Geometric Superlattice Research Articles

Geometric Nanophotonics: Light Management in Single Nanowires through Morphology.

Comprehensive control of light-matter interactions at the nanoscale is increasingly important for the development of miniaturized light-based technologies that have applications ranging from information processing to sensing. Control of light in nanoscale structures-the realm of nanophotonics-requires precise control of geometry on a few-nanometer length scale. From a chemist's perspective, bottom-up growth of nanoscale materials from chemical precursors offers a unique opportunity to design structures atom-by-atom that exhibit desired properties. In this Account, we describe our efforts to create chemically and morphologically precise Si nanowires (NWs) with designed nanophotonic properties using a vapor-liquid-solid (VLS) growth process. A synthetic technique termed "Encoded Nanowire Growth and Appearance through VLS and Etching" (ENGRAVE) combines optimized VLS growth, dopant modulation, and dopant-dependent wet-chemical etching to produce NWs with precisely designed diameter modulations, yielding lithographic-like morphological control that can vary from sinusoids to fractals. The ENGRAVE NWs thus provide a versatile playground for coupling, trapping, and directing light in a nanoscale geometry. Previously, the nanophotonic functionality of NWs primarily relied on uniform-diameter structures that exhibit Mie scattering resonances and longitudinally oriented guided modes, two key photonic properties that typically cannot be utilized simultaneously due to their orthogonality. However, when the NW diameter is controllably modulated along the longitudinal axis on a scale comparable to the wavelength of light-a geometry we term a geometric superlattice (GSL)-we found that NWs can exhibit a much richer and tunable set of nanophotonic properties, as described herein. To understand these unique properties, we first summarize the basic optical properties of uniform-diameter NWs using Mie scattering theory and dispersion relations, and we describe both conventional and relatively new microscopy methods that experimentally probe the optical properties of single NWs. Next, delving into the properties of NW GSLs, we summarize their ability to couple a Mie resonance with a guided mode at a select wavevector (or wavelength) dictated by their geometric pitch. The coupling forms a bound guided state (BGS) with a standing wave profile, which allows a NW GSL to serve as a spectrally selective light coupler and to act as optical switch or sensor. We also summarize the capacity of a GSL to trap light by serving as an ultrahigh (theoretically infinite) quality factor optical cavity with an optical bound state in the continuum (BIC), in which destructive interference prevents coupling to and from the far field. Finally, we discuss a future research outlook for using ENGRAVE NWs for nanoscale light control. For instance, we highlight research avenues that could yield light-emitting devices by interfacing a NW-based BIC with emissive materials such as quantum dots, 2D materials, and hybrid perovskite. We also discuss the design of photonic band gaps, generation of high-harmonics with quasi-BIC structures, and the possibility for undiscovered nanophotonic properties and phenomena through more complex ENGRAVE geometric designs.

Optical Bound States in the Continuum with Nanowire Geometric Superlattices.

Perfect trapping of light in a subwavelength cavity is a key goal in nanophotonics. Perfect trapping has been realized with optical bound states in the continuum (BIC) in waveguide arrays and photonic crystals; yet the formal requirement of infinite periodicity has limited the experimental realization to structures with macroscopic planar dimensions. We characterize BICs in a silicon nanowire (NW) geometric superlattice (GSL) that exhibits one-dimensional periodicity in a compact cylindrical geometry with a subwavelength diameter. We analyze the scattering behavior of NW GSLs by formulating temporal coupled mode theory to include Lorenz-Mie scattering, and we show that GSL-based BICs can trap electromagnetic energy for an infinite lifetime and exist over a broad range of geometric parameters. Using synthesized NW GSLs tens of microns in length and with variable pitch, we demonstrate the progressive spectral shift and disappearance of Fano resonances in experimental single-NW extinction spectra as a manifestation of BIC GSL modes.

Magnetic Properties of One- and Two-Dimensional Functional Materials: Oxygen Molecules Encapsulated in Single-Walled Carbon Nanotubes and Copper Ions Embedded into Phthalocyanine Sheets

Background: In this paper, we report on the topics of one-dimensional (1D) and two-dimensional (2D) functional materials. Single-Walled Carbon Nanotubes (SWCNTs) are seamless hollow cylinders made of hexagonal lattice graphite sheets. The SWCNTs have attracted considerable attention due to the applicability of their enclosed nanospaces to engineering, and many types of guest materials are encapsulated inside their 1D space, expecting unusual properties. The poly Transition Metal (TM) phthalocyanine, in which phthalocyanine units are extended in two dimensions by sharing benzene rings, is one of the examples of the TM containing 2D carbon materials. Because of strong correlation between localized d-electrons in the TM atom and delocalized π-electrons on the poly phthalocyanine frame, it is expected that spin-polarized conduction, which is useful for the spintronic applications. Objectives: The objective of the first work is to synthesize SWCNTs encapsulating oxygen molecules having spin one, whose O-O bond directions are aligned to the longitudinal direction of the SWCNTs. The objective of the second work is to synthesize Poly Cu Phthalocyanine (PCuPc) through a bottom-up method by using copper octacyanophthalocyanine as a building block and to elucidate its crystal structure and magnetic properties. Methods: SWCNTs with inner diameter of ca 0.8 nm were prepared by the CoMoCAT method, and encapsulated together with oxygen molecules (~400 Torr) into a high-purity quartz tube. To subtract the background signals of the SWCNTs and the quartz tube, we prepared the same SWCNTs inducing He gas after evacuating oxygen molecules. Magnetization measurements of these SWCNTs samples were conducted by means of a SQUID magnetometer and a pulse magnet using an induction method. PCuPc were synthesized by a solid state reaction of octacyanophthalocyanine, tetracyanobenzene, and CuCl2·2H2O in glass ampoules sealed after evacuation. The as-synthesized samples were characterized using XRD analysis and TEM microscopy. Magnetization measurement of the samples were done by using a SQUID magnetometer. Results: The intrinsic magnetization data from oxygen molecules inside the SWCNTs (temperature and magnetic field dependence) show magnetic properties typical of the spin-one Heisenberg antiferromagnet named a Haldane magnet. PCuPc and its half-filling counterpart were obtained by solid state reaction. Both magnetic susceptibility and magnetization of PCuPc are larger than those of half-filling PCuPc, but the magnitudes of the former sample are about 1.5 times larger than those of the latter one, which is expected to be twice from the geometric superlattice structure. Conclusion: We have studied magnetic properties (magnetic susceptibility and magnetization) of oxygen molecules encapsulated into Single Walled Carbon Nanotubes (SWCNTs) with diameters of about 0.8 nm, regarded as a 1D functional magnetic material, and Poly Copper Phthalocyanine (PCuPc) and poly half-filling copper phthalocyanine (half-filling PCuPc), regarded as 2D functional magnetic materials.

Analyses of orientational superlattice domains in epitaxial ZnTe thin films grown on graphene and mica

ZnTe has a favorable band alignment with CdTe and is an ideal buffer between CdTe and metal contacts used in photovoltaics. Using metalorganic chemical vapor deposition, we report epitaxial growth of ZnTe thin films on 2D substrates, namely, single crystal graphene on amorphous SiO2/Si and freshly cleaved mica(001). Despite the large in-plane lattice mismatches between ZnTe and graphene (∼75%) and between ZnTe and mica(001) (∼17%), X-ray pole figure analyses show preferred epitaxial alignments with the out-of-plane orientation along [111] for ZnTe films on both substrates. For ZnTe on graphene, besides the primary in-plane orientation of [1¯10]ZnTe//[11¯]graphene, two secondary in-plane orientations rotating ±25.28° away from the primary domain are found. A geometrical superlattice area mismatch (GSAM) model is implemented to explain the existence of the primary and secondary domains in ZnTe on graphene. For ZnTe on mica(001), only one in-plane orientational domain is found experimentally with the epitaxial relationship of [1¯10]ZnTe//[100]mica (or [1¯10]ZnTe//[21¯1¯0]mica if four-index notation is used for mica). However, the prediction of domain orientation between ZnTe and mica(001) based on the GSAM model slightly deviates from that observed experimentally. Furthermore, it should be noted that multiple order twinning domains of the primary domain are observed in both ZnTe films. While coexisting with the primary domain, each of the twinning domains is still epitaxially aligned with respect to the substrate. The in-depth understanding of ZnTe's epitaxial behaviors on graphene and mica(001) provides a valuable guidance for future studies on epitaxy of 3D zinc-blende overlayers on 2D hexagonal substrates.

Energy filtering in silicon nanowires and nanosheets using a geometric superlattice and its use for steep-slope transistors

This paper investigates energy filtering in silicon nanowires and nanosheets by resonant electron tunneling through a geometric superlattice. A geometric superlattice is any kind of periodic geometric feature along the transport direction of the nanowire or nanosheet. Multivalley quantum-transport simulations are used to demonstrate the manifestation of minibands and minibandgaps in the transmission spectra of such a superlattice. We find that the presence of different valleys in the conduction band of silicon favors a nanowire with a rectangular cross section for effective energy filtering. The obtained energy filter can consequently be used in the source extension of a field-effect transistor to prevent high-energy electrons from contributing to the leakage current. Self-consistent Schrödinger-Poisson simulations in the ballistic limit show minimum subthreshold swings of 6 mV/decade for geometric superlattices with indentations. The obtained theoretical performance metrics for the simulated devices are compared with conventional III-V superlatticeFETs and TunnelFETs. The adaptation of the quantum transmitting boundary method to the finite-element simulation of 3-D structures with anisotropic effective mass is presented in Appendixes A and B. Our results bare relevance in the search for steep-slope transistor alternatives which are compatible with the silicon industry and can overcome the power-consumption bottleneck inherent to standard CMOS technologies.

Mie-coupled bound guided states in nanowire geometric superlattices

All-optical operation holds promise as the future of computing technology, and key components include miniaturized waveguides (WGs) and couplers that control narrow bandwidths. Nanowires (NWs) offer an ideal platform for nanoscale WGs, but their utility has been limited by the lack of a comprehensive coupling scheme with band selectivity. Here, we introduce a NW geometric superlattice (GSL) that allows narrow-band guiding in Si NWs through coupling of a Mie resonance with a bound-guided state (BGS). Periodic diameter modulation creates a Mie-BGS-coupled excitation that manifests as a scattering dark state with a pronounced scattering dip in the Mie resonance. The frequency of the coupled mode, tunable from the visible to near-infrared, is determined by the pitch of the GSL. Using a combined GSL-WG system, we demonstrate spectrally selective guiding and optical switching and sensing at telecommunication wavelengths, highlighting the potential to use NW GSLs for the design of on-chip optical components.

Ferroelastic modulation and the Bloch formalism.

The key to the development of advanced materials is to understand their electronic structure-property relationship. Utilization of this understanding to design new electronic materials with desired properties led to modern epitaxial growth approaches for synthesizing artificial lattices, which for almost half a century have become the mainstay of electronic and photonic technologies. In contrast to previous scalar modulation approaches, we now study synthetic crystal lattices that have a tensor artificial modulation and develop a theory for photons and conduction band states in these lattices in a regime with an unusual departure from the familiar consequences of translational symmetry and Bloch's theorem. This study reveals that a nonmagnetic crystal lattice modulated by a purely geometrical orientational superlattice potential can lead to localized states or to spiral states for electrons and photons, as well as weakly or strongly localized states that could be used to markedly slow down the propagation of light and for optical energy storage applications.

THE GEOMETRICAL EFFECTS ON ELECTRONIC SPECTRUM AND PERSISTENT CURRENTS IN MESOSCOPIC POLYGON

In this paper, a new mesoscopic polygon which possesses smooth transition at its corners is proposed. Because of the particularity of structure, this kind of mesoscopic polygon can also be a geometrical superlattice. The geometrical effects on the electron states and persistent current are investigated comprehensively in the presence of magnetic flux. We find that the particular geometric structure of the polygon induces an effective periodic potential which results in gaps in the energy spectrum. The changes of gaps show the consistency with the geometrical two-ness of this new polygon. This electronic structure and the corresponding physical properties are found to be periodic with period ϕ0 in the magnetic flux ϕ and can be controlled by the geometric method. We also consider the Rahsba spin-orbit interaction which double the energy levels splitting and leads to an additional small zigzag in one period of the persistent current. These new phenomena may be useful for the applications in quantum device design in the future.

Lateral organization of cholesterol molecules in lipid-cholesterol assemblies.

We present results of an off-lattice simulation of a two-component planar system, as a model for lateral organization of cholesterol molecules in lipid-cholesterol assemblies. We explore the existence of "superlattice" structures even in fluid systems, in the absence of an underlying translational long-range order, and study their coupling to hexatic or bond-orientational order. We discuss our results in context of geometric superlattice theories and "condensation complexes" in understanding a variety of experiments in artificial lipid-cholesterol assemblies.

Dynamical conductivity of a quantum-wire superlattice.

The dynamical current response of a multiple-quantum-wire superlattice to a time-oscillatory external electric field is examined using Kubo's linear-response theory. Couplings of the quasi-one-dimensional electron gases with phonons (polar optic, and acoustic deformation potential) are discussed to lowest order in terms of a current-current correlation function which embodies both intrawire and interwire electron-electron Coulomb interactions. The associated dynamic screening of the electron-phonon interaction is approximated by employing the random-phase-approximation density-density correlation function for the interacting electrons of the quantum-wire superlattice. The frequency-dependent conductivity of this system is evaluated numerically, exhibiting its variations with temperature and geometrical superlattice parameters.

A non-Boltzmann balance equation approach to electronic transport in a type-I superlattice

Force and energy balance equations are derived for steady state hot electron transport in a type-I superlattice composed of periodically arranged finite-width quantum wells. The scatterings by remote and background impurities and by acoustic and polar optical phonons are taken into account, together with Coulomb interactions between intralayer electrons and interlayer electrons. The carrier mobility and electron temperature are calculated as functions of drift velocity ν up to ν=3×10 7 cm / s, showing significant nonlinearity and dependence on geometrical superlattice parameters (quantum well width and separation, etc.)