Experimental Evidences on Spin-Charge Separation

1. Experimental Evidences on Spin-Charge Separation Wei-Chun Chu Department of Physics and Astronomy, Georgia State University

2. Outline • Motivations • Luttinger liquid • 1D experiment (Auslaender) • High-Tc cuprate and visons • Vortex-memory effect experiment (Bonn) • Conclusions Department of Physics & Astronomy, Georgia State University

3. Motivations • Strongly correlated electronic system • Fundamental physics • Electronic devices • High-Tc superconducting material Department of Physics & Astronomy, Georgia State University

4. Luttinger liquid Anti-ferromagnetic chain Spin excitation (Spinon) Charge excitation (Chargon) Department of Physics & Astronomy, Georgia State University

5. 1D experiments • Tunneling between parallel wires O. M. Auslaender et al., Science 308, 88 (2005) • 1D organic conductors T. Lorenz et al., Nature 418, 614 (2002) • Carbon nanotubes M. Bockrath et al., Nature 397, 598 (1999) Department of Physics & Astronomy, Georgia State University

6. Tunneling between parallel wires Auslaender et al., Science 295, 825 (2002). Department of Physics & Astronomy, Georgia State University

7. Tunneling under B and voltage bias V d B is perpendicular to the wire plane. Assume tunneling preserves energy and momentum. Auslaender et al., Science 308, 88 (2005). Department of Physics & Astronomy, Georgia State University

8. Mapping the dispersion Department of Physics & Astronomy, Georgia State University

9. Determining Fermi velocity Department of Physics & Astronomy, Georgia State University

10. Apparent velocity Department of Physics & Astronomy, Georgia State University

11. Charge velocity and spin velocity Velocity in m/s Density in 1/m Department of Physics & Astronomy, Georgia State University

12. High-Tcsuperconductor material Cooper-pairs SCS Condensation of electron pairs Condensation of spin-0 chargons Superconductivity Department of Physics & Astronomy, Georgia State University

13. Tc and the Energy Scales T superconductivity AF x E. W. Carlson et al., cond-mat/0206217 Department of Physics & Astronomy, Georgia State University

14. Z2-gaugetheory t-J model Spin operator Electron operator Constraint on each site Department of Physics & Astronomy, Georgia State University

15. The need for visons • The third excitation. (spinon, chargon, vison) • The remnant of unpaired BCS vortices. • Electrons and Cooper-pairs -> spinon and chargons: gauge invariance. (Observables stay the same when spinon and chargon operators change signs.) • Providing another phase-shift Pi to single electron, in order to keep the wave function single-valued. T. Senthil and M. Fisher, Phys. Rev. B, 62, 7850 (2000) Department of Physics & Astronomy, Georgia State University

16. Vortex-memory effect Vison trapped T. Senthil and M. Fisher, Phys. Rev. L, 86, 292 (2001) Department of Physics & Astronomy, Georgia State University

17. Measuring trapped visons The initial magnetic flux (blue) and final magnetic flux (red). The result shows that vison escapes in less than 10s at 9.5K. If is higher than the time for electron to pass one unit cuprate lattice, than vison escape energy is less than 190K. D. A. Bonn et al., Nature, 414, 887 (2001) Department of Physics & Astronomy, Georgia State University

18. Conclusions • Theory of SCS in 1D is generally well-understood as Tomonaga-Luttinger liquid, while the situation in higher dimension is not clear. • In 1D quantum wires, two spin modes and one charge mode were found. • In high-Tc cuprates, the upper limit of vison escape energy is 190K. It reduces the possibility of this cuprate model. Department of Physics & Astronomy, Georgia State University