The strong long-range Coulomb interaction between massless Dirac fermions in graphene can drive a semimetal-insulator transition. We show that this transition is strongly suppressed when the Coulomb interaction is screened by such effects as disorder, thermal fluctuation, doping, and finite volume. It is completely suppressed once the screening factor $\mu$ is beyond a threshold $\mu_{c}$ even for infinitely strong coupling. However, such transition is still possible if there is an additional strong contact four-fermion interaction. The differences between screened and contact interactions are also discussed.Comment: 7 pages, 4 figures, to appear in Phys. Rev.

Regenerative cooling with hydrocarbon aviation fuels on board is taken as a promising technology for the thermal management system of next-generation aircraft. An improved methodology of an electrically heated tube (1 mm i.d.), i.e., applying the variable reactor tube length to carry on thermal cracking of supercritical hydrocarbon aviation fuels as the electric current heating maintains constant, was proposed to experimentally obtain detailed information on the local concentration and temperature along the microchannels of a heat exchanger. For the first time a series of experimental data on detailed local chemical compositions of cracked hydrocarbon fuel along the cooling microchannels were reported under supercritical conditions (5 MPa, 680−700 °C), and the calculated thermodynamic properties, velocity, and residence times along the tube were also reported. A modified molecular reaction model consisting of 18 species and 24 reactions was developed to predict thermal cracking of hydrocarbon aviation fuels in a wide range of cracking conversion (up to 86%). The work is significant for the design of regenerative cooling structures in predicting the local chemical compositions, estimating thermophysical properties, and coking of the cracked hydrocarbon fuels for heat transfer analysis.

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A d-wave high temperature cuprate superconductor exhibits a nematic ordering transition at zero temperature. Near the quantum critical point, the coupling between gapless nodal quasiparticles and nematic order parameter fluctuation can result in unusual behaviors, such as extreme anisotropy of fermion velocities. We study the disorder effects on the nematic quantum critical behavior and especially on the flow of fermion velocities. The disorders that couple to nodal quasiparticles are divided into three types: random mass, random gauge field, and random chemical potential. A renormalization group analysis shows that random mass and random gauge field are both irrelevant and thus do not change the fixed point of extreme velocity anisotropy. However, the marginal interaction due to random chemical potential destroys this fixed point and makes the nematic phase transition unstable.

There is an interesting proposal that the long-range Coulomb interaction in suspended graphene can generate a dynamical gap, which leads to a semimetal-insulator phase transition. We revisit this problem by solving the self-consistent Dyson-Schwinger equations of wave function renormalization and fermion gap. In order to satisfy the Ward identity, a suitable vertex function is introduced. The impact of singular velocity renormalization and that of dynamical screening on gap generation are both included in this formalism, and prove to be very important. We obtain a critical interaction strength, 3.2 < α c < 3.3, which is larger than the physical value α = 2.16 for suspended graphene. It therefore turns out that suspended graphene is a semimetal, rather than an insulator, at zero temperature.

Anisotropic Dirac cone can appear in a number of correlated electron systems, such as cuprate superconductor and deformed graphene. We study the influence of long-range Coulomb interaction on the physical properties of an anisotropic graphene by using the renormalization group method and 1/N expansion, where N is the flavor of Dirac fermions. Our explicit calculations reveal that the anisotropic fermion velocities flow monotonously to an isotropic fixed point in the lowest energy limit in clean graphene. We then incorporate three sorts of disorders, including random chemical potential, random gauge potential, and random mass, and show that the interplay of Coulomb interaction and disorders can lead to rich and unusual behaviors. In the presence of strong Coulomb interaction and random chemical potential, the fermion velocities are driven to vanish at low energies and the system turns out to be an exotic anisotropic insulator. In the presence of Coulomb interaction and other two types of disorders, the system flows to an isotropic low-energy fixed point more rapidly than the clean case, and exhibits non-Fermi liquid behaviors. We also investigate the non-perturbative effects of Coulomb interaction, focusing on how the dynamical gap is affected by the velocity anisotropy. It is found that, the dynamical gap is enhanced (suppressed) as the fermion velocities decrease (increase), but is suppressed as the velocity anisotropy increases.

A nematic quantum critical point is anticipated to exist in the superconducting dome of some hightemperature superconductors. The nematic order competes with the superconducting order and hence reduces the superconducting condensate at T = 0. Moreover, the critical fluctuations of nematic order can excite more nodal quasiparticles out of the condensate. We address these two effects within an effective field theory and show that superfluid density ρ s (T ) and superconducting temperature T c are both suppressed strongly by the critical fluctuations. The strong suppression of superconductivity provides a possible way to determine the nematic quantum critical point.