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

The Stochastic Advance-Retreat Course: An Approach to Analyse Social-Economic Evolution

The paper presents the basic theory and conceptual model for advance-retreat course and provides the analytic model the stochastic advance-retreat course and the solving method of it, discusses the relations between the endogenous resistance and subject interests increase with the periodic vibration in an advance-retreat course, gets some results, like heightening appropriately the risk-free interest rate will be favorable to subject interests’ increasing in stable, interests increasing in high-speed will result in the fast increase of resistance, the subject progress in a appropriate pace may bring the conclusion such as lasting interests increase and return with higher-level interests, etc. Finally, the empirical researches empirical, on data of USA GDP (chained) price index, has been made to the stochastic advance-retreat model, and the results show that the stochastic advance-retreat model can describe USA economic development process in recent 65 years.Economic process; advance-retreat course; the basic theory; analytic model