Unconventional behavior of Dirac fermions in three-dimensional gauge theory

Abstract

We study unconventional behavior of massless Dirac fermions due to interaction with a U(1) gauge field in three time-space dimensions. At zero chemical potential, the longitudinal and transverse components of gauge interaction are both long ranged. There is no fermion velocity renormalization since the system respects Lorentz invariance. At finite chemical potential, the Lorentz invariance is explicitly broken by the finite Fermi surface. The longitudinal gauge interaction is statically screened and becomes unimportant, whereas the transverse gauge interaction remains long ranged and leads to singular renormalization of fermion velocity. The anomalous dimension of fermion velocity is calculated by means of the renormalization group method. We then examine the influence of singular velocity renormalization on several physical quantities, and show that they exhibit different behavior at zero and finite chemical potential.

Measurement of the Electronic Thermal Conductance Channels and Heat Capacity of Graphene at Low Temperature

“…This agrees with theories for |E F | k B T , as the minimum |E F | of our samples is limited by impurity doping. For |E F | k B T , which is not accessible in this experiment, the specific heat is expected to be proportional to T 2 in the case of massless Dirac Fermions [37]. The smallest specific heat attained near the CNP is merely 10 k B µm −2 or 1000 k B for the whole sample, a factor of 9 smaller than the inferred value in state-of-the-art nano-wires used for bolometry [15].…”

Infrared behavior of dynamical fermion mass generation inQED3

“…Therefore, the transverse component of gauge boson propagator should play a more significant role than the longitudinal component at finite temperatures. This judgment is supported by the extensive recent analysis of nontrivial properties induced by gauge interaction [25][26][27][57][58][59]. Overall, the transverse component of gauge boson propagator needs to be included in an appropriate manner in the study of dynamical fermion mass generation at finite temperature, which is the motivation of our work.…”

“…Nevertheless, as illustrated in recent works on the nontrivial properties of QED 3 [25][26][27][57][58][59], the transverse component of gauge interaction plays a more important role than the longitudinal component at finite temperature, since the latter becomes short ranged after acquiring an effective thermal mass proportional to T. If T ¼ 0 and Γ ≠ 0, the longitudinal part of gauge interaction also becomes short ranged due to static screening caused by disorder scattering. In any case, the gauge invariance ensures that the transverse component of gauge interaction is strictly long ranged.…”

“…If the gauge boson acquires a finite mass, the dynamical fermion mass generation will be strongly suppressed [41]. At finite temperature, the Lorentz invariance is explicitly broken, and then the longitudinal and transverse components of gauge boson propagator behave very differently [25][26][27][57][58][59]: the former becomes short ranged due to thermal screening, whereas the latter remains long ranged as a consequence of gauge invariance. Therefore, the transverse component of gauge boson propagator should play a more significant role than the longitudinal component at finite temperatures.…”

Fermion-fermion interaction driven instability and criticality of quadratic band crossing systems with the breaking of time-reversal symmetry

“…We notice that ferocious fluctuations induced by the development of charge density wave are generally detrimental for density of states and specific heat as well compressibility of quasiparticles. It is worth pointing out that these quantities are all substantially reduced and even drive to zero while the dominant order parameter triggered by the divergent instability is large enough, hitting to the signatures of non-Fermi liquid behaviors 82,[89][90][91][92][93][94] .…”