Superglasses and the nature of disorder-induced SI transition Xiaoquan Yu Advisor: Markus Mueller 2,12,2012

Outline Introduction of spin glasses and Anderson localization. Superglasses- mean field phase diagram. Hard core boson model on a Bethe lattice with large connectivity. Finite dimension

Anderson localization

Mobility edge

Spin glasses A spin glass is a magnet with random frustrated interactions. Ferromagnetic and antiferromagnetic bonds are randomly distributed. Spin glasses display many metastable structures. Many pure states. Gaussion in one pure state

Motivations Glasses + quantum fluctuations- quantum glasses. Low temperature properties? Glasses+ superfluid ? Can two orders coexit? Motivated by some supersoild experiments: amorphous solids sustain more robust supersolidity. Disorder may be a crucial element in understanding the supersolid systems

Superglasses Model and method Self consistent equations Replica method

Phasediagram QMC Gingras et al., PRL (2010). Glassy SIT! Not BCS type! Robust to on-site disorder Exact result!

Properties of superglasses phase Local order parameters are anticorrelated Non-monotonicity behavior of superfluid order parameter

Motivation and back grounds: conception Dirty superconductor. Anderson’s theorem breaks down. Localization of bosonic particles--- Bose glass. Properties of Bosonic insulators.

Motivation and backgrounds: experiments Activated transport near the SIT D. Shahar, Z. Ovadyahu, PRB 46, 10971 (1992). J. M. Valles et al., PRL 103, 157001 (2009) Activated behavior! Indicating the exitence a boson mobility edge !

Ioffe-Mezard’s proposal M. V. Feigel'man, L. B. Ioffe, and M. Mezard, PRB (2010).  L. B. Ioffe and M. Mezard, PRL(2010). Model and cavity mean field method Cavity Hamiltonian of spin j j Order parameter of conducting phase

SI transition Susceptibility Replica method Self-average quantity Participation ratio 1-m

Mobility edge ??? Whether the pertubations relax? Matrix elements Pertubations on the boundary Fermi golden rule Should be -1

Phase diagram gc g gc g Temperature Temperature Energy Energy Ioffe – Mezard’s results Expected scenario  L. B. Ioffe and M. Mezard, PRL(2010). Temperature Temperature Energy Energy Green and red line meet at zero energy Full localization, no mobility edge! Discrete levels Continue spectrum Discrete levels Superconductor Superconductor gc g gc g

Comments If the density of state is uniform , why one should expect there is a mobility edge? Indeed, there is no mobility edge in their model! So a mobility edge never appears? It appears in a Glassy insulator!

Phase diagram Superfluid emerges without closing mobility gap! Continue spectrum Discrete levels Glassy SIT Superfluid emerges without closing mobility gap! May explain the puzzling feature (activated behavior)of transport in dirty SC films.

Thank you!