Interplay of Surface and Dirac Plasmons in Topological Insulators: The Case ofBi2Se3

Abstract

We have investigated plasmonic excitations at the surface of Bi 2 Se 3 ð0001Þ via high-resolution electron energy loss spectroscopy. For low parallel momentum transfer q ∥ , the loss spectrum shows a distinctive feature peaked at 104 meV. This mode varies weakly with q ∥ . The behavior of its intensity as a function of primary energy and scattering angle indicates that it is a surface plasmon. At larger momenta (q ∥ ∼ 0.04 Å −1 ), an additional peak, attributed to the Dirac plasmon, becomes clearly defined in the loss spectrum. Momentum-resolved loss spectra provide evidence of the mutual interaction between the surface plasmon and the [4][5][6] have promising capabilities in regard to engineering high-speed plasmonic and optoelectronic devices [7,8].The growth of TI samples belonging to the class of chalcogenides inherently involves the presence of vacancies. Thus, in most cases, the Fermi level is shifted from the bulk band gap and pinned by the bulk states occupied by doping electrons or holes. These bulk carriers give rise to their own three-dimensional electron gas (3DEG), which is well known to have plasmonic excitations characterized by the bulk plasmon energy ω p . In this matter, the frequency of the surface plasmon ω sp is related to the bulk plasmon energy ω p (for a simple planar interface ω sp ¼ ω p = ffiffiffiffiffiffiffiffiffiffiffiffi ffi 1 þ ε b p , where ε b is the dielectric constant of the background medium of the 3DEG) [9]. In turn, the value of ω p is determined by the bulk concentration of charge carriers [10]. From the reported values of the carrier concentration, the respective values of ω p , and the dielectric screening by the surrounding medium [11,12], one could expect that ω sp is in the ∼100 meV energy range and it should coexist with the collective excitation of the two-dimensional electron gas (2DEG) arising from electrons of topological surface states (the so-called Dirac plasmon) [13,14]. As a result, the intriguing interplay of the surfaceplasmon and Dirac-plasmon modes as functions of in-plane momentum q ∥ arises.Recently, optical techniques have been used [12,15,16] to investigate plasmon modes of thin films and microribbons of Bi 2 Se 3 . The Dirac plasmon has been observed in Bi 2 Se 3 microribbons [15], while the bulk plasmon has been reported in thin films [11,17,18]. However, optical techniques are not suited to the investigation of the momentum dependence of plasmonic excitations and, thus, the nature and the dispersion of low-energy collective excitations in TIs in a finite momentum range is hitherto unexplored.Here, we examine the surface collective electronic excitations in Bi 2 Se 3 by means of HREELS, which allows probing of an extended momentum range. Our HREELS measurements provide direct evidence for the coexistence of two low-energy collective modes: the surface plasmon, whose origin is due to a nonzero density of 3D doping electrons, and the Dirac plasmon of the 2DEG formed by electrons residing in a topological surface-state band. The surface plasmon, whose...

Plasmons in topological insulator cylindrical nanowires

“…We have also studied the effects of q || = 0 analyzing charge excitations where the angular degrees of freedom are more involved. It could be interesting to consider not only the presence of Dirac surface plasmons but also of other plasmon excitations 42 , in particular of surface plasmons 43 related to bulk charge carriers which have been observed very recently in EELS experiments 44,45 . Finally, it could be useful to study plasmon features at finite temperatures analyzing the effects of electronphonon couplings 46,47 , in particular, in the case of wires freely suspended or grown on a substrate 48 .…”

Optoelectronic devices, plasmonics, and photonics with topological insulators

“…76 However, attempts to directly probe spin-plasmons by means of electron energy loss spectroscopy have been unsuccessful, 60 since the predominating mode in the plasmonic spectrum is a surface plasmon arising from the bulk, free carriers. 52,60 This mode hybridizes with the spin-plasmon for momenta far from the Γ point of the Brillouin zone. 52 To selectively excite the spin-plasmon, a mechanism exploiting optical spin injection has been proposed by Raghu et al 74 (Figure 2).…”

“…An extension of the momentum range up to ∼0.3 Å 1 has been achieved by exciting the Dirac plasmon with probing electrons. 52,60 Successively, the plasmonic response of ring structures patterned in Bi 2 Se 3 films has been studied by THz spectroscopy. 61 The rings exhibit a bonding plasmon mode and an antibonding plasmon mode, whose frequency can be tuned by changing their diameter.…”

“…The two-dimensional electron gas (2DEG) formed by surface-state electrons supports a Dirac plasmon [52][53][54] with energy ω p , whose dispersion in the local approximation is as follows: 55…”

Controlling plasmon modes and damping in buckled two-dimensional material open systems

“…However, the use of MoS 2 with a large bandgap in 2DMOS is able to suppress this damping effectively. Alternatively, one could also use Bi 2 Se 3 material, 85 which is a doped topological insulator with a surface-plasmon energy around 104 meV, or a highly-doped semiconductor in 2DMOS.…”