Direct visualization of quantum dots reveals shape of quantum wave function

Direct visualization of quantum dots reveals shape of quantum wave function
Visualization of quantum dots in bilayer graphene using scanning tunneling microscopy and spectroscopy reveals a three-fold symmetry. In this three-dimensional image, the peaks represent sites of high amplitude in the waveform of the trapped electrons. Credit: Zhehao Ge, Frederic Joucken, and Jairo Velasco Jr.

Trapping and controlling electrons in bilayer graphene quantum dots yields a promising platform for quantum information technologies. Researchers at UC Santa Cruz have now achieved the first direct visualization of quantum dots in bilayer graphene, revealing the shape of the quantum wave function of the trapped electrons.


The results, published November 23 in Nano Letters, provide important fundamental knowledge needed to develop quantum information technologies based on bilayer graphene quantum dots.

“There has been a lot of work to develop this system for quantum information science, but we’ve been missing an understanding of what the electrons look like in these quantum dots,” said corresponding author Jairo Velasco Jr., assistant professor of physics at UC Santa Cruz.

While conventional digital technologies encode information in bits represented as either 0 or 1, a quantum bit, or qubit, can represent both states at the same time due to quantum superposition. In theory, technologies based on qubits will enable a massive increase in computing speed and capacity for certain types of calculations.

A variety of systems, based on materials ranging from diamond to gallium arsenide, are being explored as platforms for creating and manipulating qubits. Bilayer graphene (two layers of graphene, which is a two-dimensional arrangement of carbon atoms in a honeycomb lattice) is an attractive material because it is easy to produce and work with, and quantum dots in bilayer graphene have desirable properties.

“These quantum dots are an emergent and promising platform for quantum information technology because of their suppressed spin decoherence, controllable quantum degrees of freedom, and tunability with external control voltages,” Velasco said.

Understanding the nature of the quantum dot wave function in bilayer graphene is important because this basic property determines several relevant features for quantum information processing, such as the electron energy spectrum, the interactions between electrons, and the coupling of electrons to their environment.

Velasco’s team used a method he had developed previously to create quantum dots in monolayer graphene using a scanning tunneling microscope (STM). With the graphene resting on an insulating hexagonal boron nitride crystal, a large voltage applied with the STM tip creates charges in the boron nitride that serve to electrostatically confine electrons in the bilayer graphene.

“The electric field creates a corral, like an invisible electric fence, that traps the electrons in the quantum dot,” Velasco explained.

The researchers then used the scanning tunneling microscope to image the electronic states inside and outside of the corral. In contrast to theoretical predictions, the resulting images showed a broken rotational symmetry, with three peaks instead of the expected concentric rings.

“We see circularly symmetric rings in monolayer graphene, but in bilayer graphene the quantum dot states have a three-fold symmetry,” Velasco said. “The peaks represent sites of high amplitude

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Direct observation of a single electron’s butterfly-shaped distribution in titanium oxide

Direct observation of a single electron's butterfly-shaped distribution in titanium oxide
Figure 1. (a) Distribution of a butterfly-shaped 3d electron orbital. (b) Valence electron density distribution around the titanium (Ti3+) ion at the centre of the titanium oxide (TiO6 ) octahedron obtained by the CDFS analysis developed by the research team for this project. Credit: Shunsuke Kitou

The functions and physical properties of solid materials, such as magnetic order and unconventional superconductivity, are greatly influenced by the orbital state of the outermost electrons (valence electrons) of the constituent atoms. In other words, it could be said that the minimal unit that determines a solid material’s physical properties consists of the orbitals occupied by the valence electrons. Moreover, an orbital can also be considered a minimal unit of ‘shape,’ so the orbital state in a solid can be deduced from observing the spatially anisotropic distribution of electrons (in other words, from how the electron distribution deviates from spherical symmetry).


The orbital states in elements are basic knowledge that can be found in quantum mechanics or quantum chemistry textbooks. For example, it is known that the 3d electrons in transition elements such as iron and nickel have characteristic butterfly-type or gourd-type shapes. However, until now, it has been extremely difficult to observe the real-space distribution of such electron orbitals directly.

Now, a research collaboration between Nagoya University, University of Wisconsin-Milwaukee, Japan’s RIKEN and Institute for Molecular Science, the University of Tokyo, and the Japan Synchrotron Radiation Research Institute (JASRI), has observed the spatial distribution of a single valence electron at the center of an octahedron-shaped titanium oxide molecule, using synchrotron X-ray diffraction.

To analyze the X-ray diffraction data from the titanium oxide sample, the team developed a Fourier synthesis method in which data from each titanium ion’s inner shell electrons—which do not contribute to the compound’s physical properties—are subtracted from the total electron distribution of each ion, leaving only the butterfly-shaped valence electron density distribution. The method is called core differential Fourier synthesis (CDFS).

Direct observation of a single electron's butterfly-shaped distribution in titanium oxide
Cross-sectional view of the valence electron density distribution of Ti3+ ion obtained by (a) the CDFS analysis and (b) the first-principles calculation. Credit: Shunsuke Kitou

Furthermore, a closer look at the butterfly-shaped electron density revealed that high density remained in the central region, in contrast with bare titanium in which electrons do not exist at the center because of the node of the 3d orbital. After careful data analysis, it was found that the electron density at the center consists of the valence electrons occupying the hybridized orbital generated by the bond between titanium and oxygen. First-principles calculations confirmed this non-trivial orbital picture and reproduced the results of the CDFS analysis very well. The image directly demonstrates the well-known Kugel-Khomskii model of the relationship between the magnetic and orbital-ordered states.

The CDFS method can determine the orbital states in materials regardless of the physical properties and can be applied to almost all elements and without the need for difficult experiments or analytical techniques: the method requires neither quantum-mechanical nor informatic models, so bias introduced by analysts is minimized. The

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Fusion and Interstellar Space Travel: Direct Fusion Drive Facts

futuristic holographic nuclear fusion particles simulation

Kittiphat AbhiratvorakulGetty Images

  • Using a conceptual direct fusion drive, we could reach Saturn and Titan in just two years.
  • Titan’s liquid surface oceans and rich hydrocarbons make it an interesting target in deep space.
  • The fusion drive uses microwaved plasma to propel the ship and power its other systems.

    Experts say the right kind of propulsion system could carry spacecraft to Saturn in just two years. The direct fusion drive (DFD), a concept being developed by Princeton Plasma Physics Laboratory, would make extremely fast work of the nearly billion miles between Earth and Saturn.

    🌌You like our badass universe. So do we. Let’s explore it together.

    Researchers there say the Princeton field reversed configuration-2 (PFRC-2) drive could be the secret to feasible travel within our solar system.

    The research team chose Saturn’s moon Titan as an ideal, well, moonshot. The #1 moon in our solar system has a great deal of scientific interest because of its surface liquids, and the fact that they’re hydrocarbons means Titan could even become a refueling waystation in some far future space highway system.

    Universe Today reports:

    “[T]he engine itself exploits many of the advantages of aneutronic fusion, most notably an extremely high power-to-weight ratio,” a press release reads. “The fuel for a DFD drive can vary slightly in mass and contains deuterium and a helium-3 isotope. Essentially, the DFD takes the excellent specific impulse of electric propulsion systems and combines it with the excellent thrust of chemical rockets, for a combination that melds the best of both flight systems.”

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    In a way, this is a lot like how hybrid consumer vehicles are designed. There are times when electric provides the best, most efficient push, and there are times when fossil fuels are still the most logical choice. The PPPL direct fusion drive is being studied in two modes: one where it thrusts the entire time, and another where, like a Prius, it thrusts to get up to speed at the beginning only. The trip to Titan changes from about 2 years to about 2.5 depending on the mode.


    🚀Our Favorite LEGO Rocket Kits


    The reactor itself is relatively small, because even a larger spacecraft for our current imagination is far smaller than family

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