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

2. Department of Physics & Astronomy, Georgia State University
Outline
Motivations
Luttinger liquid
1D experiment (Auslaender)
High-Tc cuprate and visons
Vortex-memory effect experiment (Bonn)
Conclusions
2018/11/14
Department of Physics & Astronomy, Georgia State University

3. Department of Physics & Astronomy, Georgia State University
Motivations
Strongly correlated electronic system
Fundamental physics
Electronic devices
High-Tc superconducting material
2018/11/14
Department of Physics & Astronomy, Georgia State University

4. Department of Physics & Astronomy, Georgia State University
Luttinger liquid
Anti-ferromagnetic chain
Spin excitation (Spinon)
Charge excitation (Chargon)
2018/11/14
Department of Physics & Astronomy, Georgia State University

5. Department of Physics & Astronomy, Georgia State University
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)
2018/11/14
Department of Physics & Astronomy, Georgia State University

6. Tunneling between parallel wires
Auslaender et al., Science 295, 825 (2002).
2018/11/14
Department of Physics & Astronomy, Georgia State University

7. Tunneling under B and voltage bias
B is perpendicular to the wire plane.
Assume tunneling preserves energy and momentum.
Auslaender et al., Science 308, 88 (2005).
2018/11/14
Department of Physics & Astronomy, Georgia State University

8. Mapping the dispersion
2018/11/14
Department of Physics & Astronomy, Georgia State University

9. Determining Fermi velocity
2018/11/14
Department of Physics & Astronomy, Georgia State University

10. Department of Physics & Astronomy, Georgia State University
Apparent velocity
2018/11/14
Department of Physics & Astronomy, Georgia State University

11. Charge velocity and spin velocity
Velocity in m/s
Density in 1/m
2018/11/14
Department of Physics & Astronomy, Georgia State University

12. High-Tc superconductor material
Cooper-pairs
SCS
Condensation of electron pairs
Condensation of spin-0 chargons
Superconductivity
2018/11/14
Department of Physics & Astronomy, Georgia State University

13. Tc and the Energy Scales
superconductivity AF x
E. W. Carlson et al., cond-mat/
2018/11/14
Department of Physics & Astronomy, Georgia State University

14. Department of Physics & Astronomy, Georgia State University
Z2-gauge theory
t-J model
Spin operator
Electron operator
Constraint on each site
2018/11/14
Department of Physics & Astronomy, Georgia State University

15. Department of Physics & Astronomy, Georgia State University
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)
2018/11/14
Department of Physics & Astronomy, Georgia State University

16. Department of Physics & Astronomy, Georgia State University
Vortex-memory effect
Vison trapped
T. Senthil and M. Fisher, Phys. Rev. L, 86, 292 (2001)
2018/11/14
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)
2018/11/14
Department of Physics & Astronomy, Georgia State University

18. Department of Physics & Astronomy, Georgia State University
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.
2018/11/14
Department of Physics & Astronomy, Georgia State University