Acoustic plasmons in a coupled array of sheets and chains and their role in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$

There is considerable evidence that the electronic behavior of orthorhombic ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$ is dominated by energy bands associated with Cu-O sheets and chains. We discuss the long-wavelength plasmon modes expected in an array of parallel metallic sheets and chains, coupled by the Coulomb interaction and using the random-phase approximation. We show that in the a-b plane, there is a low-energy acoustic plasmon mode, in addition to the usual high-energy bulk plasmon. This new acoustic plasmon does not arise in an array of coupled layers or in an array of parallel chains. Depending as it does on electronic motion in the chains along the b axis, the frequency of the mode is highly anisotropic in the a-b plane.