Transition-Metal Pentatelluride ZrTe5_5 and HfTe5_5: a Paradigm for Large-gap Quantum Spin Hall Insulators

Quantum spin Hall (QSH) insulators, a new class of quantum matters, can support topologically protected helical edge modes inside bulk insulating gap, which can lead to dissipationless transport. A major obstacle to reach wide application of QSH is the lack of suitable QSH compounds, which should be easily fabricated and has large size of bulk gap. Here we predict that single layer ZrTe$_5$ and HfTe$_5$ are the most promising candidates to reach the large gap QSH insulators with bulk direct (indirect) band gap as large as 0.4 eV (0.1 eV), and robust against external strains. The 3D crystals of these two materials are good layered compounds with very weak inter-layer bonding and are located near the phase boundary between weak and strong topological insulators, which pave a new way to future experimental studies on both QSH effect and topological phase transitions.Comment: 16 pages, 6 figure

Essays on Market Dynamics in the Presence of Learning

I investigate how the presence of learning affects the market dynamics in three different market settings. The first chapter studies how the interplay of individual and social learning affects price dynamics. I consider a monopolist selling a new experience good over time to many buyers. Buyers learn from their own private experiences (individual learning) as well as by observing other buyers\u27 experiences (social learning). Individual learning generates ex post heterogeneity, which affects the buyers\u27 purchasing decisions and the firm\u27s pricing strategy. When learning is through good news signals, the monopolist\u27s incentive to exploit the known buyers causes experimentation to be terminated too early. After the arrival of a good news signal, the price could instantaneously go down in order to induce the remaining unknown buyer to experiment. When learning is through bad news signals, experimentation is efficient, since only the homogeneous unknown buyers purchase the experience good. The second chapter is based on the observation that workers learn at different rates about their productivity and therefore expect different wage paths across firms. We show that under strict supermodularity there is always positive assortative matching: differential learning is always dominated by the impact of productivity. Surprisingly, this holds even if learning is faster in the low type firm. The key assumption driving this result is that this is a pure Bayesian learning model.We also derive a new equilibrium condition in this class of continuous time models in addition to the common smooth-pasting and value-matching conditions. This no-deviation condition captures sequential rationality and results in a restriction on the second derivative of the value function. The third chapter develops a continuous-time war of attrition model with learning to investigate whether learning is possible to make it easier to reach an agreement. I show that with exogenous private learning, it may be easier to reach an agreement initially but it becomes more and more difficult over time. The expected delay will always be higher than the expected delay without learning. I also show that when allowing only one player to learn leads to a shorter delay than allowing both to learn

Non-collinear magnetic structure and multipolar order in Eu2_2Ir2_2O7_7

The magnetic properties of the pyrochlore iridate material Eu$_2$Ir$_2$O$_7$ (5$d^5$) have been studied based on the first principle calculations, where the crystal field splitting $\Delta$, spin-orbit coupling (SOC) $\lambda$ and Coulomb interaction $U$ within Ir 5$d$ orbitals are all playing significant roles. The ground state phase diagram has been obtained with respect to the strength of SOC and Coulomb interaction $U$, where a stable anti-ferromagnetic ground state with all-in/all-out (AIAO) spin structure has been found. Besides, another anti-ferromagnetic states with close energy to AIAO have also been found to be stable. The calculated nonlinear magnetization of the two stable states both have the d-wave pattern but with a $\pi/4$ phase difference, which can perfectly explain the experimentally observed nonlinear magnetization pattern. Compared with the results of the non-distorted structure, it turns out that the trigonal lattice distortion is crucial for stabilizing the AIAO state in Eu$_2$Ir$_2$O$_7$. Furthermore, besides large dipolar moments, we also find considerable octupolar moments in the magnetic states.Comment: 6 pages, 4 figures, supplemental material is included in the source file, accepted for publication in PR