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Register a new userPower law Kohn anomaly in undoped graphene induced by Coulomb interactions
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Phonon dispersions generically display non-analytic points, known as Kohn anomalies, due to electron-phonon interactions. We analyze this phenomenon for a zone boundary phonon in undoped graphene. When electron-electron interactions with coupling constant $beta$ are taken into account, one observes behavior demonstrating that the electrons are in a critical phase: the phonon dispersion and lifetime develop power law behavior with $beta$ dependent exponents. The observation of this signature would allow experimental access to the critical properties of the electron state, and would provide a measure of its proximity to an excitonic insulating phase.
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Dirac electrons in graphene in the presence of Coulomb interactions of strength $beta$ have been shown to display power law behavior with $beta$ dependent exponents in certain correlation functions, which we call the mass susceptibilities of the system. In this work, we first discuss how this phenomenon is intimately related to the excitonic insulator transition, showing the explicit relation between the gap equation and response function approaches to this problem. We then provide a general computation of these mass susceptibilities in the ladder approximation, and present an analytical computation of the static exponent within a simplified kernel model, obtaining $eta_0 =sqrt{1-beta/beta_c}$ . Finally we emphasize that the behavior of these susceptibilities provides new experimental signatures of interactions, such as power law Kohn anomalies in the dispersion of several phonons, which could potentially be used as a measurement of $beta$.
We investigate the effect of on-site Coulomb repulsion $U$ on the band gap of the electrically gated bilayer graphene by employing coherent potential approximation in the paramagnetic state, based on an ionic two-layer Hubbard model. We find that, while either the on-site Coulomb repulsion $U$ or the external perpendicular electric field $E$ alone will favor a gapped state in the bilayer graphene, competition between them will surprisingly lead to a suppression of the gap amplitude. Our results can be applied to understand the discrepancies of gap size reported from optical and transport measurements, as well as the puzzling features observed in angular resolved photoemission spectroscopic study.
The interplay of electron-phonon (el-ph) and electron-electron (el-el) interactions in epitaxial graphene is studied by directly probing its electronic structure. We found a strong coupling of electrons to the soft part of the A1g phonon evident by a kink at 150+/-15 meV, while the coupling of electrons to another expected phonon E2g at 195 meV can only be barely detected. The possible role of the el-el interaction to account for the enhanced coupling of electrons to the A1g phonon, and the contribution of el-ph interaction to the linear imaginary part of the self energy at high binding energy are also discussed. Our results reveal the dominant role of the A1g phonon in the el-ph interaction in graphene, and highlight the important interplay of el-el and el-ph interactions in the self energy of graphene.
A correlated material in the vicinity of an insulator-metal transition (IMT) exhibits rich phenomenology and variety of interesting phases. A common avenue to induce IMTs in Mott insulators is doping, which inevitably leads to disorder. While disorder is well known to create electronic inhomogeneity, recent theoretical studies have indicated that it may play an unexpected and much more profound role in controlling the properties of Mott systems. Theory predicts that disorder might play a role in driving a Mott insulator across an IMT, with the emergent metallic state hosting a power law suppression of the density of states (with exponent close to 1; V-shaped gap) centered at the Fermi energy. Such V-shaped gaps have been observed in Mott systems but their origins are as yet unknown. To investigate this, we use scanning tunneling microscopy and spectroscopy to study isovalent Ru substitutions in Sr$_3$(Ir$_{1-x}$Ru$_x$)$_2$O$_7$ which drives the system into an antiferromagnetic, metallic state. Our experiments reveal that many core features of the IMT such as power law density of states, pinning of the Fermi energy with increasing disorder, and persistence of antiferromagnetism can be understood as universal features of a disordered Mott system near an IMT and suggest that V-shaped gaps may be an inevitable consequence of disorder in doped Mott insulators.
We study the quantum many-body ground states of electrons on the half-filled honeycomb lattice with short- and long-ranged density-density interactions as a model for graphene. To this end, we employ the recently developed truncated-unity functional renormalization group (TU-fRG) approach which allows for a high resolution of the interaction vertex wavevector dependence. We connect to previous lattice quantum Monte Carlo (QMC) results which predict a stabilization of the semimetallic phase for realistic emph{ab initio} interaction parameters and confirm that the application of a finite biaxial strain can induce a quantum phase transition towards an ordered ground state. In contrast to lattice QMC simulations, the TU-fRG is not limited in the choice of tight-binding and interaction parameters to avoid the occurrence of a sign problem. Therefore, we also investigate a range of parameters relevant to the realistic graphene material which are not accessible by numerically exact methods. Although a plethora of charge density waves arise under medium-range interactions, we find the antiferromagnetic spin-density wave to be the prevailing instability for long-range interactions. We further explore the impact of an extended tight-binding Hamiltonian with second-nearest neighbor hopping and a finite chemical potential for a more accurate description of the band structure of graphenes $p_z$ electrons.
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