Acoustic phonon modes of rectangular quantum wires

Nishiguchi, Norihiko; Ando, Yoshihiro; Wybourne, M. N.

doi:10.1088/0953-8984/9/27/007

Cited by 117 publications

(121 citation statements)

References 21 publications

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“…Above about these temperatures additional optical modes of vibration with higher cutoff frequencies 15 would be excited and contribute to the heat conduction in the wire ͑we have not added the contribution of these modes͒. Hence, this plateau will be seen only when the higher optical phonon branches are well separated from the shear mode frequency S,min .…”

Section: Thermal Conductancementioning

confidence: 99%

Lattice thermal conductance in nanowires at low temperatures: Breakdown and recovery of quantization

2005

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The quantization of lattice thermal conductance g normalized by g 0 = 2 k B 2 T /3h ͑the universal quantum of thermal conductance͒ was recently predicted theoretically to take an integer value over a finite range of temperature and then observed experimentally in nanowires with catenoidal contacts. The prediction of this quantization by Rego and Kirczenow ͓Phys. Rev. Lett. 81, 232 ͑1998͔͒ relies on a study of only dilatational ͑longitudinal͒ vibrational mode in the wires. We study the thermal conductance in catenoidal wires by explicitly calculating the transmission rates of the six distinct vibrational modes ͑four acoustic and two low-lying optical modes͒ and applying the Landauer formula for the one-dimensional thermal transport in the ballistic regime. In a temperature range similar to the one predicted by Rego and Kirczenow, we find the presence of a plateau in g / g 0 . However, below this temperature range g / g 0 is modified-that is, the quantization is brokendue to imperfect transmission of the acoustic modes of vibration. Our new observation is that, as temperature goes down further, the recovery of the quantization of g / g 0 should occur. These results are found assuming GaAs as a wire material, but we also make similar calculations for silicon nitride wires used experimentally.

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Section: Thermal Conductancementioning

confidence: 99%

Lattice thermal conductance in nanowires at low temperatures: Breakdown and recovery of quantization

2005

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“…Phonons then are no longer a mere source of dissipation but become experimentally controllable with the possibility, e.g., to create phonon confinement 18,34,35,36 or the analogon of quantum optical phenomena such as coherent and squeezed phonon states. 37,38,39,40 The paper is organized as follows: in section II, we introduce the model and derive a master equation for the density operator.…”

Section: Introductionmentioning

confidence: 99%

Steering of a bosonic mode with a double quantum dot

Brandes

Lambert

2003

Phys. Rev. B

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We investigate the transport and coherence properties of a double quantum dot coupled to a single damped boson mode. Our numerically results reveal how the properties of the boson distribution can be steered by altering parameters of the electronic system such as the energy difference between the dots. Quadrature amplitude variances and the Wigner function are employed to illustrate how the state of the boson mode can be controlled by a stationary electron current through the dots.

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“…To compare with experiment we first subtract the measured conductance from the ideal conductance predicted using the cutoff frequencies calculated numerically by using the xyz approach [14] and d 60 nm and W 160 nm: this gives us an estimate of the effect of scattering which we can compare with our calculated scattering. The data processed in this way (Fig.…”

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confidence: 99%

Effect of Phonon Scattering by Surface Roughness on the Universal Thermal Conductance

2001

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The effect of phonon scattering by surface roughness on the thermal conductance in mesoscopic systems at low temperatures is calculated using full elasticity theory. The low frequency behavior of the scattering shows novel power law dependences arising from the unusual properties of the elastic modes. This leads to new predictions for the low temperature depression of the thermal conductance below the ideal universal value. Comparison with the data of Schwab et al. [Nature (London) 404, 974 (2000)] suggests that surface roughness on a scale of the width of the thermal pathway is important in the experiment. DOI: 10.1103/PhysRevLett.87.115502 PACS numbers: 63.22. +m, 63.50. +x, 68.65. -k Thermal transport in mesoscopic systems at low temperatures shows universal properties analogous to the quantized electrical conductance [1]. Theoretical analyses of phonon transport when the thermal wavelength becomes comparable to the dimensions of the thermal pathway predict a thermal conductance K that is independent of many of the details of the geometry and material properties [2], and a universal value for K͞T N 0 p 2 k 2 B ͞3h at low enough temperatures [3,4]. (Here N 0 is the number of modes with zero frequency at long wavelengths, equal to 4 for a single, free-standing elastic beam.) These predictions have since been connected to more general results on bounds on entropy transport at low temperatures [5] and to thermal transport by particles of arbitrary statistics [6]. The recent confirmation of the universal thermal conductance in tiny silicon nitride devices [7] is an experimental tour de force. Although verifying the predictions of a universal value of K͞T at low enough temperatures, the experiments showed values of K͞T that decrease as the temperature increases in the range of 0.08 to 0.2 K, before beginning to rise at higher temperatures as more vibrational modes that can carry the heat are excited.We [8] and others [9,10] have previously studied a simplified treatment of this problem using a scalar model for the elastic waves. However, elastic waves in confined geometries have many unusual features, such as modes with a quadratic dispersion relation v~k 2 at small wave numbers k and regions of anomalous dispersion dv͞dk , 0, that are not captured in this simple model and might be expected to have a strong influence on the low temperature transport.In this Letter we study the general problem of the scattering of phonons by rough surfaces for a rectangular cross-section elastic beam using three-dimensional elasticity theory. The scattering of the low frequency modes that contribute to the conductance at low temperatures depends on the detailed properties of the elastic modes, and we find novel power law dependences for the frequency dependence of the scattering off unstructured roughness that are not those anticipated by simple analogy with Rayleigh scattering. In turn this low frequency behavior yields a depression of K͞T at low temperatures with unexpected power laws, with a faster decrease of K͞T as the temp...

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Acoustic phonon modes of rectangular quantum wires

Cited by 117 publications

References 21 publications

Lattice thermal conductance in nanowires at low temperatures: Breakdown and recovery of quantization

Lattice thermal conductance in nanowires at low temperatures: Breakdown and recovery of quantization

Steering of a bosonic mode with a double quantum dot

Effect of Phonon Scattering by Surface Roughness on the Universal Thermal Conductance

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