Scientists Visualize Electron Crystals In A Quantum Superposition

Princeton scientists are utilizing progressive methods to visualize electrons in graphene, a single atomic layer of carbon atoms. They’re discovering that robust interactions between electrons in excessive magnetic fields drive them to type uncommon crystal-like constructions much like these first acknowledged for benzene molecules within the 1860s by chemist August Kekulé. These crystals exhibit a spatial periodicity that corresponds to electrons being in a quantum superposition.

Illustration of two sites of graphene lattice.  

Credit: Image courtesy of the researchers

The experiments additionally present the Kekulé quantum crystals have defects that don’t have an analog to these of unusual crystals made up of atoms. These findings make clear the complicated quantum phases electrons can type due to their interplay, which underlies a variety of phenomena in lots of supplies.

Physicists realized to manage how electrons work together with each other by way of the appliance of a powerful magnetic subject and, most not too long ago, by stacking a number of layers of graphene on prime of one another. In truth, the invention of graphene within the first decade of the 21st century—a discovery that led to a Nobel Prize in physics in 2010—opened a brand new area for exploring the physics of electrons, particularly for analyzing how electrons behave collectively.

A vortex of Kekule pattern. The left panel shows the change of Kekule pattern in space. The bottom right panel illustrates the texture of the vortex extracted from the left panel that resembles a hurricane. 

Credit: Image courtesy of the researchers

Now, Princeton researchers led by Ali Yazdani, the Class of 1909 Professor of Physics and director of the Middle for Complicated Supplies at Princeton College, have found that the robust interplay between electrons in graphene drives them to type crystal constructions with complicated patterns decided by quantum superposition—electrons residing at a number of atomic websites on the similar time. The experiment, not too long ago printed in Science, additionally reveals that this novel quantum crystal hosts unique deformations that correspond to the twisting and winding of the electrons’ wavefunction.

Graphene consists of a single layer of carbon atoms organized in a two-dimensional hexagonal, or honeycomb-like, lattice. It’s produced in a deceptively easy however painstaking method. Graphite, the identical materials present in pencils, is progressively exfoliated strip by strip-till this single-atom-thin layer of carbon is reached.

“Earlier research have proven that graphene demonstrates novel electrical properties,” Yazdani mentioned. “However by no means earlier than have researchers been capable of peer so deeply and with such spatial decision into the character of quantum states.”

To attain this unparalleled degree of decision, Yazdani’s group used a tool referred to as a scanning tunneling microscope (STM). This gadget depends on a phenomenon referred to as “quantum tunneling,” the place voltage is used to funnel electrons between the sharp metallic tip of the microscope and the pattern only some ångströms away. The microscope makes use of this tunneling present quite than gentle to view the world of electrons on the atomic scale. Yazdani’s microscopes function in a really excessive vacuum to maintain the pattern floor clear and at very low temperatures to permit for prime decision measurements, unperturbed by thermal agitation.

The microscope can also be capable of viewing electrons as they attain their lowest power states dominated by their quantum properties. Within the presence of a magnetic subject, the microscope can be utilized to find out the spatial construction of the quantized power degree.

“One of many particular properties of graphene is its conduct in a magnetic subject, when electrons are compelled to orbit across the magnetic subject in a circle,” mentioned Yazdani. “This quantizes their energies, leading to quantization of graphene’s electrical properties.”

Quantization of power refers back to the creation of discrete values of power, with no intermediate values, which is an attribute of quantum physics, versus classical physics, the place steady power values is permitted.

The researchers centered their consideration on the quantized degree with the bottom power in graphene, for which earlier analysis first reported by Phuan Ong, Eugene Higgins Professor of Physics at Princeton, had revealed some uncommon electrical properties. This degree dominates {the electrical} properties when there aren’t any extra fees added or far away from graphene—in different phrases when the cost is impartial. Ong had proven that electrons “freeze” when the cost is impartial, and the graphene layer acts as an insulator with the appliance of a magnetic subject. The character of this frozen state of electrons in graphene has been a thriller for nearly a decade, since Ong’s preliminary discovery.

“The insulating state that we discovered puzzled everybody and strongly challenged the prevailing theories at the moment,” mentioned Ong, who was not concerned within the present analysis. “It remained a permanent puzzle for 13 years till the gorgeous outcomes obtained by Yazdani. The brand new outcomes resolve the puzzle in a really thrilling trend.” 

Yazdani and his workforce used the microscope to map the wave function of the bottom quantized power degree within the presence of a magnetic subject. The researchers discovered complicated patterns of electron waves when graphene was tuned to an impartial state with a close-by electrical gate.

In metals, electrons’ wavefunction is unfold all through the crystal, whereas in a traditional insulator, electrons are frozen with no specific choice to the crystal construction of the atomic websites. At very low fields, STM photographs confirmed electron wavefunctions of graphene selecting one of many sub-lattice websites over the opposite. Extra importantly, by rising the magnetic subject, an outstanding bond-like sample is noticed, which corresponds to electrons’ wavefunction residing in a quantum superposition. This means an electron occupies the 2 inequivalent websites at a similar time.

Particularly, the picture corresponded to the bond-like construction first acknowledged by Kekulé for benzene. This consists of alternating single and double bonds. In a single bond, one electron from every atom binds with its neighbor electron; in a double bond, two electrons from every atom take part.

Folks have speculated that electrons could type such Kekulé patterns,” mentioned Yazdani, “however now we’re seeing it for the primary time. One could not distinguish this state of electrons some other means until it’s imaged.” 

The researchers then used the microscope to map the uniformity of the Kekulé crystal and its properties close to imperfections, or defects within the graphene. One outstanding discovery they made was close to cost defects the place they discovered the Kekulé sample to evolve repeatedly in its patterns across the defect on the graphene floor.

Teaming up with Michael Zaletel of the College of California, Berkeley, the workforce developed a technique for extracting from the STM knowledge the mathematical properties of the quantum wavefunction of electrons, so-called part angles describing their quantum superposition. The evaluation revealed outstanding winding of one among these part angles across the defect and correlated modifications within the different angles.

“When the group utilized their approach to measure the phase-angle above a defect within the substrate, they discovered a ‘vortex’ within the Kekulé sample, which is sort of a hurricane round which the phase-angle winds round by 12 hours [as on a clock],” mentioned Zaletel. “When making predictions about such quantum, nanoscale, objects, you hardly ever assume you may have the pleasure to essentially ‘see’ an image of them, however the group has been capable of just do that.”

The workforce believes that the methods they’ve developed to uncover this uncommon quantum crystal of electrons in a powerful magnetic subject can have functions elsewhere within the subject. Different two-dimensional supplies and their stack can exhibit comparable quantum crystals with novel defects. The workforce goals to use their methodology to a wider class of such supplies.

Along with Yazdani and Zaletel, contributors to the research included authors Xiaomeng Liu, Gelareh Farahi and Cheng-Li Chiu, all on the Joseph Henry Laboratories and Division of Physics, Princeton College; Zlatko Papic, College of Physics and Astronomy, College of Leeds, United Kingdom; and Kenji Watanabe and Takashi Taniguchi of the Nationwide Institute for Materials Science in Japan.

The research, “Visualizing damaged symmetry and topological defects in a quantum Corridor ferromagnet,” by Xiaomeng Liu, Gelareh Farahi, Cheng-Li Chiu, Zlatko Papic, Kenji Watanabe, Takashi Taniguchi, Michael Zaletel, and Ali Yazdani, was printed Dec. 2, 2021, within the journal Science.