We present a study of the compressibility, κ, of a two-dimensional hole system which exhibits a metal-insulator phase transition at zero magnetic field. It has been observed that dκ dp changes sign at the critical density for the metal-insulator transition. Measurements also indicate that the insulating phase is incompressible for all values of B. Finally, we show how the phase transition evolves as the magnetic field is varied and construct a phase diagram in the density-magnetic field plane for this system. 73.40.Hm, 71.30+h, 72.20.My Recently, we are seeing a growing body of experimental evidence supporting a metal-insulator quantum phase transition in a number of two-dimensional electron 1 and hole systems 2 where coulomb interactions are strong and particle mobility is quite high. These experiments are of interest because of the prevailing theory of noninteracting particle systems in two dimensions which states that only insulating behavior should be seen at all densities for even the smallest amount of disorder in the system.3 In order to further understand the nature of the unusual phase transition, it is important to study the thermodynamic properties near the transition. One particular question is whether there is any signature for the phase transition in a thermodynamic measurement. Theoretically, within the framework of Fermi liquid, one does not expect any qualitative change in the thermodynamic properties.4 On the other hand, recent theories for strong interacting systems 5,6 have predicted that there should be profound consequences in thermodynamic measurements.In this paper, we address this issue by presenting a measurement of one of the fundamental thermodynamic quantities: the thermodynamic density of states (or equivalently, the compressibility) of a strongly interacting two-dimensional hole system (2DHS). We report evidence that the compressibility measurement indeed provides an unambiguous signature for the metalinsulator transition (MIT). The insulating phase is incompressible. Furthermore, we show that the phase transition at B = 0 is intimately related to the quantum Hall state to insulator transition for the lowest Landau level in a finite magnetic field.Traditionally, to obtain the density of states (DOS) or the compressibility of a 2D electron system, capacitance between the 2D electrons and the gate is measured. 7-10This capacitance can be modeled as the geometrical capacitance in series with a quantum capacitance. The quantum capacitance per unit area c q is related to the DOS dn dµ by c q = e 2 dn dµ , or to κ by c q = n 2 e 2 κ where µ is the chemical potential and n is the carrier density. One major drawback of this method is that, in the low magnetic field limit, the quantum capacitance is much larger than the geometric capacitance. For two capacitors in series, small uncertainty in the geometric capacitance can lead to a large quantitative error (even a sign error) in the extracted κ. In a pioneering experiment by Eisenstein et al.11 , the penetration of the electric field thr...

By tracking the delocalized states of the two-dimensional hole gas in a p-type GaAs/AlGaAs heterostructure as a function of magnetic field, we mapped out a phase diagram in the density -magnetic field plane. We found that the energy of the delocalized state from the lowest Landau level flattens out as the magnetic field tends toward zero. This finding is different from that for the two-dimensional electron system in an n-type GaAs/AlGaAs heterostructure where delocalized states diverge in energy as B goes to zero indicating the presence of only localized states below the Fermi energy. The possible connection of this finding to the recently observed metal-insulator transition at B = 0 in the two-dimensional hole gas systems is discussed.Typeset using REVT E X 1

We have measured compressibility of a two-dimensional hole gas in p-GaAs/AlGaAs heterostructure, grown on a (100) surface, in the presence of a tilted magnetic field. It turns out that the parallel component of magnetic field affects neither the spin splitting nor the density of states. We conclude that: (a) g-factor in the parallel magnetic field is nearly zero in this system; and (b) the level of the disorder potential is not sensitive to the parallel component of the magnetic field.

Key words: quantum gates, cooper pair box, quantum computing

Presented in this work is a comparative study of the thermodynamic compressibility of two different two dimensional systems in GaAs/AlGaAs heterostructures. In the two-dimensional hole system, electron-electron interactions are strong and possibly the reason for an anomalous temperature dependence in the resistivity that is reminiscent of metallic behavior which is known not to exist in a non-interacting two dimensional Fermi gas. The other system is a twodimensional electron system where interactions are much weaker and whose transport properties have been understood in the context of scaling theory. The thermodynamic compressibility of both systems are measured. An unequivocal signature for a phase transition is found in the compressibility measurements for the hole system. In contrast, a very different, non-singular behavior is observed in the electron system. The experimental results are compared with a recent theoretical work.