Observation of a ν=1/2 fractional quantum Hall state in a double-layer electron system

Abstract

We report the observation, for the first time, of a fractional quantum Hall state at v -1/2 Landaulevel filling in a low disorder, double-layer electron system realized in a 680-A-wide GaAs/AlGaAs single quantum well. A nearly vanishing diagonal resistance and a Hall resistance quantized at 2h/e 2 to within 0.3% are observed at -15 T and -26 mK. The activated temperature dependence of the diagonal resistance minimum yields a quasiparticle excitation energy gap of 230 mK.In a standard hierarchy picture [1], assuming that the two-dimensional (2D) electrons are all spin polarized, the fractional quantum Hall (FQH) states can only be realized at Landau-level filling factors (v) with odd denominators. This restriction to odd denominators is a result of the Fermi statistics which requires antisymmetry under particle exchange. If the condition of a spin-polarized ground state is relaxed, FQH states at even-denominator v become possible [2]. This is the explanation given by Haldane and Rezayi [3] for the experimental observation of the v -5/2 FQH state [4] which has been seen only at relatively low magnetic fields where the Zeeman energy is small [5]. For other even-denominator fillings, and especially for v = l/2, although many transport anomalies have been reported for the 2D electron systems in GaAs/Al v Gaiv As heterostructures [6-8], no evidence of a FQH state has yet been found [9]. Another candidate for the possible observation of an even-denominator FQH state [10] is a double-layer electron system (DLES) where the layer index can be treated as a pseudospin to take into account the additional degrees of freedom. Recent numerical studies [11,12] show that the FQH state at v=l/2 can be stabilized in a DLES with an appropriate CMB, where d is the separation between the layers and Ig^ih/eB)^2is the magnetic length. Experimentally, a DLES can be realized in a double quantum-well structure [13] where two sheets of electrons are separated by a high band-gap barrier, or in a wide, single, quantum well [14] where the electrons are separated by their own electrostatic repulsion. Experiments in these systems have shown that strong magnetic fields can destroy or weaken [13,14] the integral quantum Hall (IQH) states at odd v corresponding to the symmetric-antisymmetric energy gap (ASAS); this phenomenon has been attributed to the competition between the interwell and intrawell Coulomb interactions [15,16]. However, no observation of a v-\/2 FQH state has been reported in a DLES prior to this work.In this Letter, we present IQH and FQH effect data in a high-quality DLES realized in a wide, single, GaAs quantum well. We observe a well-developed FQH state at v=l/2 with a nearly vanishing diagonal resistance (R xx ) and a Hall resistance (R xx ) quantized at 2h/e 2 to within 0.3%. The temperature-activated behavior of R xx allows us to determine the energy gap for the quasiparti-

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

“…In the intermediate regime d ∼ 2 − 6, the incompressibility of the system is observed in various experiments [19][20][21][22] . However, its precise origin is still a long-standing subject.…”

“…Although such a possibility was predicted about 20 years ago [16][17][18][24][25][26][27] , convincing and comprehensive evidence directly from a microscopic description was missed until our work. Second, the previously found FQH ν T = 1/2 plateau in single wide QW experiments 19,21,22 , where the tunneling strength is taken to be considerable, is most likely to be captured by the MR Pfaffian state and in favor of a nontrivial p x + ip y pairing mechanism. By reducing the effec- tive tunneling (through tuning electron density), the system undergoes a transition from the non-Abelian MR Pfaffian to the weak p-wave pairing (331) Halperin state, while the Hall conductance keeps unchanged.…”

“…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. [16][17][18][24][25][26][27][28][29][30][31] In this paper, we consider a two-component FQH system with N e electrons (as illustrated in Fig.…”

“…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).…”

Fractional quantum Hall effect of two-dimensional electrons in high-mobility Si/SiGe field-effect transistors

“…Celebrated examples include Skyrmions in systems with small Zeeman splitting [6,7], even-denominator FQH states [8,9], and the excitonic superfluid in bilayer systems [10]. While much effort towards the understanding of the roles of spins, layers, and subbands in the FQH regime has been made using high-quality GaAs quantum wells, experimental studies on the effects of valleys have been relatively sparse, only a few reports on 2D electrons in Si [11,12] and AlAs [13][14][15][16] available, partly due to the less impressive material quality of multi-valley semiconductors.…”