1 M ay 2 00 1 New non - Fermi liquid type behavior given by a two band system in normal phase

We are reporting a new non-Fermi liquid type normal phase that has a well defined Fermi energy, but without showing any non-regularity in the momentum distribution function nk in the whole momentum space, the sharp Fermi momentum concept being undefinable. The system contains a natural built in gap that is visible in the physical properties of the system at nonzero temperatures. The presence of a flat band in multi-band interacting Fermi systems with more than half filling is the key feature leading to such a ground state, which is not restricted to one spatial dimension and emerges in the proximity of an insulating phase. PACS No. 05.30.Fk, 67.40.Db, 71.10.-w, 71.10.Hf, 71.10.Pm Typeset using REVTEX 1 Our understanding of the behavior of interacting fermionic many-body systems is intimately connected to the concept of Fermi-liquid introduced by Landau many decades ago [1]. In a normal state that preserves all symmetry properties of the high temperature phase of a fermionic system, the Fermi liquid behavior has been clearly observed in the normal state of He3 and simple metals [2]. It has the meaning that in spite of the inter-particle interactions, the low energy behavior of the system can be well described within a picture of weakly interacting quasi-particles [3]. This picture can be also mathematically formulated [4]. In these terms, in a normal Fermi liquid: a) There is a one-to-one correspondence between the non-interacting one particle states and interacting single-particle states. This is concretely obtained by describing the interacting system using a perturbation theory that is convergent up to infinite order. b) The single particle Green-functions have a quasiparticle pole that gives rise to a discontinuity of the momentum distribution function nk at the Fermi surface whose position is specified by a sharp Fermi momentum value ~kF . c) The residual quasi-particle interactions can be described by a small number of parameters, called Landau parameters, which can be deduced from a microscopic theory taking into account non-divergent two-particle vertex functions [5]. In the last decade however nonFermi liquid behavior has been observed experimentally in the normal phase of a variety of materials, including higher than one dimensional systems of large interest. Examples are: high temperature superconductors [6], heavy-fermions [7], layered systems [8], quasi-one dimensional conductors, doped semiconductors, systems with impurities, materials presenting proximity to metal-insulator transition [3], etc. These results are often discussed in terms of multi-band models [9], the presence of a some kind of gap in the normal phase being clearly established in many cases and subject of intensive studies [9,10]. The last decade witnessed a huge intellectual effort [11] for the understanding of the non-Fermi liquid behavior in the normal phase [12] of fermionic systems. On the theoretical side however, for pure systems, the existence of a non-Fermi liquid in a normal phase has been exactly proved only for the one dimensional case (i.e. Luttinger liquid [13]). So far, the possibility of extending the proof to two spatial dimensions has not been demonstrated rigorously. In fact, a rigorous 2 theory of a non-Fermi liquid normal state in higher than one spatial dimensions is missing. For this reason, the theoretical understanding of different phenomena observed in the materials listed above is relatively poor and theoretical advance in this subject is badly needed. Our work on the periodic Anderson model (PAM) at nonzero and finite on-site Coulomb repulsion (U) (a prototype of two-band systems containing strong correlation effects) was motivated by this state of affairs. We are presenting in this Letter for the first time, an exact solution for this model. The solution present in a restricted (but continuous and infinite domain of the phase diagram) represents a new type of non-Fermi liquid behavior in a normal phase for a system that has a built in gap. The obtained ground state energy cannot be expressed as a sum of contributions of the on-site Hamiltonian terms, and the ground state expectation value of the kinetic energy terms is nonzero and negative [14]. The state emerges in the vicinity of a Mott insulating phase in a continuous domain of concentration above 3/4 filling and has a well defined Fermi energy, but the Fermi momentum cannot be defined, nk being without any non-regularity in momentum space. The property is due to the emergence of a flat band in a multi-band system with more than half filling and can be extended in an exact manner to two spatial dimensions [15]. Such features have been observed experimentally, e.g., in ARPES data, which, even for high-Tc materials often reflect main bands without any sharp characteristics in nk [16] or necessitate the assumption of the presence of flat bands [17]. Band structure calculations for layered systems often show a Fermi level positioned exactly at the bottom of a conduction band with a relatively large effective mass around its minimum, below which a gap is present [8]. Connections between the emergence of superconductivity and flat dispersions were also clearly pointed out in Ref. [18]. Flat-band features are present in heavy-fermion systems as well [19], and can be even produced by squashing carbon nanotubes [20]. We consider two bands denoted by b = c, f , the starting 1D Hamiltonian being Ĥ = Ĥ0+Û . The Hubbard term is Û = U ∑ i n̂ f i,↑n̂ f i,↓ and we have Ĥ0 = T̂c+T̂f+Êf+Ĥh with the kinetic energies T̂b = tb ∑