Spinon Phonon Interaction and Ultrasonic Attenuation in Quantum Spin Liquids

Several experimental candidates for quantum spin liquids have been discovered in the past few years which appear to support gapless fermionic $S = {1\over 2}$ excitations called spinons. The spinons may form a Fermi sea coupled to a $U(1)$ gauge field, and may undergo a pairing instability. We show that despite being charge neutral, the spinons couple to phonons in exactly the same way that electrons do in the long wavelength limit. Therefore we can use sound attenuation to measure the spinon mass and lifetime. Furthermore, transverse ultrasonic attenuation is a direct probe of the onset of pairing because the Meissner effect of the gauge field causes a "rapid fall" of the attenuation at $T_c$ in addition to the reduction due to the opening of the energy gap. This phenomenon, well known in clean superconductors, may reveal the existence of the U(1) gauge field.Comment: 4+epsilon pages of main text + 12 pages of supplementary materia

Application of the z-transform to composite materials

Applications of the z-transform were made earlier to interfacial electron transfer involving semi-infinite solids, e.g., semiconductor/liquid and metal/liquid interfaces and scanning tunneling microscopy. It is shown how the method is readily adapted to treat composite materials, such as solid/solid interfaces or "molecular wire"/solid interfaces