Congjun Wu University of California, San Diego Quaternionic states of matter from synthetic gauge fields ISCAP Taiyuan, Jun 16, 2014 Collaborators: Yi Li (UCSDPrinceton), X. F. Zhou (USTC, Hefei) 2 ˆ e 1 ˆ e S Q-BEC with Hopf invariant 3D Q-analytic Landau level
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Congjun Wu University of California, San Diego
Quaternionic states of matter from synthetic gauge fields
ISCAP Taiyuan,
Jun 16, 2014
Collaborators: Yi Li (UCSD Princeton), X. F. Zhou (USTC, Hefei)
2e
1e
S
Q-BEC with Hopf invariant 3D Q-analytic Landau level
2
AcknowledgementCollaborations on related topics: Vincent Liu, Zi Cai, Luming Duan, Yue Yu, K. Intrilligator, S. C. Zhang.
Helpful discussions with Jorge Hirsch, Kazuki Hasebe, T. L. Ho, Jiang-ping Hu, Nai Phuan Ong, Cenke Xu, Kun Yang, Yue Yu, S. C. Zhang, Fei Zhou
Support from NSF-DMR, AFOSR.
Ref. 1) Y. Li, X. F. Zhou, C. Wu, arxiv1205.2162.2) Y. Li, C. Wu, PRL 110, 216802 (2013), arxiv:1103.5422.3) Y. Li, Xiangfa Zhou, C. Wu, Phys. Rev. B 85, 125122 (2012).4) Review on synthetic SO coupling: X. F. Zhou, Y. Li, Z. Cai, C. Wu, J
Phy. B 46, 134001 (2013).
Other related work1) C. Wu, I. Mondragon-Shem, X. F. Zhou, Chin. Phys. Lett. 28, 097102, 2011(arXiv:0809.3532).
2) Y. Li, S. C. Zhang, C. Wu, PRL 111, 186803(2013).3) Y. Li, K. Intrilligator, Y. Yu, C. Wu, PRB 85, 85132(2012).
Outline
• Real numbers complex numbers quaternions (Q).
• Bosons: real (positive) BEC complex BEC Q-BEC
unconventional symm. beyond the “no-node” theorem.
• More formally and rigorously, c.f. Perron-Frobenius theorem.
Conventional BEC (invariant under rotations, s-wave-like)
1212
• “No-node” theorem forbids unconventional symmetries, say, p, d, etc.
• Cf. conventional superconductivity: the pair WF belongs to the trivial (s-wave) representation of the rotation group.
)()()(
21
21 kekdrrrrik
k
k
• High Tc d-wave superconductivity tested by phase sensitive Josephson junction experiment by Van Harlingen et al.
Unconventional BEC: beyond “no-node”
• The condensate wavefunction belongs to a non-trivial (non-s-wave) representation of the lattice point group.
)(r
• No-node theorem does NOT apply to excited states.
• Example: the p-orbital bands can have degenerate band minima.
Interaction selects complex p+ip UBEC:
W. V. Liu, and C. Wu, PRA, 2006; Zi Cai, C. Wu, PRA 84, 033635(2011).Review: C. Wu, Mod. Phys. Lett. 23, 1(2009). Wirth, Olschlager, Hemmerich, Nat. Phys. 2011, N. Y. Kim, et al, Nat. Phy. Physics 2010.
13
)()()(21
rirrKK
K1 K2
-K1-K2
• Solid state experiments: d-wave BEC in exiton-polarition lattices (Kim, Yamamoto, Wu)
Outline
• Real numbers complex numbers quaternions (Q).
• Bosons: real (positive) BEC complex BEC Q-BEC
unconventional symm. beyond the “no-node” theorem.