Regular-triangle trimer and charge order preserving the Anderson condition in the pyrochlore structure of CsW2O6

Abstract

Since the discovery of the Verwey transition in magnetite, transition metal compounds with pyrochlore structures have been intensively studied as a platform for realizing remarkable electronic phase transitions. We report on a phase transition that preserves the cubic symmetry of the β-pyrochlore oxide CsW2O6, where each of W 5d electrons are confined in regular-triangle W3 trimers. This trimer formation represents the self-organization of 5d electrons, which can be resolved into a charge order satisfying the Anderson condition in a nontrivial way, orbital order caused by the distortion of WO6 octahedra, and the formation of a spin-singlet pair in a regular-triangle trimer. An electronic instability due to the unusual three-dimensional nesting of Fermi surfaces and the strong correlations of the 5d electrons characteristic of the pyrochlore oxides are both likely to play important roles in this charge-orbital-spin coupled phenomenon.

Perfect flat band with chirality and charge ordering out of strong spin-orbit interaction

“…Still, the evaluated energy splitting of E 1 − E 2 ∼0.2eV is as large as the bandwidth of our system (see Appendix A), which is compatible with the first principles band structure given in Ref. [33] where we roughly evaluate t ∼ 0.06 eV by their bandwidth.…”

“…The SOC-induced flat band clarifies the origin of the trimerized charge ordering observed in CsW 2 O 6 33 . Figure 1(d) shows the mean field phase diagram at quarterfilling, corresponding to two electrons per tetrahedron.…”

“…In the low temperature phase II, we expect the trimer flat band state, which has a Mott gap. This explains the sharp increase of the resistivity at the transition temperature 33 . There shall be a stiff pseudo-spin chirality formed by a tiny magnetic moment, indicating that the system breaks the time reversal symmetry.…”

“…The analytical many body flat band wave function give access to the important but the most unreachable physical regime, the effectively strongest correlation, where they optimize their form in a way to avoid the loss of the Coulomb energy. This mechanism explains the exotic trimerized charge ordering found in 5d pyrochlore CsW 2 O 6 33 , where one-quarter of the pyrochlore sites become perfectly vacant. On each triangle, there appears a stiff spin chirality inextricably linked to the flat band formation, which may provide another platform for testing the interplay of strong correlation and spin topology.…”

Charge-ordered state satisfying the Anderson condition in LiRh2O4 arising from local dimer order

“…Structural symmetry breaking caused by the ordering of electronic multiple degrees of freedom coupled to the lattice, occurs ubiquitously in transition metal compounds [1][2][3]. Examples include iron chalcogenides/pnictides superconductors [4][5][6] and materials forming exotic low-temperature orbital molecules [7][8][9][10][11][12][13][14][15][16][17][18]. Recently, it was found that symmetry breaking can occur locally, as a precursor, even above the transition temperature [18][19][20][21][22][23][24][25][26].…”