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arXiv:cond-mat/0209018 · Physical Review Letters

“Fingered” Patterns in Electron Droplets in Nonuniform Magnetic Fields

Taylor L. Hughes, A. D. Klironomos, Alan T. Dorsey

Published May 15, 2003• 1 citation
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Abstract

A semiclassical analysis of a two-dimensional electron droplet in a high, nonuniform magnetic field predicts that the droplet will form "fingered" patterns upon increasing the number of electrons. We construct explicit examples of these patterns using methods first developed for the flow of two-dimensional viscous fluids. We complement our analytical results with Monte Carlo simulations of the droplet wave function, and find that at the point where the semiclassical analysis predicts a cusp on the interface, the droplet fissions-a type of "quantum breakup" phenomenon.

DOI
10.1103/physrevlett.90.196802

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A semiclassical analysis of a two-dimensional electron droplet in a high, nonuniform magnetic field predicts that the droplet will form "fingered" patterns upon increasing the number of electrons. We construct explicit examples of these patterns using methods first developed for the flow of two-dimensional viscous fluids. We complement our analytical results with Monte Carlo simulations of the droplet wave function, and find that at the point where the semiclassical analysis predicts a cusp on the interface, the droplet fissions-a type of "quantum breakup" phenomenon.
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Ultradilute quantum droplets are intriguing new state of matter, in which the attractive mean-field force can be balanced by the repulsive force from quantum fluctuations to avoid collapse. Here, we present a microscopic theory of ultradilute quantum droplets in low-dimensional two-component Bose-Bose mixtures, by generalizing the conventional Bogoliubov theory to include the bosonic pairing arising from the inter-species attraction. Our pairing theory is fully equivalent to a variational approach and hence gives an upper bound for the energy of quantum droplets. In one dimension, we find that the energy calculated by the pairing theory is in an excellent agreement with the latest diffusion Monte Carlo simulation {[}Phys. Rev. Lett. \textbf{122}, 105302 (2019){]}, for nearly all the interaction strengths at which quantum droplets exist. In two dimensions, we show that quantum droplets disappear and may turn into a soliton-like many-body bound state, when the inter-species attraction exceeds a critical value. Below the threshold, the pairing theory predicts more or less the same results as the Bogoliubov theory derived by Petrov and Astrakharchik {[}Phys. Rev. Lett. \textbf{117}, 100401 (2016){]}. The predicted energies from both theories are higher than the diffusion Monte Carlo results, due to the weak inter-species attraction and the increasingly important role played by the beyond-Bogoliubov-approximation effect in two dimensions. Our pairing theory provides an ideal starting point to understand interesting ground-state properties of quantum droplets, including their shape and collective oscillations.
We report thermodynamic magnetization measurements of two-dimensional electrons in several high-mobility Si metal-oxide-semiconductor field-effect transistors. We provide evidence for an easily polarizable electron state in a wide density range from insulating to deep into the metallic phase. The temperature and magnetic field dependence of the magnetization is consistent with the formation of large-spin droplets in the insulating phase. These droplets melt in the metallic phase with increasing density and temperature, though they survive up to large densities.
The magnetic critical properties of two-dimensional Ising spin glasses are controversial. Using an exact ground-state determination, we extract the properties of clusters flipped when a uniform field is increased continuously. We show that these clusters have many holes but otherwise have statistical properties similar to those of zero-field droplets. A detailed analysis gives for the magnetization exponent $\ensuremath{\delta}\ensuremath{\approx}1.30\ifmmode\pm\else\textpm\fi{}0.02$ using lattice sizes up to $80\ifmmode\times\else\texttimes\fi{}80$; this is compatible with the droplet model prediction, $\ensuremath{\delta}=1.282$. The reason for previous disagreements stems from the need to analyze both singular and analytic contributions in the low-field regime.