Thermal conductivity of suspended pristine graphene measured by Raman spectroscopy

The thermal conductivity of suspended single-layer graphene was measured as a function of temperature using Raman scattering spectroscopy on clean samples prepared directly on a prepatterned substrate by mechanical exfoliation without chemical treatments. The temperature at the laser spot was monitored by the frequency of the Raman 2$D$ band of the Raman scattering spectrum, and the thermal conductivity was deduced by analyzing heat diffusion equations assuming that the substrate is a heat sink at ambient temperature. The obtained thermal conductivity values range from $\sim$1800 Wm$^{-1}$K$^{-1}$ near 325 K to $\sim$710 Wm$^{-1}$K$^{-1}$ at 500 K.Comment: 4pages, 3 figure

Linking emergent phenomena and broken symmetries through one-dimensional objects and their dot/cross products

The symmetry of the whole experimental setups, including specific sample environments and measurables, can be compared with that of specimens for observable physical phenomena. We, first, focus on one-dimensional (1D) experimental setups, independent from any spatial rotation around one direction, and show that eight kinds of 1D objects (four; vectorlike, the other four; director-like), defined in terms of symmetry, and their dot and cross products are an effective way for the symmetry consideration. The dot products form a Z2xZ2xZ2 group with Abelian additive operation, and the cross products form a Z2xZ2 group with Abelian additive operation or Q8, a non-abelian group of order eight, depending on their signs. Those 1D objects are associated with characteristic physical phenomena. When a 3D specimen has Symmetry Operational Similarity (SOS) with (identical or lower, but not higher, symmetries than) an 1D object with a particular phenomenon, the 3D specimen can exhibit the phenomenon. This SOS approach can be a transformative and unconventional avenue for symmetry-guided materials designs and discoveries.Comment: 12 pages, 6 figure