Terahertz Conductivity of Twisted Bilayer Graphene

Abstract

Using terahertz time-domain spectroscopy, the real part of optical conductivity [σ1(ω)] of twisted bilayer graphene was obtained at different temperatures (10 -300 K) in the frequency range 0.3 -3 THz. On top of a Drude-like response, we see a strong peak in σ1(ω) at ∼2.7 THz. We analyze the overall Drude-like response using a disorder-dependent (unitary scattering) model, then attribute the peak at 2.7 THz to an enhanced density of states at that energy, that is caused by the presence of a van Hove singularity arising from a commensurate twisting of the two graphene layers.Compared to single-layer graphene (SLG), where there are two non-equivalent lattice sites (A and B), bilayer graphene (BLG) has two SLGs stacked in the third direction. In the most common Bernal (AB) stacking of BLG, adjacent layers are rotated by 60 • , so that the B atoms of layer 2 (B ′ ) sits directly on top of A atoms in layer 1 (A), and B and A ′ atoms are in the center of the hexagons of the opposing layer. Electrons can then hop between these two A sites with a hopping energy t ⊥ . In the undoped case, though both SLG and BLG are gapless semi-metals, carriers in SLG exhibit linear dispersion, while those in BLG show quadratic dispersion. An energy gap in SLG opens up due to finite geometry effects, but its control has proven to be unreliable [1]. On the other hand, the electronic gap in BLG can be reliably opened and controlled by an applied electric field, shown theoretically and demonstrated experimentally [2][3][4][5], and promises interesting applications. Both SLG and BLG however, are sensitive to disorder. Hence, to realize graphene-based optoelectronic devices, an understanding of the temperature and disorder effects in the transport and spectroscopic properties of BLG is needed. Temperature and disorder-dependent conductivity of BLG have been derived theoretically [1,6]. Experimentally, spectroscopies (from terahertz (THz) to visible) and ultrafast dynamics of various flavors of graphene have been reported, such as SLG, few and many-layer graphene, and graphite [7][8][9][10][11]. For example, Fourier-transform infrared spectroscopy (FTIR) on large-area SLG grown by chemical vapor deposition (CVD) revealed a Drude-like frequency dependence of the spectral density from THz to mid-infrared at different carrier concentrations [12]. In addition, graphene plasmons, which lie in the THz range, are strongly coupled to the interband electronic transitions and decay by exciting interband electron-hole pairs [13]. Hence knowledge of graphene's electromagnetic response, as a function of disorder, in the THz frequency range is critical for applications such as graphene-based THz oscillators [14].

Terahertz conductivity of topological surface states in Bi1.5Sb0.5Te1.8Se1.2

“…Finally, the transmission (of 1-THz component) through one pass of one (top or bottom) surface layer is exp (− αt surf ) ~ 98.3%. This THz transmission of ~98% is consistent with that of single-layer graphene25 or bilayer graphene26. Whether this similarity is due to the common Dirac-cone feature in their band structures, is an intriguing question.…”

Electronic properties of graphene-based bilayer systems

“…Thus, the peak at ω ∼ = 2.64 THz was observed experimentally using terahertz time-domain spectroscopy in Ref. [442]. The twist angle of the sample studied in the latter work was estimated as θ ∼ = 1.16…”

“…The response of the tBLG on the ac electromagnetic field has been studied both experimentally [441,442,443] and theoretically [440,444,445,344]. In Ref.…”

Electron-phonon scattering and in-plane electric conductivity in twisted bilayer graphene

“…The parameters α ν of the phonon spectrum, Eq. (16)(17)(18), describe the in-plane elastic properties of the twist bilayer and can be obtained directly from the phonon dispersion of graphene or graphite, which has been studied extensively both theoretically [55][56][57][58][59] as well as experimentally [60][61][62] . Comparing the phonon dispersion of graphene and graphite reveals that the in-plane elastic properties α ν are robust against different stacking configurations of graphene layers and therefore the same values can be used for the twist bilayer.…”