Dynamical conductivity in multiply-degenerate point-nodal semimetal CoSi

We investigate the dynamical conductivity in multiply-degenerate point-nodal semimetal CoSi. In the semimetal, the band structure holds point nodes at the $\Gamma$ and R points in the Brillouin zone and more than three bands touch at the nodes. Around the nodes, electronic states are predicted to be described as the multifold chiral fermion, a new class of fermion. We show that the dynamical conductivity exhibits a characteristic spectrum corresponding to the band structure and the chiral fermionic states. The dynamical conductivity of CoSi is calculated as a function of photon energy by using the first-principles band calculation and linear response theory. We show that a dip structure in the low photon-energy region is attributed to not only the band structure but also the chirality of electronic states. The chirality leads to the prohibition of transition between the lower and upper bands of threefold chiral fermion and thus the transition between the middle and lower bands is relevant to the dynamical conductivity. This transition property is different from the Dirac and Weyl semimetals, the other point-nodal semimetals, where the excitation between the upper and lower bands is relevant to the dynamical conductivity. We discuss the relation between the prohibition and the dip structure by using an effective Hamiltonian describing threefold chiral fermion.Comment: 8 pages, 5 figure

Robustness of Gapless Interface State in a Junction of Two Topological Insulators

We theoretically study subgap states appearing at the interface between two three-dimensional topological insulators which have different configurations in the spin-orbit interactions from each other. The coupling of spin $\boldsymbol{\sigma}$ with momenta $\boldsymbol{p}$ is configured by a material dependent $3\times 3$ matrix $\boldsymbol{\Lambda}$ as ${\sigma}^\mu {\Lambda}_\mu^\nu p_\nu$. We show that the spectra of the interface suggap states depend strongly on the relative choices of $\boldsymbol{\Lambda}$ in the two topological insulators. In particular, we focus on properties of gapless states which appear when $\boldsymbol{\Lambda}$ in two topological insulators are connected by the inversion in momentum space. We also discuss the robustness of the gapless states under perturbations breaking the time-reversal symmetry or the band-inversion symmetry by the numerical simulation.Comment: 13 pages, 9 figure

Dry minor mergers and size evolution of high-z compact massive early-type galaxies

Recent observations show evidence that high-z (z\sim 2 - 3) early-type galaxies (ETGs) are more compact than those with comparable mass at z\sim 0. Such a size evolution is most likely explained by the `Dry Merger Sceanario'. However, previous studies based on this scenario are not able to consistantly explain both the properties of the high-z compact massive ETGs and the local ETGs. We investigate the effect of multiple sequential dry minor mergers on the size evolution of the compact massive ETGs. From an analysis of the Millennium Simulation Database, we show that such minor (stellar mass ratio $M_{2}/M_{1} < 1/4$) mergers are extremely common during hierarchical structure formation. We perform N-body simulations of sequential minor mergers with parabolic and head-on orbits, including a dark matter component and a stellar component. Typical mass ratios of the minor mergers are $1/20 < M_{2}/M_{1} < 1/10$. We show that sequential minor mergers of compact satellite galaxies are the most efficient at promoting size growth and decreasing the velocity dispersion of the compact massive ETGs in our simulations. The change of stellar size and density of the merger remnants is consistent with recent observations. Furthermore, we construct the merger histories of candidates for the high-z compact massive ETGs using the Millennium Simulation Database, and estimate the size growth of the galaxies by the dry minor merger scenario. We can reproduce the mean size growth factor between $z=2$ and $z=0$, assuming the most efficient size growth obtained during sequential minor mergers in our simulations. However, we note that our numerical result is only valid for merger histories with typical mass ratios between 1/20 and 1/10 with parabolic and head-on orbits, and that our most efficient size growth efficiency is likely to an upper limit.Comment: 23 pages, 15 figures, accepted for MNRAS, Fig. 5 is fixe