectric devices.

Strain effects on the spin polarization of edge currents in MoS2 zig-zag nanoribbons

The strain effects on the edge-state transport of the zigzag monolayer for a molybdenum disulfide nanoribbon are investigated numerically using a six-band tight-binding model with KWANT, where the strain effect was absorbed into the modified hopping coefficients. For metallic edge-states in a zigzag nanoribbon, introducing both an intrinsic spin–orbit coupling and local exchange field effects breaks the spin degeneracy and spin inversion symmetry to enable spin selective transport. Changes in the energy dispersion of the metallic edge-states due to uniaxial strain are asymmetric with respect to the strain direction. Transitions from metallic to insulating edge modes occur for a tensile strain of approximately 5% along the x -direction, but no such transition has been observed up to a tensile strain of 10% along the y -direction. The edge-current transmission and spin-polarized edge-currents are determined primarily by details of the energy dispersion of edge-states and are strongly affected by the incident energy of carriers for a given strain. The fully spin-polarized edge-currents can be obtained by modulating both the Fermi energy and gate potential. The results provide useful information to implement a spin-polarized current as a potential solution for wearable spin devices. • The strain effects on the edge-state transport for a molybdenum disulfide nanoribbon. • Asymmetric change of the energy dispersion of the edge states with respect to the strain direction. • Transitions from metallic to insulating edge modes due to tensile strains. • The spin-polarized edge currents in a three terminal field effect transistor.

Edge states of topological acoustic phonons in graphene zigzag nanoribbons

The tight-binding method is an effective way to study topological insulators. However, an intrinsic element, i.e., the acoustic sum rule (ASR) in phonon systems, has often been overlooked when constructing the Wannier tight-binding phonon Hamiltonian, which results in edge states of acoustic modes rarely observed in previous works. In the present work, we show that the topological acoustic edge states in graphene need to be assessed by ASR. Interestingly, when the inversion-time-reversal symmetry is broken, the distributions of some edge states will mutate from two edges of the nanoribbon to one edge. Moreover, some other topological phonon modes, which are different from previous reports, have also been observed. Our results would shed light on the method for searching topological phonon states, and provide effective strategies for designing phononic devices.

New disordered anyon phase of doped graphene zigzag nanoribbon

We investigate interacting disordered zigzag nanoribbons at low doping, using the Hubbard model to treat electron interactions within the density matrix renormalization group and Hartree-Fock method. Extra electrons that are inserted into an interacting disordered zigzag nanoribbon divide into anyons. Furthermore, the fractional charges form a new disordered anyon phase with a highly distorted edge spin density wave, containing numerous localized magnetic moments residing on the zigzag edges, thereby displaying spin-charge separation and a strong non-local correlation between the opposite zigzag edges. We make the following new predictions, which can be experimentally tested: (1) In the low doping case and weak disorder regime, the soft gap in the tunneling density of states is replaced by a sharp peak at the midgap energy with two accompanying peaks. The e^-/2 fractional charges that reside on the boundary of the zigzag edges are responsible for these peaks. (2) We find that the midgap peak disappears as the doping concentration increases. The presence of e^-/2 fractional charges will be strongly supported by the detection of these peaks. Doped zigzag ribbons may also exhibit unusual transport, magnetic, and inter-edge tunneling properties.

Topological properties, entropies, stabilities and spectra of armchair versus zigzag coronene-like nanoribbons

A coronene-like graphitic nanoribbon was recently synthesised as a potential candidate for applications in nanoelectornics due to its unique structural characteristics in contrast with other nanomaterials. It is a planar, thin, finite, and quasi-one-dimensional carbon-based material with novel characteristics. The coronene-like graphitic nanoribbon is constructed using multiple units of a finite dimensional coronene structure linked together in a chain of armchair and zigzag isomers. In this article, we compute the topological properties based on distance and degrees of armchair and zigzag nanoribbon isomers by adopting the orthogonal partition techniques. Our results on entropy measures demonstrate that armchair and zigzag nanoribbon isomers exhibit isentropic structures. We have computed the vertex partitions, C NMR and ESR spectra using distance degree sequence vectors and spectra of armchair and zigzag isomers. Furthermore graph spectral properties of the two isomers are computed which reveal that the zigzag nanoribbons are kinetically more stable than the corresponding armchair isomers.