Particle-hole asymmetry of fractional quantum Hall states in the second Landau level of a two-dimensional hole system

In a two-dimensional electron system (2DES) subjected to a perpendicular magnetic field B the Coulomb interaction between the charge carriers leads to the emergence of prototype many body ground states unknown in any other condensed matter system. Well known examples of such ground states are the fractional quantum Hall states (FQHS) of the lowest Landau level (LL) [1] which are understood in terms of Laughlin’s wavefunction [2] and Jain’s composite fermion theory [3]. Another example yet to be understood is the even denominator � = 5=2 FQHS in the second LL [4–17]. According to an intriguing proposal this state arises from a p-wave pairing of composite fermions described by the Pfaffian wavefunction. In contrast to the FQHS of the Jain sequence, the � = 5=2 Moore-Read Pfaffian [18–20] and its particle-hole conjugate anti-Pfaffian [21–23] are predicted to have quasiparticles which obey non-Abelian statistics and might be harnessed for topological quantum computing [24, 25]. Other recent theoretical work on the � = 5=2 FQHS, however, proposes an explanation which does not involve the Pfaffian [26–28]. In the second LL besides the � = 5=2 FQHS there are numerous FQHS observed at odd denominator LL filling factors of which the most prominent ones are the � = 7=3 and 8=3 FQHS [5–17]. The 7=3 and 8=3 FQHS obey the odd denominator rule of the Jain sequence and the existence of their counterparts in the lowest LL at � = 1=3 and 2=3, respectively, might suggest that they are of the Laughlin-Jain type. Numerical work found, however, either an absence of Laughlin correlations or no incompressibility at � = 7=3 [29–35]. Theories based on Laughlin’s wavefunction have been refined since by the inclusion of non-ideality factors of real samples such as finite layer thickness [36] and LL mixing [28] and find that the Laughlin state is a good candidate for the � = 7=3 FQHS in certain conditions. Other theories find that the odd denominator FQHS of the second LL are more exotic [37–39]. These theories extend ideas used in the construction of the Pfaffian wavefunction to odd denominator FQHS and therefore predict non-Abelian quasiparticle excitations. Thus not only the even but also the odd denominator FQHS of the second LL remain under intense scrutiny. To date FQHS in the second LL have only been convincingly observed in 2DES. We report in this Letter the first FQHS observed in the second LL of a twodimensional hole system (2DHS) at � = 8=3. This was possible because of recent progress in the growth of exceptional quality Carbon-doped 2DHS [40–44] and of achievement of ultra low charge carrier temperature. The 8=3 FQHS has an energy gap of 40 mK and, to our surprise, its particle-hole symmetric pair at � = 7=3 is missing. This observation is contrary to that in electron samples where the � = 7=3 FQHS is typically more robust than the � = 8=3 FQHS.