Topological Insulator in an Atomic Liquid

We demonstrate theoretically an atomic liquid phase that supports topologically nontrivial electronic structure. A minimum two-orbital model of liquid topological insulator in two dimensions is constructed within the framework of tight-binding molecular dynamics. As temperature approaches zero, our simulations show that the atoms crystallize into a triangular lattice with nontrivial band topology at high densities. Thermal fluctuations at finite temperatures melt the lattice, giving rise to a liquid state which inherits the nontrivial topology from the crystalline phase. The electronic structure of the resultant atomic liquid is characterized by a nonzero Bott index. Our work broadens the notion of topological materials, and points to a new systematic approach for searching topological phases in amorphous and liquid systems.Comment: 5 pages, 4 figure

Noncoplanar magnetic ordering driven by itinerant electrons on the pyrochlore lattice

Exchange interaction tends to favor collinear or coplanar magnetic orders in rotationally invariant spin systems. Indeed, such magnetic structures are usually selected by thermal or quantum fluctuations in highly frustrated magnets. Here we show that a complex noncoplanar magnetic order with a quadrupled unit cell is stabilized by itinerant electrons on the pyrochlore lattice. Specifically we consider the Kondo-lattice and Hubbard models at quarter filling. The electron Fermi 'surface' at this filling factor is topologically equivalent to three intersecting Fermi circles. Perfect nesting of the Fermi lines leads to magnetic ordering with multiple wavevectors and a definite handedness. The chiral order might persist without magnetic order in a chiral spin liquid at finite temperatures.Comment: 5 pages, 4 figure

Dipolar order by disorder in the classical Heisenberg antiferromagnet on the kagome lattice

Ever since the experiments which founded the field of highly frustrated magnetism, the kagome Heisenberg antiferromagnet has been the archetypical setting for the study of fluctuation induced exotic ordering. To this day the nature of its classical low-temperature state has remained a mystery: the non-linear nature of the fluctuations around the exponentially numerous harmonically degenerate ground states has not permitted a controlled theory, while its complex energy landscape has precluded numerical simulations at low temperature. Here we present an efficient Monte Carlo algorithm which removes the latter obstacle. Our simulations detect a low-temperature regime in which correlations saturate at a remarkably small value. Feeding these results into an effective model and analyzing the results in the framework of an appropriate field theory implies the presence of long-range dipolar spin order with a tripled unit cell.Comment: 5 pages, 4 figure