Fermions between one and two dimensions

When fermions are confined to move only in one dimension, as in a chain, th en they form a Luttinger Liquid which differs fundamentally from the Landau Fermi Liquid that occurs in higher dimensions. If chains are combined to f orm ladders, one finds surprisingly that the properties of fermionic ladder s depend essentially on their width. Ladder can be divided in two classes, those with odd and even numbers of legs. To date this behavior has been obs erved only in certain cuprate materials and the ideal of lightly doped and perfectly formed ladders has not been realized. The synthesis of materials with ladder structures should lead to interesting new physics.