Fermi Velocity Renormalization Research Articles

Fermi velocity renormalization and dynamical gap generation in graphene

We study the renormalization of the Fermi velocity by the long-range Coulomb interactions between the charge carriers in the Dirac-cone approximation for the effective low-energy description of the electronic excitations in graphene at half filling. Solving the coupled system of Dyson-Schwinger equations for the dressing functions in the corresponding fermion propagator with various approximations for the particle-hole polarization we observe that Fermi velocity renormalization effects generally lead to a considerable increase of the critical coupling for dynamical gap generation and charge-density wave formation at the semimetal-insulator transition.

Dynamical breakdown of parity and time-reversal invariance in the many-body theory of graphene

We show that, at sufficiently large strength of the long-range Coulomb interaction, a mass term breaking parity (so-called Haldane mass) is dynamically generated in the many-body theory of Dirac fermions describing the graphene layer. While the tendency towards chiral symmetry breaking is stronger than for the dynamical breakdown of parity at spatial dimension D > 2, we find that the situation is reversed at D = 2. The need to regularize the many-body theory in a gauge-invariant manner (taking the limit D = 2 - \epsilon) is what leads to the dominance of the parity-breaking pattern in graphene. We compute the critical coupling for the generation of a parity-breaking mass from the finite radius of convergence of the ladder series supplemented with electron self-energy corrections, finding a value quite close to the effective interaction strength for graphene in vacuum after including Fermi velocity renormalization and static RPA screening of the Coulomb interaction.

Anomalous superfluid density in quantum critical superconductors.

When a second-order magnetic phase transition is tuned to zero temperature by a nonthermal parameter, quantum fluctuations are critically enhanced, often leading to the emergence of unconventional superconductivity. In these "quantum critical" superconductors it has been widely reported that the normal-state properties above the superconducting transition temperature T(c) often exhibit anomalous non-Fermi liquid behaviors and enhanced electron correlations. However, the effect of these strong critical fluctuations on the superconducting condensate below T(c) is less well established. Here we report measurements of the magnetic penetration depth in heavy-fermion, iron-pnictide, and organic superconductors located close to antiferromagnetic quantum critical points, showing that the superfluid density in these nodal superconductors universally exhibits, unlike the expected T-linear dependence, an anomalous 3/2 power-law temperature dependence over a wide temperature range. We propose that this noninteger power law can be explained if a strong renormalization of effective Fermi velocity due to quantum fluctuations occurs only for momenta k close to the nodes in the superconducting energy gap Δ(k). We suggest that such "nodal criticality" may have an impact on low-energy properties of quantum critical superconductors.

Luttinger liquid physics from the infinite-system density matrix renormalization group

We study one-dimensional spinless fermions at zero and finite temperature $T$ using the density-matrix renormalization group. We consider nearest- as well as next-nearest-neighbor interactions; the latter render the system inaccessible by a Bethe ansatz treatment. Using an infinite-system algorithm we demonstrate the emergence of Luttinger liquid physics at low energies for a variety of static correlation functions as well as for thermodynamic properties. The characteristic power-law suppression of the momentum distribution $n(k)$ function at $T=0$ can be directly observed over several orders of magnitude. At finite temperature, we show that $n(k)$ obeys a scaling relation. The Luttinger liquid parameter and the renormalized Fermi velocity can be extracted from the density response function, the specific heat, or the susceptibility without the need to carry out any finite-size analysis. We illustrate that the energy scale below which Luttinger liquid power laws manifest vanishes as the half-filled system is driven into a gapped phase by large interactions.

Electronic ground-state properties of strained graphene

We consider the effect of the Coulomb interaction in strained graphene using tight-binding approximation together with the Hartree-Fock interactions. The many-body energy dispersion relation, anisotropic Fermi velocity renormalization and charge compressibility in the presence of uniaxial strain are calculated. We show that the quasiparticle quantities are sensitive to homogenous strain and indeed, to its sign. The charge compressibility is enhanced by stretching and suppressed by compressing a graphene sheet. We find a reduction of Fermi velocity renormalization along the direction of graphene deformation, in good agreement with the recent experimental observation.

An atlas of carbon nanotube optical transitions

Electron-electron interactions are significantly enhanced in one-dimensional systems, and single-walled carbon nanotubes provide a unique opportunity for studying such interactions and the related many-body effects in one dimension. However, single-walled nanotubes can have a wide range of diameters and hundreds of different structures, each defined by its chiral index (n,m), where n and m are integers that can have values from zero up to 30 or more. Moreover, one-third of these structures are metals and two-thirds are semiconductors, and they display optical resonances at many different frequencies. Systematic studies of many-body effects in nanotubes would therefore benefit from the availability of a technique for identifying the chiral index of a nanotube based on a measurement of its optical resonances, and vice versa. Here, we report the establishment of a structure-property 'atlas' for nanotube optical transitions based on simultaneous electron diffraction measurements of the chiral index and Rayleigh scattering measurements of the optical resonances of 206 different single-walled nanotube structures. The nanotubes, which were suspended across open slit structures on silicon substrates, had diameters in the range 1.3-4.7nm. We also use this atlas as a starting point for a systematic study of many-body effects in the excited states of single-walled nanotubes. We find that electron-electron interactions shift the optical resonance energies by the same amount for both metallic and semiconducting nanotubes, and that this shift (which corresponds to an effective Fermi velocity renormalization) increases monotonically with nanotube diameter. This behaviour arises from two sources: an intriguing cancellation of long-range electron-electron interaction effects, and the dependence of short-range electron-electron interactions on diameter.

Band symmetries and singularities in twisted multilayer graphene

The electronic spectra of rotationally faulted graphene bilayers are calculated using a continuum formulation for small fault angles that identifies two distinct electronic states of the coupled system. The low-energy spectra of one state features a Fermi velocity reduction, which ultimately leads to pairwise annihilation and regeneration of its low-energy Dirac nodes. The physics in the complementary state is controlled by pseudospin selection rules that prevent a Fermi velocity renormalization and produce second generation symmetry-protected Dirac singularities in the spectrum. These results are compared with previous theoretical analyses and with experimental data.

Exact diagonalization study of 2D Hubbard model on honeycomb lattice: Semi-metal to insulator transition

Phase transition in a honeycomb lattice is studied by the means of the two-dimensional Hubbard model and the exact diagonalization dynamical mean field theory at zero temperature. At low energies, the dispersion relation is shown to be a linear function of the momentum. In the limit of weak interactions, the system is in the semi-metal phase. By increasing the on site interaction a semi-metal to insulator transition takes place in the paramagnetic phase. Calculation of double occupancy shows such a phase transition is of the second order. The respective phase transition point and critical on-site interaction are determined using renormalized Fermi velocity factor.

The dielectric environment dependent exchange self-energy of the energy structure in graphene

We theoretically calculate the energy dispersion in the presence of the screened exchange self-energy in extrinsic monolayer graphene. It is found that the exchange self-energy enhances the renormalized Fermi velocity. With decreasing the dielectric constant, the screening effect and the electron correlation effect increase which induces the Fermi velocity increasing. The screened exchange energy has an energy shift at the Dirac points. The self-energy from the valance band carriers gives the main contribution to the effective energy. We also discuss the electron density dependence of the self-energy.

Effect of gap opening on the quasiparticle properties of doped graphene sheets

We present numerical calculations of the effect of gap opening on the quasiparticle properties of a doped graphene sheet within G0W -RPA approximation. We present results of the renormalized Fermi velocity suppression and the renormalization constant over a broad range of the energy gap values. We find that the renormalized velocity is density independent at large density values which is in agreement with recent experimental observations. We also show that the inelastic quasiparticle lifetime decreases by increasing the gap value. Finally, we show that the inelastic mean free path reduces by increasing the gap values but in the range of the typical gap values it is large enough and transport remains in the semi-ballistic regime.

Effect of Holstein phonons on the optical conductivity of gapped graphene

We study the optical conductivity of a doped graphene when a sublattice symmetry breaking is occurred in the presence of the electron-phonon interaction. Our study is based on the Kubo formula that is established upon the retarded self-energy. We report new features of both the real and imaginary parts of the quasiparticle self-energy in the presence of a gap opening. We find an analytical expression for the renormalized Fermi velocity of massive Dirac Fermions over broad ranges of electron densities, gap values and the electron-phonon coupling constants. Finally we conclude that the inclusion of the renormalized Fermi energy and the band gap effects are indeed crucial to get reasonable feature for the optical conductivity.

Fermi velocity renormalization in doped graphene

AbstractWe present an ab initio study of the graphene quasi‐particle band structure within GW approximation. In particular we studied the renormalization of the Fermi velocity vF as function of the electrostatic doping. We show that within local density approximation (LDA) the Fermi velocity is substantially renormalized by correlation effects and that this renormalization rapidly decreases with doping. We discuss our results in the light of recent experiments on graphene and intercalate graphite.

The effect of sublattice symmetry breaking on the electronic properties of doped graphene

Motivated by a number of recent experimental studies, we have carried out the microscopic calculation of the quasi-particle (QP) self-energy and spectral function in doped graphene when symmetry breaking of the sublattices occurs. Our systematic study is based on the many-body G0W approach that is established on the random phase approximation and on graphene's massive Dirac equation continuum model. We report extensive calculations of both the real and imaginary parts of the QP self-energy in the presence of a gap opening. We also present results for spectral function, renormalized Fermi velocity and band gap renormalization of massive Dirac fermions over a broad range of electron densities. We further show that mass generating in graphene washes out the plasmaron peak in the spectral weight.

Fermi Surface Topology and Low-Lying Quasiparticle Dynamics of ParentFe1+xTe/SeSuperconductor

We report the first photoemission study of Fe1+xTe - the host compound of the newly discovered iron-chalcogenide superconductors. Our results reveal a pair of nearly electron- hole compensated Fermi pockets, strong Fermi velocity renormalization and an absence of a spin-density-wave gap. A shadow hole pocket is observed at the "X"-point of the Brillouin zone which is consistent with a long-range ordered magneto-structural groundstate. No signature of Fermi surface nesting instability associated with Q= pi(1/2, 1/2) is observed. Our results collectively reveal that the Fe1+xTe series is dramatically different from the undoped phases of the high Tc pnictides and likely harbor unusual mechanism for superconductivity and quantum magnetic order.

Electron−Phonon Interactions in Graphene, Bilayer Graphene, and Graphite

Using first-principles techniques, we calculate the renormalization of the electron Fermi velocity and the vibrational lifetimes arising from electron-phonon interactions in doped bilayer graphene and in graphite and compare the results with the corresponding quantities in graphene. For similar levels of doping, the Fermi velocity renormalization in bilayer graphene and in graphite is found to be approximately 30% larger than that in graphene. In the case of bilayer graphene, this difference is shown to arise from the interlayer interaction. We discuss our findings in the light of recent photoemission and Raman spectroscopy experiments.

Tilted anisotropic Dirac cones in quinoid-type graphene andα−(BEDT-TTF)2I3

We investigate a generalized two-dimensional Weyl Hamiltonian, which may describe the low-energy properties of mechanically deformed graphene and of the organic compound $\ensuremath{\alpha}\text{\ensuremath{-}}{(\text{BEDT-TTF})}_{2}{\text{I}}_{3}$ $[\text{BEDT-TTF}=\text{bis}(\text{ethylene}\text{dithio)tetrathiafulvalene}]$ under pressure. The associated dispersion has generically the form of tilted anisotropic Dirac cones. The tilt arises due to next-nearest-neighbor hopping when the Dirac points, where the valence band touches the conduction band, do not coincide with crystallographic high-symmetry points within the first Brillouin zone. Within a semiclassical treatment, we describe the formation of Landau levels in a strong magnetic field, the relativistic form of which is reminiscent of that of graphene, with a renormalized Fermi velocity due to the tilt of the Dirac cones. These relativistic Landau levels, experimentally accessible via spectroscopy or even a quantum-Hall-effect measurement, may be used as a direct experimental verification of Dirac cones in $\ensuremath{\alpha}\text{\ensuremath{-}}{(\text{BEDT-TTF})}_{2}{\text{I}}_{3}$.

Quasiparticle properties of graphene in the presence of disorder

We calculate the quasiparticle properties of chiral two-dimensional Dirac electrons in graphene within the Landau Fermi Liquid scheme based on G W approximation in the presence of disorder. Disorder effects due to charged impurity scattering play a crucial role in density dependence of quasiparticle quantities. Mode-coupling approach to scattering rate and self-energy in G W approximation for quasiparticle renormalized Fermi velocity and spin-antisymmetric Landau Fermi parameter incorporating the many-body interactions and the disorder effects show reduction of these quantities by 5%–15% at available experimental charge carrier density region.

Role of Strong Correlation in the Recent Angle-Resolved Photoemission Spectroscopy Experiments on Cuprate Superconductors

Motivated by recent photoemission experiments on cuprates, the low-lying excitations of a strongly correlated superconducting state are studied numerically. It is observed that along the nodal direction these low-lying one-particle excitations show a linear momentum dependence for a wide range of excitation energies and, thus, they do not present a kinklike structure. The nodal Fermi velocity v(F), as well as other observables, are systematically evaluated directly from the calculated dispersions, and they are found to compare well with experiments. It is argued that the parameter dependence of v(F) is quantitatively explained by a simple picture of a renormalized Fermi velocity.

Fermi-liquid theory for anisotropic superconductors

This article develops a quantitative quasiparticle model of the low-temperature properties of d-wave superconductors which incorporates both Fermi-liquid effects and band-structure effects. The Fermi-liquid interaction effects are found to be classifiable into strong and negligible renormalizaton effects, for symmetric and antisymmetric combinations of the energies of $k\uparrow$ and $-k\downarrow$ quasiparticles, respectively. A particularly important conclusion is that the leading clean-limit temperature-dependent correction to the superfluid density is not renormalized by Fermi-liquid interactions, but is subject to a Fermi velocity (or mass) renormalization effect. This leads to difficulties in accounting for the penetration depth measurements with physically acceptable parameters, and hence reopens the question of the quantitative validity of the quasiparticle picture.

Upper critical field of Ti andα−TiAlalloys: Evidence of an intrinsic type-II superconductivity in pure Ti

The upper critical field ${H}_{c2}$ of $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Ti}}_{1\ensuremath{-}x}{\mathrm{Al}}_{x}(0<~x<~0.1)$ alloys has been investigated in detail. The behaviors can well be described by the theory of type-II superconductors. The electronic specific heat deduced from the superconducting properties is in excellent agreement with previous calorimetric measurements. However, the Fermi velocity obtained here is substantially lower than predicted by band calculation. The present work gives clear evidence that pure Ti is an intrinsic type-II superconducting element due to its very low renormalized Fermi velocity.