Abstract
Dirac-like electrons in solid state have been of great interest since they exhibit many peculiar physical behaviors analogous to relativistic mechanics. Among them, carriers in graphene and surface states of topological insulators are known to behave as massless Dirac fermions with a conical band structure in the two-dimensional momentum space, whereas electrons in semimetal bismuth (Bi) are expected to behave as massive Dirac-like fermions in the three-dimensional momentum space, whose dynamics is of particular interest in comparison with that of the massless Dirac fermions. Here, we demonstrate that an intense terahertz electric field transient accelerates the massive Dirac-like fermions in Bi from classical Newtonian to the relativistic regime; the electrons are accelerated approaching the effective “speed of light” with the “relativistic” beta β = 0.89 along the asymptotic linear band structure. As a result, the effective electron mass is enhanced by a factor of 2.4.
Highlights
(THz) time-domain spectroscopy, which is free from thermal effect
As shown by arrows to visualize the magnitude of the transmittance, Bi becomes more transparent for the large maximum THz electric field
The transmittance is averaged over 0.4–1.1 THz, through Bi film on Si substrate relative to that through the bare Si substrate
Summary
The film was deposited on a Si (111)–7 × 7 reconstructed surface[20], and post-annealed at 350 K to improve the crystallinity. Because of the approximate lattice matching of the Si surface with lattice constant of Bi, we could obtain a highly flat single-crystalline Bi film, whose quality was evaluated by a RHEED measurement and an atomic force microscope (AFM). Highresistivity Si is used as the substrate to avoid a nonlinear effect of the substrate under intense THz field irradiation[22]. Using Eq (5) in the main text, we calculated the kinetic momentum of electrons irradiated under an intense THz field transient. The values used in the calculation are c = 5 × 105 m/s 19, Γ = 20 × 1012 s−1 23, n = 7 × 1018 cm−3 23, m0 = 1 × 10−2 × me (me = 9.1 × 10−31 kg)[11], and Eg = 40 meV at 300 K12
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