Ground state of a two-dimensional lattice system with a long-range interparticle repulsion: Stripe formation and effective lowering of dimension

Abstract

It has been shown that effective lowering of dimension underlies ground-state space structure and properties of two-dimensional lattice systems with a long-range interparticle repulsion. On the basis of this fact a rigorous general procedure has been developed to describe the ground state of the systems.PACS number(s): 64.60. Cn,

Low-temperature thermodynamics of two-dimensional electron gas on disordered host lattice

“…Here a 0 is mean host-lattice spacing, l a /c e d 0 1 1 ( ) / mean inter-particle distance, e the average Coulomb energy per particle, d dimension of the system and c e is electron concentration. As was shown in [1], in zero-temperature limit and in the case of c e << 1, the charge carriers forms ordered structure -generalized Wigner crystal (GWC). The ground state (GS) structure of GWC is fully described in terms of one-dimensional (1D) theory developed by Hubbard [2][3][4].…”

“…Besides, even in the case of regular host-lattice the theory developed in [1] is inapplicable for concentration range1 2 1 / c e < < . The proposed method allows us to fill this gap.…”

“…Besides analytical approaches to such system investigations (see, for example [1][2][3][4]9,10]), an interest to the numerical studies has grown rapidly during the last decade. This interest is caused by the fact that the analytical theories are mainly focused on 1D systems and based on very rough simplifying models that leads, as the result, to qualitative estimations only.…”

Wigner-like crystallization of Anderson-localized electron systems with low electron densities

“…In such a case the space structure of the Anderson-localized electron system is in fact the same as that of the self-localized systems discussed in Sec. 1, i.e., it is an incommensurate electron structure [3] (the potential wells are regularly arranged) or plain Wigner crystal [4] (a disordered arrangement of the wells). Hence, for sufficiently small g the AWG is bound to turn into a structure of the self-localized type at some critical n n e c = 2 meeting the condition D~dE C .…”

“…At present much attention is being given to electron/hole lattice systems with so small an overlap integral that tunneling of the charge carriers between the host-lattice sites is supressed by their mutual Coulomb repulsion. Under these conditions a Coulomb self-localization of the electrons/holes inevitably takes place, bringing about their ordering in the following two cases: 1) If the host lattice is regular, an incommensurate electron/hole structure is generally formed for any charge carrier density [2,3]. 2) If the host lattice is disordered, but the mean separation of its sites, a 0 , is much less than that of the electrons/holes r, the ground-state space structure of the lattice gas of the charge carriers, though disordered, is obviously close to the corresponding Wigner crystal lattice (WCL), since the WCL spacing a r W~, while the random charge carriers' displacements from the WCL sites are~a 0 .…”