Interface Hamiltonian Research Articles

Topological invariants for interface modes

This article concerns topologically non-trivial interface Hamiltonians that find many applications in materials science and geophysical fluid flows. The non-trivial topology manifests itself in the existence of topologically protected, asymmetric edge states at the interface between two two-dimensional half spaces. The asymmetric transport is characterized by a quantized interface conductivity. The objective of this article is to compute such a conductivity and show its stability under perturbations. We present two methods. The first one computes the conductivity using the winding number of branches of absolutely continuous spectrum of the interface Hamiltonian. This calculation is independent of any bulk properties but requires a sufficient understanding of the spectral decomposition of the Hamiltonian. In the fluid flow setting, it also applies in cases where the so-called bulk-interface correspondence fails. The second method establishes a bulk-interface correspondence between the interface conductivity and a so-called bulk-difference invariant. We introduce the bulk-difference invariants characterizing pairs of half spaces. We then relate the interface conductivity to the bulk-difference invariant by means of a Fedosov–Hörmander formula, which computes the index of a related Fredholm operator and is obtained using semiclassical calculus. The two methods are used to compute invariants for representative 2 × 2 and 3 × 3 systems of equations that appear in the applications.

Probing predictions due to the nonlocal interface Hamiltonian: Monte Carlo simulations of interfacial fluctuations in Ising films.

Extensive Monte Carlo simulations have been performed on an Ising ferromagnet under conditions that would lead to complete wetting in a semi-infinite system. We studied an L×L×D slab geometry with oppositely directed surface fields so that a single interface is formed and can undergo a localization-delocalization transition. Under the chosen conditions the interface position is, on average, in the middle of the slab, and its fluctuations allow a sensitive test of predictions that the effective interactions between the interface and the confining surfaces are nonlocal. The decay of distance dependent correlation functions are measured within the surface, in the middle of the slab, and between middle and the surface for slabs of varying thickness D. From Fourier transforms of these correlation functions a nonlinear correlation length is extracted, and its behavior is found to confirm theoretical predictions for D>6 lattice spacings.

Critical Ising model with boundary magnetic field: RG interface and effective Hamiltonians

Critical 2D Ising model with a boundary magnetic field is arguably the simplest QFT that interpolates between two non-trivial fixed points. We use the diagonalising Bogolyubov transformation for this model to investigate two quantities. Firstly we explicitly construct an RG interface operator that is a boundary condition changing operator linking the free boundary condition with the one with a boundary magnetic field. We investigate its properties and in particular show that in the limit of large magnetic field this operator becomes the dimension 1/16 primary field linking the free and fixed boundary conditions. Secondly we use Schrieffer-Wolff method to construct effective Hamiltonians both near the UV and IR fixed points.

Capillary wave theory of adsorbed liquid films and the structure of the liquid-vapor interface.

In this paper we try to work out in detail the implications of a microscopic theory for capillary waves under the assumption that the density is given along lines normal to the interface. Within this approximation, which may be justified in terms of symmetry arguments, the Fisk-Widom scaling of the density profile holds for frozen realizations of the interface profile. Upon thermal averaging of capillary wave fluctuations, the resulting density profile yields results consistent with renormalization group calculations in the one-loop approximation. The thermal average over capillary waves may be expressed in terms of a modified convolution approximation where normals to the interface are Gaussian distributed. In the absence of an external field we show that the phenomenological density profile applied to the square-gradient free energy functional recovers the capillary wave Hamiltonian exactly. We extend the theory to the case of liquid films adsorbed on a substrate. For systems with short-range forces, we recover an effective interface Hamiltonian with a film height dependent surface tension that stems from the distortion of the liquid-vapor interface by the substrate, in agreement with the Fisher-Jin theory of short-range wetting. In the presence of long-range interactions, the surface tension picks up an explicit dependence on the external field and recovers the wave vector dependent logarithmic contribution observed by Napiorkowski and Dietrich. Using an error function for the intrinsic density profile, we obtain closed expressions for the surface tension and the interface width. We show the external field contribution to the surface tension may be given in terms of the film's disjoining pressure. From literature values of the Hamaker constant, it is found that the fluid-substrate forces may be able to double the surface tension for films in the nanometer range. The film height dependence of the surface tension described here is in full agreement with results of the capillary wave spectrum obtained recently in computer simulations, and the predicted translation mode of surface fluctuations reproduces to linear order in field strength an exact solution of the density correlation function for the Landau-Ginzburg-Wilson Hamiltonian in an external field.

Gradient Dynamics Description for Films of Mixtures and Suspensions: Dewetting Triggered by Coupled Film Height and Concentration Fluctuations

A thermodynamically consistent gradient dynamics model for the evolution of thin layers of liquid mixtures, solutions, and suspensions on solid substrates is presented which is based on a film-height- and mean-concentration-dependent free energy functional. It is able to describe a large variety of structuring processes, including coupled dewetting and decomposition processes. As an example, the model is employed to investigate the dewetting of thin films of liquid mixtures and suspensions under the influence of effective long-range van der Waals forces that depend on solute concentration. The occurring fluxes are discussed, and it is shown that spinodal dewetting may be triggered through the coupling of film height and concentration fluctuations. Fully nonlinear calculations provide the time evolution and resulting steady film height and concentration profiles.

Renormalization group calculations for wetting transitions of infinite order and continuously varying order: Local interface Hamiltonian approach

We study the effect of thermal fluctuations on the wetting phase transitions of infinite order and of continuously varying order, recently discovered within a mean-field density-functional model for three-phase equilibria in systems with short-range forces and a two-component order parameter. Using linear functional renormalization group calculations within a local interface Hamiltonian approach, we show that the infinite-order transitions are robust. The exponential singularity (implying 2-α(s)=∞) of the surface free energy excess at infinite-order wetting as well as the precise algebraic divergence (with β(s)=-1) of the wetting layer thickness are not modified as long as ω<2, with ω the dimensionless wetting parameter that measures the strength of thermal fluctuations. The interface width diverges algebraically and universally (with ν([perpendicular])=1/2). In contrast, the nonuniversal critical wetting transitions of finite but continuously varying order are modified when thermal fluctuations are taken into account, in line with predictions from earlier calculations on similar models displaying weak, intermediate, and strong fluctuation regimes.

Stability of thin liquid films and sessile droplets under confinement

The stability of nonvolatile thin liquid films and of sessile droplets is strongly affected by finite size effects. We analyze their stability within the framework of density functional theory using the sharp kink approximation, i.e., on the basis of an effective interface Hamiltonian. We show that finite size effects suppress spinodal dewetting of films because it is driven by a long-wavelength instability. Therefore nonvolatile films are stable if the substrate area is too small. Similarly, nonvolatile droplets connected to a wetting film become unstable if the substrate area is too large. This instability of a nonvolatile sessile droplet turns out to be equivalent to the instability of a volatile drop which can attain chemical equilibrium with its vapor.

Geometry-Controlled Interface Localization-Delocalization Transition in Block Copolymers

Lamellar copolymers confined into a film of thickness D by two stripe-patterned surfaces, which are rotated against each other by a twist angle α, form lamellar domains that register and align with the respective chemical surface patterns. The two domains of thickness x and D-x are separated by an interface that resembles a twist grain boundary. At small twist angles α or strong selectivity of the surface patterns, this interface fluctuates around the middle of the film, x≈D/2, while the interface is localized at one of the surfaces, x≈0 or x≈D, in the opposite limit. These two morphologies are separated by an interface localization-delocalization transition (ILDT) that can be controlled by the twist angle α. For thin films, we find a second-order ILDT while the ILDT is first-order for large D values. A phenomenological interface Hamiltonian is used to relate the findings to the ILDT of symmetric mixtures, and the predictions are confirmed by molecular simulation.

Optical anisotropy of InAs/GaSb broken-gap quantum wells

We investigate in detail the optical anisotropy of absorption of linearly polarized light in InAs/GaSb quantum wells grown on GaSb along the [001] direction, which can be used as an active region of different laser structures. The energy level positions, the wave functions, the optical matrix elements, and the absorption coefficients are calculated using the eight-band k center dot p model and the Burt-Foreman envelope function theory. In these calculations, the Schrodinger and Poisson equations are solved self-consistently taking the lattice-mismatched strain into account. We find that a realistic Hamiltonian, which has the C (2v) symmetry, results in considerable anisotropy of optical matrix elements for different directions of light polarization and different directions of the initial-state in-plane wave vector, including low-symmetry directions. We trace how the optical matrix elements and absorption are modified when spin-orbit interaction and important symmetry breaking mechanisms are taken into account (structural inversion asymmetry, bulk inversion asymmetry, and interface Hamiltonian). These mechanisms result in an almost 100% anisotropy of the absorption coefficients as the light polarization vector rotates in the plane of the structure and in a plane normal to the interfaces.

Spin-related phenomena in InAs/GaSb quantum wells

We have studied theoretically the influence of symmetry breaking mechanisms: structural inversion asymmetry, bulk inversion asymmetry, relativistic and non-relativistic interface Hamiltonian and warping on spin split of levels Delta E and optical absorption of linearly polarized light in asymmetrical quantum wells made from zincblende materials grown on [001] direction. The AlSb/InAs/GaSb/AlSb broken-gap quantum wells with hybridized electron-hole states sandwiched by the AlSb barriers have been considered. We have obtained substantial contributions of these effects into the absolute values of spin split of electron and hole states and spinflip optical transitions for the initial state in-plane wave vectors along low symmetry directions such as [12].

Simulation Evidence for Nonlocal Interface Models: Two Correlation Lengths Describe Complete Wetting

Monte Carlo simulations of (fluctuating) interfaces in Ising models confined between competing walls at temperatures above the wetting transition are presented and various correlation functions probing the interfacial fluctuation are computed. Evidence for the nonlocal interface Hamiltonian approach of A. O. Parry et al. [Phys. Rev. Lett. 93, 086104 (2004)] is given. In particular, we show that two correlation lengths exist with different dependence on the distance D between the walls.

Intersubband optical transitions in InAs/GaSb quantum wells

The effects of electron-hole hybridization, structural asymmetry with respect to spatial inversion, bulk asymmetry, and the interface Hamiltonian upon the optical absorption of linearly polarized light in broken-gap heterostructures are treated with the use of the eight-band Burt-Foreman envelope function theory and the self-consistent solution of the Schrodinger equation and the Poisson equation. The broken-gap heterostructures, specifically, the AlSb/InAs/GaSb/AlSb quantum wells, grown along the [001] direction offer promise for the fabrication of various devices. The anisotropy induced by the above-listed effects in the dispersion relations of size-quantization subbands and in optical matrix elements is established. The bulk asymmetry and the interface Hamiltonian modify the selection rules for intersubband transitions on the exposure of the structures to linearly polarized light. As a result, the initially forbidden spin-flip transitions are allowed. This brings about a large number of peaks in the dependence of the absorption coefficient on the photon energy, if the light polarization vector is directed along the axis of growth of the structure. If the light polarization vector is in the plane of the structure, the bulk asymmetry and the interface Hamiltonian induce strong longitudinal anisotropy of the absorption due to the hybridization of states with oppositely oriented spins. These effects are comprehensively studied for optical transitions involving hybridized electron-hole states in quantum wells grown on InAs.

“Elastic” fluctuation-induced effects in smectic wetting films

The Li-Kardar field theory approach is generalized to wetting smectic films and the “elastic” fluctuation-induced interaction is obtained between the external flat bounding surface and distorted IA (isotropic liquid-smectic A) interface acting as an “internal” (bulk) boundary of the wetting smectic film under the assumption that the IA interface is essentially “softer” than the surface smectic layer. This field theory approach allows calculating the fluctuation-induced corrections in Hamiltonians of the so-called “correlated” liquids confined by two surfaces, in the case where one of the bounding surfaces is “rough” and with different types of surface smectic layer anchoring. We obtain that in practice, the account of thermal displacements of the smectic layers in a wetting smectic film reduces to the addition of two contributions to the IA interface Hamiltonian. The first, so-called local contribution describes the long-range thermal “elastic” repulsion of the fluctuating IA interface from the flat bounding surface. The second, so-called nonlocal contribution is connected with the occurrence of an “elastic” fluctuation-induced correction to the stiffness of the IA interface. An analytic expression for this correction is obtained.

From density to interface fluctuations: The origin of wavelength dependence in surface tension

The height-height correlation function for a fluctuating interface between two coexisting bulk phases is derived by means of general equilibrium properties of the corresponding density-density correlation function. A wavelength-dependent surface tension gamma(q) can be defined and expressed in terms of the direct correlation function c(r,r;{'}) , the equilibrium density profile rho_{0}(r) , and an operator which relates density to surface configurations. Neither the concept of an effective interface Hamiltonian nor the difference in pressure is needed to determine the general structure of the height-height correlations or gamma(q) , respectively. This result generalizes the Mecke-Dietrich surface tension gamma_{MD}(q) [Phys. Rev. E 59, 6766 (1999)] and modifies recently published criticism concerning gamma_{MD}(q) [Tarazona, Checa, and Chacón, Phys. Rev. Lett. 99, 196101 (2007)].

Optical absorption of polarized light in InAs/GaSb quantum wells

Using an eight-band k ⋅ p model Hamiltonian with the Burt–Foreman envelope function theory, we have investigated the optical absorption of both linearly and circularly polarized light, as well as related phenomena in InAs/GaSb broken-gap quantum wells grown along the [0 0 1] direction, with emphasis on the effects of electron–hole hybridization and the various symmetry-breaking mechanisms such as structural inversion asymmetry, bulk inversion asymmetry and interface Hamiltonian. The optical matrix elements exhibit unusual angular dependence in close connection with the spin-flip transitions which are originally forbidden. The spin split of the 2e subband results in two profound absorption peaks for the 1hh–2e transition for both linearly polarized and circularly polarized light. A large lateral optical anisotropy appears in the absorption coefficient of linearly polarized light, which can reach almost 100% with a reducing thickness of the quantum well. For the absorption of circularly polarized light, we found a large enhancement of electron spin polarization in the upper 2e subband, which was generally considered as forbidden if the polarization is along the direction perpendicular to the plane-of-light incidence.

Dimensionally hybrid Green's functions for impurity scattering in the presence of interfaces

A previous calculation of Green's function ( E - H ) - 1 for an interface Hamiltonian which interpolates between two and three dimensions is generalized to include scattering from perturbations both on and off the interface.

Effect of nonrelativistic interface Hamiltonian on optical transitions in broken-gap heterostructures

Using the Burt-Foreman envelope function theory and an eight-band k p model, we have extended our previous work on optical transitions in InAs/GaSb quantum wells grown along the [001] direction by ...

Intrusion of fluids into nanogrooves

We study the shape of gas-liquid interfaces forming inside rectangular nanogrooves (i.e., slit-pores capped on one end). On account of purely repulsive fluid-substrate interactions the confining walls are dry (i.e., wet by vapor) and a liquid-vapor interface intrudes into the nanogrooves to a distance determined by the pressure (i.e., chemical potential). By means of Monte Carlo simulations in the grand-canonical ensemble (GCEMC) we obtain the density rho(z) along the midline (x = 0) of the nanogroove for various geometries (i.e., depths D and widths L) of the nanogroove. We analyze the density profiles with the aid of an analytic expression which we obtain through a transfer-matrix treatment of a one-dimensional effective interface Hamiltonian. Besides geometrical parameters such as D and L , the resulting analytic expression depends on temperature T , densities of coexisting gas and liquid phases in the bulk rho g,l(x) and the interfacial tension gamma. The latter three quantities are determined in independent molecular dynamics simulations of planar gas-liquid interfaces. Our results indicate that the analytic formula provides an excellent representation of rho(z) as long as L is sufficiently small. At larger L the meniscus of the intruding liquid flattens. Under these conditions the transfer-matrix analysis is no longer adequate and the agreement between GCEMC data and the analytic treatment is less satisfactory.

Dimensionally hybrid Green's functions and density of states for interfaces

The energy dependent Green's function ( E - H ) - 1 for an interface Hamiltonian which interpolates between two and three dimensions can be calculated explicitly. This yields an expression for the density of states ϱ ( E ) in the system which interpolates continuously between the two-dimensional ϱ ( E ) = constant behavior for high energies and the three-dimensional ϱ ( E ) ∝ E behavior for low energies. The relation between electron density and Fermi energy in the system also interpolates between the two-dimensional and three-dimensional equations.

Effects of bulk inversion asymmetry and low interface symmetry on the optical properties of broken-gap heterostructures

We have studied the influence of bulk inversion asymmetry (BIA) and the relativistic part of the low-symmetry interface Hamiltonian (IH) on intersubband optical transitions, induced by linearly polarized light, between strongly hybridized electron-hole states in asymmetrical $\mathrm{In}\mathrm{As}∕\mathrm{Ga}\mathrm{Sb}$ broken-gap quantum wells grown along the [001] direction. The self-consistent calculations were performed using the Burt-Foreman envelope function theory and a sophisticated eight-band $\mathbf{k}∙\mathbf{p}$ model Hamiltonian. We found that the BIA and the IH can activate originally forbidden spin-flip optical transitions, and that the strength of the corresponding optical matrix elements depends on the light polarization direction and the quasiparticle in-plane wave vector. Both the BIA and the IH contribute significantly to this effect. When the initial electron-hole states are strongly hybridized, the spin-flip optical transition probability can be of the same order as the probability of the spin-conserved transitions. The BIA results in interface-localized terms in the optical matrix elements due to the material-dependent Kane's $B$ parameter and produces a strong in-plane anisotropy in the absorption of light polarized along the [11] and $[1\overline{1}]$ directions. The IH also contributes to this effect. We found that the primary contribution to the optical anisotropy comes from the BIA-induced mechanism.