quasi-1D Systems Research Articles

Tunable electronic correlation effects in nanotube-light interactions

Electronic many-body correlation effects in one-dimensional (1D) systems such as carbon nanotubes have been predicted to strongly modify the nature of photoexcited states. Here we directly probe this effect using broadband elastic light scattering from individual suspended carbon nanotubes under electrostatic gating conditions. We observe significant shifts in optical transition energies, as well as line broadening, as the carrier density is increased. The results demonstrate the role of screening of many-body electronic interactions on the different length scales, a feature inherent to quasi-1D systems. Our findings further demonstrate the possibility of electrical tuning of optical transitions and provide a basis for understanding of various optical phenomena in carbon nanotubes and other quasi-1D systems in the presence of charge carrier doping.

Hidden modes in open disordered media: analytical, numerical, and experimental results

We explore numerically, analytically, and experimentally the relationship between quasi-normal modes (QNMs) and transmission resonance (TR) peaks in the transmission spectrum of one-dimensional (1D) and quasi-1D open disordered systems. It is shown that for weak disorder there exist two types of the eigenstates: ordinary QNMs which are associated with a TR, and hidden QNMs which do not exhibit peaks in transmission or within the sample. The distinctive feature of the hidden modes is that unlike ordinary ones, their lifetimes remain constant in a wide range of the strength of disorder. In this range, the averaged ratio of the number of transmission peaks to the number of QNMs is insensitive to the type and degree of disorder and is close to the value which we derive analytically in the weak-scattering approximation. The physical nature of the hidden modes is illustrated in simple examples with a few scatterers. The analogy between ordinary and hidden QNMs and the segregation of superradiant states and trapped modes is discussed. When the coupling to the environment is tuned by an external edge reflectors, the superradiance transition is reproduced. Hidden modes have been also found in microwave measurements in quasi-1D open disordered samples. The microwave measurements and modal analysis of transmission in the crossover to localization in quasi-1D systems give a ratio of close to In diffusive quasi-1D samples, however, falls as the effective number of transmission eigenchannels M increases. Once is divided by M, however, the ratio is close to the ratio found in 1D.

Low-Energy Electron Potentiometry: Contactless Imaging of Charge Transport on the Nanoscale.

Charge transport measurements form an essential tool in condensed matter physics. The usual approach is to contact a sample by two or four probes, measure the resistance and derive the resistivity, assuming homogeneity within the sample. A more thorough understanding, however, requires knowledge of local resistivity variations. Spatially resolved information is particularly important when studying novel materials like topological insulators, where the current is localized at the edges, or quasi-two-dimensional (2D) systems, where small-scale variations can determine global properties. Here, we demonstrate a new method to determine spatially-resolved voltage maps of current-carrying samples. This technique is based on low-energy electron microscopy (LEEM) and is therefore quick and non-invasive. It makes use of resonance-induced contrast, which strongly depends on the local potential. We demonstrate our method using single to triple layer graphene. However, it is straightforwardly extendable to other quasi-2D systems, most prominently to the upcoming class of layered van der Waals materials.

Reversals of the large-scale circulation in quasi-2D Rayleigh–Bénard convection

We report an experimental study of the large-scale circulation (LSC) reversal in quasi-2D turbulent thermal convection, in which the aspect ratio ${\it\Gamma}$ ($=\text{height}/\text{length}$ of a rectangular box) is used as a parameter to perturb the stability of the LSC. It is found that the mean time interval $\langle {\it\tau}\rangle$ between two successive reversals increases strongly with increasing ${\it\Gamma}$. A stochastic model is proposed to incorporate the effect of the corner rolls. In the model, the aspect ratio serves as a tuning parameter for the relative weight of the corner rolls that damp the LSC. The model predictions for the shape of the bistable states of the system and $\langle {\it\tau}\rangle$ agree excellently with the experimental results, with $\langle {\it\tau}\rangle$ having an unexpected stretched exponential Rayleigh number dependence, ${\sim}\!\exp (Ra^{{\it\alpha}})$. We further show quantitatively that the main damping force of the LSC in a quasi-2D system is from the corner rolls rather than the viscous drag from the sidewalls, which bridges the difference found in quasi-2D and 3D systems.

Nanowire Lasers

Abstract:We review principles and trends in the use of semiconductor nanowires as gain media for stimulated emission and lasing. Semiconductor nanowires have recently been widely studied for use in integrated optoelectronic devices, such as light-emitting diodes (LEDs), solar cells, and transistors. Intensive research has also been conducted in the use of nanowires for subwavelength laser systems that take advantage of their quasione- dimensional (1D) nature, flexibility in material choice and combination, and intrinsic optoelectronic properties. First, we provide an overview on using quasi-1D nanowire systems to realize subwavelength lasers with efficient, directional, and low-threshold emission. We then describe the state of the art for nanowire lasers in terms of materials, geometry, andwavelength tunability.Next,we present the basics of lasing in semiconductor nanowires, define the key parameters for stimulated emission, and introduce the properties of nanowires. We then review advanced nanowire laser designs from the literature. Finally, we present interesting perspectives for low-threshold nanoscale light sources and optical interconnects. We intend to illustrate the potential of nanolasers inmany applications, such as nanophotonic devices that integrate electronics and photonics for next-generation optoelectronic devices. For instance, these building blocks for nanoscale photonics can be used for data storage and biomedical applications when coupled to on-chip characterization tools. These nanoscale monochromatic laser light sources promise breakthroughs in nanophotonics, as they can operate at room temperature, can potentially be electrically driven, and can yield a better understanding of intrinsic nanomaterial properties and surface-state effects in lowdimensional semiconductor systems.

Charge density waves and phonon-electron coupling inZrTe3

Charge-density-wave (CDW) order has long been interpreted as arising from a Fermi-surface instability in the parent metallic phase. While phonon-electron coupling has been suggested to influence the formation of CDW order in quasi-two-dimensional (quasi-2D) systems, the presumed dominant importance of Fermi-surface nesting remains largely unquestioned in quasi-1D systems. Here we show that phonon-electron coupling is also important for the CDW formation in a model quasi-1D system ZrTe$_3$. Our joint experimental and computational study reveals that particular lattice vibrational patterns possess exceedingly strong coupling to the conduction electrons, and are directly linked to the lattice distortions associated with the CDW order. The dependence of the coupling matrix elements on electron momentum further dictates the opening of (partial) electronic gaps in the CDW phase. Since lattice distortions and electronic gaps are the defining signatures of CDW order, our result demonstrates that the conventional wisdom based on Fermi-surface geometry needs to be substantially supplemented by phonon-electron coupling even in the simplest quasi-1D case. As prerequisites for the CDW formation, the highly anisotropic electronic structure and strong phonon-electron coupling in ZrTe$_3$ give rise to a distinct Raman scattering effect, namely, measured phonon linewidths depend on the direction of momentum transfer in the scattering process.

Polar molecule reactive collisions in quasi-1D systems

We study polar molecule scattering in quasi-one-dimensional geometries. Elastic and reactive collision rates are computed as a function of collision energy and electric dipole moment for different confinement strengths. The numerical results are interpreted in terms of first order scattering and of adiabatic models. Universal dipolar scattering is also discussed. Our results are relevant to experiments where control of the collision dynamics through one-dimensional confinement and an applied electric field is envisioned.

Limits to Metallic Conduction in Atomic-Scale Quasi-One-Dimensional Silicon Wires

The recent observation of ultralow resistivity in highly doped, atomic-scale silicon wires has sparked interest in what limits conduction in these quasi-1D systems. Here we present electron transport measurements of gated Si:P wires of widths 4.6 and 1.5 nm. At 4.6 nm we find an electron mobility, μ(el)≃60 cm²/V s, in excellent agreement with that of macroscopic Hall bars. Metallic conduction persists to millikelvin temperatures where we observe Gaussian conductance fluctuations of order δG∼e²/h. In thinner wires (1.5 nm), metallic conduction breaks down at G≲e²/h, where localization of carriers leads to Coulomb blockade. Metallic behavior is explained by the large carrier densities in Si:P δ-doped systems, allowing the occupation of all six valleys of the silicon conduction band, enhancing the number of 1D channels and hence the localization length.

Effective transport equations in quasi 1D systems

The mapping methods reducing 2D or 3D transport equations in quasi 1D structures onto the longitudinal coordinate x are revisited. The general formalism based on homogenization is explained on the simplest case, diffusion in a 2D channel of varying width A(x). Then its modifications to diffusion in an external field (Smoluchowski equation), and nonzero mass of the particles (Klein-Kramers equation) are demonstrated. A special attention is payed to the role of the “natural” curvilinear coordinates, connected with the stationary flow, in the mapping and derivation of the effective equations.

Nonlinear transport in quasi-one-dimensional Nb2PdS5 nanowires

Nb2PdS5 is a newly discovered quasi-one-dimensional (quasi-1D) superconductor with a high upper critical field along the chain direction. Here, we report the size-dependent electronic properties of Nb2PdS5 nanowires obtained by ultrasonically cleaving the bulk crystals. The nanowires exhibit a superconductor to insulator transition as the cross-sectional area decreases. Moreover, for the thinner nanowires with insulating state, the transport properties exhibit a power-law dependence on both temperature and bias voltage at an intermediate temperature (<30 K), followed by a conduction saturation below 10 K. We found that such an apparent power-law behavior can be described by the extended variable range hopping theory developed recently for the multichannel quasi-1D systems, where the localization of electrons is expected to be dominant instead of the Luttinger liquid nature.

Parity-dependent localization inNstrongly coupled chains

Anderson localization of wave-functions at zero energy in quasi-1D systems of $N$ disordered chains with inter-chain coupling $t$ is examined. Localization becomes weaker than for the 1D disordered chain ($t=0$) when $t$ is smaller than the longitudinal hopping $t'=1$, and localization becomes usually much stronger when $t\gg t'$. This is not so for all $N$. We find "immunity" to strong localization for open (periodic) lateral boundary conditions when $N$ is odd (a multiple of four), with localization that is weaker than for $t=0$ and rather insensitive to $t$ when $t \gg t'$. The peculiar $N$-dependence and a critical scaling with $N$ is explained by a perturbative treatment in $t'/t$, and the correspondence to a weakly disordered effective chain is shown. Our results could be relevant for experimental studies of localization in photonic waveguide arrays.

A semispectral approach for the efficient calculation of scattering matrices in quasi-1D quantum systems and transmission coefficients for the Landauer formula

This paper proposes the semispectral method for the calculation of the scattering matrices for the charge carriers in quasi-one-dimensional quantum systems described by the Schrodinger equation. An efficient and accurate calculation method is achieved by adding of reference solutions at selected energy points to the eigenfunction expansion of the Green's function. A numerical simulation of the quantum wire with the square cross-section in transverse electric field was performed by different methods. The example problem of a quantum wire in a transverse electric field is used to compare the semispectral method with alternative approaches. We find that the semispectral method reliably converges and is significantly faster than the direct solution while the eigenfunction expansion approach has convergence issues. These results allow us to propose the semispectral method as a universal and efficient approach to calculation of the transmission coefficients for the Landauer formula as well as other scattering-based entities.

Velocity Anomaly of a Driven Tracer in a Confined Crowded Environment

We consider a discrete model in which a tracer performs a random walk biased by an external force, in a dense bath of particles performing symmetric random walks constrained by hard-core interactions. We reveal the emergence of a striking velocity anomaly in confined geometries: in quasi-1D systems such as stripes or capillaries, the velocity of the tracer displays a long-lived plateau before ultimately dropping to a lower value. We develop an analytical solution that quantitatively accounts for this intriguing behavior. Our analysis suggests that such a velocity anomaly could be a generic feature of driven dynamics in quasi-1D crowded systems.

Behavior of entanglement entropy in interacting quasi-one-dimensional systems and its consequences for their efficient numerical study

The density matrix renormalization group (DMRG) method allows an efficient computation of the properties of interacting 1D quantum systems. Two-dimensional (2D) systems, capable of displaying much richer quantum behavior, generally lie beyond its reach except for very small system sizes. Many of the physical properties of 2D systems carry into the quasi-1D case, for which, unfortunately, the standard 2D DMRG algorithm fares little better. By finding the form of the entanglement entropy in quasi-1D systems, we directly identify the reason for this failure. Using this understanding, we explain why a modified algorithm, capable of cleverly exploiting this behavior of the entanglement entropy, can accurately reach much larger system sizes. We demonstrate the power of this method by accurately finding quantum critical points in frustration induced magnetic transitions, which remain inaccessible using the standard DMRG or the Monte Carlo methods.

CDW fluctuations and the pseudogap in the single-particle conductivity of quasi-1D Peierls CDW systems: II

The current-dipole Kubo formula for the dynamical conductivity of interacting multiband electronic systems derived in Kupčić et al (2013 J. Phys.: Condens. Matter 25 145602) is illustrated on the Peierls model for quasi-one-dimensional systems with the charge-density-wave (CDW) instability. Using the microscopic representation of the Peierls model, it is shown in which way the scattering of conduction electrons by CDW fluctuations affects the dynamical conductivity at temperatures above and well below the CDW transition temperature. The generalized Drude formula for the intraband conductivity is derived in the ordered CDW state well below the transition temperature. The natural extension of this formula to the case where the intraband memory function is dependent on frequency and wave vectors is also presented. It is shown that the main adventage of such a memory-function conductivity model is that it can be easily extended to study the dynamical conductivity and the electronic Raman scattering in more complicated multiband electronic systems in a way consistent with the law of conservation of energy. The incoherent interband conductivity in the CDW pseudogap state is briefly discussed as well.

The single-channel regime of transport through random media.

The propagation of light through samples with random inhomogeneities can be described by way of transmission eigenchannels, which connect incoming and outgoing external propagating modes. Although the detailed structure of a disordered sample can generally not be fully specified, these transmission eigenchannels can nonetheless be successfully controlled and used for focusing and imaging light through random media. Here we demonstrate that in deeply localized quasi-1D systems, the single dominant transmission eigenchannel is formed by an individual Anderson-localized mode or by a ‘necklace state’. In this single-channel regime, the disordered sample can be treated as an effective 1D system with a renormalized localization length, coupled through all the external modes to its surroundings. Using statistical criteria of the single-channel regime and pulsed excitations of the disordered samples allows us to identify long-lived localized modes and short-lived necklace states at long and short time delays, respectively.

Divergence of the long-wavelength collective diffusion coefficient in quasi-one- and quasi-two-dimensional colloidal suspensions.

We report the results of experimental studies of the short-time-long-wavelength behavior of collective particle displacements in quasi-one-dimensional (q1D) and quasi-two-dimensional (q2D) colloid suspensions. Our results are reported via the q → 0 behavior of the hydrodynamic function H(q) that relates the effective collective diffusion coefficient D(e)(q), with the static structure factor S(q) and the self-diffusion coefficient of isolated particles D(0): H(q) ≡ D(e)(q)S(q)/D(0). We find an apparent divergence of H(q) as q → 0 with the form H(q) ∝ q(-γ) (1.7 < γ < 1.9) for both q1D and q2D colloid suspensions. Given that S(q) does not diverge as q → 0 we infer that D(e)(q) does. This behavior is qualitatively different from that of the three-dimensional H(q) and D(e)(q) as q → 0, and the divergence is of a different functional form from that predicted for the diffusion coefficient in one-component one-dimensional and two-dimensional fluids not subject to boundary conditions that define the dimensionality of the system. We provide support for the contention that the boundary conditions that define a confined system play a very important role in determining the long-wavelength behavior of the collective diffusion coefficient from two sources: (i) the results of simulations of H(q) and D(e)(q) in quasi-1D and quasi-2D systems and (ii) verification, using data from the work of Lin, Rice and Weitz [Phys. Rev. E 51, 423 (1995)], of the prediction by Bleibel et al., arXiv:1305.3715, that D(e)(q) for a monolayer of colloid particles constrained to lie in the interface between two fluids diverges as q(-1) as q → 0.

Non-Equilibrium Phase Behaviour in Giant Lipid Vesicles Following Very Rapid Temperature Changes

Artificial lipid bilayers are useful models of biological membranes, appealing for applicative purposes, and an interesting example of quasi-2D liquid systems on which to investigate new physics. It is well known that ternary-component lipid membranes, depending on the relevant thermodynamic parameters (composition, temperature and pressure), can show phase coexistence between two liquid phases, Lo and Ld, that can be imaged by fluorescence microscopy.We have performed experiments observing both equilibrium and non-equilibrium morphology of lipid phases. Specifically we have investigated a new dynamical regime in which we follow the diffusive mixing of miscible phases, and observe pattern formation out of equilibrium. This has been possible thanks to the development of a method to induce rapid temperature changes, by infrared irradiation. In this fashion, a temperature change can be imposed faster (in about 1s) than the diffusive time over relevant lengthscales (several 10s).Our observations are that the line tension rapidly vanishes upon heating the system above the miscibility transition temperature. After a few seconds, the spectrum of the interface fluctuations becomes very different from the equilibrium capillary waves, growing in amplitude and losing the characteristic 1/wave-vector2 equilibrium form. The interface from then blurs out, resembling fractal growth fronts, until the phases are fully mixed.The same fast temperature change allows us to very rapidly cool the system. This extends previous measurements by other groups, giving insight into processes that take place over the first few seconds of phase separation.Investigating these non-equilibrium conditions is relevant because biological membranes in living systems are not in a steady state: they are continually subject to rapid changes in composition, temperature and curvature, and their response is known to couple into a variety of biochemical processes by mediating protein binding and interactions.

Classification of engineered topological superconductors

I perform a complete classification of two-dimensional, quasi-one-dimensional (1D) and 1D topological superconductors which originate from the suitable combination of inhomogeneous Rashba spin–orbit coupling, magnetism and superconductivity. My analysis reveals alternative types of topological superconducting platforms for which Majorana fermions are accessible. Specifically, I observe that for quasi-1D systems with Rashba spin–orbit coupling and time-reversal violating superconductivity, such as for instance due to a finite Josephson current flow, Majorana fermions can emerge even in the absence of magnetism. Furthermore, for the classification I also consider situations where additional ‘hidden’ symmetries emerge, with a significant impact on the topological properties of the system. The latter generally originate from a combination of space group and complex conjugation operations that separately do not leave the Hamiltonian invariant. Finally, I suggest alternative directions in topological quantum computing for systems with additional unitary symmetries.

Space group symmetry applied to SCF calculations with periodic boundary conditions and Gaussian orbitals

Space group symmetry is exploited and implemented in density functional calculations of extended systems with periodic boundary conditions. Our scheme for reducing the number of two-electron integrals employs the entire set of operations of the space group, including glide plains and screw axes. Speedups observed for the Fock matrix formation in simple 3D systems range from 2X to 9X for the near field Coulomb part and from 3X to 8X for the Hartree-Fock-type exchange, the slowest steps of the procedure, thus leading to a substantial reduction of the computational time. The relatively small speedup factors in special cases are attributed to the highly symmetric positions atoms occupy in crystals, including the ones tested here, as well as to the choice of the smallest possible unit cells. For quasi-1D systems with most atoms staying invariant only under identity, the speedup factors often exceed one order of magnitude reaching almost 70X (near-field Coulomb) and 57X (HFx) for the largest tested (16,7) single-walled nanotube with 278 symmetry operations.