Physicists have discovered a new quantum state in elemental solids

Data visualization representation of the surface and edge electron quantum states of gray arsenic crystals obtained using scanning tunneling microscopy from the Department of Physics at Princeton University. Image source: Image based on STM data simulations prepared by Shafayat Hossain and Zahid Hasan's group at Princeton University's Topological Quantum Matter Laboratory.

Physicists have observed a new quantum effect in crystalline materials called "hybrid topology". This discovery opens up a range of new possibilities for the next generation of quantum science and engineering to develop efficient materials and technologies.

The discovery was published in the journal Nature, when scientists at Princeton University discovered that an elemental solid crystal made up of arsenic (As) atoms had an unprecedented form of topological quantum behavior. They were able to explore and image this new quantum state using scanning tunneling microscopy (STM) and optical emission spectroscopy, a technique used to determine the relative energy of electrons in molecules and atoms.

This state combines or "mixes" two forms of topological quantum behavior—edge states and surface states—which are two types of quantum two-dimensional electronic systems. These have been observed in previous experiments, but have never been simultaneously mixed in the same material to form a new state of matter.

"This discovery was completely unexpected," said M. Zahid Hassan, a professor of physics at Princeton University who led the study. Zahid Hasan) said. "No one predicted it theoretically until it was observed.

In recent years, the study of the topological state of matter has attracted great attention from physicists and engineers, and is currently the focus of many international attention and research. This field of study combines quantum physics with topology, a branch of theoretical mathematics that explores geometric properties that can be deformed but not changed in nature.

For more than a decade, scientists have been using bismuth (Bi)-based topological insulators to demonstrate and explore exotic quantum effects in bulk solids, primarily by fabricating composite materials, such as mixing Bi with selenium (Se). However, this experiment is the first time that topological effects have been found in crystals composed of the element As.

"The search for and discovery of new topological properties of matter has become one of the most stalked treasures in modern physics, both from the perspective of fundamental physics and from the perspective of the next generation of quantum science and engineering," Hassan said. "The discovery of this new topological state in elemental solids is made possible by several innovative experimental advances and instrumentation at our Princeton Laboratory.

Elemental solids are a valuable experimental platform for testing a variety of topological concepts. So far, bismuth is the only element with a rich topology, leading to two decades of intensive research activities. This is due in part to the cleanliness and ease of synthesis of the material. However, the richer topological phenomena currently found in arsenic may pave the way for new and ongoing research directions.

"We have demonstrated for the first time that, similar to different related phenomena, different topological sequences can interact and generate new and interesting quantum phenomena," Hassan said.

Topological materials are the main components used to study the mysteries of quantum topology. The device acts as an insulator inside it, which means that the electrons inside cannot move freely and hence do not conduct electricity.

However, the electrons at the edge of the device can move freely, which means they are electrically conductive. In addition, due to the special properties of the topology, the electrons flowing along the edges are not hindered by any defects or deformations. This type of device not only has the potential to improve technology, but also to better understand matter itself by probing quantum electronic properties.

Hasan notes that there is a strong interest in using topological materials for real-world applications. However, two important developments need to be made before this can be achieved. First, quantum topological effects must manifest themselves at higher temperatures. Second, it is necessary to find a simple elemental material system that can carry topological phenomena (e.g., silicon in traditional electronics).

"In our lab, we're working in both directions – we're looking for simpler material systems that are easy to fabricate and where fundamental topological effects can be found," Hasan said. "We're also looking at how to make these effects survive at room temperature.

Background of the experiment

The roots of this discovery lie in the operation of the quantum Hall effect, a topological effect that was the subject of the 1985 Nobel Prize in Physics. Since then, topological phases have been studied and many novel quantum materials with topological electronic structures have been discovered. Most notably, Daniel Tsui, Arthur Legrand Dotty Professor Emeritus of Electrical Engineering at Princeton University, was awarded the 1998 Nobel Prize in Physics for his discovery of the fractional quantum Hall effect.

Similarly, F. Duncan Haldane, Eugene Higgins Professor of Physics at Princeton University. Duncan Haldane was awarded the 2016 Nobel Prize in Physics for his theoretical discoveries of topological phase transitions and a two-dimensional (2D) topological insulator. Subsequent theoretical developments have shown that topological insulators can be based on spin-orbit interactions of electrons, taking the form of two copies of the Haldane model.

Hasan and his research team have been following in the footsteps of these researchers, studying other aspects of topological insulators and finding new states of matter. This led them to discover the first example of a three-dimensional (3D) topological insulator in 2007. Since then, Hassan and his team have been searching for a new topology that can also be run at room temperature.

"Proper atomic chemistry and structural design, combined with first-principles theory, is a critical step in making speculative predictions of topological insulators a reality in high-temperature environments," Hassan said.

"There are hundreds of quantum materials, and we need intuition, experience, material-specific calculations, and intensive experimental efforts to finally find materials suitable for deep exploration. This led us on a decade-long journey to study many bismuth-based materials, leading to many fundamental discoveries.

experiment

At least in principle, bismuth-based materials are able to maintain the topological state of matter at high temperatures. However, these require complex material preparation under ultra-high vacuum conditions, so the researchers decided to explore several other systems. Postdoctoral researcher Dr. Shafayat Hossain suggested using a crystal made of arsenic because it can grow in a cleaner form than many bismuth compounds.

When Yuxiao Jiang, a graduate student in Hussein and Hassan's group, rotated the STM to the arsenic sample, they saw a dramatic observation – grey arsenic is a metallic form of arsenic with both a topological surface state and an edge state.

"We were surprised. Ash arsenic should only be in a superficial state. But when we examine the atomic step edges, we also find a beautiful conductive edge pattern," Hussain said.

"An isolated single-layer stepped edge should not have a gap-free edge pattern," added Jiang, co-first author of the study.

This is the result of calculations by Frank Schindler, a postdoctoral researcher and condensed matter theorist at Imperial College London, and Rajibul Islam, a postdoctoral researcher at the University of Alabama in Birmingham, Alabama. Both are co-first authors of the paper.

"Once the edge is placed on top of the bulk sample, the surface state hybridizes with the gap state on the edge and forms a gap-free state," Schindler says.

"It's the first time we've seen such a hybrid," he added.

Physically, this gap-free state at the edge of the ladder is not expected for strong topological insulators or higher-order topological insulators, but only applies to hybrid materials where two quantum topologies exist at the same time. This gap-free state is also distinct from the surface or hinge state in strong and higher-order topological insulators, respectively. This means that the experimental observations of the Princeton team immediately indicate a topological state that has never been observed before.

David Hsieh, chair of the physics department at Caltech and a researcher who was not involved in the study, noted the study's innovative conclusions.

"Typically, we think of the band structure of a material as belonging to one of several different topological categories, each of which is associated with a specific type of boundary state," Hsieh said. "This work shows that certain materials can be divided into two categories at the same time. The most interesting thing is that the boundary states that emerge from these two topologies can interact and be reconstructed into a new quantum state, not just a superposition of its parts.

The researchers further confirmed the scanning tunneling microscope measurements with the system's high-resolution, angle-resolved optical emission spectra.

"The gray As sample was very clean, and we found a clear feature of the topological surface state," said Zi-Jia Cheng, a graduate student in Hasan's group and co-first author of the paper, who made some light emission measurements.

The combination of multiple experimental techniques allowed the researchers to probe the unique decent-edge correspondence associated with the mixed topological state and confirmed the experimental results.

Significance of the findings

The implications of this finding are twofold. Observations of the combined topological edge patterns and surface states pave the way for the design of new topological electron transport channels. This could enable the design of new quantum information science or quantum computing devices.

Researchers at Princeton University have demonstrated that topological edge patterns exist only on specific geometries compatible with crystal symmetry, providing an avenue for designing various forms of future nanodevices and spin-based electronics.

From a broader perspective, society benefits when new materials and properties are discovered, Hassan said. In quantum materials, the identification of elemental solids as material platforms, such as antimony with strong topology or bismuth with higher-order topology, has led to the development of novel materials that have greatly benefited the field of topological materials.

"We envision arsenic with a unique topology that could serve as a new platform of similar level for the development of novel topological materials and quantum devices that are not currently available with existing platforms," Hasan said.

The Princeton team has been designing and building novel experiments for more than 15 years for the exploration of topological insulator materials. For example, between 2005 and 2007, Hasan's team used new experimental methods to discover the topological order of three-dimensional bismuth-antimony bulk solids, semiconductor alloys, and related topological Dirac materials.

This led to the discovery of topological magnetic materials. Between 2014 and 2015, they discovered and developed a new class of topological materials called magnetic Weyl semimetals.

The researchers believe that this discovery will open the door to future research possibilities and applications of quantum technologies, especially in so-called "green" technologies.

"Our research is a step forward in demonstrating the potential of topological materials for energy-efficient applications in quantum electronics," Hasan said.

More information: M. Zahid Hasan, Hybrid Topological Quantum States in Elemental Solids, Nature (2024). DOI： 10.1038/s41586-024-07203-8.www.nature.com/articles/s41586-024-07203-8

Journal Information: Nature