Interaction of Phonons and Dirac Fermions on the Surface of Bi2Se3: A Strong Kohn Anomaly

We report the first measurements of phonon dispersion curves on the (001) surface of the strong three-dimensional topological insulator Bi2Se3. The surface phonon measurements were carried out with the aid of coherent helium beam surface scattering techniques. The results reveal a prominent signature of the exotic metallic Dirac fermion quasi-particles, including a strong Kohn anomaly. The signature is manifest in a low energy isotropic convex dispersive surface phonon branch with a frequency maximum of 1.8 THz, and having a V-shaped minimum at approximately 2kF that defines the Kohn anomaly. Theoretical analysis attributes this dispersive profile to the renormalization of the surface phonon excitations by the surface Dirac fermions. The contribution of the Dirac fermions to this renormalization is derived in terms of a Coulomb-type perturbation model

Temperature-Dependent Anomalies in the Structure of the (001) Surface of LiCu2O2

Surface corrugation functions, derived from elastic helium atom scattering (HAS) diffraction patterns at different temperatures, reveal that the Cu2+ rows in the (001) surface of LiCu2O2 undergo an outward displacement of about 0.15 {\AA} as the surface was cooled down to 140 K. This is probably the first time that isolated one-dimensional magnetic ion arrays were realized, which qualifies the Li1+Cu2+O2-2 surface as a candidate to study one-dimensional magnetism. The rising Cu2+ rows induce a surface incommensurate structural transition along the a-direction. Surface equilibrium analysis showed that the surface Cu2+ ions at bulk-like positions experience a net outward force along the surface normal which is relieved by the displacement. Temperature-dependent changes of the surface phonon dispersions obtained with the aid of inelastic HAS measurements combined with surface lattice dynamical calculations are also reported.Comment: 4 pages, 7 figure

Interaction Properties of the Periodic and Step-like Solutions of the Double-Sine-Gordon Equation

The periodic and step-like solutions of the double-Sine-Gordon equation are investigated, with different initial conditions and for various values of the potential parameter $\epsilon$. We plot energy and force diagrams, as functions of the inter-soliton distance for such solutions. This allows us to consider our system as an interacting many-body system in 1+1 dimension. We therefore plot state diagrams (pressure vs. average density) for step-like as well as periodic solutions. Step-like solutions are shown to behave similarly to their counterparts in the Sine-Gordon system. However, periodic solutions show a fundamentally different behavior as the parameter $\epsilon$ is increased. We show that two distinct phases of periodic solutions exist which exhibit manifestly different behavior. Response functions for these phases are shown to behave differently, joining at an apparent phase transition point.Comment: 17pages, 15 figure