We study the low-energy density of states of Dirac fermions in disordered d-wave superconductor. At zero energy, a finite density of states is obtained via the mechanism of dynamical mass generation in an effective (1+1)-dimensional relativistic field theory.
Extensive investigations show that QED$_{3}$ exhibits dynamical fermion mass generation at zero temperature when the fermion flavor $N$ is sufficiently small. However, it seems difficult to extend the theoretical analysis to finite temperature. We st
udy this problem by means of Dyson-Schwinger equation approach after considering the effect of finite temperature or disorder-induced fermion damping. Under the widely used instantaneous approximation, the dynamical mass displays an infrared divergence in both cases. We then adopt a new approximation that includes an energy-dependent gauge boson propagator and obtain results for dynamical fermion mass that do not contain infrared divergence. The validity of the new approximation is examined by comparing to the well-established results obtained at zero temperature.
We perform a detailed renormalization group analysis to study a (2+1)-dimensional quantum field theory that is composed of two interacting scalar bosons, which represent the order parameters for two continuous phase transitions. This sort of field th
eory can describe the competition and coexistence between distinct long-range orders, and therefore plays a vital role in statistical physics and condensed matter physics. We first derive and solve the renormalization group equations of all the relevant physical parameters, and then show that the system does not have any stable fixed point in the lowest energy limit. Interestingly, this conclusion holds in both the ordered and disordered phases, and also at the quantum critical point. Therefore, the originally continuous transitions are unavoidably turned to first-order due to ordering competition. Moreover, we examine the impacts of massless Goldstone boson generated by continuous symmetry breaking on ordering competition, and briefly discuss the physical implications of our results.
While a broad profile of the Fe K$alpha$ emission line is frequently found in the X-ray spectra of typical Seyfert galaxies, the situation is unclear in the case of Narrow Line Seyfert 1 galaxies (NLS1s)---an extreme subset which are generally though
t to harbor less massive black holes with higher accretion rates. In this paper, the ensemble property of the Fe K$alpha$ line in NLS1s is investigated by stacking the X-ray spectra of a large sample of 51 NLS1s observed with {it XMM-Newton}. The composite X-ray spectrum reveals a prominent, broad emission feature over 4--7 keV, characteristic of the broad Fe K$alpha$ line. In addition, there is an indication for a possible superimposing narrow (unresolved) line, either emission or absorption, corresponding to Fe XXVI or Fe XXV, respectively. The profile of the broad emission feature can well be fitted with relativistic broad-line models, with the line energy consistent either with 6.4 keV (i.e., neutral Fe) or with 6.67 keV (i.e., highly ionized Fe), in the case of the narrow line being emission and absorption, respectively. Interestingly, there are tentative indications for low or intermediate values of the average spins of the black holes ($a<0.84$), as inferred from the profile of the composite broad line. If the observed feature is indeed a broad line rather than resulting from partial covering absorption, our results suggest that a relativistic Fe line may in fact be common in NLS1s; and there are tentative indications that black holes in NLS1s may not spin very fast in general.
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.
We study chiral phase transition and confinement of matter fields in (2+1)-dimensional U(1) gauge theory of massless Dirac fermions and scalar bosons. The vanishing scalar boson mass, $r=0$, defines a quantum critical point between the Higgs phase an
d the Coulomb phase. We consider only the critical point $r=0$ and the Coulomb phase with $r > 0$. The Dirac fermion acquires a dynamical mass when its flavor is less than certain critical value $N_{f}^{c}$, which depends quantitatively on the flavor $N_{b}$ and the scalar boson mass $r$. When $N_{f} < N_{f}^{c}$, the matter fields carrying internal gauge charge are all confined if $r eq 0$ but are deconfined at the quantum critical point $r = 0$. The system has distinct low-energy elementary excitations at the critical point $r=0$ and in the Coulomb phase with $r eq 0$. We calculate the specific heat and susceptibility of the system at $r=0$ and $r eq 0$, which can help to detect the quantum critical point and to judge whether dynamical fermion mass generation takes place.
