A Luttinger Liquid in Box.pdfVIP

a r X i v : c o n d - m a t / 0 3 0 2 6 2 5 v 2 [ c o n d - m a t .s t r - e l ] 1 M a r 2 0 0 3 A Luttinger Liquid in a Box Fabrizio Anfuso1, 2 and Sebastian Eggert1 1Institute of Theoretical Physics, Chalmers University of Technology and Go?teborg University, S-412 96 Go?teborg, Sweden 2Physics Dept., University of Bologna, INFM and INFN, I-40127 Bologna, Italy (Dated: February 2, 2008) We study a Luttinger Liquid in a finite one-dimensional wire with box-like boundary conditions by considering the local distribution of the single particle spectral weight. This corresponds to the experimental probability of extracting a single electron at a given place and energy, which can be interpreted as the square of an electron wave-function. For the non-interacting case, this is given by a standing wave at the Fermi wave-vector. In the presence of interactions, however, the wave-functions obtain additional structure with a sharp depletion near the edges and modulations throughout the wire. In the spinful case, these modulations correspond to the separate spin- and charge-like excitations in the system. PACS numbers: 71.10.Pm, 73.21.Hb,73.63.-b The problem of a particle in a one-dimensional box is a classic example in almost any quantum mechanics text-book since it gives a pedagogical introduction to the concept of energy quantization and provides a complete visualization of the corresponding wave-functions. It is however only recently that this problem has gained true experimental relevance due to the progress in constructing smaller and more refined structures to confine electrons in dots and wires. It is for example now possible to resolve the electron wave functions in a finite piece of carbon nanotube by Scanning Tunneling Microscopy (STM) experiments [1, 2, 3]. Most experimental realizations of one-dimensional electron boxes contain many electrons in a Fermi sea, but it is possible to study a single particle excitation on top of such a ground state configuratio