Berlin 2018 – wissenschaftliches Programm
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TT: Fachverband Tiefe Temperaturen
TT 82: Topological Insulators II (joint session TT/MA)
TT 82.6: Vortrag
Donnerstag, 15. März 2018, 10:45–11:00, A 053
Wigner oscillations and fractional Wigner oscillations in Luttinger liquids — •Niccolo Traverso Ziani and Bjoern Trauzettel — Institut für Theoretische Physik, Universität Würzburg
In finite electronic systems, when electron-electron interactions dominate over kinetic energy, electrons tend to form regular lattices, called Wigner molecules. While the study of the Wigner molecule in three and two spatial dimensions is most often carried out numerically, in one dimension the Luttinger liquid theory allows for analytical results. In one dimension, when interaction strength is increased from the noninteracting regime, a crossover between finite size Friedel oscillations (with wavevector 2kF) and Wigner oscillations (with wavevector 4kF) is found in the average density. Moreover, in a range of intermediate interactions, increasing temperature favours Wigner oscillations over Friedel ones. Importantly, for strong interactions, the Wigner molecule becomes an almost classical state and any dependence on the spin degree of freedom is lost. This behaviour is antithetical to the concept of spin-momentum locking characterizing the helical edges of two-dimensional topological insulators (helical Luttinger liquids). The compromise between strong interactions and spin-momentum locking leads, in helical systems, to a Wigner oscillation of fermions with fractional charge e/2. This fractional oscillation is also characterized by strongly anisotropic spin-spin correlations. In a finite size setup the fractional charges have a nontrivial interplay with Jackiw-Rebbi fractional solitons.