Fig. 1. Schematic of graphene structure^[11]. (a) Atomic lattice and reciprocal lattice; (b) electronic band structure; (c) electron effective mass as a function of doping concentration, where the Fermi velocity is extracted from experimental fitting; (d) density of states distribution

Fig. 2. Defect and phonon effects in graphene. (a) Chemical potential distribution in graphene on a silicon substrate^[16]; (b) chemical potential distribution in graphene on an hBN substrate^[17]; (c) temperature-dependent resistivity under varying gate voltages^[18]; (d) thermal conductivity measurement^[19]

Fig. 3. Gurzhi effect in graphene. (a) Multi-terminal Hall bar device geometry^[10]; (b) temperature dependence of nonlocal resistance in the Hall bar, exhibiting a pronounced nonmonotonic behavior^[10]; (c) obstacle-induced Gurzhi effect measurement setup^[32];(d) temperature-dependent resistance in the obstacle-embedded structure^[32]

Fig. 4. Quantum-critical conductivity in graphene^[37]. (a) Schematic of zero-momentum mode and finite-momentum mode; (b) on-chip terahertz spectroscopy setup with coplanar waveguide; (c) scattering rate versus temperature at charge neutrality; (d) universal scaling of conductivity with normalized frequency

Fig. 5. Breakdown of the Wiedemann-Franz law in graphene^[41]. (a) Thermal conductivity measurements under different doping conditions and temperatures; (b) Lorenz ratio as a function of carrier density and temperature

Fig. 6. Poiseuille flow in Dirac fluid^[43]: (a)(c) Hall electric field profiles at T=7.5 K and T=75 K, respectively; (b)(d) reconstructed current density profiles under different transport mechanisms; (e) quantum spin magnetometry setup for spatially resolved current imaging; (f) current density map

Fig. 7. Vortex flow in graphene^[44]: (a)(b) Schematic of the nano-scale scanning superconducting quantum interference device measurement setup; (c)(e) laminar flow imaging and corresponding streamline pattern; (d)(f) vortex flow imaging and streamline pattern

Fig. 8. Vortex flow in graphene^[45]. (a)(c) Negative nonlocal resistance measurement setup and corresponding results; (b) vortex imaging apparatus; (d) current density profiles under varying doping levels

Fig. 9. Energy wave dynamics in graphene^[49]: (a)‒(e) Spatially resolved propagation profiles of energy waves under varying carrier densities; (f)(g) energy wave dispersion relations