Stability of semi-metals : (partial) classification of semi-metals
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1 : (partial) classification of semi-metals Eun-Gook Moon Department of Physics, UCSB EQPCM 2013 at ISSP, Jun 20, 2013
2 Collaborators Cenke Xu, UCSB Yong Baek, Kim Univ. of Toronto Leon Balents, KITP B.J. Yang Riken L. Savary UCSB N. Nagaosa, Riken
3 Refs : 1. Non-Fermi liquids and topological phases : EGM, Xu, Kim, and Balents (arxiv : ) 2. All-in All-out magnetic phase transition in pyrochlore structures : Savary, EGM, and Balents (to appear) 3. Topological quantum phase transitions in noncentrosymmetic systems : Yang, et. al. (EGM) (PRL ) 4. Stability of semi-metals : EGM et. al. (to appear)
4 Motivation Amounts of charge excitations Insulators : charge gapped systems Metals : large amounts of low energy excitations Imura, Yoshida (06/07), Furusaki (06/10), Maciejko (06/11), Oshikawa (06/18), and many other talks in the symposium
5 Motivation Amounts of charge excitations Insulators : charge gapped systems Semi-metals Metals : large amounts of low energy excitations Imura, Yoshida (06/07), Furusaki (06/10), Maciejko (06/11), Oshikawa (06/18), and many other talks in the symposium
6 Motivation Amounts of charge excitations Band Insulators Textbook examples (topological or not) Semi-metals Fermi Liquids Simple metals Mott Insulators Correlated or not? Correlated Metals Interaction Magnetism, spin liquids, etc. Heavy Fermions Non-Fermi liquids
7 Characteristics of semi-metals Semi-metals Finite number of band touching points in Brillouin zone (ex : graphene) - Existence of gapless excitations - Symmetry is more important. (protecting symmetries) - Interaction effect is more important than insulators. - Physical properties show different behaviors. K and K points sub-lattice symmetry quantum critical phase zero Landau Level
8 Strategy - Consider symmetric semi-metals. - Investigate Coulomb interaction effects. - Break symmetries and obtain different class of semi-metals. Symmetric semi-metals : energy dispersion is isotropic near gapless points. (only one dynamic critical exponent is necessary.) Coulomb interaction effects : two types of interactions - Short range Coulomb interaction (ex : Hubbard U) - Long range Coulomb interaction (V(r) ~ 1/r ) High momentum (energy) degrees of freedom induces the two types of interactions
9 Effective action of the symmetric semi-metals spatial dimension Short-range Coulomb Long-range Coulomb Scaling dimensions Non-interacting fixed point : Stability critical dimension : : irrelevant contact interactions : relevant contact interactions
10 Classification of the symmetric semi-metals Notation : (dnzm) phase (n spatial dimension and m dynamical critical exponent) Non-interacting fixed points under contact interactions - stable for (d2z1, d3z1, d3z2) - marginal for (d1z1, d2z2, d3z3) - unstable for (d1z2, d1z3, d2z3) Density of states : Long-range Coulomb interaction effects??
11 Classification of the symmetric semi-metals Density of states : constant at the stability critical dimensions. screening of the long range Coulomb interaction. cf ) Thomas-Fermi screening in metallic systems. Polarization function = Long-range Coulomb interaction : irrelevant at the stability critical dimensions.
12 Classification of the symmetric semi-metals Coulomb interaction : marginally irrelevant (QED types) Coulomb interaction : relevant (interaction is cruical.) Simple estimation At long distance (low energy), Coulomb interaction is dominant.
13 Classification of the symmetric semi-metals (d3z2) semi-metals - short-range Coulomb interaction : irrelevant - long-range Coulomb interaction : relevant But, virtual screening process eventually becomes dominant at long range physics. Thus, the ground state becomes non-fermi liquid.
14 Classification of the symmetric semi-metals
15 Classification of the symmetric semi-metals Renormalization group picture : (d1z1), (d2z1), (d3z1), (d2z2) (e, g) (d3z2) (e, g) (d1z2), (d1z3), (d2z3) (e, g)
16 Derivative phases from the symmetric semi-metals By breaking protecting symmetries, anisotropic semi-metals are achieved. Spatial scaling is anisotropic.
17 Quantum phase transitions around the semi-metals Especially, the (d3z2) semi-metal has exotic phase transitions due to its special characteristics. Example : AIAO phase transition around the (d3z2) Quantum critical Linear Weyl with AIAO LAB Emergent anisotropy and emergent symmetries. Savary et. al. (to appear)
18 Summary Stability of semi-metals under Coulomb interactions are studied. In symmetric semi-metals, four stable weakly(non) interacting semi-metals are possible. In symmetric semi-metals, one interacting semi-metal phase is found. Unstable phases might be gapped or might become interacting semi-metals. (Fractionalization of electrons is possible.) Anisotropic semi-metals are achieved by breaking protecting symmetries. Exotic quantum phase transitions around the semi-metals are realized.
19 Future work Strongly interacting semi-metals Quantum critical behavior in semi-metals Impurity problems in semi-metals Physical quantities (optical conductivity, susceptibility, etc.) Crossover to small Fermi pocket systems.
20 Thank you for your attention.
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