Abstract
What is the fate of the ground state of a two-dimensional electron system (2DES) at very low Landau level filling factors ($\nu$) where interaction reigns supreme? An ordered array of electrons, the so-called Wigner crystal, has long been believed to be the answer. It was in fact the search for the elusive Wigner crystal that led to the discovery of an unexpected, incompressible liquid state, namely the fractional quantum Hall state at $\nu=1/3$. Understanding the competition between the liquid and solid ground states has since remained an active field of fundamental research. Here we report experimental data for a new two-dimensional system where the electrons are confined to an AlAs quantum well. The exceptionally high quality of the samples and the large electron effective mass allow us to determine the liquid-solid phase diagram for the two-dimensional electrons in a large range of filling factors near $\simeq 1/3$ and $\simeq 1/5$. The data and their comparison with an available theoretical phase diagram reveal the crucial role of Landau level mixing and finite electron layer thickness in determining the prevailing ground states.
Highlights
The ground state of an interacting, low-disorder twodimensional electron system (2DES) in a large perpendicular magnetic field (B) has been of continued interest for decades
Note that the 2D holes in GaAs and 2D electrons in ZnO have an effective mass (m∗) which is larger than m∗ of GaAs 2D electrons by a factor of ∼ 6 [24], leading to a larger LL mixing (LLM) parameter κ, defined as the ratio of the Coulomb energy and t√he LL separation: κ = (e2/4π 0 lB)/(heB/m∗), where lB = h/eB is the magnetic length, and is the dielectric constant
Comparing the experimental data with the theoretical w = 4lB liquid-solid boundary, we find agreement with the liquid states predicted in the calculations
Summary
The ground state of an interacting, low-disorder twodimensional electron system (2DES) in a large perpendicular magnetic field (B) has been of continued interest for decades. Our data provide a κ vs ν phase diagram for the liquid-solid states in a large range of fillings (1/5 ν 1/3) and LLM (4 κ 12); note that the typical value for κ in GaAs 2DESs is 1.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have