Exciton Condensation in Bilayer Quantum Hall Systems

Abstract

The condensation of excitons, bound electron-hole pairs in a solid, into a coherent collective electronic state was predicted over 50 years ago. Perhaps surprisingly, the phenomenon was first observed in a system consisting of two closely-spaced parallel two-dimensional electron gases in a semiconductor double quantum well. At an appropriate high magnetic field and low temperature, the bilayer electron system condenses into a state resembling a superconductor, only with the Cooper pairs replaced by excitons comprised of electrons in one layer bound to holes in the other.In spite of being charge neutral, the transport of excitons within the condensate gives rise to several spectacular electrical effects. This article describes these phenomena and examines how they inform our understanding of this unique phase of quantum electronic matter.

Coulomb drag

“…They have been used to investigate properties of electron-electron scattering in low-density 2D electron systems Kellogg et al, 2002a); signatures of metal-insulator transition in dilute 2D hole systems (Jörger et al, 2000a,b;Pillarisetty et al, 2002Pillarisetty et al, , 2005a; quantum coherence of electrons (Kim et al, 2011;Price et al, 2008Price et al, , 2007 and composite fermions (Price et al, 2010); exciton effects in electron-hole bilayers Keogh et al, 2005;Morath et al, 2009;Seamons et al, 2009); exotic bilayer collective states (Eisenstein, 2014), especially the quantum Hall effect (QHE) at the total filling factor ν T = 1 (Finck et al, 2010;Kellogg et al, 2003Kellogg et al, , 2002bSchmult et al, 2010;Spielman et al, 2004;Tutuc et al, 2009); compressible quantum Hall (QH) states at half-integer filling factor (Muraki et al, 2004;Zelakiewicz et al, 2000); integer QH regime (Lok et al, 2002); Luttinger liquid effects (Debray et al, 2001;Laroche et al, 2008Laroche et al, , 2014; Wigner crystallization in quantum wires (Yamamoto et al, 2002(Yamamoto et al, , 2006(Yamamoto et al, , 2012; and one-dimensional (1D) sub-bands in quasi 1D wires (Debray et al, 2000;Laroche et al, 2011). More generally, interlayer interaction and corresponding transport properties have been studied in hybrid devices comprising a quantum wire and a quantum dot (Krishnaswamy et al, 1999); a SC film and a 2D electron gas (Farina et al, 2004); Si metal-oxide-semiconductor systems …”

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

“…This allows d/ℓ B and ∆ SAS / e 2 ǫℓB to be tuned continuously in a single sample. To illustrate the typical parameter range that can be accessed, we note that at ν = 1/2 + 1/2 it has been possible to vary d/ℓ B in range 1.2-4, while the interlayer tunneling ∆ SAS can be either completely suppressed or as large as 0.1e 2 /ǫℓ B [58]. The width of individual layers in this case is less than d. On the other hand, in wide QWs one controls independently the width of the entire well and the tunneling amplitude ∆ SAS .…”

Fractional quantum Hall bilayers at half filling: Tunneling-driven non-Abelian phase

“…Compared to single-component systems, multicomponent FQH systems with extra degrees of freedom offer additional tunable parameters and allow the observation of richer quantum phase diagrams [14][15][16][17][18] . The internal degrees of freedom correspond to realistic experimental circumstances, for example, layers, subbands or spins in GaAs quantum wells (QWs) [19][20][21][22][23] , spins or valleys in graphene or AlAs, which lead to effective multilayers separated by layer distance d with electrons' tunneling t ⊥ between layers (Fig. 1).…”

“…Two most notable examples of the multicomponent FQH effects are the observation of quantized Hall plateaus at total filling factors ν T = 1/2 and ν T = 1 in double QW and wide QW systems. The ν T = 1 state 23 is believed to favor a symmetry-breaking state with spontaneous interlayer phase coherence, which induces a remarkable exciton condensation. The ν T = 1/2 state [19][20][21][22] has turned out to be more interesting and controversial, as it can be an Abelian Halperin FQH state, but also be a possible platform for realizing non-Abelian anyonic statistics, which has been pursued persistently in the past.…”