Condensed Matter Physics

The concept of topological insulator refers to a unique class of materials, which have insulating bulk but gapless transport channels at the edge or surface. The physical origin of the topological insulator is the strong spin-oribit coupling, which is in fact a combination of the quantum theory and relativistic theory. Due to the existence of the particular surface or edge states, the TIs possess many novel phenomenon and have great potential in the application of spintronic devices and topological quantum computation.

My previous works focus on the following several aspects: (1) In order to observe the novel phenomenon in experiment, it is essential to find the proper materials with such type of properties. Combining the first principle calculation with the analytical k.p theory, we search for both three-dimensional (3D) and two-dimensional (2D) TIs in different families of materials. For 3D TIs, we have found Bi2Se3 family, TlBiTe2 family and LaBiTe2 family, while for 2D TIs (QSH insulator), we have shown InAs/GaSb quantum well is a possible candidate. Experimentally Bi2Se3 family and TlBiTe2 family have been confirmed to be 3D TIs, while researchers also find strong evidence of 2D TI for InAs/GaSb quantum wells. Particularly, the work on Bi2Se3 family has stimulated a lot of experiment effort in this family of materials, which has become the hottest materials in the field of TIs. (2) We also investigate several novel effects in TIs, which include the quantum anomalous Hall effect in Mn doped HgTe quantum wells, the 3D-2D oscillatory crossover of TI thin film, the charge and spin transport of helical liquid at the edge of 2D TI, the magnetic impurity and Ruderman-Kittel-Kasuya-Yosida interaction at the surface of 3D TI, and so on. (3) We propose a superconductor-TI sandwich structure, which can be utilized to realize helical Dirac-majorana interferometer, enabling the observation of the helical majorana fermion in the topological superconductor (TSC). Now I'm interested in the following topics. (1) New topological materials and topological phases. Up to now the 2D quantum spin Hall effect has only been observed in $HgTe$ system and 3D TI has only been realized in $Bi_xSb_{1-x}$ and $Bi_2Se_3$ type of materials. There still exist disadvantages for the present materials. For example, the gap of 2D TI $HgTe/CdTe$ quantum well is only $sim 20meV$, far below room temperature, which may prevent the $HgTe/CdTe$ system from the device application. There also exist other elements with strong SOC, therefore one may ask whether or not there exist some other materials with non-trivial topological phases. Further the new materials may introduce new properties, such as strong correlation, into the system, which may lead to new topological phases, thus it will be quite interesting and important to search for new TI materials systematically. Up to now, only the materials with s- and p-orbital electron have been carefully studied. Although there are also some proposals about d-electron, however a systematic research of d and f electron has not been considered, hence we may pay more attention to these types of materials. To search for new materials, the first principle calculation should be combined with analytical method, which has been successfully used to predict the $Bi_2Se_3$ family. (2) Weyl fermion. In analog to the 2D gapless Dirac cone in graphene, Weyl fermion is in fact a 3D gapless Dirac cone. Weyl fermion has definite chirality and in a lattice system, they always appear in pairs. Just like the flat edge state at the zigzag edge of graphene, the surface state of the system with Weyl fermions will possess a Fermi arc for the surfaces along some directions. Actually the Weyl fermion can be regarded as a 3D generalization of the 2D quantum anomalous Hall effect. Here we are interested in the physical consequence of the Weyl fermions and also how to realize it in the realistic materials. (3) Topological superconductors (TSCs) and majorana fermion. The topological non-trivial phase is not limitted to the topological insulator and another example is topological superconductors, which has superconducting gap in the bulk but gapless mode at the edge/surface. These topologically non-trivial edge/surface states are protected by the bulk superconducting gap. Unlike the TI, which has been observed in experiment, the TSCs with majorana bound state or edge (surface) states have never been confirmed although several experimental achievable approaches have been proposed. The main difficulty of the experiment is how to identify a clear signiture for the majorana fermion. We will collaborate with the experimentalist and hope to investigate the TI system coexisting with superconductivity and to search for a ``smoking gun'' signiture of the majorana fermion.

C. Brune, C. Liu, A. Novik, E. M. Hankiewicz, H. Buhmann, Y. Chen, X. Qi, Z. Shen, S. Zhang and L. Molenkamp, "Quantum Hall Effect from the Topological Surface States of Strained Bulk HgTe," Phys. Rev. Lett. **106**, 126803 (2011)

C. Liu and B. Trauzettel, "Helical Dirac-Majorana interferometer in a superconductor-topological insulator sandwich structure," Phys. Rev. B Rapid Comm. **83**, 220510 (2011)

C. Liu, X. Qi, H. Zhang, X. Dai, Z. Fang and S. Zhang, "Model Hamiltonian for Topological Insulators," Phys. Rev. B **82**, 045122 (2010)

B. Yan, C. Liu, H. Zhang, C. Yam, X. Qi, T. Frauenheim and S. Zhang, "Theoretical Prediction of Topological Insulators in Thallium-based III-V-VI2 Ternary Chalcogenides," Europhys. Lett. **90**, 37002 (2010)

B. Yan, H. Zhang, C. Liu, X. Qi, T. Frauenheim and S. Zhang, "Theoretical prediction of topological insulator in ternary rare earth chalcogenides," Phys. Rev. B Rapid Comm. **82**, 161108 (2010)

C. Liu, H. Zhang, B. Yan, X. Qi, X. Dai, Z. Fang and S. Zhang, "Oscillatory crossover from two dimensional to three dimensional topological insulators," Phys. Rev. B Rapid Comm. **81**, 041307 (2010)

H. Zhang, C. Liu, X. Qi, X. Deng, X. Dai, S. Zhang and Z. Fang, "Electronic structures and surface states of the topological insulator Bi1-xSbx," Phys. Rev. B **80**, 085307 (2009)

J. Maciejko, C. Liu, Y. Oreg, X. Qi, C. Wu and S. Zhang, "Kondo Effect in the Helical Edge Liquid of the Quantum Spin Hall State," Phys. Rev. Lett. **102**, 256803 (2009)

Q. Liu, C. Liu, C. Xu, X. Qi and S. Zhang, "Magnetic Impurities on the Surface of a Topological Insulator," Phys. Rev. Lett. **102**, 156603 (2009)

H. Zhang, C. Liu, X. Qi, X. Dai, Z. Fang and S. Zhang, "Topological insulators in Bi2Se3, Bi2Te3 and Sb2Te3 with a single Dirac cone on the surface," Nature Phys. **5**, 438 (2009)

C. Liu, X. Qi, X. Dai, Z. Fang and S. Zhang, "Quantum Anomalous Hall Effect in Hg1-yMnyTe Quantum Wells," Phys. Rev. Lett. **102**, 146802 (2008)

C. Liu, T. L. Hughes, X. Qi, K. Wang and S. Zhang, "Quantum Spin Hall Effect in Inverted Type II Semiconductors," Phys. Rev. Lett. **100**, 236601 (2008)