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Hesselmann {it et al}.~question one of our conclusions, namely, the suppression of Fermi velocity at the Gross-Neveu critical point for the specific case of vanishing long-range interactions and at zero energy. The possibility they raise could occur in any finite-size extrapolation of numerical data. While we cannot definitively rule out this possibility, we provide mathematical bounds on its likelihood.
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While many physical properties of graphene can be understood qualitatively on the basis of bare Dirac bands, there is specific evidence that electron-electron (EE) and electron-phonon (EP) interactions can also play an important role. We discuss strategies for extracting separate images of the EE and EP interactions as they present themselves in the electron spectral density and related self-energies. While for momentum, $k$, equal to its Fermi value, $k_F$, a composite structure is obtained which can be difficult to separate into its two constituent parts, at smaller values of $k$ the spectral function shows distinct incoherent sidebands on the left and right of the main quasiparticle line. These image respectively the EE and EP interactions, each being most prominent in its own energy window. We employ a maximum entropy inversion technique on the self energy to reveal the electron-phonon spectral density separate from the excitation spectrum due to coulomb correlations. Our calculations show that this technique can provide important new insights into inelastic scattering processes in graphene.
Two-dimensional electron systems with fascinating properties exist in multilayers of standard semiconductors, on helium surfaces, and in oxides. Compared to the two-dimensional (2D) electron gases of semiconductors, the 2D electron systems in oxides are typically more strongly correlated and more sensitive to the microscopic structure of the hosting lattice. This sensitivity suggests that the oxide 2D systems are highly tunable by hydrostatic pressure. Here we explore the effects of hydrostatic pressure on the well-characterized 2D electron system formed at LaAlO$_{3}$ -SrTiO$_{3}$ interfaces[1] and measure a pronounced, unexpected response. Pressure of $sim$2 GPa reversibly doubles the 2D carrier density $n_{s}$ at 4 K. Along with the increase of $n_{s}$, the conductivity and mobility are reduced under pressure. First-principles pressure simulations reveal the same behavior of the carrier density and suggest a possible mechanism of the mobility reduction, based on the dielectric properties of both materials and their variation under external pressure.
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.
Surfaces and interfaces offer new possibilities for tailoring the many-body interactions that dominate the electrical and thermal properties of transition metal oxides. Here, we use the prototypical two-dimensional electron liquid (2DEL) at the SrTiO$_3$(001) surface to reveal a remarkably complex evolution of electron-phonon coupling with the tunable carrier density of this system. At low density, where superconductivity is found in the analogous 2DEL at the LaAlO$_3$/SrTiO$_3$ interface, our angle-resolved photoemission data show replica bands separated by 100,meV from the main bands. This is a hallmark of a coherent polaronic liquid and implies strong long-range coupling to a single longitudinal optical phonon mode. In the overdoped regime the preferential coupling to this mode decreases and the 2DEL undergoes a crossover to a more conventional metallic state with weaker short-range electron-phonon interaction. These results place constraints on the theoretical description of superconductivity and allow for a unified understanding of the transport properties in SrTiO$_3$-based 2DELs.
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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