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We propose a tunable acoustic filter using superlattices constructed by random stacking of solid and fluid layers. Acoustic waves are localized in the random superlattices (RSLs) and the transmission rates substantially decay to 0 except for the resonance transmissions where the acoustic waves are delocalized. The transmission rates become unity for the resonance transmissions. The resonance frequencies depend on the layer thicknesses, and we can modulate the transmission spectra from transparent to opaque, and vice versa, modifying the layer thicknesses. We numerically illustrate the changes in the transport properties for the aluminum/water RSLs, and suggest to exploit the RSLs for the tunable acoustic filters.

We propose a tunable acoustic filter using superlattices constructed by random stacking of solid and fluid layers. Acoustic waves are localized in the random superlattices (RSLs) and the transmission rates substantially decay to 0 except for the resonance transmissions where the acoustic waves are delocalized. The transmission rates become unity for the resonance transmissions. The resonance frequencies depend on the layer thicknesses, and we can modulate the transmission spectra from transparent to opaque, and vice versa, modifying the layer thicknesses. We numerically illustrate the changes in the transport properties for the aluminum/water RSLs, and suggest to exploit the RSLs for the tunable acoustic filters.

Numerically investigating mode-conversion effects of phonons on Anderson localization in random superlattices, we make it clear the changes in localization properties when the LA and TA phonons which independently show Anderson localization for the normal incidence interact as the incident angles increase. The mode conversions which occur for oblique propagation at small incident angles induce collaboration among the phonons, giving rise to extension of the localization length or delocalization, depending on the system size. On the other hand, at large incident angles, the transmission decay becomes larger than for the normal incidence. In contrast to the small incident angles, the transmission decay and transmission fluctuations become independent of the incident phonon modes and show the frequency dependences that are not predictable from those at the small incident angles, evidencing that the coupled modes of phonons are formed by the mode conversions.

Numerically investigating mode-conversion effects of phonons on Anderson localization in random superlattices, we make it clear the changes in localization properties when the LA and TA phonons which independently show Anderson localization for the normal incidence interact as the incident angles increase. The mode conversions which occur for oblique propagation at small incident angles induce collaboration among the phonons, giving rise to extension of the localization length or delocalization, depending on the system size. On the other hand, at large incident angles, the transmission decay becomes larger than for the normal incidence. In contrast to the small incident angles, the transmission decay and transmission fluctuations become independent of the incident phonon modes and show the frequency dependences that are not predictable from those at the small incident angles, evidencing that the coupled modes of phonons are formed by the mode conversions.

It is well known that phonon modes become sensitive to the geometry of an object when the phonon wavelengths are comparable to the objects physical length scale. In contrast, the sensitivity of phonon modes toward topology is much less explored and understood. In this paper we discuss the effects of topology on phonon modes using a finite thickness Möbius band of centerline radius a as the model system. The phonon modes are derived using the xyz algorithm based on Riemannian geometry. From the boundary conditions and paritywe identify two sets ofmodeswithwave numbers q = n 2a described by odd and even integers n. Modes characterized by odd integers have flexural vibrations whereas those characterized by even integers exhibit dilatational and shear/torsional motion. While the phonon dispersion at large wave numbers agrees with that of structures having simple topology (rings and wires), at low frequencies and wave numbers the Möbius topology introduces significant differences. Uniquely, we find three of the four phonon branches do not go to zero frequency with decreasing wave number, but converge on a finite frequency.Weidentify a new form of vibrational pattern resembling incomplete breathing modes and discuss the ramifications of the modified spectrum, including a local increase in the density of states and the existence of a phonon band gap.

It is well known that phonon modes become sensitive to the geometry of an object when the phonon wavelengths are comparable to the objects physical length scale. In contrast, the sensitivity of phonon modes toward topology is much less explored and understood. In this paper we discuss the effects of topology on phonon modes using a finite thickness Möbius band of centerline radius a as the model system. The phonon modes are derived using the xyz algorithm based on Riemannian geometry. From the boundary conditions and paritywe identify two sets ofmodeswithwave numbers q = n 2a described by odd and even integers n. Modes characterized by odd integers have flexural vibrations whereas those characterized by even integers exhibit dilatational and shear/torsional motion. While the phonon dispersion at large wave numbers agrees with that of structures having simple topology (rings and wires), at low frequencies and wave numbers the Möbius topology introduces significant differences. Uniquely, we find three of the four phonon branches do not go to zero frequency with decreasing wave number, but converge on a finite frequency.Weidentify a new form of vibrational pattern resembling incomplete breathing modes and discuss the ramifications of the modified spectrum, including a local increase in the density of states and the existence of a phonon band gap.

We propose a rectifier of elastic waves in a thin plate, which is made of an elastically isotropic material containing a periodic array of triangular holes as scatterers, and demonstrate numerically that it works both for the symmetric and anti-symmetric Lamb waves as well as shear horizontal waves. The rectification is caused by the geometric effects on wave scattering due to the asymmetric scatterers, while the interplay between the mode conversion and interference effects among the scattered waves owing to the periodic arrangement of scatterers complicates it. The mechanism makes it possible to rectify the typical elastic waves in the system above the threshold frequency corresponding to the wavelength equivalent to the periodicity of scatterers.

We propose a rectifier of elastic waves in a thin plate, which is made of an elastically isotropic material containing a periodic array of triangular holes as scatterers, and demonstrate numerically that it works both for the symmetric and anti-symmetric Lamb waves as well as shear horizontal waves. The rectification is caused by the geometric effects on wave scattering due to the asymmetric scatterers, while the interplay between the mode conversion and interference effects among the scattered waves owing to the periodic arrangement of scatterers complicates it. The mechanism makes it possible to rectify the typical elastic waves in the system above the threshold frequency corresponding to the wavelength equivalent to the periodicity of scatterers.

We investigate the effects on the transport characteristics of a single electron transistor caused by dynamic deformations of the device configuration due to phonons. We formulate the electron-phonon interaction that originates from changes in capacitances and tunnel resistances caused by the breathing and oblong vibrations of the island that forms part of the transistor. We derive transport properties by means of the master equation. For a single electron transistor with a gold nanoparticle island with a radius of 1 nm, we demonstrate the contribution to the transport properties that originates from tunneling channels associated with THz phonon emission and absorption.

We investigate the effects on the transport characteristics of a single electron transistor caused by dynamic deformations of the device configuration due to phonons. We formulate the electron-phonon interaction that originates from changes in capacitances and tunnel resistances caused by the breathing and oblong vibrations of the island that forms part of the transistor. We derive transport properties by means of the master equation. For a single electron transistor with a gold nanoparticle island with a radius of 1 nm, we demonstrate the contribution to the transport properties that originates from tunneling channels associated with THz phonon emission and absorption.

We investigate theoretically the transport characteristics of a single electron transistor affected by the dynamic deformation of the device configuration due to phonons. By considering changes in capacitances and tunnel resistances caused by the breathing and oblong vibrations of the island that forms part of the transistor, we formulate the electron-phonon interaction peculiar to the device and derive its transport properties by means of the master equation. For a single electron transistor with a gold nano particle island of radius 1 nm, we demonstrate the contribution to the transport properties that originates from tunneling channels associated with THz phonon emission and absorption.

We investigate theoretically the transport characteristics of a single electron transistor affected by the dynamic deformation of the device configuration due to phonons. By considering changes in capacitances and tunnel resistances caused by the breathing and oblong vibrations of the island that forms part of the transistor, we formulate the electron-phonon interaction peculiar to the device and derive its transport properties by means of the master equation. For a single electron transistor with a gold nano particle island of radius 1 nm, we demonstrate the contribution to the transport properties that originates from tunneling channels associated with THz phonon emission and absorption.

We study theoretically acoustic phonon modes in nanowire superlattices (NWSLs) composed of cubic materials. We classify the acoustic phonon modes in rectangular and square cross-section NWSLs, based on group theory. For NWSLs consisting of GaAs and AlAs, we calculate numerically the dispersion relations of each phonon mode and corresponding displacement fields. We examine the effects of both the lateral confinement and superlattice modulation along the wire axis. The results suggest that peculiar electron–phonon interactions occur because the vibrations of both the lateral and longitudinal confining potentials induce scattering potential in addition to the deformation and piezoelectric potentials.

We study theoretically acoustic phonon modes in nanowire superlattices (NWSLs) composed of cubic materials. We classify the acoustic phonon modes in rectangular and square cross-section NWSLs, based on group theory. For NWSLs consisting of GaAs and AlAs, we calculate numerically the dispersion relations of each phonon mode and corresponding displacement fields. We examine the effects of both the lateral confinement and superlattice modulation along the wire axis. The results suggest that peculiar electron–phonon interactions occur because the vibrations of both the lateral and longitudinal confining potentials induce scattering potential in addition to the deformation and piezoelectric potentials.

We theoretically investigate shuttle instability induced by an ac gate in a nanoelectromechanical single-electron transistor containing a moveable grain. The ac gate causes periodic variations of charge on the grain, which turn (in the bias field) to driving force of grain vibrations. The forced grain vibrations and related electron transport show drastic and hysteretic changes for variations of the bias or the gate frequency due to transitions in transport mechanisms between tunneling and shuttling.

We theoretically investigate shuttle instability induced by an ac gate in a nanoelectromechanical single-electron transistor containing a moveable grain. The ac gate causes periodic variations of charge on the grain, which turn (in the bias field) to driving force of grain vibrations. The forced grain vibrations and related electron transport show drastic and hysteretic changes for variations of the bias or the gate frequency due to transitions in transport mechanisms between tunneling and shuttling.

We propose a system for rectification of acoustic waves. The system consists of an array of triangular holes drilled in an elastically isotropic material. Assuming the propagation of transverse acoustic waves with polarization parallel to the holes, we confirm numerically that the rectification of acoustic waves occurs even in the frequency region with corresponding wavelength comparable to the dimensions of the scatterers. The rectification effects appear above a threshold frequency due to the Bragg diffraction owing to the periodic structures. The threshold frequency depends on the structural parameters, which enables the realization of a tunable rectifier.

We propose a system for rectification of acoustic waves. The system consists of an array of triangular holes drilled in an elastically isotropic material. Assuming the propagation of transverse acoustic waves with polarization parallel to the holes, we confirm numerically that the rectification of acoustic waves occurs even in the frequency region with corresponding wavelength comparable to the dimensions of the scatterers. The rectification effects appear above a threshold frequency due to the Bragg diffraction owing to the periodic structures. The threshold frequency depends on the structural parameters, which enables the realization of a tunable rectifier.

RAPID COMMUNICATIONS, A blockade phenomenon for electron transport in a freely suspended single-electron transistor (SET) is predicted. Voltages applied for its operation induce electromechanical forces acting on the SET, giving rise to structural deformation and collapse over a critical voltage. The electric characteristics become sensitive to charge fluctuations on the SET at the onset of the structural instability, leading to changes in the electrical characteristics that hinder electron transport through the SET around the zero-bias-voltage region.

A blockade phenomenon for electron transport in a freely suspended single-electron transistor (SET) is predicted. Voltages applied for its operation induce electromechanical forces acting on the SET, giving rise to structural deformation and collapse over a critical voltage. The electric characteristics become sensitive to charge fluctuations on the SET at the onset of the structural instability, leading to changes in the electrical characteristics that hinder electron transport through the SET around the zero-bias-voltage region., RAPID COMMUNICATIONS

Random telegraph noise in the electric current produced by shot noise is predicted for an array of movable colloid particles by Monte Carlo and molecular dynamics calculations. The electron transport is attributed to the shuttle mechanism where moving colloid particles carry charges. The colloid-particle motion induced by the source-drain voltage shows periodic and/or quasiperiodic vibrations, and the current value depends on the vibration modes. Shot noise that is uncorrelated with the colloid-particle motion causes transitions between the periodic and quasiperiodic vibration modes, resulting in random switching between the current levels corresponding to the vibration modes.

Random telegraph noise in the electric current produced by shot noise is predicted for an array of movable colloid particles by Monte Carlo and molecular dynamics calculations. The electron transport is attributed to the shuttle mechanism where moving colloid particles carry charges. The colloid-particle motion induced by the source-drain voltage shows periodic and/or quasiperiodic vibrations, and the current value depends on the vibration modes. Shot noise that is uncorrelated with the colloid-particle motion causes transitions between the periodic and quasiperiodic vibration modes, resulting in random switching between the current levels corresponding to the vibration modes.

The gate voltage dependence of a single-electron transistor using the shuttle mechanism in which a vibrating conductive nanoparticle carries charges between the electrodes is studied theoretically and with numerical simulations. Two types of gate voltage effect on the transport properties are demonstrated: one is direct modulation of the current via modification in the tunneling rate, giving rise to shift of ] I/]V peaks on the step-like current, splitting of the current steps and periodic behavior of the current with the change in gate voltage. Another is an indirect effect due to a shift in the range of the nanoparticle vibration induced by the gate voltage. The latter effect stops the shuttle mechanism at a large gate voltage, leading to the conduction gap which widens in proportion to the gate voltage.

The gate voltage dependence of a single-electron transistor using the shuttle mechanism in which a vibrating conductive nanoparticle carries charges between the electrodes is studied theoretically and with numerical simulations. Two types of gate voltage effect on the transport properties are demonstrated: one is direct modulation of the current via modification in the tunneling rate, giving rise to shift of ] I/]V peaks on the step-like current, splitting of the current steps and periodic behavior of the current with the change in gate voltage. Another is an indirect effect due to a shift in the range of the nanoparticle vibration induced by the gate voltage. The latter effect stops the shuttle mechanism at a large gate voltage, leading to the conduction gap which widens in proportion to the gate voltage.

Electron scattering due to confined and extended acoustic phonons is analytically investigated for a quasi-one-dimensional GaAs quantum wire embedded within bulk AlAs. It is found that the deformation coupling between electrons and confined phonons is extremely small in comparison with that between electrons and extended phonons. Consequently, the electron scattering processes are governed by the extended phonons, and the magnitude and electron energy dependence of the scattering rates are almost the same as those due to the usual three-dimensional bulk phonons.

Electron scattering due to confined and extended acoustic phonons is analytically investigated for a quasi-one-dimensional GaAs quantum wire embedded within bulk AlAs. It is found that the deformation coupling between electrons and confined phonons is extremely small in comparison with that between electrons and extended phonons. Consequently, the electron scattering processes are governed by the extended phonons, and the magnitude and electron energy dependence of the scattering rates are almost the same as those due to the usual three-dimensional bulk phonons.

We study the extended acoustic-phonon modes in a cylindrical GaAs quantum wire embedded in bulk AlAs. There are two kinds of resonant acoustic-phonon modes related to the wire dimensions: one is entirely extended in the system and the other is almost confined in the wire. Displacement of extended phonon modes in the wire region is enhanced for the resonant modes. The dispersion relations of these resonant modes have subband structures similar to those of confined phonon modes in free-standing wires. Owing to the resonant modes, the extended phonon modes, in the wire region, have characters of confined phonon modes in a free-standing wire rather than the usual bulk phonon modes.

We study the extended acoustic-phonon modes in a cylindrical GaAs quantum wire embedded in bulk AlAs. There are two kinds of resonant acoustic-phonon modes related to the wire dimensions: one is entirely extended in the system and the other is almost confined in the wire. Displacement of extended phonon modes in the wire region is enhanced for the resonant modes. The dispersion relations of these resonant modes have subband structures similar to those of confined phonon modes in free-standing wires. Owing to the resonant modes, the extended phonon modes, in the wire region, have characters of confined phonon modes in a free-standing wire rather than the usual bulk phonon modes.

Confined and interface acoustic phonon modes in a cylindrical quantum wire embedded in another material are analytically investigated based on the elastic continuum model by means of the potential theory. Confined acoustic phonon modes are coupled modes of bulk-longitudinal and transverse acoustic waves, classified into torsional, dilatational, and flexural modes due to the rotational symmetry of the modes. Dispersions of the confined modes have subband structures with finite cutoff frequencies owing to quantization of wave vectors in the lateral direction. The density of confined phonon states becomes, as a result, a staircaselike structure. As for the interface modes, regions of material parameters for the possible existence of interface modes are investigated. We found that the existence of interface modes in a quantum wire–surrounding system becomes more sensitive to the combinations of materials than that for a plane interface.

Confined and interface acoustic phonon modes in a cylindrical quantum wire embedded in another material are analytically investigated based on the elastic continuum model by means of the potential theory. Confined acoustic phonon modes are coupled modes of bulk-longitudinal and transverse acoustic waves, classified into torsional, dilatational, and flexural modes due to the rotational symmetry of the modes. Dispersions of the confined modes have subband structures with finite cutoff frequencies owing to quantization of wave vectors in the lateral direction. The density of confined phonon states becomes, as a result, a staircaselike structure. As for the interface modes, regions of material parameters for the possible existence of interface modes are investigated. We found that the existence of interface modes in a quantum wire–surrounding system becomes more sensitive to the combinations of materials than that for a plane interface.

We study both analytically and numerically phonon transmission fluctuations and localization in partially ordered superlattices with correlations among neighboring layers. In order to generate a sequence of layers with a varying degree of order we employ a model proposed by Hendricks and Teller as well as partially ordered versions of deterministic aperiodic superlattices. By changing a parameter measuring the correlation among adjacent layers, the Hendricks-Teller superlattice exhibits a transition from periodic ordering, with alternating layers, to the phase-separated opposite limit, including many intermediate arrangements and the completely random case. In the partially ordered versions of deterministic superlattices, there is short-range order (among any N consecutive layers) and long-range disorder, as in the N-state Markov chains. The average and fluctuations in the transmission, the backscattering rate, and the localization length in these multilayered systems are calculated based on the superlattice structure factors we derive analytically. The standard deviation of the transmission versus the average transmission lies on a universal curve irrespective of the specific type of disorder of the superlattice. We illustrate these general results by applying them to several GaAs-AlAs superlattices for the proposed experimental observation of phonon universal-transmission fluctuations.

We analytically study phonon transmission and localization in random superlattices by using a Green’s-function approach. We derive expressions for the average transmission rate and localization length, or Lyapunov exponent, in terms of the superlattice-structure factor. This is done by considering the backscattering of phonons, due to the complex mass-density fluctuations, which incorporates all of the forward-scattering processes. These analytical results are applied to two types of random superlattices and compared with numerical simulations based on the transfer-matrix method. Our analytical results show excellent agreement with the numerical data. A universal relation for the transmission fluctuations versus the average transmission is derived explicitly, and independently confirmed by numerical simulations. The transient of the distribution of transmission to the log-normal distribution for the localized phonons is also studied.

We analytically study phonon transmission and localization in random superlattices by using a Green’s-function approach. We derive expressions for the average transmission rate and localization length, or Lyapunov exponent, in terms of the superlattice-structure factor. This is done by considering the backscattering of phonons, due to the complex mass-density fluctuations, which incorporates all of the forward-scattering processes. These analytical results are applied to two types of random superlattices and compared with numerical simulations based on the transfer-matrix method. Our analytical results show excellent agreement with the numerical data. A universal relation for the transmission fluctuations versus the average transmission is derived explicitly, and independently confirmed by numerical simulations. The transient of the distribution of transmission to the log-normal distribution for the localized phonons is also studied.

We study both analytically and numerically phonon transmission fluctuations and localization in partially ordered superlattices with correlations among neighboring layers. In order to generate a sequence of layers with a varying degree of order we employ a model proposed by Hendricks and Teller as well as partially ordered versions of deterministic aperiodic superlattices. By changing a parameter measuring the correlation among adjacent layers, the Hendricks-Teller superlattice exhibits a transition from periodic ordering, with alternating layers, to the phase-separated opposite limit, including many intermediate arrangements and the completely random case. In the partially ordered versions of deterministic superlattices, there is short-range order (among any N consecutive layers) and long-range disorder, as in the N-state Markov chains. The average and fluctuations in the transmission, the backscattering rate, and the localization length in these multilayered systems are calculated based on the superlattice structure factors we derive analytically. The standard deviation of the transmission versus the average transmission lies on a universal curve irrespective of the specific type of disorder of the superlattice. We illustrate these general results by applying them to several GaAs-AlAs superlattices for the proposed experimental observation of phonon universal-transmission fluctuations.

Lattice vibrations on two-dimensional Penrose lattices are investigated numerically. The resultant spectra exhibit several peaks similar to those of disordered systems. From the dependence of the vibrational phase difference and the distribution of the local elastic energy on the different boundary conditions, it is found that the lattice vibrations of this system seem to be isotropic and localized above a certain critical frequency. The spectral peaks are attributed to van Hove singularities and localization.

The previous theory on the thermal boundary resistance between small particles and liquid He II Phys. Rev. B 24 6421 (1981) is extended to the case for normal liquid 3He in terms of Landau Fermi-liquid theory. It is shown that the toroidal-mode phonons in small particles contribute to the heat flow through the excitation of transverse zero sound in contrast to the case of liquid He II. The calculated resistances exhibit a T-3 behavior above some temperature which depends on the size and elastic property of the small particle. In this temperature regime, the calculated results for silver and copper particles agree well with the observed resistances in both magnitude and temperature dependence. At lower temperatures the theory predicts exponentially increasing resistances with decreasing temperature as in the case for liquid He II. The relative contributions to the heat flow due to longitudinal and transverse zero sound are obtained as a function of temperature.

The previous theory on the thermal boundary resistance between small particles and liquid He II Phys. Rev. B 24 6421 (1981) is extended to the case for normal liquid 3He in terms of Landau Fermi-liquid theory. It is shown that the toroidal-mode phonons in small particles contribute to the heat flow through the excitation of transverse zero sound in contrast to the case of liquid He II. The calculated resistances exhibit a T-3 behavior above some temperature which depends on the size and elastic property of the small particle. In this temperature regime, the calculated results for silver and copper particles agree well with the observed resistances in both magnitude and temperature dependence. At lower temperatures the theory predicts exponentially increasing resistances with decreasing temperature as in the case for liquid He II. The relative contributions to the heat flow due to longitudinal and transverse zero sound are obtained as a function of temperature.

Lattice vibrations on two-dimensional Penrose lattices are investigated numerically. The resultant spectra exhibit several peaks similar to those of disordered systems. From the dependence of the vibrational phase difference and the distribution of the local elastic energy on the different boundary conditions, it is found that the lattice vibrations of this system seem to be isotropic and localized above a certain critical frequency. The spectral peaks are attributed to van Hove singularities and localization.