Quantum Transport in One-Dimensional Nanostructures

Contact Charis Quay (cquayhl@) or Joseph Sulpizio (jopizio@) for more information.

We study electron-electron interactions and quantum effects in one-dimensional (1D) systems by fabricating devices using various nanofabrication techniques and performing low-temperature transport measurements.  Currently, we are studying devices made from carbon nanotubes, peapods, and cleaved edge overgrowth wires.

Overview of 1D Interacting Quantum Systems

Although interactions between particles such as electrons are present in higher-dimensional systems (dimension >1), many systems can amazingly be effectively described in terms of nearly independent particles as a Fermi liquid.  In the Fermi liquid theory treatment of an electronic system, the fundamental excitations are no longer electrons.  Instead, the excitations are termed quasiparticles, which are "dressed" electrons with surrounding charge-density fluctuations.  The quasiparticle description leads to some important differences from completely independent electron descriptions (Landau parameters), but quasiparticle excitations are essentially non-interacting, and many higher-dimensional systems can therefore be described in terms of independent particles.

In 1D interacting systems, the Fermi liquid treatment is no longer valid.  A simple cartoon (below) helps clarify this important difference between 1D and higher dimensions.  In a 1D interacting system, a particle cannot move unless all the other particles move as well, since the reduced dimensionality prevents the particles from moving around the others as in higher-dimensional systems.  Therefore, in 1D with interactions, the excitations are collective, and an independent particle description is certainly not applicable.

Figure 1. (a) Independent quasiparticle excitations in higher dimensions and (b) a 1D system forced to behave collectively due to interactions between particles [1].

The interacting 1D quantum state is then a correlated non-Fermi liquid state, and is described theoretically as a Luttinger liquid. The Luttinger liquid has many fascinating physical properties that differ from normal Fermi liquids, and is one of the few exactly soluble many-body problems.

Tunable Tunnel Barriers in Single-Walled Carbon Nanotubes

Carbon nanotubes are predicted theoretically to exhibit Luttinger liquid behavior, and this has been observed experimentally [2, 3].  We are currently fabricating carbon nanotube devices with tunable tunnel barriers using lithographically-defined metal gate electrodes.  By studying transport in these devices, we aim to probe the electron-electron interactions and further test the predictions of Luttinger liquid theory.  In particular, applying a voltage to the narrow metal gate electrode will locally deplete the region of the nanotube directly beneath the gate, creating a tunnel barrier [4].  By varying this gate voltage, the transmission coefficient, τ, of the tunnel barrier can be tuned.  We hope to carefully study tunelling transport in a Luttinger liquid in various regimes of barrier transmission.  A schematic of our device is shown below. 

Figure 2. Schematic of a nanotube tunable tunnel barrier device. Regions 1 and 2 are the source and drain, and region 3 is an insulating ALD layer.

SEM images of completed devices.

Carbon nanotube peapods are carbon nanotubes filled with another carbon allotrope called buckyballs (or buckminsterfullerene). Buckyballs look like footballs (soccer balls) with a carbon atom at every vertex (see picture below). Sparsely filled nanotubes allow us to look at slightly perturbed one-dimensional systems, while nanotubes completely filled with buckyballs are ideal for studying electrons in nicely periodic one-dimensional potentials. TEM images of our peapods are shown below.

Figure 3. (a) Structure of a buckyball [5] and (b) TEM images of our peapods.

Cleaved Edge Overgrowth Wires

Almost a decade ago now, researchers began fabricating one-dimensional wires from GaAs/AlGaAs 2DEG (two-dimensional electron gases) using an ingenious technique called cleaved edge overgrowth. [6] In this process, a conventional 2DEG is first grown by molecular beam epitaxy (MBE). (Fig. 3a) Metal gates and tick marks indicating the site of a future cleave are then fabricated on the surface of the wafer using standard photolithography techniques. The wafer is then re-introduced to the MBE chamber where it is cleaved and a second 2DEG layer sequence is grown onto the edge. (Fig. 3b) Each gate can be used to deplete the 2DEG under it, forming a wire at the edge of the wafer, which is contacted through the 2DEG on either side (Fig. 3c).

Figure 4. Cleaved edge overgrowth. (a) 2DEG is grown by MBE and cleaved after defining metal gates. (b) A 2nd MBE layer is grown onto the edge, (c) forming a gated 1D wire contacted through the 2DEG.

Together with collaborators at Bell Labs, we are studying cleaved edge overgrowth hole wires in GaAs. Holes in GaAs differ from electrons in having higher effective masses; this is expected to enhance the interactions between the particles leading, it is hoped, to more easily observable 1D behaviour. Holes also experience larger spin-orbit couplings compared to electrons. In 2D, this leads to the formation of two bands of 'heavy' and 'light' holes, but it is not as yet clear what should happen in 1D.

[1] T. Giamarchi Quantum Physics in One Dimension (Oxford Univ. Press, New York, 2004).
[2] M. Bockrath et al., Nature 397, 598 (1999).
[3] Z. Yao et al., Nature 402, 273 (1999).
[4] M. J. Biercuk et al., Phys. Rev. Lett. 94, 026801 (2005).
[5] http://www.godunov.com/Bucky/fullerene.html
[6] A. Yacoby, H. L. Stormer, K. W. Baldwin, L. N. Pfeiffer, K. W. West, Solid State Comm. 101, 77-81 (1997).