Thermodynamic Signature of a Two-Dimensional Metal-Insulator Transition

Abstract

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...

Singular or non-Fermi liquids

“…Compressibility (Ä) measurements [81,129] in the region around n = n c show a rapid change in Ä −1 from the negative value characteristic of high r s metallic state to positive values-see Fig. 79.…”

Thermal correction to resistivity in dilute 2D Si-based systems

“…Usually, this behavior is explained [22] in terms of conventional Hartree-Fock exchange omitted in our simple approach. However, for extremely low 2D density the inverse compressibility data always exhibits an abrupt upturn which cannot be explained [23] within HartreeFock scenario. We argue that the above feature has the natural explanation within our model(see dashed line in Fig.3) since d = d 0 exp(−1/ |ξ|) at ξ < 0, |ξ| ≪ 1 and, hence, exhibits T-activated behavior.…”

“…At fixed temperature Fig.3 represents the depen- Then, upon decreasing of 2DEG density( i.e. µ → 0) the experimental data [21,22,23] exhibit diminish and, furthermore, the negative inverse compressibility compared to d 0 . Usually, this behavior is explained [22] in terms of conventional Hartree-Fock exchange omitted in our simple approach.…”

“…These findings are consistent with experimental observations. [22,23] We now address the question of parallel field magnetoresistivity. The energy spectrum modified with respect to valley [24] Fig.4a, inset.…”

“…It is of particular interest the 2DEG compressibility, K = dN dµ = − d 2 Ω dµ 2 , known to be a fundamental quantity generally more amenable to theoretical and experimental analysis. [21,22,23] For noninteracting 2DEG system Eq. (3) yields…”