David K. Campbell

Localizing Energy Through Nonlinearity and Discreteness

Intrinsic localized modes have been theoretical constructs for more than a decade. Only recently have they been observed in physical systems as distinct as charge-transfer solids, Josephson junctions, photonic structures, and micromechanical oscillator arrays.

Transport properties of pristine few-layer black phosphorus by van der Waals passivation in an inert atmosphere.

Ultrathin black phosphorus is a two-dimensional semiconductor with a sizeable band gap. Its excellent electronic properties make it attractive for applications in transistor, logic and optoelectronic devices. However, it is also the first widely investigated two-dimensional material to undergo degradation upon exposure to ambient air. Therefore a passivation method is required to study the intrinsic material properties, understand how oxidation affects the physical properties and enable applications of phosphorene. Here we demonstrate that atomically thin graphene and hexagonal boron nitride can be used for passivation of ultrathin black phosphorus. We report that few-layer pristine black phosphorus channels passivated in an inert gas environment, without any prior exposure to air, exhibit greatly improved n-type charge transport resulting in symmetric electron and hole transconductance characteristics.

Resonance structure in kink-antikink interactions in φ4 theory

Abstract We present new numerical and theoretical results concerning kink-antikink collisions in the classical (nonintegrable) φ 4 field model in one-dimensional space. Earlier numerical studies of such collisions revealed that, over a small range of initial velocities, intervals of initial relative velocity for which the kink and antikink capture one another alternate with regions for which the interaction concludes with escape to infinite separation. We describe the results of a new high-precision computer simulation that significantly extends and refines these observations of escape “windows”. We also discuss a simple theoretical mechanism that appears to account for this structure in a natural way. Our picture attributes the alternation phenomenon to a nonlinear resonance between the orbital frequency of the bound kink-antikink pair and the frequency of characteristic small oscillations of the field localized at the moving kink and antikink centers. Our numerical simulation also reveals long-lived small-scale oscillatory behavior in the time dependence of kink and antikink velocity following those collisions that do not lead to capture. We account for this fine structure in terms of the interaction between kink (and antikink) motion and small amplitude “radiation” generated during and after the collision. We discuss possible implications of our results for physical systems.

Kink-antikink interactions in the double sine-Gordon equation

We study numerically the interactions of a kink (K) and an antikink (K) in the double sine-Gordon equation with potential V(φ) = −4[ - cos(φ/2) + η cos φ]/[1 + |4η|]. As a function of initial velocity in the KK collisions, we observe and analyze quantitatively a rich structure of “resonances” in most ranges of η.

Exactness of semiclassical bound state energies for supersymmetric quantum mechanics

Abstract We show that the structure of supersymmetric quantum mechanics motivates a modified semiclassical quantization condition for one-dimensional hamiltonians. Writing certain well-known quantum systems in supersymmetric form, we discover that this quantization rule gives the exact energy eigenvalues for several potentials for which conventional WKB does not give exact results.

Soliton Excitations in Polyacetylene and Relativistic Field Theory Models

A continuum model of a Peierls-dimerized chain, as described generally by Brazovskii and discussed for the case of polyacetylene by Takayama, Lin-Liu and Maki (TLM), is considered. The continuum (Bogliubov-de Gennes) equations arising in this model of interacting electrons and phonons are shown to be equivalent to the static, semiclassical equations for a solvable model field theory of self-coupled fermions-the N = 2 Gross-Neveu model. Based on this equivalence we note the existence of soliton defect states in polyacetylene that are additional to, and qualitatively different from, the amplitude “kinks” commonly discussed. The new solutions do not have the topological stability of kinks but are essentially conventional strong-coupling polarons in the dimerized chain. They carry spin (12) and charge (±e). In addition, we discuss further areas in which known field theory results may apply to a Peierls-dimerized chain, including relations between phenomenological φ4 and continuum electron-phonon models, and the structure of the fully quantum versus mean field theories.

Kink-antikink interactions in a modified sine-Gordon model

We study numerically the interactions of a kink (K) and an antikink (K) in a parametrically modified sine-Gordon model with potential V(φ) = (1 − r)2(1 − cosφ)/(1 + r2 + 2rcosφ). As the parameter r is varied from the pure sine-Gordon case (r = 0) to values for which the model is not completely integrable (r ≠ 0), we find that a rich structure arises in the KK collisions. For some regions of r(−0.20⪅r<0) this structure is very similar to that observed in KK interactions in the φ4 model, and we show that the theory recently suggested for these collisions also applies quantitatively to the modified sine-Gordon model. In other regions of r we observe new scattering phenomena, which we present in detail numerically and discuss in a qualitative manner analytically.

Bond-order-wave phase and quantum phase transitions in the one-dimensional extended Hubbard model

We use a stochastic series-expansion quantum Monte Carlo method to study the phase diagram of the one-dimensional extended Hubbard model at half-filling for small to intermediate values of the on-site U and nearest-neighbor V repulsions. We confirm the existence of a novel, long-range-ordered bond-order-wave (BOW) phase recently predicted by Nakamura [J. Phys. Soc. Jpn. 68, 3123 (1999)] in a small region of the parameter space between the familiar charge-density-wave (CDW) state for

Polyacetylene and relativistic field-theory models

V\ensuremath{\gtrsim}U/2

Theory of coexisting charge and spin-density waves in (TMTTF)(2)Br, (TMTSF)(2)PF6, and alpha-(BEDT-TTF)(2)MHg(SCN)(4)

and the state with dominant spin-density-wave (SDW) fluctuations for