Physica B 359–361 (2005) 1421–1423 X-ray scattering on quantum cross-bars Igor Kuzmenko à Department of Physics, Ben-Gurion University, Beer-Sheva 84105, Israel Abstract X-ray scattering on quantum cross-bars (QCB) leads to creation of QCB plasmon. Such a process corresponds to a sharp peak of frequency dependence of the differential scattering cross-section. The peak frequency strongly depends on the direction of the scattered light. As a result, 1D!2D cross-over can be observed in the scattering spectrum. It manifests itself in special directions as an appearance of doublets instead of a single line. r 2005 Elsevier B.V. All rights reserved. PACS: 73.90.+f; 78.67.n; 77.22.Gm Keywords: Luttinger liquid; Dimensional cross-over; X-ray scattering Double square quantum cross-bars (QCB) is a novel artificial nanoobject which represents actu- ally a double 2D periodic grid with period a formed by two super-imposed crossing arrays of parallel conducting quantum wires or metallic single wall carbon nanotubes [1–3]. From the topological point of view, QCB is an object with intermediate dimensionality. Therefore, its spectral properties are not treated in terms of purely 1D or purely 2D electron liquid theory. QCB with electrostatic interaction in the crosses possesses the Luttinger liquid (LL) properties at low energies and momenta [4], and a rich Bose-type excitation spectrum (plasmon modes) beyond the LL fixed point [5]. The main spectral features are related to various 1D!2D dimensional cross-over effects. These effects can be observed by methods of infrared (IR) spectroscopy [6] which are mostly oriented to probe a characteristic QCB frequency region. Here, we report on another method of X- ray scattering to probe QCB spectrum. This method is mostly oriented to study characteristic values of QCB wave number. The simplest process contributing to the scatter- ing is an annihilation of an incident photon and creation of a scattered photon and QCB plasmon (Fig. 1). Let k (k 0 ) be momentum of the incident (scattered) photon. Then the plasmon momentum is Q ¼ K  K 0 ; where K denotes the projection of photon momentum k onto QCB plane. If the QCB plasmon frequency oðQÞ coincides with photon ARTICLE IN PRESS www.elsevier.com/locate/physb 0921-4526/$ - see front matter r 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2005.01.433 à Tel.: 972 8 647 2419; fax: 972 8 647 2904. E-mail address: igorkuz@bgumail.bgu.ac.il.