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

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

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

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

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

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

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

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

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

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

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

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

Tc and the Energy Scales superconductivity AF x E. W. Carlson et al., cond-mat/0206217 2018/11/14 Department of Physics & Astronomy, Georgia State University

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

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

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

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

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