A recent experience detailed in the review Nature challenges our view of the behavior of electrons in quantum materials. Using stacked layers of a material called tungsten ditelluride, the researchers observed two-dimensional electrons behaving as if they were in one dimension – and in the process created what the researchers claim is a new state electronics of matter.
“It really is a whole new horizon,” said Sanfeng Wuassistant professor of physics at princeton university and the main author of the article. “We were able to create a new electronic phase with this experiment – basically, a new kind of metallic state.”
Our current understanding of the behavior of interacting electrons in metals can be described by a theory that works well with two-dimensional and three-dimensional systems, but fails when it comes to describing the interaction of electrons in a single dimension.
“This theory describes the majority of metals we know of,” Wu said. different in certain characteristic quantities, such as mass and magnetic moment.”
In one-dimensional systems, however, this “Fermi’s liquid theory” gives way to another theory, “Luttinger’s liquid theory”, to describe the interaction between electrons.
“Luttinger’s liquid theory provides a basic starting point for understanding interacting electrons in one dimension,” Wu said. they start not acting like free electrons.”
Fermi’s liquid theory was first proposed by Nobel laureate LD Landau. Luttinger’s theory went through a long process of refinement before it was widely accepted by physicists. A theoretical model was first proposed by Japanese Nobel laureate Shinichiro Tomonaga in the 1950s, Wu said, and was formulated independently by J. M. Luttinger later in 1963. Luttinger, however, provided an inadequate solution and so Princeton mathematician and physicist Elliott Lieb, now the physics professor emeritus Eugene Higgins, took up the challenge in 1965, eventually providing a correct solution. Another physicist and Nobel laureate, F. Duncan Haldane, a professor of physics at Princeton’s Sherman Fairchild University, later used the model in 1981 to understand one-dimensional metal interaction effects. Haldane coined the term “Luttinger liquids” and laid the foundation for modern Luttinger liquid theory as a general description of one-dimensional metals.
For a long time, these two theories – Fermi’s liquid theory and Luttinger’s liquid theory – have been central to our understanding of the behavior of electrons in condensed matter physics, depending on their dimensionality.
But there have been hints that electron interactions are much more complex than this simple classification. Philip Anderson, another Nobel laureate and Princeton physicist, proposed in the 1990s that there might be some “exotic” cases in which the behavior of electrons in two-dimensional systems, on rare occasions, might also follow the predictions of Luttinger’s liquid theory. In other words, although electrons in two-dimensional systems are usually explained by Fermi’s liquid theory, Anderson wondered if these electrons might counterintuitively behave like a Luttinger’s liquid, as if they were in a one-dimensional system.
It was largely hypothetical. There was no experience that could be linked to these exotic cases, Wu said.
Through experimentation, Wu and his team discovered that electrons in a specially created two-dimensional material structure, when cooled to very low temperatures, suddenly began to behave as predicted by Luttinger’s liquid theory. In other words, they acted like correlated electrons in a one-dimensional state.
The researchers conducted their experiment using a material called tungsten ditelluride (WTe2), a laminated semi-metal. A semi-metal is a compound that has intermediate properties that place it between metals and insulators. Princeton researchers Leslie Schoop, Assistant Professor of Chemistry, and Robert Cava, Russell Wellman Moore Professor of Chemistry, and their teams have created the highest quality tungsten ditelluride crystals. Wu’s team then created single atomic layers of this material and stacked two of them vertically for study.
“We stacked tungsten ditelluride monolayers on top of each other and used a 5 or 6 degree angle twist,” said Pengjie Wang, co-first author of the article and postdoctoral research associate. This created a large rectangular lattice called a moiré pattern, which resembles a common French textile design.
The team originally planned to observe how the twist angle would affect other types of quantum phenomena in tungsten ditelluride. But what they found amazed them.
“At first, we were confused by the results,” Wang said. “But it turned out to be true.”
The researchers observed that the electrons, instead of acting freely, began to pack strongly into a linear array indicative of electrons in a one-dimensional system.
“What you have here is really a two-dimensional metallic state that is not described by the standard Fermi liquid theory,” Wu said. dimensions described by Luttinger’s liquid theory.”
Guo Yuco-first author of the paper and a graduate student in electrical and computer engineering, described the material properties as being remarkably switchable between uniform in all directions (isotropic) or highly varying in physical properties when measured in different directions (anisotropic).
“What is unique about our twisted bilayer tungsten ditelluride system is that, unlike most other single-layer materials and their moiré superlattices which are isotropic, the moiré pattern of our sample is highly anisotropic. , crucial for hosting one-dimensional physics,” Yu. said.
A new metallic phase might appear to have many practical applications, but Wu cautioned that this is preliminary research. Before such applications can be realized, he said, more work needs to be done.
Nevertheless, Wu is optimistic about the future. “It could help open a whole new window to look at new quantum phases of matter,” he said. “In the years to come, we will see many new discoveries coming out of this research.”
Besides Wu, Wang, Yu, Schoop, and Cava, other Princeton contributors were physics graduate student Yanyu Jia and Shivaji L. Sondhi, a former professor in the physics department at Princeton and now at Oxford University; and Shiming Lei, Sebastian Klemenz, F. Alexandre Cevallos, and Ratnadwip Singha from the Department of Chemistry. Yves H. Kwan and Siddharth A. Parameswaran, Rudolf Peierls Center for Theoretical Physics, University of Oxford, and Trithep Devakul, Department of Physics, Massachusetts Institute of Technology, also contributed. Additional contributions came from Kenji Watanabe of the Functional Materials Research Center and Takashi Taniguchi of the International Center for Nanoarchitectural Materials, both at the National Institute of Materials Science in Tsukuba, Japan.
“One-Dimensional Luttinger Liquids in a Two-Dimensional Moire Network”, Pengjie Wang, Guo Yu, Yves H. Kwan, Yanyu Jia, Shiming Lei, Sebastian Klemenz, F. Alexandre Cevallos, Ratnadwip Singha, Trithep Devakul, Kenji Watanabe, Takashi Taniguchi, Shivaji L Sondhi, Robert J. Cava, Leslie M. Schoop, Siddharth A. Parameswaran, and Sanfeng Wu was published May 4 in the journal Nature (https://doi.org/10.1038/s41586-022-04514-6).
This research was supported by the National Science Foundation through a CAREER award (DMR-1942942) and the Princeton University Materials Research Science and Engineering Center (DMR-2011750). Characterization of the device and analysis of the data was partially supported by the Office of Naval Research through a Young Investigator Award (N00014-21-1-2804). Additional support came from the Eric and Wendy Schmidt Transformative Technology Fund at Princeton. The first measurements were made at the National High Magnetic Field Laboratory, which is supported by NSF cooperative agreement no. DMR-1644779 and the State of Florida. Support also came from the Elemental Strategy Initiative led by MEXT, Japan, grant number JPMXP0112101001, JSPS grant number KAKENHI JP20H00354 and CREST (JPMJCR15F3), JST. Additional support came from the EPiQS initiative of the Gordon and Betty Moore Foundation through grant no. GBMF9064 to LMS, the David and Lucile Packard Foundation, the Sloan Foundation and the Princeton Catalysis Initiative, and the European Research Council under the Horizon 2020 research and innovation program through grant agreement no. 804213-TMCS. And finally, additional support came from the Gordon and Betty Moore Foundation through grant no. GBMF8685 towards the theoretical program of Princeton and by an international professorship Leverhulme in Oxford.
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One-dimensional Luttinger liquids in a two-dimensional moire lattice
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