Two new Raman modes below 100 cm(-1) are observed in twisted bilayer graphene grown by chemical vapor deposition. The two modes are observed in a small range of twisting angle at which the intensity of the G Raman peak is strongly enhanced, indicating that these low energy modes and the G Raman mode share the same resonance enhancement mechanism, as a function of twisting angle. The ~94 cm(-1) mode (measured with a 532 nm laser excitation) is assigned to the fundamental layer breathing vibration (ZO' mode) mediated by the twisted bilayer graphene lattice, which lacks long-range translational symmetry. The dependence of this mode's frequency and line width on the rotational angle can be explained by the double resonance Raman process that is different from the previously identified Raman processes activated by twisted bilayer graphene superlattice. The dependence also reveals the strong impact of electronic-band overlaps of the two graphene layers. Another new mode at ~52 cm(-1), not observed previously in the bilayer graphene system, is tentatively attributed to a torsion mode in which the bottom and top graphene layers rotate out-of-phase in the plane.

The Jahn–Teller effect (JTE) is defined and the historical background of the Jahn–Teller theorem is briefly discussed. The E⊗β system, an electronic doublet coupled to a single mode of vibration, is introduced as an elementary example and is used to illustrate features characteristic of Jahn–Teller systems. The spin resonance of Cu++ in various materials is considered and the particular case of Cu++ in a cubic crystal field is used to introduce the E⊗ε Jahn–Teller system. The linear and quadratic E⊗ε systems are discussed, and the linear case is used to illustrate the appearance of the Berry phase in a quantum system. The role of the Jahn–Teller effect in high-temperature superconductivity is also discussed. In particular, the JTE-based superconductivity theories of Englman et al. [Physica C 169, 314–324 (1990)] and Weber et al. [Physica C 162/164, 307–312 (1989)] are briefly reviewed. The possible roles of the Jahn–Teller effect in C60 (buckminsterfullerene) and superconducting K3C60 are also considered.

Two infrared (IR)-active vibrational modes, observed at 93 and 113 cm(-1) in Raman scattering, are evidence of an inversion symmetry breakdown in thin (~10 nm) nanoplates of topological insulator Bi(2)Te(3) as-grown on SiO(2). Both Raman and IR modes are preserved after typical device fabrication processes. In nanoplates transferred to another SiO(2) substrate via contact printing, however, the IR modes are absent, and the Raman spectra are similar to those from bulk samples. The differences between as-grown and transferred nanoplates may result from nanoplate-substrate interactions.

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Topological insulators are novel quantum materials with metallic surface transport, but insulating bulk behavior. Often, topological insulators are dominated by bulk contributions due to defect induced bulk carriers, making it difficult to isolate the more interesting surface transport characteristics. Here, we report the synthesis and characterization of nanosheets of topological