Disordering of a quantum Hall superfluid M.V. Milovanovic, Institute of Physics, Belgrade, Serbia

The quantum Hall bilayer A fundamental problem of: Superfluid disordering in 2+1 dimensions!

d (distance between layers) small Superfluid Appropriate quasiparticles CBs (composite bosons)‏ Th: Wen and Zee,PRL 69, 1811(1992) …, Exp: Spielman et al., PRL 84, 5808 (2000)…

Theory of Moon et al. PRB 51, 5138 (1995) Quantum Mechanical view of electron – spinor states, Ground state is a condensate of same spin states – phase coherence k = angular momentum in disc geometry essentially XY model physics – physics of superfluid expect: (1) Goldstone mode (2) elementary charged vortices-merons (3) finite T BKT transition fixed relative number of particles state =

d large Fermi-liquid-like state Approprite quasiparticles CFs (composite fermions)‏ Th: B.I. Halperin, P.A. Lee, and N. Read, PRB 47, 7312 (1993),…, Exp: R.L. Willett et al., PRL 71, 3846 (1993),…

Experiments Spielman et al., PRL 87, (2001)Kellogg et al., PRL 93, (2004)

Discrepancies from ideal superfluid – “imperfect superfluid” Kellogg et al., PRL 93, (2004) Experiments

drag – evolution with d persistance of intercorrelations for large d Kellogg et al., PRL 90, (2003)

Experiments – transition at finite T Conductance at zero bias G(0) vs. T, d Phase boundary at ν T = 1 Champagne et al., PRL 100, (2008)

What about intermediate distances, how transition proceeds? What is the superfluid disordering that results in ?

Two paradigms of superfluid disordering: (1) BKT (2D XY) dipole unbinding (2) λ (3D XY) condensation of loops

AB M.V.Milovanovic, Bull. Am. Phys. Soc. 48 (2003); S.H. Simon, E.H. Rezayi, and M.V. Milovanovic, PRL 91, (2003)‏

(a) and (c) superfluid (b) dsf., com. – vortex metal (d) dsf., incom. – top. phase? M.V.Milovanovic, PRB 75, (2007), Z. Papic and M.V. Milovanovic, PRB 75, (2007)‏ (I) (II)

Chern-Simons linear response (a)‏(b)‏

(a) (b): vortex metal – (I) universality class (a): neutral fermion pairs in dual (Laughlin plasma) picture (a) (b) BKT unbinding or dipole dissociation M.V.Milovanovic and Z.Papic, PRB 79, (2009)

(a):

exactly rewritten as: Fock space of neutral fermions:

Stern and Halperin proposal with phase separation (fermi liquid puddles inside superfluid) explains drag experiments by deriving semicircle law - A.Stern and B.I. Halperin, PRL 88, (2002) But also (a) and (b) (homogenous wave functions) in a Chern-Simons response conform to semicircle law!

semicircle law S.H.Simon et al., PRL 91, (2003) ( case case (b): Z. Papic and M.V. Milovanovic, PRB 75, (2007)‏

( MM (c) © (c): spin-wave (phonon) contribution- in (II) universalty class B Bogoliubov:Chern-Simons: from wave functions: 1+1 neutral fermion (I) (II) Lopez, Fradkin PRB 51, 4347 (1995);Jiang,Ye PRB74, (2006)

(c) (d): topological phase? -(II) univesality class (d): M.V.Milovanovic and Z.Papic, PRB 79, (2009)

use bosonic CFT analogies:

Excitations :

There must be also a branch of gapless excitations topological phase is of the kind described by BF Chern-Simons theory But But! can be any real number, also zero by CFT analogies:

(1) impurities in exps. on bilayer cause BKT disordering via pairs of neutral fermions (they lock charged elementary merons)‏ (2) we may hope that sufficiently clean bilayer systems may serve as generators (via loop condensation) of (quasi) topological phases described by doubled Chern-Simons theories