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Scientists Map Elusive Physics Phenomena Using Hubbard Model Simulator

Individuals can interpret the behavior of quantum particles by envisaging a pinball game, but instead of a single metal ball, there are scores of balls that all bounce off one another and their surroundings.

Cornell researchers stacked two atomic monolayers of a semiconductor—tungsten disulfide and tungsten diselenide—to create a moiré superlattice that acts as a simulator for the Hubbard model. This simplified system enables the team to better understand the essential physics of many interacting quantum particles. Image Credit: Cornell University.

For a long time, physicists have been trying to analyze this interactive system of powerfully correlated particles, which can potentially shed light on the strange physics phenomena, such as magnetism and high-temperature superconductivity.

One typical technique is to produce a simplified model that is capable of recording the essence of such particle interactions. In 1963, a team of physicists, which included Martin Gutzwiller, Junjiro Kanamori, and John Hubbard who worked separately, recommended what came to be known as the Hubbard model. This model describes the fundamental physics of several interacting quantum particles.

But the solution to the Hubbard model only exists in a single dimension (1D). For many years, physicists have attempted to achieve the Hubbard model in two dimensions (2D) or three dimensions (3D) by developing quantum simulators that can imitate it.

A collaboration headed by Cornell University has effectively developed a quantum simulator using ultrathin monolayers that overlap to create a moiré pattern. This solid-state platform was then used by the researchers to map an age-old enigma in physics—that is, the phase diagram of the triangular lattice Hubbard model.

The researchers’ study, titled “Simulation of Hubbard Model Physics in WSe2/WS2 Moiré Superlattices,” was published in the Nature journal on March 18th, 2020. Postdoctoral associate Yanhao Tang is the lead author of the study.

The study was headed by Kin Fai Mak, an associate professor of physics in the College of Arts and Sciences and the co-senior author of the study, together with Jie Shan, a professor of applied and engineering physics in the College of Engineering.

Both scientists are members of the Kavli Institute at Cornell for Nanoscale Science and came to Cornell University via the provost’s Nanoscale Science and Molecular Engineering (NEXT Nano) initiative. The researchers’ shared laboratory concentrates on the physics of atomically thin quantum materials.

The duo’s laboratory has collaborated with the study’s co-author Allan MacDonald, a physics professor at the University of Texas at Austin and who conceptualized in 2018 that a Hubbard model simulator can be achieved by stacking a pair of atomic monolayers of semiconductors—the kind of materials that Mak and Shan have been investigating for 10 years.

What we have done is take two different monolayers of this semiconductor, tungsten disulfide (WS2) and tungsten diselenide (WSe2), which have a lattice constant that is slightly different from each other. And when you put one on top of the other, you create a pattern called a moiré superlattice.

Kin Fai Mak, Study Co-Senior Author and Associate Professor, Department of Physics, The College of Arts and Sciences, Cornell University

The moiré superlattice appears similar to an array of interlocking hexagons, and the scientists placed a single electron in each site, or juncture, in the crosshatch pattern. Such electrons are often held in place by the energy barrier that exists between the sites. However, these electrons have sufficient kinetic energy that, at times, can jump across this energy barrier and communicate with adjacent electrons.

If you don’t have this interaction, everything is actually well understood and sort of boring,” added Mak. “But when the electrons hop around and interact, that’s very interesting. That’s how you can get magnetism and superconductivity.”

Since electrons are known to have a negative charge and repel one another, the resulting interactions turn out to be more and more complicated when so many of them are active; this underscores the need for a streamlined system to interpret the behavior of electrons.

We can control the occupation of the electron at each site very precisely. We then measure the system and map out the phase diagram. What kind of magnetic phase is it? How do the magnetic phases depend on the electron density?

Kin Fai Mak, Study Co-Senior Author and Associate Professor, Department of Physics, The College of Arts and Sciences, Cornell University

To date, the scientists have utilized the quantum simulator to make a couple of major discoveries—that is, mapping the magnetic phase diagram of the system and visualizing a Mott insulating state. Mott insulators are a group of materials that are expected to conduct electricity and act like metals but instead work like insulators. Physicists had predicted that such a phenomenon could be demonstrated by the Hubbard model.

Another significant phenomenon being studied by the scientists is the magnetic ground state of Mott insulators. There are other types of quantum simulators, like the one that utilizes cold atom systems as well as an artificial lattice produced by laser beams. But according to Mak, the simulator developed by his research team has a clear advantage of being a “true many-particle simulator” that can control or adjust the density of particles easily.

Additionally, the system can reach relatively lower effective temperatures and evaluate the model’s thermodynamic ground states. Meanwhile, the novel simulator is not so effective at adapting the interactions between electrons when the same site is shared by them.

We want to invent new techniques so that we can also control the on-site repulsion of two electrons. If we can control that, we will have a highly tunable Hubbard model in our lab. We may then obtain the complete phase diagram of the Hubbard model.

Kin Fai Mak, Study Co-Senior Author and Associate Professor, Department of Physics, The College of Arts and Sciences, Cornell University

Others who contributed to the study include PhD student Lizhong Li, postdoctoral associates Tingxin Li and Yang Xu, and scientists from the National Institute for Materials Science in Tsukuba, Japan and Columbia University.

The study was mainly supported by the U.S. Department of Energy.


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