Carbon nanotube arrays are designed to investigate the behaviour of electrons in low‑dimensional systems. By arranging well‑aligned 1D nanotubes into a 2D film, the researchers create a coupled‑wire structure that allows them to study how electrons move and interact as the system transitions between different dimensionalities. Using a gate electrode positioned on top of the array, the researchers were able to tune both the carrier density (number of electrons and holes in a unit area) and the strength of electron–electron interactions, enabling controlled access to regimes. The nanotubes behave as weakly coupled 1D channels where electrons move along each nanotube, as a 2D Fermi liquid where the electrons can move between nanotubes behaving like a conventional metal, or as a set of quantum‑dot‑like islands showing Coulomb blockade where at low carrier densities sections of the nanotubes become isolated.

The dimensional transitions are set by two key temperatures: T₂D, where electrons begin to hop between neighbouring nanotubes, and T₁D, where the system behaves as a Luttinger liquid which is a 1D state in which electrons cannot easily pass each other and therefore move in a strongly correlated, collective way. Changing the number of holes in the nanotubes changes how strongly the tubes interact with each other. This controls when the system stops acting like separate 1D wires and when strong interactions make parts of the film break up into isolated regions that show Coulomb blockade.

The researchers built a phase diagram by looking at how the conductance changes with temperature and voltage, and by checking how well it follows power‑law behaviour at different energy ranges. This approach allows them to identify the boundaries between Tomonaga–Luttinger liquid, Fermi liquid and Coulomb blockade phases across a wide range of gate voltages and temperatures.

Overall, the work demonstrates a continuous crossover between 2D, 1D and 0D electronic behaviour in a controllable nanotube array. This provides an experimentally accessible platform for studying correlated low‑dimensional physics and offers insights relevant to the development of nanoscale electronic devices and future carbon nanotube technologies.

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Structural approach to charge density waves in low-dimensional systems: electronic instability and chemical bonding Jean-Paul Pouget and Enric Canadell (2024)