Nonlinear optical response of twisted bilayer graphene

Twist dependent magneto-optical response in twisted bilayer graphene

“…We find that TBG exhibits no universal magneto-optical conductivity and the magnitude ranges from [0-6.5]σ 0 where σ 0 = e 2 /4 is the universal conductivity for SLG. This is well within the reported low frequency range of [0-10]σ 0 at E F = 0.4 eV for the linear optical conductivities for TBG [13,34,44,49,61]. Secondly it is found that the responses in each region increase with twist angle.…”

“…Firstly, so as to not include higher-order n F -terms one must ensure the electric field is adequately low. Given nonlinear magneto-optical effects (Kerr rotations) are shown to manifest for photon frequencies 75 THz [50] and higher-order harmonics require fields of E ≈ 10 6 -10 8 V m −1 in order to be comparable with the linear terms [48,49], we restrict ourselves to the THz frequency region and applied fields of the order 10 4 -10 5 V m −1 . Secondly, for the semiclassical description of carriers to break down and quantum behaviour to dictate transport phenomena the magnetic field must be strong enough so that B L [54].…”

“…Experimentally, numerous spectroscopy methods such as Raman spectroscopy [29][30][31], angle-resolved photoemission spectroscopy [32], optical reflection spectroscopy [33] and terahertz time domain spectroscopy [34] have verified these properties. As a direct result of this featurerich electronic structure, many transport properties have been explored, including but not limited to: plasmon resonance [35], circular dichroism [36], chiral response [37][38][39], topologically protected zero modes [40], Mott insulating and superconductivity [41], THz photogalvanic response [42,43], strong optical response accompanied by symmetry dependent selection rules [13, 35-37, 44, 45], second harmonic generation (SHG) [46], Rabi oscillations [47] and more recently a strong nonlinear response optical response has been revealed in both the terahertz (THz)-far infrared (FIR) and mid infrared (MIR)-near infrared (NIR) regions [48,49]. (2) 1 and a (2) 2 ) and the bottom layer (spanned by a (1) 1 and a (1) 2 ) at different twist angles.…”

“…To study the magneto-optical response and its dependence on both twist angle and Fermi level we adopt a semiclassical formalism to derive a general expression for the low-energy magneto-optical response of TBG including effects from both the Berry curvature and the magnetic moment [57]. In the low field region where the linear electric field response dominates [11,12,49,[58][59][60] we employ a linearised Boltzmann equation to isolate the transverse and longitudinal conductivities up to the second order in magnetic field and up to the linear order in electric field. The crux of this method lies in approximating electronic quantities from the system with B = 0 : H B =0 (k)|ũ s,r (k) = ˜ s,r |ũ s,r (k) by explicitly computable quantities from the system with B = 0 : H(k)|u s,r (k) = s,r |u s,r (k) .…”

Optical properties and plasmons in moiré structures

“…As mentioned in the previous section, the TBG transition energies are notably influenced by the twist angle [239,240]. Consequently, for a constant twist angle, the activation or deactivation of one-and two-photon resonances can be achieved by adjusting the incident wavelength.…”