Transcript H. Lee
Quantum state that never condenses Dung-Hai Lee U.C. Berkeley Condense = develop some kind of order As a solid develops order, some symmetry is broken. Spin rotational symmetry is broken ! Ice crystal Superfluid Neutron star Expanding universe Examples of order Metals do break any symmetry, but they are not stable at zero temperature. Metals always turn into some ordered states with symmetry breaking as T 0. Metals are characterized by the Fermi surface Different types of Fermi surface instability lead to different order. Cooper instability superconductivity Fermi surface nesting instability spin density wave, or charge density wave Landau’s paradigm • Ordered state is characterized by the symmetry that is broken. • All ordered states originate from the metallic state due to Fermi surface instability. Metal Superconductivity Charge density wave Spin density wave Is it possible for a solid not to develop any order at zero temperature ? Insulators with integer filling factor are good candidates Fermion band insulator Boson Mott insulator Mott insulator Boson Mott insulator Fermion Mott insulator Insulating due to repulsion between particles. Examples of electron band insulator C, Si, Ge, GaAs, … An example of electron Mott insulator YBa2Cu3O6 – the parent compound of high temperature superconductor CuO2 sheet An example of boson Mott insulator: optical lattice of neutral atoms Greiner et al, Nature 02 Why are we interested in insulators ? Doping make them very useful ! Most of the time, doping make the particle mobile, hence can conduct. Doped band insulator A Silicon chip Doped Mott insulators Doping Mott insulators has produced many materials with interesting properties. Doped YBa2Cu3O6 High Tc superconductors Doped LaMnO3 Colossal magneto-resistive materials Is it possible that a solid remains insulating after doping ? Yes An interesting fact: all insulators with fractional filling factor break some kind of symmetry hence exhibit some kind of order. fermion Antiferromagnet Dimmerization boson Why is uncondensed insulator so rare at fractional filling ? Oshikawa’s theorem If the system is insulating, and if the filling factor = p/q, the ground state is q-fold degenerate. Usually the required degeneracy is achieved by long range order. Can a fractional filled insulator exist without symmetry breaking ? Oshikawa PRL 2000 It is generally believed that featureless insulators will have very unusual properties. Such as fractional-charge excitations … Anderson’s spin liquid idea Resonating singlet patterns + +... Spin liquid is a featureless insulator (at half filling) with no long range order ! It has S=1/2 excitations (spinons). It exists in the parent state of high-temperature superconductors. Anderson, Science 1987 Condensed matter physicists have searched for such insulators for 20 years. The usual search guide line is “frustration”. ? A new idea: symmetry protected uncondensed quantum state Filling factor =1/3 Melts crystal order but never changes the C-M position preserve 3fold degeneracy. The Quantum effect The fractional quantumHall Hall effect Rxx = VL /I; Rxy = VH /I One example of this type of state is the fractional quantum Hall liquid Lee & Leinaas, PRL 2004 Another example is the quantum dimer liquid Moessner & Sondhi, PRL, 2001 All existing models in the literature that exhibit uncondensed quantum state conserve the center-of-mass position and momentum.