Superglasses and the nature of disorder-induced SI transition

Xiaoquan YuAdvisor: 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 glassesA spin glass is a magnet with random frustrated interactions.

Spin glasses display many metastable structures.

Ferromagnetic and antiferromagnetic bonds are randomly distributed.

Gaussion in one pure state

Many pure states.

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

Robust to on-site disorderNot BCS type!

Gingras et al., PRL (2010).

QMC

Glassy SIT!

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

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 !

Activated transport near the SIT

Ioffe-Mezard’s proposal

• Model and cavity mean field method

Order parameter of conducting phase

M. V. Feigel'man, L. B. Ioffe, and M. Mezard, PRB (2010). L. B. Ioffe and M. Mezard, PRL(2010).

Cavity Hamiltonian of spin jj

• SI transition

Susceptibility

Replica method

Self-average quantity

Participation ratio

1-m

• Mobility edge Whether the pertubations relax?

Fermi golden rule

Pertubations on the boundary Matrix elements

???

Should be -1

Phase diagram

Superconductor

g

Temperature

Energy

Discrete levels

gc

Green and red line meet at zero energy

g gc

Temperature

Full localization, no mobility edge!Discrete levels

Continue spectrum

Energy

Ioffe – Mezard’s results

Superconductor

Expected scenario

L. B. Ioffe and M. Mezard, PRL(2010).

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

Continue spectrum

Discrete levels

Superfluid emerges without closing mobility gap! Glassy SIT

May explain the puzzling feature (activated behavior)of transport in dirty SC films.

Thank you!