Ordering Phenomena in Solids

Introduction

 

Charge Order

Chargeorder01

Charge order can be understood as self-organization of charge carriers in a superstructure. In a less than completely filled conduction band charge disproportionation is observed. The charge carriers arrange themselves in distinct patterns. In case of static charge order and if it includes all charge carriers of the conduction band, the charge ordered state is insulating. Most well known example is the stripe order in transition metal oxides like La2-x-yNdySrxCuO4 or La2-xSrxNiO4 (see figure on the right). Holes are accumulating in one-dimensional stripes in the domain walls separating antiferromagnetic regions. Spin and charge order in these materials has attracted attention of many scientists because they are closely related to high-temperature superconductors. In high-temperature superconductors like La2-xSrxCuO4 indications of fluctuation spin and charge stripes were observed, which however do not order statically.

In the recent years, the increased interest in charge-order transitions lead to more and more research activities in this field. The focus was on the nickelates and cuprates where the competition between magnetic exchange interaction and Coulomb repulsion results in spin and charge stripes, on systems with mixed valences like the vanadates, or on the manganates where charge order is competing with orbital order. Charge order occurs not only in anorganic transition-metal oxides but also in organic charge-transfer salts. Here, the intersite Coulomb repulsion V is the driving force. If V exceeds a certain value, the charge carriers arrange themselves in a way that they have the largest possible distance from each other. An easy example is a one-dimensional system with a quarter-filled conduction band: in the charge order state, the charge carriers alternatingly do occupy or do not occupy a lattice site. The quasi one-dimensional organic TMTTF charge-transfer salts, which have a 3/4-filled conduction band (or 1/4-filled hole band) are such systems. In the quasi two-dimensional BEDT-TTF salts more complicated two-dimensional charge-order patterns are formed. The advantage of low-dimensional organic charge-transfer salts is that parameters like Coulomb repulsion, dimensionality, or band filling can be easily tuned by exchanging atoms of the donor molecules or the anions.