Pentagonal Lattice Research Articles

Two-Dimensional Pentagonal Materials with Parabolic Dispersion and High Carrier Mobility

Materials with high carrier mobility, represented by graphene, have garnered significant interest. However, the zero band gap arising from linear dispersion cannot achieve an ideal on–off ratio in field-effect transistors (FETs), limiting practical applications in certain fields. In contrast, parabolic dispersion usually exhibits extremely high carrier mobility and an appropriate band gap. In this work, we predicted a planar pentagonal lattice composed entirely of pentagons (namely penta-MX2 monolayer), where M = Ni, Pd and Pt, X = group V elements. Using first-principles calculations, we demonstrated a parabolic dispersion within this framework, which results in intriguing phenomena, such as a direct band gap (0.551–1.105 eV) and extraordinary high carrier mobility. For penta-MX2 monolayer, the carrier mobility can attain ~1 × 108 cm2 V−1 s−1 (PBE), surpassing those of black phosphorene, graphene and 2D hexagonal materials. This monolayer also displays anisotropic mechanical properties and significant absorption peaks in the ultraviolet spectrum. Remarkably, 2D penta-MX2 monolayers are promising for successful experimental exfoliation, particularly when X is a nitrogen element, opening up new possibilities for designing two-dimensional semiconductor materials characterized by high carrier mobility.

Tuning the Electronic Bandgap of Penta-Graphene from Insulator to Metal Through Functionalization: A First-Principles Calculation.

We performed first-principles density functional theory (DFT) calculations to numerically investigate the electronic band structures of penta-graphene (PG), a novel two-dimensional carbon material with a pentagonal lattice structure, and its chemically functionalized forms. Specifically, we studied hydrogenated PG (h-PG), fluorinated PG (f-PG), and chlorinated PG (Cl-PG). We used the generalized gradient approximation (GGA) and the hybrid Heyd-Scuseria-Ernzerhof (HSE06) exchange-correlation functional in the DFT-based software VASP to capture electronic properties accurately. Our results indicate that hydrogenation and fluorination increased the indirect bandgap of PG from 3.05 eV to 4.97 eV and 4.81 eV, respectively, thereby effectively transforming PG from a semiconductor to an insulator. In contrast, we found that chlorination closed the bandgap, thus indicating the metallic behavior of Cl-PG. These results highlight the feasibility of tuning the electronic properties of PG through functionalization, offering insight into designing new materials for nanoelectronic applications.

Pentagonal two-dimensional lattices.

Pentagonal two-dimensional lattices.

Vacancy Ordering in Ultrathin Copper Oxide Films on Cu(111).

Oxide thin films grown on metal surfaces have wide applications in catalysis and beyond owing to their unique surface structures compared to their bulk counterparts. Despite extensive studies, the atomic structures of copper surface oxides on Cu(111), commonly referred to as "44" and "29", have remained elusive. In this work, we demonstrated an approach for the structural determination of oxide surfaces using element-specific scanning tunneling microscopy (STM) imaging enhanced by functionalized tips. This approach enabled us to resolve the atomic structures of "44" and "29" surface oxides, which were further corroborated by noncontact atomic force microscopy (nc-AFM) measurements and Monte Carlo (MC) simulations. The stoichiometry of the "44" and "29" frameworks was identified as Cu23O16 and Cu16O11, respectively. Contrary to the conventional hypothesis, we observed ordered Cu vacancies within the "44" structure manifesting as peanut-shaped cavities in the hexagonal lattice. Similarly, a combination of Cu and O vacancies within the "29" structure leads to bean-shaped cavities within the pentagonal lattice. Our study has thus resolved the decades-long controversy on the atomic structures of "44" and "29" surface oxides, advancing our understanding of copper oxidation processes and introducing a robust framework for the analysis of complex oxide surfaces.

Local Spin Frustration and Order in Fractional Cairo Pentagonal Lattice Under Magnetic Fields

Pentagonal lattices with an odd number of vertices are known to exhibit spin frustration, where the orientation of the spins in the ground state is not uniquely determined. In this study, we focus on a lattice created by incorporating fractals within a Cairo pentagonal lattice. We refer to this lattice as cairoflake lattice, analogous to the well-known fractal pentaflake. We use the Monte Carlo method to study an antiferromagnetic Ising model in a magnetic field for the ground state of the cairoflake lattice. Our findings reveal a separation of the spin order state and the frustration-induced disorder state in the paramagnetic phase near the magnetic-field-induced ferromagnetic phase.

Irreversibility of 2D Linear CA and Garden of Eden

In this paper, we consider a pentagonal lattice and we investigate the rule matrix with null boundary condition for two-dimensional cellular automata with the field [Formula: see text] (the set of integers modulo [Formula: see text]) and analyze their characteristics. Moreover, an algorithm of computing the rank of rule matrix with null boundary condition for von Neumann neighborhood is developed. Finally, necessary and sufficient conditions for the existence of Garden of Eden configurations for two-dimensional cellular automata are obtained.

Canonical Monte Carlo multispin cluster method

We present a new Canonical Multispin-flip Cluster Monte Carlo algorithm for Ising model and describe efficient implementations for hybrid supercomputer. Our method takes advantage of the computing architecture for parallel and multi-threaded operations and uses a sequential cluster state update scheme. Due to the peculiarity of the implementation, the method is more effective for models with a restricted radius of interaction. It is based on combining a random selection of spin cluster by the Monte Carlo method with a complete enumeration of the all states of the selected cluster. To show how it works we applied our method to models of interacting magnetic Ising-moments: ferromagnetic Ising model, the Edwards–Anderson spin glass model, dipolar spin ice on hexagonal and pentagonal Cairo lattices.

Nonlinear photonic disclination states

Higher-order topological insulators are unusual materials that can support topologically protected states, whose dimensionality is lower than the dimensionality of the structure at least by 2. Among the most intriguing examples of such states are zero-dimensional corner modes existing in two-dimensional higher-order insulators. In contrast to corner states, recently discovered disclination states also belong to the class of higher-order topological states but are bound to the boundary of the disclination defect of the higher-order topological insulator and can be predicted using the bulk-disclination correspondence principle. Here, we present the first example of the nonlinear photonic disclination state bifurcating from its linear counterpart in the disclination lattice with a pentagonal or heptagonal core. We show that nonlinearity allows us to tune the location of the disclination states in the bandgap and notably affects their shapes. The structure of the disclination lattice is crucial for the stability of these nonlinear topological states: for example, disclination states are stable in the heptagonal lattice and are unstable nearly in the entire gap of the pentagonal lattice. Nonlinear disclination states reported here are thresholdless and can be excited even at low powers. Nonlinear zero-energy states coexisting in these structures with disclination states are also studied. Our results suggest that disclination lattices can be used in the design of various nonlinear topological functional devices, while disclination states supported by them may play an important role in applications, where strong field confinement together with topological protection are important, such as the design of topological lasers and enhancement of generation of high harmonics.

Order and disorder, crossovers, and phase transitions in dipolar artificial spin ice on the Cairo lattice.

We study the thermodynamic properties of the magnetic dipolar spin ice on a 2D pentagonal Cairo lattice by using the numerical Metropolis and the complete enumeration methods. We use the model of point Ising-like dipoles considering long-range interactions with up to 100 nearest neighbors and with periodic boundary conditions. There are two explicit peaks both in the temperature behavior of the heat capacity and in the magnetic susceptibility. The low-temperature peak is caused only by long-range interactions and is not present in the model where each dipole interacts only with four nearest neighbors. The height of the peak depends logarithmically on the quantity of dipoles, which indicates a phase transition. The nature of the low-temperature phase transition is related to the transformation from order to disorder in orthogonal sublattices while maintaining the spin ice state and the spin ice rule in the sublattice of crosses. The high-temperature heat capacity peak is associated with the melting of spin ice, i.e., with the crossover from spin ice to paramagnetic chaos. Its height is constant and does not depend on the quantity of dipoles. It is shown that the choice of the radius of the dipole-dipole interaction has a significant effect on the statistical properties of the model. The model may even show the appearance of the long-range order and the phase transition in the case of long-range interaction or its absence in the case of short-range interaction.

Theoretical exploration of mechanical and superconducting properties of two-dimensional Cairo penta- BP2 : A first-principles study

Two-dimensional (2D) Cairo pentagon materials have attracted tremendous interest due to their exotic physical properties. Based on first-principles calculations, we predict that monolayer penta-${\mathrm{BP}}_{2}$ is a promising Cairo pentagon-based 2D material simultaneously harboring a negative Poisson ratio and intrinsic superconductivity. The Poisson ratio exhibits strong anisotropy with alternating positive-negative signs, and its value along the diagonal direction is more negative than that of pentagraphene. The medium-strength coupling between the Fermi-surface electrons and a phonon mode majorly originating from the ${\mathrm{P}}_{2}$ dimers leads to a superconducting transition estimated to occur at ${T}_{\mathrm{c}}\ensuremath{\sim}7.7\phantom{\rule{0.28em}{0ex}}\mathrm{K}$. Moreover, we find that fluorination/chlorination can efficiently engineer the superconductivity and mechanical properties of penta-${\mathrm{BP}}_{2}$: achieving higher ${T}_{\mathrm{c}}$ of 9.6/10.5 K, turning Poisson's ratio from negative to positive and enhancing Young's modulus. These results render penta-${\mathrm{BP}}_{2}$ an appealing platform to investigate unique superconductivity and mechanical properties in the Cairo pentagon lattice.

Irreversibility of 2d Linear Ca on Pentagonal Lattice Over Periodic Boundary Condition and Garden of Eden

Irreversibility of 2d Linear Ca on Pentagonal Lattice Over Periodic Boundary Condition and Garden of Eden

Magnetization process of the S = 1/2 Heisenberg antiferromagnet on the floret pentagonal lattice

We study the S = 1/2 Heisenberg antiferromagnet on the floret pentagonal lattice by numerical diagonalization method. This system shows various behaviours that are different from that of the Cairo-pentagonal-lattice antiferromagnet. The ground-state energy without magnetic field and the magnetization process of this system are reported. Magnetization plateaux appear at one-ninth height of the saturation magnetization, at one-third height, and at seven-ninth height. The magnetization plateaux at one-third and seven-ninth heights come from interactions linking the sixfold-coordinated spin sites. A magnetization jump appears from the plateau at one-ninth height to the plateau at one-third height. Another magnetization jump is observed between the heights corresponding to the one-third and seven-ninth plateaux; however the jump is away from the two plateaux, namely, the jump is not accompanied with any magnetization plateaux. The jump is a peculiar phenomenon that has not been reported.

Ferromagnetic coupling in a two-dimensional Cairo pentagonal Ni2(TCNQ)2 lattice

Magnetism has revolutionized important technologies, and continues to bring forth new phenomena in emergent materials and reduced dimensions. Here, using first-principles calculations, we demonstrate that the already-synthesized two-dimensional (2D) Ni-tetracyanoquinodimethane (Ni2(TCNQ)2) lattice is a stable ferromagnetism material with multiple spin-polarized Dirac cones. The conical bands in proximity of the Fermi level can be tuned by external tensile strain and show the fourfold degenerate electronic states at the critical tensile strain of ∼2.35 %, whose energy dispersion is consistent with 2D Cairo pentagonal lattice. In addition, spin-orbital coupling can open a band gap at the Dirac point of A, leading to topologically nontrivial electronic states characterized by the non-zero Chern number and the edge states of nanoribbon. Our results offer versatile platforms for the realization of massless spintronics with full-spin polarization in 2D Cairo pentagonal Ni2(TCNQ)2 Lattice.

Topological Insulating Phase in Single-Layer Pentagonal Covalent Organic Frameworks: A Reticular Design Using Metal Phthalocyanine

Organic topological insulators have received tremendous attention lately due to their designability and highly chemical diversity. In this work, we propose an isoreticular series of single-layer π-conjugated covalent organic frameworks with the Cairo pentagonal tiling, termed mcm-ZnPc-1, mcm-ZnPc-2, mcm-ZnPc-3, and mcm-ZnPc-3N, where mcm is the crystal net’s symbol and ZnPc stands for zinc phthalocyanine. First-principles calculations using density functional theory show that mcm-ZnPc-1 and mcm-ZnPc-2 are trivial insulators with band gaps of 0.96 and 1.18 eV, respectively. Interestingly, expanding the π-conjugated system of mcm-ZnPc-2, followed by a chemical substitution, results in mcm-ZnPc-3 and mcm-ZnPc-3N with a distorted Dirac point and a quadratic band-crossing point in their band structures, respectively. The topological analyses indicate that mcm-ZnPc-3N is a Z2 topological insulator with a nontrivial gapless edge state. Our tight-binding model for the pentagonal lattice suggests that the topologically trivial-to-nontrivial transition can be attributed to the sufficient electronic coupling between two adjacent linkers and to the fact that the band-crossing point locates at the Fermi level. Remarkably, we show that replacing Zn in mcm-ZnPc-3N with Cd and Hg can substantially enlarge the nontrivial band gap from 0.3 meV up to 10 meV due to strong spin–orbit coupling strengths although a biaxial strain is necessary to tune the Fermi level of mcm-HgPc-3N in order to enter its topological insulating phase. Our proposed materials are predicted to be dynamically, thermally, and mechanically stable, thus paving the way for their experimental realization. This work not only introduces the pentagonal lattice as a building motif for framework structures but also demonstrates a strategy to engineer the exotic band structure of organic materials.

Polarization-independent wavelength splitter based on silicon nanowire embedded dual-core pentagonal lattice photonic crystal fiber for optical communication systems

A silicon nanowire embedded dual-core pentagonal photonic crystal fiber (PCF)-based polarization-independent wavelength splitter is proposed. The proposed PCF structure is analyzed using the finite element method. The wavelength splitting behavior of the PCF is investigated using the coupled-mode theory. The structural parameters of the PCF are optimized to achieve a coupling length ratio of 2. For the proposed PCF of length 102 μm, the cross-talk (CT) of −48.27 and −61.54 dB and CT bandwidth of 29.3 and 37.7 nm at 1.3 and 1.55 μm for X-polarization mode is achieved. However, the proposed PCF of length 115.5 μm attained the CT of −42.83 and −46.74 dB and CT bandwidth of 27.6 and 34.5 nm at 1.3 and 1.55 μm, respectively for Y-polarization mode. The polarization-independent wavelength splitter is achieved with the proposed PCF of length 108.75 μm. The proposed PCF-based wavelength splitter will be an inevitable candidate for integrated optical systems.

Low-energy states, ground states, and variable frustrations of the finite-size dipolar Cairo lattices.

To investigate the influence of geometric frustration on the properties of low-energy configurations of systems of ferromagnetic nanoislands located on the edges of the Cairo lattice, the model of interacting Ising-like magnetic dipoles is used. By the method of complete enumeration, the densities of states of the Cairo pentagonal lattices of a finite number of Ising-like point dipoles are calculated. The calculated ground and low-energy states for systems with a small number of dipoles can be used to solve the problem of searching for the ground states in a system with a relatively large number of dipoles. It is shown that the ground-state energy of the Cairo pentagonal lattices exhibits nonmonotonic behavior on one of the lattice parameters. The lattice parameters can be used to control the degree of geometric frustration. For the studied lattices of a finite number of Ising dipoles on the Cairo lattice in the ground-state configurations, a number of closed pentagons is observed, which are different from the obtained maximum closed pentagons. The magnetic order in the ground-state configurations obeys the ice rule and the quasi-ice rules.

Experimental determination of the magnetic interactions of frustrated Cairo pentagon lattice materials

We present inelastic neutron scattering measurements of the Cairo pentagon lattice magnets Bi$_2$Fe$_4$O$_9$ and Bi$_4$Fe$_5$O$_{13}$F, supported by high field magnetisation measurements of Bi$_2$Fe$_4$O$_9$. Using linear spin wave theory and mean field analyses we determine the spin exchange interactions and single-ion anisotropy in these materials. The Cairo lattice is geometrically frustrated and consists of two inequivalent magnetic sites, both occupied by Fe$^{3+}$ ions and connected by two competing nearest neighbour interactions. We found that one of these interactions, coupling nearest neighbour spins on the three-fold symmetric sites, is extremely strong and antiferromagnetic. These strongly coupled dimers are then weakly coupled to a framework formed from spins occupying the other inequivalent site. In addition we found that the Fe$^{3+}$ $S=5/2$ spins have a non-negligible single-ion anisotropy, which manifests as a spin anisotropy gap in the neutron spectrum and a spin-flop transition in high field magnetisation measurements.

Low‐Symmetry PdSe2 for High Performance Thermoelectric Applications

AbstractAs an emerging member in 2D materials, pentagonal palladium diselenide (PdSe2) has interesting ambipolar charge transport behavior with high air‐stability and shows great potential in nanoelectronics and optoelectronics. Moreover, the puckered pentagon structure in PdSe2 results in an intrinsic low lattice thermal conductivity, which makes PdSe2 a superior material prospect for thermoelectric (TE) applications. However, its TE properties have yet to be experimentally demonstrated. Here, the TE transport in 2D PdSe2 with a low‐symmetry pentagonal lattice is probed for the first time. By thickness‐engineering, it is demonstrated that the TE property of PdSe2 can be effectively manipulated due to its sensitive dependence on the interlayer coupling originating from the special lattice structure. The TE performance can be largely enhanced benefiting from the high band convergence and quantum confinement in thinner PdSe2 flakes. A power factor as high as 1.5 mW m−1 K−2 can be achieved for a PdSe2 flake with a thickness of 5 nm. This work provides the first TE study on a pentagonal lattice as opposed to hexagonal lattices that dominate the 2D layered material family. The unique lattice structure with special interlayer interaction in PdSe2 opens up new pathways for TE applications, low‐dimensional electronics, and quantum devices.

Ground-state phases and spin textures of spin–orbit-coupled dipolar Bose–Einstein condensates in a rotating toroidal trap* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11475144 and 11047033), the Natural Science Foundation of Hebei Province, China (Grant Nos. A2019203049 and A2015203037), the University Science and Technology Foundation of Hebei Provincial Department of Education, China (Grant No. Z2017056), Science

We investigate the ground-state phases and spin textures of spin–orbit-coupled dipolar pseudo-spin-1/2 Bose–Einstein condensates in a rotating two-dimensional toroidal potential. The combined effects of dipole–dipole interaction (DDI), spin–orbit coupling (SOC), rotation, and interatomic interactions on the ground-state structures and topological defects of the system are analyzed systematically. For fixed SOC strength and rotation frequency, we provide a set of phase diagrams as a function of the DDI strength and the ratio between inter- and intra-species interactions. The system can show rich quantum phases including a half-quantum vortex, symmetrical (asymmetrical) phase with quantum droplets (QDs), asymmetrical segregated phase with hidden vortices (ASH phase), annular condensates with giant vortices, triangular (square) vortex lattice with QDs, and criss-cross vortex string lattice, depending on the competition between DDI and contact interaction. For given DDI strength and rotation frequency, the increase of the SOC strength leads to a structural phase transition from an ASH phase to a tetragonal vortex lattice then to a pentagonal vortex lattice and finally to a vortex necklace, which is also demonstrated by the momentum distributions. Without rotation, the interplay of DDI and SOC may result in the formation of a unique trumpet-shaped Bloch domain wall. In addition, the rotation effect is discussed. Furthermore, the system supports exotic topological excitations, such as a half-skyrmion (meron) string, triangular skyrmion lattice, skyrmion–half-skyrmion lattice, skyrmion–meron cluster, skyrmion–meron layered necklace, skyrmion–giant-skyrmion necklace lattice, and half-skyrmion–half-antiskyrmion necklace.

Topological defects in rotating spin–orbit-coupled dipolar spin-1 Bose–Einstein condensates

We consider the topological defects and spin structures of spin-1 Bose–Einstein condensates with spin–orbit coupling (SOC) and dipole–dipole interaction (DDI) in a rotating harmonic plus quartic trap. The combined effects of SOC, DDI and rotation on the ground-state phases of the system are analyzed. Our results show that for fixed rotation frequency structural phase transitions can be achieved by adjusting the magnitudes of the SOC and DDI. A ground-state phase diagram is given as a function of the SOC and DDI strengths. It is shown that the system exhibits rich quantum phases including vortex string phase with isolated density peaks (DPs), triangular (square) vortex lattice phase with DPs, checkerboard phase, and stripe phase with hidden vortices and antivortices. For given SOC and DDI strengths, the system can display pentagonal vortex lattice with DPs, vortex necklace with DPs, and exotic topological structure composed of multi-layer visible vortex necklaces, a hidden giant vortex and hidden vortex necklaces, depending on the rotation frequency. In addition, the system sustains fascinating novel spin textures and skyrmion excitations, such as an antiskyrmion pair, antiskyrmion-half-antiskyrmion (antiskyrmion–antimeron) cluster, skyrmion–antiskyrmion lattice, skyrmion–antiskyrmion cluster, skyrmion–antiskyrmion–meron–antimeron lattice, double-layer half-antiskyrmion necklaces, and composite giant-antiskyrmion–antimeron necklaces.