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The entanglement entropy of the incompressible states of a realistic quantum Hall system in the second Landau level are studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy, which is believed to carry information about topologic order in the ground state, was extracted for filling factors nu = 12/5 and nu = 7/3. While it is difficult to make strong conclusions about nu = 12/5, the nu = 7/3 state appears to be very consistent with the topological entanglement entropy for the k=4 Read-Rezayi state. The effect of finite thickness corrections to the Coulomb potential used in the direct diagonalization are also systematically studied.
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Specific heat has had an important role in the study of superfluidity and superconductivity, and could provide important information about the fractional quantum Hall effect as well. However, traditional measurements of the specific heat of a two-dimensional electron gas are difficult due to the large background contribution of the phonon bath, even at very low temperatures. Here, we report measurements of the specific heat per electron in the second Landau level by measuring the thermalization time between the electrons and phonons. We observe activated behaviour of the specific heat of the 5/2 and 7/3 fractional quantum Hall states, and extract the entropy by integrating over temperature. Our results are in excellent agreement with previous measurements of the entropy via longitudinal thermopower. Extending the technique to lower temperatures could lead to detection of the non-Abelian entropy predicted for bulk quasiparticles at 5/2 filling
We present activation gap measurements of the fractional quantum Hall effect (FQHE) in the second Landau level. Signatures for 14 (5) distinct incompressible FQHE states are seen in a high (low) mobility sample with the enigmatic 5/2 even denominator FQHE having a large activation gap of $sim$600 ($sim$300mK) in the high (low) mobility sample. Our measured large relative gaps for 5/2, 7/3, and 8/3 FQHE indicate emergence of exotic FQHE correlations in the second Ladau level, possibly quite different from the well-known lowest Landau level Laughlin correlations. Our measured 5/2 gap is found to be in reasonable agreement with the theoretical gap once finite width and disorder broadening corrections are taken into account.
We have investigated the behavior of electronic phases of the second Landau level under tilted magnetic fields. The fractional quantum Hall liquids at $ u=$2+1/5 and 2+4/5 and the solid phases at $ u=$2.30, 2.44, 2.57, and 2.70 are quickly destroyed with tilt. This behavior can be interpreted as a tilt driven localization of the 2+1/5 and 2+4/5 fractional quantum Hall liquids and a delocalization through melting of solid phases in the top Landau level, respectively. The evolution towards the classical Hall gas of the solid phases is suggestive of antiferromagnetic ordering.
Quasiparticles, which obey non abelian statistics, were predicted to exist in different physical systems, but are yet to be observed directly. Possible candidate states, which are expected to support such quasiparticles, are the { u}=8/3, { u}=5/2 and { u}=7/3 fractional quantum Hall states (in the second Landau level). The non abelian quasiparticles are expected to carry charge and a unique form of a chiral neutral edge mode. Recent measurements in the { u}=5/2 state detected quasiparticle charge e/4 and an upstream (opposite to charge transport) chiral neutral mode; both agreeing with a non abelian anti-Pfaffian state; although not excluding the possibility of edge reconstruction as the source for the detected upstream neutral mode and a different type of state. Here we present results of detailed measurements of charge and neutral modes in the main three quantum Hall states of the second Landau level. For the { u}=8/3 state we found a quasiparticle charge e/3 and an upstream neutral mode - excluding the possibility of a non abelian Read-Rezayi state and supporting a Laughlin-like state. Such exclusion holds for the hole-conjugate { u}=7/3 state as well, in which no upstream neutral mode was detected. This also proves that edge reconstruction was not present in the { u}=7/3 state, suggesting its absence also in { u}=5/2 state and thus supporting further the non abelian anti Pfaffian state.
For certain measurements, the Corbino geometry has a distinct advantage over the Hall and van der Pauw geometries, in that it provides a direct probe of the bulk 2DEG without complications due to edge effects. This may be important in enabling detection of the non-Abelian entropy of the 5/2 fractional quantum Hall state via bulk thermodynamic measurements. We report the successful fabrication and measurement of a Corbino-geometry sample in an ultra-high mobility GaAs heterostructure, with a focus on transport in the second and higher Landau levels. In particular, we report activation energy gaps of fractional quantum Hall states, with all edge effects ruled out, and extrapolate the conductivity prefactor from the Arrhenius fits. Our results show that activated transport in the second Landau level remains poorly understood. The development of this Corbino device opens the possibility to study the bulk of the 5/2 state using techniques not possible in other geometries.
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