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Register a new userThree-dimensional Dirac fermions in quasicrystals as seen via optical conductivity
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The optical conductivity of quasicrystals is characterized by two features not seen in ordinary metallic systems. There is an absence of the Drude peak and the interband conductivity rises linearly from a very low value up to normal metallic levels over a wide range of frequencies. The absence of a Drude peak has been attributed to a pseudogap at the Fermi surface but a detailed explanation of the linear behavior has not been found. Here we show that the linear conductivity, which seems to be universal in all Al based icosahedral quasicrystal families, as well as their periodic approximants, follows from a simple model that assumes that the entire Fermi surface is gapped except at a finite set of Dirac points. There is no evidence of a semiconducting gap in any of the materials suggesting that the Dirac spectrum is massless, protected by topology leading to a Weyl semimetal. This model gives rise to a linear conductivity with only one parameter, the Fermi velocity. This picture suggests that decagonal quasicrystals should, like graphene, have a frequency independent conductivity, without a Drude peak. This is in accord with the experimental data as well.
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We use determinant quantum Monte Carlo (DQMC) simulations to study the role of electron-electron interactions on three-dimensional (3D) Dirac fermions based on the $pi$-flux model on a cubic lattice. We show that the Hubbard interaction drives the 3D Dirac semimetal to an antiferromagnetic (AF) insulator only above a finite critical interaction strength and the long-ranged AF order persists up to a finite temperature. We evaluate the critical interaction strength and temperatures using finite-size scaling of the spin structure factor. The critical behaviors are consistent with the (3+1)d Gross-Neveu universality class for the quantum critical point and 3D Heisenberg universality class for the thermal phase transitions. We further investigate correlation effects in birefringent Dirac fermion system. It is found that the critical interaction strength $U_c$ is decreased by reducing the velocity of the Dirac cone, quantifying the effect of velocity on the critical interaction strength in 3D Dirac fermion systems. Our findings unambiguously uncover correlation effects in 3D Dirac fermions, and may be observed using ultracold atoms in an optical lattice.
We study excitonic effects in two-dimensional massless Dirac fermions with Coulomb interactions by solving the ladder approximation to the Bethe-Salpeter equation. It is found that the general 4-leg vertex has a power law behavior with the exponent going from real to complex as the coupling constant is increased. This change of behavior is manifested in the antisymmetric response, which displays power law behavior at small wavevectors reminiscent of a critical state, and a change in this power law from real to complex that is accompanied by poles in the response function for finite size systems, suggesting a phase transition for strong enough interactions. The density-density response is also calculated, for which no critical behavior is found. We demonstrate that exciton correlations enhance the cusp in the irreducible polarizability at $2k_F$, leading to a strong increase in the amplitude of Friedel oscillations around a charged impurity.
A Dirac-Fermi liquid (DFL)--a doped system with Dirac spectrum--is an important example of a non-Galilean-invariant Fermi liquid (FL). Real-life realizations of a DFL include, e.g., doped graphene, surface states of three-dimensional (3D) topological insulators, and 3D Dirac/Weyl metals. We study the optical conductivity of a DFL arising from intraband electron-electron scattering. It is shown that the effective current relaxation rate behaves as $1/tau_{J}propto left(omega^2+4pi^2 T^2right)left(3omega^2+8pi^2 T^2right)$ for $max{omega, T}ll mu$, where $mu$ is the chemical potential, with an additional logarithmic factor in two dimensions. In graphene, the quartic form of $1/tau_{J}$ competes with a small FL-like term, $proptoomega^2+4pi^2 T^2$, due to trigonal warping of the Fermi surface. We also calculated the dynamical charge susceptibility, $chi_mathrm{c}({bf q},omega)$, outside the particle-hole continua and to one-loop order in the dynamically screened Coulomb interaction. For a 2D DFL, the imaginary part of $chi_mathrm{c}({bf q},omega)$ scales as $q^2omegaln|omega|$ and $q^4/omega^3$ for frequencies larger and smaller than the plasmon frequency at given $q$, respectively. The small-$q$ limit of $mathrm{Im} chi_mathrm{c}({bf q},omega)$ reproduces our result for the conductivity via the Einstein relation.
To probe the charge scattering mechanism in Cd$_{3}$As$_{2}$ single crystal, we have analyzed the temperature and magnetic field dependence of the Seebeck coefficient ($S$). The large saturation value of $S$ at high field clearly demonstrates the linear energy dispersion of three-dimensional Dirac fermion. A wide tunability of the charge scattering mechanism has been realized by varying the strength of the magnetic field and carrier density via In doping. With the increase in magnetic field, the scattering time crosses over from being nearly energy independent to a regime of linear dependence. On the other hand, the scattering time enters into the inverse energy-dependent regime and the Fermi surface strongly modifies with 2% In doping at Cd site. With further increase in In content from 2 to 4%, we did not observe any Shubnikov-de Haas oscillation up to 9 T field, but the magnetoresistance is found to be quite large as in the case of undoped sample.
Relativistic massless Dirac fermions can be probed with high-energy physics experiments, but appear also as low-energy quasi-particle excitations in electronic band structures. In condensed matter systems, their massless nature can be protected by crystal symmetries. Classification of such symmetry-protected relativistic band degeneracies has been fruitful, although many of the predicted quasi-particles still await their experimental discovery. Here we reveal, using angle-resolved photoemission spectroscopy, the existence of two-dimensional type-II Dirac fermions in the high-temperature superconductor La$_{1.77}$Sr$_{0.23}$CuO$_4$. The Dirac point, constituting the crossing of $d_{x^2-y^2}$ and $d_{z^2}$ bands, is found approximately one electronvolt below the Fermi level ($E_mathrm{F}$) and is protected by mirror symmetry. If spin-orbit coupling is considered, the Dirac point degeneracy is lifted and the bands acquire a topologically non-trivial character. In certain nickelate systems, band structure calculations suggest that the same type-II Dirac fermions can be realised near $E_mathrm{F}$.
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