More Designer Electrons- Artificial Molecular Graphene used to Mimic Higgs Field and Relativity

Researchers arranged carbon monoxide molecules to form the same hexagonal pattern found in graphene, except that they could adjust molecular spacing slightly. They placed individual molecules of carbon monoxide onto a copper sheet. The material’s electrons behave remarkably like relativistic particles, with a “speed of light” that they can adjust. Additionally, the researchers could change the spacing between molecules in a way that the masses of the quasiparticles changed, or cause them to behave as though they are interacting with electric and magnetic fields—without actually applying those fields to the material.

Manoharan has indicated that his team will be working on using the new material as a test bed for future exploitation as well as creating new nanoscale materials with new properties.

This is a follow up to the design electron article from yesterday

Manoharan lab covers their own work here

The work could lead to new materials and devices.

Graphical summary of this work. Artificial “molecular” graphene is fabricated via atom manipulation, and then imaged and locally probed via scanning tunneling microscopy (STM). Guided by theory, we fabricate successively more exotic variants of graphene. From left to right: pristine graphene exhibiting emergent massless Dirac fermions; graphene with a Kekulé distortion dresses the Dirac fermions with a scalar gauge field that creates mass; graphene with a triaxial strain distortion embeds a vector gauge field which condenses a time-reversal-invariant relativistic quantum Hall phase. In the theory panel, images are color representations of the strength of the carbon-carbon bonds (corresponding to tight-binding hopping parameters t), and the curves shown are calculated electronic density of states (DOS) from tight-binding (TB) theory. In the experiment panel, images are STM topographs acquired after molecular assembly, and the curves shown are normalized conductance spectra obtained from the associated nanomaterial.

In this work we combine a central tenet of condensed matter physics—how electronic band structure emerges from a periodic potential in a crystal—with the most advanced imaging and atomic manipulation techniques afforded by the scanning tunnelling microscope. We synthesize a completely artificial form of graphene (“molecular graphene”) in which Dirac fermions can be materialized, probed, and tailored in ways unprecedented in any other known materials. We do this by using single molecules, bound to a two-dimensional surface, to craft designer potentials that transmute normal electrons into exotic charge carriers. With honeycomb symmetry, electrons behave as massless relativistic particles as they do in natural graphene. With altered symmetry and texturing, these Dirac particles can be given a tunable mass, or even be married with a fictitious electric or magnetic field (a so-called gauge field) such that the carriers believe they are in real fields and condense into the corresponding ground state. We show an array of new phenomena emerging from: patterning Dirac carrier densities with atomic precision, without need for conventional gates (corresponding to locally uniform electric fields which adjust chemical potential); spatially texturing the electron bonds such that the Dirac point is split by an energy gap (corresponding to a nonuniform scalar gauge field); straining the bonds in such a way that a quantum Hall effect emerges even without breaking time-reversal symmetry (corresponding to a vector gauge field). Along the way, we make use of several theoretical predictions for real graphene which have never been realized in experiment

Nature – Designer Dirac fermions and topological phases in molecular graphene

Phantom Fields

A version of molecular graphene in which the electrons respond as if they’re experiencing a very high magnetic field (red areas) when none is actually present. Scientists from Stanford and SLAC National Accelerator Laboratory calculated the positions where carbon atoms in graphene should be to make its electrons believe they were being exposed to a magnetic field of 60 Tesla, more than 30 percent higher than the strongest continuous magnetic field ever achieved on Earth. (A 1 Tesla magnetic field is about 20,000 times stronger than the Earth’s.) The researchers then used a scanning tunneling microscope to place carbon monoxide molecules (black circles) at precisely those positions. The electrons responded by behaving exactly as expected — as if they were exposed to a real field, but no magnetic field was turned on in the laboratory. Image credit: Hari Manoharan / Stanford University.

Schrödinger Meets Dirac

Visualization depicting the transformation of an electron moving under the influence of the non-relativistic Schrödinger equation (upper planar quantum waves) into an electron moving under the prescription of the relativistic Dirac equation (lower honeycomb quantum waves). The light blue line shows a quasiclassical path of one such electron as it enters the molecular graphene lattice made of carbon monoxide molecules (black/red atoms) positioned individually by an STM tip (comprised of iridium atoms, dark blue). The path shows that the electron becomes trapped in synthetic chemical bonds that bind it to a honeycomb lattice and allow it to quantum mechanically tunnel between neighboring honeycomb sites, just like graphene. The underlying electron density in a honeycomb pattern (lower part of image, yellow-orange) is the quantum superposition formed from all such electron paths as they transmute into a new tunable species of massless Dirac fermions. Image credit: Hari Manoharan / Stanford University.

Designer Electrons

This graphic shows the effect that a specific pattern of carbon monoxide molecules (black/red) has on free-flowing electrons (orange/yellow) atop a copper surface. Ordinarily the electrons behave as simple plane waves (background). But the electrons are repelled by the carbon monoxide molecules, placed here in a hexagonal pattern. This forces the electrons into a honeycomb shape (foreground) mimicking the electronic structure of graphene, a pure form of carbon that has been widely heralded for its potential in future electronics. The molecules are precisely positioned with the tip of a scanning tunneling microscope (dark blue). Image credit: Hari Manoharan / Stanford University.

Molecular Graphene PNP Junction Device

Stretching or shrinking the bond lengths in molecular graphene corresponds to changing the concentrations of Dirac electrons present. This image shows three regions of alternating lattice spacing sandwiched together. The two regions on the ends contain Dirac “hole” particles (p-type regions), while the region in the center contains Dirac “electron” particles (n-type region). A p-n-p structure like this is of interest in graphene transistor applications. Image credit: Hari Manoharan / Stanford University.

The observation of massless Dirac fermions in monolayer graphene has generated a new area of science and technology seeking to harness charge carriers that behave relativistically within solid-state materials. Both massless and massive Dirac fermions have been studied and proposed in a growing class of Dirac materials that includes bilayer graphene, surface states of topological insulators and iron-based high-temperature superconductors. Because the accessibility of this physics is predicated on the synthesis of new materials, the quest for Dirac quasi-particles has expanded to artificial systems such as lattices comprising ultracold atoms. Here we report the emergence of Dirac fermions in a fully tunable condensed-matter system—molecular graphene—assembled by atomic manipulation of carbon monoxide molecules over a conventional two-dimensional electron system at a copper surface5. Using low-temperature scanning tunnelling microscopy and spectroscopy, we embed the symmetries underlying the two-dimensional Dirac equation into electron lattices, and then visualize and shape the resulting ground states. These experiments show the existence within the system of linearly dispersing, massless quasi-particles accompanied by a density of states characteristic of graphene. We then tune the quantum tunnelling between lattice sites locally to adjust the phase accrual of propagating electrons. Spatial texturing of lattice distortions produces atomically sharp p–n and p–n–p junction devices with two-dimensional control of Dirac fermion density and the power to endow Dirac particles with mass. Moreover, we apply scalar and vector potentials locally and globally to engender topologically distinct ground states and, ultimately, embedded gauge fields wherein Dirac electrons react to ‘pseudo’ electric and magnetic fields present in their reference frame but absent from the laboratory frame. We demonstrate that Landau levels created by these gauge fields can be taken to the relativistic magnetic quantum limit, which has so far been inaccessible in natural graphene. Molecular graphene provides a versatile means of synthesizing exotic topological electronic phases in condensed matter using tailored nanostructures.

14 pages of supplemental material

Molecular graphene assembly

Molecular graphene assembly. A movie shows the nanoscale assembly sequence of an electronic honeycomb lattice by manipulating individual CO molecules on the Cu(111) two-dimensional electron surface state with the STM tip. The video comprises 52 topographs (30 × 30 nm2, bias voltage V = 10 mV, tunnel current I = 1 nA) acquired during the construction phase and between manipulation steps.

Tunable Pseudomagnetic Field

Molecular Manipulation

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