Tunable Hubbard Lattices in Semiconductor Nanowire Networks

One of the most important outstanding questions in physics is arguably the understanding of correlated electrons in condensed matter.

The theoretical framework is given by the Hubbard model, however, no analytical solutions have been found and numerical treatments are challenging and controversial.

Although great progress has been made in experimental implementations of the Hubbard model in cold atom lattices and ion traps, the most interesting regime of low temperature and strong interactions, presumably accounting for the physics of High-Tc superconductors, is yet to be realized.

In this project a new experimental platform is proposed for realizing tunable lattices of coupled quantum dots (QDs) by combining Molecular Beam Epitaxy crystal growth of semiconductor nanostructures, state-of-the-art semiconductor processing, and low-temperatures quantum transport.

Macroscopic networks of ultra-high quality InAs nanowires will be combined with epitaxial integration of dielectric layers and gate metals. The gates thereby retain the ultimate limit of uniformity; overcoming previous problems with QD arrays.

Conservative estimates of the on-site Coulomb interaction ~100-200Kelvin and with fully gate-tunable tunnel couplings, the strongly interacting, low-T regime is easily reachable.

Both square and honeycomb lattices will be realized and the macroscopic properties will studied by transport and quantum capacitance spectroscopy at mK temperatures, and in addition, the currents will be locally probed by scanning SQUID microscopy.

Furthermore, by a new concept for gating, we achieve tunable spatial modulation of tunnel couplings, and thereby enable in situ tunable gauge fields, tunable disorder, and controlled symmetry breaking. A proof-of-concept experiment is discussed.

If successful, the results will have major impact on physics, technology and material science by providing a tunable model of the foundation of solid state physics.