Walter E Lawrence

Accessibility of quantum effects in mesomechanical systems

We explore the quantum aspects of an elastic bar supported at both ends and subject to compression. If strain rather than stress is held fixed, the system remains stable beyond the buckling instability, supporting two potential minima. The classical equilibrium transverse displacement is analogous to a Ginsburg-Landau order parameter, with strain playing the role of temperature. We calculate the quantum fluctuations about the classical value as a function of strain. Excitation energies and quantum fluctuation amplitudes are compared for silicon beams and carbon nanotubes.

Static buckling and actuation of free-standing mesoscale beams

We discuss the static buckling and actuation of free-standing mesoscopic beams. As the length-to-width aspect ratio of the beams is increased, the buckled shapes become more complex. Mechanical actuation confirms that the complex shapes are stable equilibria and that metastable equilibria also exist. This is consistent with a nonlinear elastic continuum model, which incorporates asymmetry in higher order buckling modes. Preliminary results indicate that, in addition to purely mechanical actuation, electromechanical mode-mode transitions can be induced by utilizing fabricated electrodes.

Crossover between quantum and thermal regimes of free-standing nanostructures

Mesomechanical systems offer the possibility to observe and control certain quantum effects. Here we develop a phonon description of transverse motion of a mesoscopic beam with fixed endpoints. We obtain expressions for the fundamental frequencies and quantum fluctuation amplitudes of these structures when subjected to longitudinal compression. We show how the frequencies and fluctuation amplitudes scale with physical dimensions and give estimates for the crossover temperatures which characterize the transition between quantum and thermal regimes.

Phonon description and the Euler buckling instability of a mesoscopic bar at fixed strain

Abstract The quantum theory of a mesoscopic beam subjected to fixed compressional strain is discussed from the perspective of phonons and other excitations that emerge from the buckling instability. It is argued that despite the anharmonicity inherent in this instability, elementary excitations maintain their integrity because (i) modes higher than the fundamental remain harmonic through the instability, and (ii) the quantum vibrational frequency of the fundamental, ( E 1 − E 0 )/ℏ, does not vanish. It is determined by a Landau-like effective potential which is quartic at critical strain. Beyond the buckling instability, phonons recover their harmonic character while a distinct form of excitation evolves associated with the broken symmetry. For a beam of rectangular cross-section these are tunneling modes; for a tube of circular cross-section they are rotational.

Compressional mode softening and Euler buckling patterns in mesoscopic beams

We describe a sequence of Euler buckling instabilities associated with the transverse modes of a mesoscopic beam subjected to compressional strain. As the strain is increased, successively higher normal mode frequencies are driven to zero; each zero signals an instability in the corresponding normal mode that can be realized if all lower instabilities are suppressed by constraints. When expressed in terms of the critical buckling modes, the potential energy functional takes the form of a multimode Ginzburg–Landau system that describes static equilibria in the presence of symmetry breaking forces. This model is used to analyse the complex equilibrium shapes that have been observed experimentally in strained mesoscopic beams. Theoretically predicted critical strain values agree with the appearances of higher order mode structures as the length-to-width aspect ratio increases. The theory also predicts upper bounds on the individual mode amplitudes that are consistent with the data. Based on insights from the theory, we suggest possible origins of the buckling patterns.

Novel buckled shapes of free-standing mesoscopic beams

We discuss the observation of novel buckled shapes of free-standing mesoscopic beams fabricated using conventional electron-beam lithography and plasma etching. As the length-to-width aspect ratio of the beams is increased the buckled shapes become more complex. Based on analysis of beams in the low aspect ratio regime using a nonlinear elastic continuum model, we obtain an upper bound on the magnitude of the fundamental mode asymmetry and relate this to higher-order asymmetry. We also observe an electromechanical mode-mode transition using capacitively coupled gates.

Phonon mediated electron-electron scattering in aluminium: A first detailed calculation

Abstract A microscopic calculation of the phonon mediated electron-electron scattering rate (SR) has been performed with realistic Fermi surface and phonon spectrum for the first time. This confirms the results of earlier approximate calculations 1,2 that the contributions from exchange of virtual phonons dominates the usual Coulomb interaction. The dense mesh of our calculation reveals a surprisingly strong (20 to 1) anisotropy for the T 2 coefficient of the electron-electron SR. We also obtain a more complete picture of the temperature dependent electron-phonon SR.