What is 2DQMM?

The purpose of this workshop is to determine the applicability of engineered arrays of dopants in semiconductors, placed with atomic precision, for the study of many-body quantum effects in condensed matter physics. This fabrication procedure gives full control over the array symmetry, spacing and carrier density, as well as control over the bandwidth and band filling. More importantly, manipulation of the number of dopants in a node of the array affords control over the strength of the interactions. Demonstrated techniques, using phosphorus donors in a silicon host, form the basic ingredients for a tunable Fermi-Hubbard system, a canonical many-body quantum system.

Scanning probe microcopy enables a high degree of control over tip positioning, making it possible to pattern a regular distribution of dopants, where the details of the design are determined with near atomic precision. This degree of precision can be realized using phosphorus atoms, and potentially other donors and acceptors such as boron, in a silicon host. This technique relies on a silicon surface terminated with an atomically-ordered layer of hydrogen atoms.  An STM tip is used to selectively remove hydrogen atoms from the surface, resulting in patterned regions of chemically activated sites.  Deposition of appropriate molecular species containing dopants chemisorb only to the lithographically patterned regions.  These dopants are then incorporated into the surface layer of the silicon matrix and silicon is overgrown to protect the atomically-patterned layer.  Additional in-plane support electronics such as source, drain, and gate electrodes can also be patterned using this technique to both probe and manipulate the dopant array.

Recent studies of other tailored systems that provide insight into many-body quantum effects includes a number of alternative approaches, including cold atoms or ions trapped in an optical lattice, superconducting circuits, quantum dots, and photonic lattices. A key advantage of the dopants-in-semiconductors approach is that the accessible energy scales for both electron kinetic energy and electron-electron interaction energy are large relative to the system temperature, and could give unprecedented access to exotic low-temperature phases. However, as a result of the fabrication method itself, some key risks are –it is slow, which limits system size, and it is not atomically perfect, which introduces disorder. Broadly, the critical mission of this workshop is to identify where the opportunities and risks for atomically-precise dopants-in-semiconductor lie relative to the other alternative approaches, and relative to theoretical need in addressing real materials problems.

Some relevant papers

Iulia Buluta and Franco Nori, “Quantum Simulators” Science 326 pp.108-111, (2009). DOI: 10.1126/science.1177838

“We present an overview of how quantum simulators may become a reality in the near future as the required technologies are now within reach. Quantum simulators, relying on the coherent control of neutral atoms, ions, photons, or electrons, would allow studying problems in various fields including condensed-matter physics, high-energy physics, cosmology, atomic physics, and quantum chemistry.”

I. M. Georgescu, S. Ashhab, and Franco Nori, “Quantum Simulation” Rev. Modern Physics 86 153-185 (2014). DOI: 10.1103/RevModPhys.86.153

“A number of quantum systems such as neutral atoms, ions, polar molecules, electrons in semiconductors, superconducting circuits, nuclear spins, and photons have been proposed as quantum simulators. This review outlines the main theoretical and experimental aspects of quantum simulation and emphasizes some of the challenges and promises of this fast-growing field.”

A. Mazurenko, C. S. Chiu, G. Ji, M. F. Parsons, M. Kanász-Nagy, R. Schmidt, F. Grusdt, E. Demler, D. Greif, and M. Greiner, “A cold-atom Fermi–Hubbard antiferromagnet,” Nature, vol. 545, no. 7655, pp. 462–466, May 2017. DOI:10.1038/nature22362

Here we report the realization of an antiferromagnet in a repulsively interacting Fermi gas on a 2D square lattice of approximately 80 sites.”

P. Barthelemy and L. M. K. Vandersypen, “Quantum Dot Systems: a versatile platform for quantum simulations” Ann. Phys., 525, (10–11), pp. 808–826, (2013). DOI: 10.1002/andp.201300124

“Quantum dot systems have shown to be widely tunable quantum systems, that can be efficiently controlled electrically. This tunability and the versatility of their design makes them very promising quantum simulators.”

N. H. Le, A. J. Fisher, and E. Ginossar, “An extended Hubbard model for mesoscopic transport in donor arrays in silicon,” pp. 1–13, 2017  http://arxiv.org/abs/1707.01876.

“Arrays of dopants in silicon are promising platforms for the quantum simulation of the Fermi- Hubbard model.”

J. Salfi, J. A. Mol, R. Rahman, G. Klimeck, M. Y. Simmons, L. C. L. Hollenberg, and S. Rogge, “Quantum simulation of the Hubbard model with dopant atoms in silicon,” Nat. Commun., vol. 7, p. 11342, 2016. DOI:10.1038/ncomms11342

“We find separation-tunable Hubbard interaction strengths that are suitable for simulating strongly correlated phenomena in larger arrays of dopants, establishing dopants as a platform for quantum simulation of the Hubbard model.”

E. Prati, K. Kumagai, M. Hori, and T. Shinada, “Band transport across a chain of dopant sites in silicon over micron distances and high temperatures.,” Sci. Rep., vol. 6, p. 19704, 2016. DOI:10.1038/srep19704

“By employing an atomic chain consists of an array of 20 atoms implanted along the channel of a silicon transistor with length of 1 µm, we extend to such unprecedented distance both the single electron quantum transport via sequential tunneling, and to room temperature the features of the Hubbard bands.”