Polarons in highly doped atomically thin graphitic materials

Polaron spectral functions are computed for highly doped graphene-on-substrate and other atomically thin graphitic systems using the diagrammatic Monte Carlo technique. The specific aim is to investigate the effects of interaction on spectral functions when the symmetry between sub-lattices of a honeycomb lattice has been broken by the substrate or ionicity, inducing a band gap. Introduction of electron-phonon coupling leads to several polaronic features, such as band-flattening and changes in particle lifetimes. At the K point, differences between energies on each sub-lattice increase with electron-phonon coupling, indicating an augmented transport gap, while the spectral gap decreases slightly. Effects of phonon dispersion and long-range interactions are investigated, and found to lead to only quantitative changes in spectra

Electron and phonon dispersions of the two dimensional Holstein model: Effects of vertex and non-local corrections

I apply the newly developed dynamical cluster approximation (DCA) to the calculation of the electron and phonon dispersions in the two dimensional Holstein model. In contrast to previous work, the DCA enables the effects of spatial fluctuations (non-local corrections) to be examined. Approximations neglecting and incorporating lowest-order vertex corrections are investigated. I calculate the phonon density of states, the renormalised phonon dispersion, the electron dispersion and electron spectral functions. I demonstrate how vertex corrections stabilise the solution, stopping a catastrophic softening of the $(\pi,\pi)$ phonon mode. A kink in the electron dispersion is found in the normal state along the $(\zeta,\zeta)$ symmetry direction in both the vertex- and non-vertex-corrected theories for low phonon frequencies, corresponding directly to the renormalised phonon frequency at the $(\pi,0)$ point. This kink is accompanied by a sudden drop in the quasi-particle lifetime. Vertex and non-local corrections enhance the effects at large bare phonon frequencies.Comment: I am posting reprints of the final submitted versions of previous articles to improve access. Here ARPES "kinks" are discussed. Article was published in 2003. 17 pages, 9 figure

Breakdown of Migdal--Eliashberg theory via catastrophic vertex divergence at low phonon frequency

We investigate the applicability of Migdal--Eliashberg (ME) theory by revisiting Migdal's analysis within the dynamical mean-field theory framework. First, we compute spectral functions, the quasi-particle weight, the self energy, renormalised phonon frequency and resistivity curves of the half-filled Holstein model. We demonstrate how ME theory has a phase-transition-like instability at intermediate coupling, and how the Engelsberg--Schrieffer (ES) picture is complicated by low-energy excitations from higher order diagrams (demonstrating that ES theory is a very weak coupling approach). Through consideration of the lowest-order vertex correction, we analyse the applicability of ME theory close to this transition. We find a breakdown of the theory in the intermediate coupling adiabatic limit due to a divergence in the vertex function. The region of applicability is mapped out, and it is found that ME theory is only reliable in the weak coupling adiabatic limit, raising questions about the accuracy of recent analyses of cuprate superconductors which do not include vertex corrections.Comment: 19 pages, 10 figures, accepted for publication in Journal of Low Temperature Physic

Quantum simulation of electron-phonon interactions in strongly deformable materials

We propose an approach for quantum simulation of electron-phonon interactions using Rydberg states of cold atoms and ions. We show how systems of cold atoms and ions can be mapped onto electron-phonon systems of the Su-Schrieffer-Heeger type. We discuss how properties of the simulated Hamiltonian can be tuned and how to read physically relevant properties from the simulator. In particular, use of painted spot potentials offers a high level of tunability, enabling all physically relevant regimes of the electron-phonon Hamiltonian to be accessed.Comment: To appear in New Journal of Physic

Superlight small bipolarons

Recent angle-resolved photoemission spectroscopy (ARPES) has identified that a finite-range Fr\"ohlich electron-phonon interaction (EPI) with c-axis polarized optical phonons is important in cuprate superconductors, in agreement with an earlier proposal by Alexandrov and Kornilovitch. The estimated unscreened EPI is so strong that it could easily transform doped holes into mobile lattice bipolarons in narrow-band Mott insulators such as cuprates. Applying a continuous-time quantum Monte-Carlo algorithm (CTQMC) we compute the total energy, effective mass, pair radius, number of phonons and isotope exponent of lattice bipolarons in the region of parameters where any approximation might fail taking into account the Coulomb repulsion and the finite-range EPI. The effects of modifying the interaction range and different lattice geometries are discussed with regards to analytical strong-coupling/non-adiabatic results. We demonstrate that bipolarons can be simultaneously small and light, provided suitable conditions on the electron-phonon and electron-electron interaction are satisfied. Such light small bipolarons are a necessary precursor to high-temperature Bose-Einstein condensation in solids. The light bipolaron mass is shown to be universal in systems made of triangular plaquettes, due to a novel crab-like motion. Another surprising result is that the triplet-singlet exchange energy is of the first order in the hopping integral and triplet bipolarons are heavier than singlets in certain lattice structures at variance with intuitive expectations. Finally, we identify a range of lattices where superlight small bipolarons may be formed, and give estimates for their masses in the anti-adiabatic approximation.Comment: 31 pages. To appear in J. Phys.: Condens. Matter, Special Issue 'Mott's Physics

Statistical physics of cerebral embolization leading to stroke

We discuss the physics of embolic stroke using a minimal model of emboli moving through the cerebral arteries. Our model of the blood flow network consists of a bifurcating tree, into which we introduce particles (emboli) that halt flow on reaching a node of similar size. Flow is weighted away from blocked arteries, inducing an effective interaction between emboli. We justify the form of the flow weighting using a steady flow (Poiseuille) analysis and a more complicated nonlinear analysis. We discuss free flowing and heavily congested limits and examine the transition from free flow to congestion using numerics. The correlation time is found to increase significantly at a critical value, and a finite size scaling is carried out. An order parameter for non-equilibrium critical behavior is identified as the overlap of blockages' flow shadows. Our work shows embolic stroke to be a feature of the cerebral blood flow network on the verge of a phase transition.Comment: 11 pages, 11 figures. Major rewrite including improved justification of the model and a finite size scalin

Effects of lattice geometry and interaction range on polaron dynamics

We study the effects of lattice type on polaron dynamics using a continuous-time quantum Monte-Carlo approach. Holstein and screened Froehlich polarons are simulated on a number of different Bravais lattices. The effective mass, isotope coefficients, ground state energy and energy spectra, phonon numbers, and density of states are calculated. In addition, the results are compared with weak and strong coupling perturbation theory. For the Holstein polaron, it is found that the crossover between weak and strong coupling results becomes sharper as the coordination number is increased. In higher dimensions, polarons are much less mobile at strong coupling, with more phonons contributing to the polaron. The total energy decreases monotonically with coupling. Spectral properties of the polaron depend on the lattice type considered, with the dimensionality contributing to the shape and the coordination number to the bandwidth. As the range of the electron-phonon interaction is increased, the coordination number becomes less important, with the dimensionality taking the leading role.Comment: 16 pages, 12 figure

Unconventional pairing in bipolaronic theories

Various mechanisms have been put forward for cuprate superconductivity, which fit largely into two camps: spin-fluctuation and electron-phonon (el-ph) mechanisms. However, in spite of a large effort, electron-phonon interactions are not fully understood away from clearly defined limits. To this end, we use a numerically exact algorithm to simulate the binding of bipolarons. We present the results of a continuous-time quantum Monte-Carlo (CTQMC) algorithm on a tight-binding lattice, for bipolarons with arbitrary interaction range in the presence of strong coulomb repulsion. The algorithm is sufficiently efficient that we can discuss properties of bipolarons with various pairing symmetries. We investigate the effective mass and binding energies of singlet and triplet real-space bipolarons for the first time, and discuss the extensions necessary to investigate $d$-symmetric pairs.Comment: Submitted to M2S-HTSC VIII, Dresden 2006, 2 page

Extending the theory of phonon-mediated superconductivity in quasi-2D

I present results from an extended Migdal-Eliashberg theory of electron-phonon interactions and superconductivity. The history of the electron-phonon problem is introduced, and then study of the intermediate parameter regime is justified from the energy scales in the cuprate superconductors. The Holstein model is detailed, and limiting cases are examined to demonstrate the need for an extended theory of superconductivity. Results of the extended approximation are shown, including spectral functions and phase diagrams. These are discussed with reference to Hohenberg's theorem, the Bardeen-Cooper-Schrieffer theory and Coulomb repulsion

<i>d</i>-wave superconductivity from electron-phonon interactions

I examine electron-phonon mediated superconductivity in the intermediate coupling and phonon frequency regime of the quasi-two-dimensional Holstein model. I use an extended Migdal-Eliashberg theory that includes vertex corrections and spatial fluctuations. I find a d-wave superconducting state that is unique close to half filling. The order parameter undergoes a transition to s-wave superconductivity on increasing filling. I explain how the inclusion of both vertex corrections and spatial fluctuations is essential for the prediction of a d-wave order parameter. I then discuss the effects of a large Coulomb pseudopotential on the superconductivity (such as is found in contemporary superconducting materials like the cuprates), which results in the destruction of the s-wave states, while leaving the d-wave states unmodified