Luttinger Liquid Behavior of 3He Atoms

Published March 13, 2023

The illustration shows a cross section of a hexagonal nanochannel.

Using the NMR techniques and ultra-low temperature facilities at the MagLab, atoms of a pure isotope of helium showed experimental signs of the Luttinger liquid theory, an exact quantum mechanical solution of interacting fermions in one-dimension.

What did scientists discover?

At ultra-low temperatures - from 1K down to below 0.01K - ³He atoms demonstrated a clear experimental signature of the Luttinger liquid theory, an exact quantum mechanical solution of interacting fermions in one-dimension.

Using the unique ultra-low-temperature nuclear magnetic resonance (NMR) techniques at the MagLab’s High B/T facility to probe a one-dimensional (1D) system built from ³He atoms confined to a one-dimensional region that is only 1 nanometer in diameter. This is achieved by inert 4He atoms that line the interior of a hollow nanotube (see Figure).

Why is this important?

Although Fermi liquid theory works very well in understanding the properties of three-dimensional fermion systems such as electrons in metals and liquid ³He at very low temperatures, Fermi liquid theory completely breaks down in the case of 1D fermion systems. Instead, the dynamics of 1D systems are believed to be characterized by interactions described by the Luttinger liquid theory. Numerous experimental efforts have focused on searching for signatures of a Luttinger liquid in electron systems. Due to instabilities in electron systems arising from the fact that electrons are charged particles, definitive evidence for the existence of a Luttinger liquid has remained elusive. This user research represents one of the first investigations of dynamics in a charge-neutral 1D fermion system that has been sufficiently cooled to ultra-low temperatures where experimental signatures of the Luttinger liquid can be detected.

Who did the research?

Donald Candela¹, Johnny Adams^2,3, Chao Huan^2,3, Naoto Masuhara^2,3, Neil S. Sullivan^2,3

¹University of Massachusetts, Amherst; ²National MagLab; 3University of Florida;

Why did they need the MagLab?

This research requires ultra-low temperatures, high-homogeneity magnetic fields, and the instrumentation and expertise required to perform NMR measurements under such extreme conditions, a combination that can only be met at the MagLab’s High B/T facility.