In this work we report the opening of an energy gap at the filling factor $ u=3+1/3$, firmly establishing the ground state as a fractional quantum Hall state. This and other odd-denominator states unexpectedly break particle-hole symmetry. Specifical
ly, we find that the relative magnitudes of the energy gaps of the $ u=3+1/3$ and $3+1/5$ states from the upper spin branch are reversed when compared to the $ u=2+1/3$ and $2+1/5$ counterpart states in the lower spin branch. Our findings raise the possibility that the former states have a non-conventional origin.
High quality strongly correlated two-dimensional (2D) electron systems at low temperatures $Trightarrow 0$ exhibits an apparent metal-to-insulator transition (MIT) at a large $r_s$ value around 40. We have measured the magnetoresistance of 2D holes i
n weak perpendicular magnetic field in the vicinity of the transition for a series of carrier densities ranging from $0.2-1.5times10^{10}$ $cm^{-2}$. The sign of the magnetoresistance is found to be charge density dependent: in the direction of decreasing density, the sign changes from being positive to negative across a characteristic value that coincides with the critical density of MIT.
Comparing the results of transport measurements of strongly correlated two-dimensional holes in a GaAs heterojunction-insulated-gate field-effect-transistor obtained before and after a brief photo-illumination, the light-induced disorder is found to
cause qualitative changes suggesting altered carrier states. For charge concentrations ranging from $3times10^{10}$ $cm^{-2}$ down to $7times10^{8}$ cm$^{-2}$, the post-illumination hole mobility exhibits a severe suppression for charge densities below $2times10^{10}$ cm$^{-2}$, while almost no change for densities above. The long-ranged nature of the disorder is identified. The temperature dependence of the conductivity is also drastically modified by the disorder reconfiguration from being nonactivated to activated.
Detailed measurements of the longitudinal thermopower of two-dimensional electrons in the first excited Landau level are reported. Clear signatures of numerous fractional quantized Hall states, including those at $ u = 5/2$ and 7/3, are observed in t
he magnetic field and temperature dependence of the thermopower. An abrupt collapse of the thermopower is observed below about $T= 40$ mK at those filling factors where re-entrant insulating electronic states have been observed in conventional resistive transport studies. The thermopower observed at $ u = 5/2$ is discussed in the context of recent theories which incorporate non-abelian quasiparticle exchange statistics.
Spectroscopic methods involving the sudden injection or ejection of electrons in materials are a powerful probe of electronic structure and interactions. These techniques, such as photoemission and tunneling, yield measurements of the single particle
density of states (SPDOS) spectrum of a system. The SPDOS is proportional to the probability of successfully injecting or ejecting an electron in these experiments. It is equal to the number of electronic states in the system able to accept an injected electron as a function of its energy and is among the most fundamental and directly calculable quantities in theories of highly interacting systems. However, the two-dimensional electron system (2DES), host to remarkable correlated electron states such as the fractional quantum Hall effect, has proven difficult to probe spectroscopically. Here we present an improved version of time domain capacitance spectroscopy (TDCS) that now allows us to measure the SPDOS of a 2DES with unprecedented fidelity and resolution. Using TDCS, we perform measurements of a cold 2DES, providing the first direct measurements of the single-particle exchange-enhanced spin gap and single particle lifetimes in the quantum Hall system, as well as the first observations of exchange splitting of Landau levels not at the Fermi surface. The measurements reveal the difficult to reach and beautiful structure present in this highly correlated system far from the Fermi surface.
