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Weyl Semimetals (WSM) for Electronics Applications

New synthesized materials open the way to govern the density of helicity, axial charge, and its flow, axial current.

The major factor determining transport properties of solids is the number of electron states in a vicinity of Fermi level. In equilibrium, no macroscopic flow of electrons exists and, therefore, in order to create such flow, electrons must be excited over their equilibrium distribution. However, electrons with energies well below the Fermi level (compared to the characteristic energy scale kBT, where kB is the Boltzmann constant and T is the temperature), cannot acquire small excitation energy. Indeed, in this case, they would have energy corresponding to already occupied states, which is prohibited by the Pauli principle. In turn, well above the Fermi level, where excitation of electrons is not constrained by the Pauli principle, the electron states are not populated, thus making their contribution to the response negligible.

Figure 1. The band diagrams of (a) conductor and (b) semiconductor (or dielectric) in a vicinity of the extremal points of the valence and conduction bands.

An elementary classification of materials as conductors and insulators is, therefore, based on the relation between the Fermi level and the energy bands characterizing electron states in the solid. In metals, such as copper or silver, the Fermi level is inside the band and, therefore, metals have high electric and thermal conductivities. In insulators, for instance, silicon dioxide (SiO2) or crystal sodium chloride (NaCl), the Fermi level is inside the wide, conventionally more than 4 eV, bandgap separating valence and conduction (below and above the Fermi level, respectively) bands, for example, ∆ ≈ 8.9 eV in SiO2 and ∆ ≈ 8.5 eV in NaCl.

Such picture establishing a relation between the band diagram of a solid and its transport properties is sufficient for dealing with materials with sharp conducting or insulating properties. However, it requires refinement when the band gap is not too wide (∆ is smaller than 4 eV). Materials with 0 < ∆ < 4 eV are semiconductors, for example, silicon (Si, ∆ ≈ 1.1 eV) and gallium arsenide (GaAs, ∆ ≈ 1.5 eV). Since the Fermi level is essentially the electrochemical potential for electrons, its position on the band diagram noticeably depends on doping (concentration of donor or acceptor impurities) and the external electric potential. These are core properties laying in the ground of semiconductor electronics.

Further decreasing of the gap width results in overlap of the valence and conduction bands. Such materials are called semimetals. Usually, for instance in bismuth (Bi) and graphite (an allotrope of carbon, C), this occurs when the extremal points of the bands are located at points with different momenta. In this case, the direct gap, the separation between points in conduction and valence bands with the same momentum, preserves. As a result, the electron density of states at the energy range corresponding to overlapping bands is small and the materials demonstrate properties characteristic for both semiconductors and metals.

Figure 2. The band diagram of graphene in the tight-binding approximation demonstrating the emergence of the Dirac points. The inset shows a vicinity of one of the points, where the energy spectrum has the form of Dirac cones.

Recently, a series of new materials enriching the canonical understanding of solids started to attract significant attention. Among them, a special place is taken by semimetals with the extremal points of the conduction and valence bands residing at the same momentum and separated by a small or even absent gap. The important feature of such materials is that near the extremal points of the valence and conduction bands, the electron states with a good accuracy are described by a Dirac equation generalized to account for a possible lack of rotational symmetry. As a result, the dynamics of low-energy excitations is similar to ultrarelativistic quantum particles. This brings concepts that previously were thought of only in the context of very high energies into the “everyday” energy range.

The most famous and well-studied example of such materials is graphene, a one-atom thick carbon layer. Due to its lattice structure, the band diagram of graphene has distinctive Dirac cones touching each other at the -points of the Brillouin zone (Figure 2). Due to the linear dispersion law near these points, electrons behave like massless fermions. Such particles are called Weyl fermions after the physicist who first considered the massless limit of the Dirac equation. Respectively, the touching point of the conduction and valence bands is called the Weyl point.

This work was done by Professor Pinaki Mazumder of the University of Michigan for the Air Force Research Laboratory. AFRL-0287

Topics:
Aerospace Electronic equipment Electronics Electronics & Computers Materials Materials properties Semiconductors Semiconductors & ICs
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Weyl Semimetals (WSM) for Electronics Applications

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    Aerospace & Defense Technology Magazine

    This article first appeared in the February, 2020 issue of Aerospace & Defense Technology Magazine (Vol. 5 No. 1).

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    Overview

    The document titled "Weyl Semimetals (WSM) for Electronics Applications" is a final report authored by Pinaki Mazumder from the University of Michigan, covering research conducted from September 15, 2016, to March 14, 2018. Sponsored by the Air Force Office of Scientific Research (AFOSR), the report delves into the properties and potential applications of Weyl semimetals, a class of materials that exhibit unique electronic characteristics due to their topological nature.

    Weyl semimetals are significant in the field of condensed matter physics as they bridge the gap between high-energy physics and practical electronic applications. The discovery of Dirac materials has introduced phenomena typically associated with high-energy physics into the realm of everyday energy scales, making them relevant for technological advancements. The report emphasizes the importance of understanding the effects of boundary conditions on the states of Weyl fermions, which are crucial for harnessing the unique properties of these materials.

    One key focus of the research is the behavior of electron states in Dirac materials with anti-dots, which are structures that can take the form of cavities in three-dimensional materials or holes in two-dimensional materials. The study investigates how these anti-dots influence localized states in Dirac materials, which has garnered significant attention for potential engineering applications. Dr. Erementchouk's contribution to the research involved developing a model that explains the formation of defect states bound to anti-dots in transition metal dichalcogenides, such as MoS₂. Numerical simulations using density functional theory (DFT) revealed the emergence of defect levels within the band structure of pristine MoS₂ and other similar materials.

    The report outlines the implications of these findings for future electronic applications, suggesting that the unique properties of Weyl semimetals could lead to advancements in various technologies, including quantum computing and spintronics. Overall, the document serves as a comprehensive overview of the research conducted on Weyl semimetals, highlighting their potential to revolutionize electronic materials and devices through their distinctive electronic properties and behaviors.

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