Generalization of the theory of three-dimensional quantum Hall effect of Fermi arcs in Weyl semimetal

The quantum Hall effect (QHE), which is usually observed in two-dimensional systems, was predicted theoretically and observed experimentally in three-dimensional (3D) topological semimetal. However, there are some inconsistencies between the theory and the experiments showing the theory is imperfect. Here, we generalize the theory of the 3D QHE of Fermi arcs in Weyl semimetal. Through calculating the sheet Hall conductivity of a Weyl semimetal slab, we show that the 3D QHE of Fermi arcs can occur in a large energy range and the thickness dependences of the QHE in different Fermi energies are distinct. When the Fermi energy is near the Weyl nodes, the Fermi arcs give rise to the QHE which is independent of the thickness of the slab. When the Fermi energy is not near the Weyl nodes, the two Fermi arcs form a complete Fermi loop with the assistance of bulk states giving rise to the QHE which is dependent on the sample thickness. We also demonstrate how the band anisotropic terms influence the QHE of Fermi arcs. Our theory complements the imperfections of the present theory of 3D QHE of Fermi arcs.     

Breakup of the Fermi surface near the mott transition in low-dimensional systems

We investigate the Mott transition in weakly coupled one-dimensional (1D) fermionic chains. Using a generalization of dynamical mean field theory, we show that the Mott gap is suppressed at some critical hopping t{ perpendicular}{c2}. The transition from the 1D insulator to a 2D metal proceeds through an intermediate phase where the Fermi surface is broken into electron and hole pockets. The quasiparticle spectral weight is strongly anisotropic along the Fermi surface, both in the intermediate and metallic phases. We argue that such pockets would look like "arcs" in photoemission experiments.     

Wilson's renormalization group applied to 2D lattice electrons in the presence of van Hove singularities

The weak coupling instabilities of a two dimensional Fermi system are investigated for the case of a square lattice using a Wilson renormalization group scheme to one loop order. We focus on a situation where the Fermi surface passes through two saddle points of the single particle dispersion. In the case of perfect nesting, the dominant instability is a spin density wave but d-wave superconductivity as well as charge or spin flux phases are also obtained in certain regions in the space of coupling parameters. The low energy regime in the vicinity of these instabilities can be studied analytically. Although saddle points play a major role (through their large contribution to the single particle density of states), the presence of low energy excitations along the Fermi surface rather than at isolated points is crucial and leads to an asymptotic decoupling of the various instabilities. This suggests a more mean-field like picture of these instabilities, than the one recently established by numerical studies using discretized Fermi surfaces. Received 11 April 2001 and Received in final form 6 September 2001     

Effect of hole doping on the electronic structure and the Fermi surface in the Hubbard model within norm-conserving cluster pertubation theory

The concentration dependences of the band structure, spectral weight, density of states, and Fermi surface in the paramagnetic state are studied in the Hubbard model within cluster pertubation theory with 2 × 2 clusters. Representation of the Hubbard X operators makes it possible to control conservation of the spectral weight in constructing cluster perturbation theory. The calculated value of the ground-state energy is in good agreement with the results obtained using nonperturbative methods such as the quantum Monte Carlo method, exact diagonalization of a 4 × 4 cluster, and the variational Monte Carlo method. It is shown that in the case of hole doping, the states in the band gap (in-gap states) lie near the top of the lower Hubbard band for large values of U and near the bottom of the upper band for small U. The concentration dependence of the Fermi surface strongly depends on hopping to second (t′) and third (t″) neighbors. For parameter values typical of HTSC cuprates, the existence of three concentration regions with different Fermi surfaces is demonstrated. It is shown that broadening of the spectral electron density with an energy resolution typical of contemporary ARPES leads to a pattern of arcs with a length depending on the concentration. Only an order-of-magnitude decrease in the linewidth makes it possible to obtain the true Fermi surface from the spectral density. The kinks associated with strong electron correlations are detected in the dispersion relation below the Fermi level.     

Holographic Fermi arcs and a d-wave gap

We study fermion correlators in a holographic superfluid with a d-wave (spin two) order parameter. We find that, with a suitable bulk Majorana coupling, the Fermi surface is anisotropically gapped. At low temperatures the gap shrinks to four nodal points. At high temperatures the Fermi surface is partially gapped generating four Fermi arcs.     

Cuprate Fermi orbits and Fermi arcs: the effect of short-range antiferromagnetic order

We consider the effect of a short antiferromagnetic correlation length xi on the electronic band structure of the underdoped cuprates. Starting with a Fermi-surface topology consistent with magnetic-quantum-oscillation data, we show that a reduced xi gives an asymmetric broadening of the quasiparticle dispersion, resulting in simulated ARPES data very similar to those observed in experiment. Predicted features include "Fermi arcs" close to ak=(pi/2,pi/2), where a is the in-plane lattice parameter, without the need to invoke a d-wave pseudogap order parameter. The statistical variation in the k-space areas of the reconstructed Fermi-surface pockets causes the quantum oscillations to be strongly damped, even in very strong magnetic fields, in agreement with experiment.     

Kink in the dispersion of layered strontium ruthenates

We present detailed energy dispersions near the Fermi level along the high symmetry line GammaX on the monolayer and bilayer strontium ruthenates Sr2RuO4 and Sr3Ru2O7, determined by high-resolution angle-resolved photoemission spectroscopy. A kink in the dispersion is clearly shown for the both ruthenates. The energy position of the kink and the slope in the low-energy part near the Fermi level are almost identical between them, whereas the dispersion in the high-energy part varies, like the behavior of the kink for the cuprate superconductors.     

The holographic fermions dual to massive gravity

We investigate the properties of the spectral function of the fermionic operator in the field theory which is dual to a 4-dimensional massive gravity. We first study the Fermi surface and the dispersion relation in the dual boundary theory. We find that as the massive parameters is decreased, the Fermi momentum becomes lower and the low energy excitation near Fermi surface behaves more like non-Fermi liquid. Then, we introduce a dipole coupling in the bulk theory and explore the emergence of a gap in the fermionic spectral function. It is found that larger critical dipole coupling is needed to open the gap than that in Einstein gravity. Accordingly, in the field theory dual to massive gravity, it requires stronger negative dipole coupling to generate the marginal Fermi liquid.     

Evolution of the Fermi surface of d-wave superconductors in the presence of thermal phase fluctuations

One of the most puzzling aspects of the high Tc superconductors is the appearance of Fermi arcs in the normal state of the underdoped cuprate materials. These are loci of low energy excitations covering part of the Fermi surface that suddenly appear above Tc instead of the nodal quasiparticles. Based on a semiclassical theory, we argue that partial Fermi surfaces arise naturally in a d-wave superconductor that is destroyed by thermal phase fluctuations. Specifically, we show that the electron spectral function develops a square root singularity at low frequencies for wave vectors positioned on the bare Fermi surface. We predict a temperature dependence of the arc length that can partially account for the results of recent angle resolved photoemission experiments.     

Protected nodes and the collapse of Fermi arcs in high-T{c} cuprate superconductors

Angle resolved photoemission on underdoped Bi2Sr2CaCu2O8 reveals that the magnitude and d-wave anisotropy of the superconducting state energy gap are independent of temperature all the way up to T{c}. This lack of T variation of the entire k-dependent gap is in marked contrast to mean field theory. At T{c} the point nodes of the d-wave gap abruptly expand into finite length "Fermi arcs." This change occurs within the width of the resistive transition, and thus the Fermi arcs are not simply thermally broadened nodes but rather a unique signature of the pseudogap phase.     

Fermi arc formation by chiral spin textures in high-temperature superconductors

In angle-resolved photoemission spectroscopy pseudogap phenomenon in high-temperature superconductors is observed as Fermi arcs, or truncated Fermi surface. Here I argue that the hole induced chiral spin texture scenario naturally leads to Fermi arcs by including hole hopping processes. Disappearance of part of the Fermi surface is associated with the effect of the coherence factor. Suppressed spectral weight of the holes turns out to be an electron-like component which has weight near (π,0) only and has some charge instability.     

Fermi arcs in the superconducting clustered state for underdoped cuprate superconductors

The one-particle spectral function of a state formed by superconducting (SC) clusters is studied via Monte Carlo techniques. The clusters have similar SC amplitudes but randomly distributed phases. This state is stabilized by competition with the antiferromagnetism expected to be present in the cuprates and after quenched disorder is introduced. A Fermi surface composed of disconnected segments, i.e., Fermi arcs, is observed between the critical temperature T_(c) and the cluster formation temperature scale T*.     

One-dimensional energy dispersion of single-walled carbon nanotubes by resonant electron scattering

We characterized the energy band dispersion near the Fermi level in single-walled carbon nanotubes using low-temperature scanning tunneling microscopy. Analysis of energy-dependent standing wave oscillations, which result from quantum interference of electrons resonantly scattered by defects, yields a linear energy dispersion near E(F), and indicates the importance of parity in scattering for armchair single-walled carbon nanotubes. Additionally, these data provide values of the tight-binding overlap integral and Fermi wave vector, in good agreement with previous work, but indicate that the electron coherence length is substantially shortened.     

Charge order driven by Fermi-arc instability and its connection with pseudogap in cuprate superconductors

The recently discovered charge order is a generic feature of cuprate superconductors, however, its microscopic origin remains debated. Within the framework of the fermion-spin theory, the nature of charge order in the pseudogap phase and its evolution with doping are studied by taking into account the electron self-energy (then the pseudogap) effect. It is shown that the antinodal region of the electron Fermi surface is suppressed by the electron self-energy, and then the low-energy electron excitations occupy the disconnected Fermi arcs located around the nodal region. In particular, the charge order state is driven by the Fermi-arc instability, with a characteristic wave vector corresponding to the hot spots of the Fermi arcs rather than the antinodal nesting vector. Moreover, although the Fermi arc increases its length as a function of doping, the charge order wave vector reduces almost linearity with the increase of doping. The theory also indicates that the Fermi arc, charge order and pseudogap in cuprate superconductors are intimately related to each other, and all of them emanates from the electron self-energy due to the interaction between electrons by the exchange of spin excitations.     

Fermi Arcs and DC Transport in Nanowires of Dirac and Weyl Semimetals

The transport properties and electron states in cylinder nanowires of Dirac and Weyl semimetals are studied paying special attention to the structure and properties of the surface Fermi arcs. The latter make the electric charge and current density distributions in nanowires strongly nonuniform as the majority of the charge density is accumulated at the surface. It is found that a Weyl semimetal wire also supports a magnetization current localized mainly at the surface because of the Fermi arcs contribution. By using the Kubo linear response approach, the direct current (DC) conductivity is calculated and it is found that its spatial profile is nontrivial. By explicitly separating the contributions of the surface and bulk states, it is shown that when the electric chemical potential and/or the radius of the wire is small, the electron transport is determined primarily by the Fermi arcs and the electrical conductivity is much higher at the surface than in the bulk. Due to the rise of the surface-bulk transition rate, the relative contribution of the surface states to the total conductivity gradually diminishes as the chemical potential increases. In addition, the DC conductivity at the surface demonstrates noticeable peaks when the Fermi level crosses energies of the surface states.     

A cellular dynamical mean field theory approach to Mottness

We investigate the properties of a strongly correlated electron system in the proximity of a Mott insulating phase within the Hubbard model, using a cluster generalization of the dynamical mean field theory. We find that Mottness is intimately connected with the existence in momentum space of a surface of zeros of the single particle Green’s function. The opening of a Mott-Hubbard gap at half filling and the opening of a pseudogap at finite doping are necessary elements for the existence of this surface. At the same time, the Fermi surface may change topology or even disappear. Within this framework, we provide a simple picture for the appearance of Fermi arcs. We identify the strong short-range correlations as the source of these phenomena and we identify the cumulant as the natural irreducible quantity capable of describing this short-range physics. We develop a new version of the cellular dynamical mean field theory based on cumulants that provides the tools for a unified treatment of general lattice Hamiltonians.     

Evolution of the normal state of a strongly interacting Fermi gas from a pseudogap phase to a molecular Bose gas

Wave-vector resolved radio frequency spectroscopy data for an ultracold trapped Fermi gas are reported for several couplings at T(c), and extensively analyzed in terms of a pairing-fluctuation theory. We map the evolution of a strongly interacting Fermi gas from the pseudogap phase into a fully gapped molecular Bose gas as a function of the interaction strength, which is marked by a rapid disappearance of a remnant Fermi surface in the single-particle dispersion. We also show that our theory of a pseudogap phase is consistent with a recent experimental observation as well as with quantum Monte Carlo data of thermodynamic quantities of a unitary Fermi gas above T(c).     

Phonon dispersion curves for niobium

Conclusion The experimentally measured phonon dispersion relation for niobium is very complex. This complexity may be due to the incomplete electronicd shells which make an important contribution to very large cohesive energy, and its likely effect on the phonon frequencies. Also the anomalies in the dispersion curves may be due to the departure of the Fermi surface from sphericity. In the present study none of the above effects is included explicitly and so theory fails to achieve exact agreement with the experimental data. Finally, we would like to put a concluding remark that an appropriate microscopic treatment given tod electron could explain the phonon dispersion curves of transition metal like niobium.One of the authors (ARJ) would like to express his appreciation to Professor M. K. Agarwal (Head of the Department) for his support and encouragement to carry out this work. Thanks are also due to Sardar Patel University for providing computer facilities.     

Perspective of Galactic dark matter subhalo detection on Fermi from the EGRET observation

The perspective of the detectability of Galactic dark matter subhaioes on the Fermi satellite is investigated in this work.Under the assumptions that dark matter annihilation accounts for the "GeV excess" of the Galactic diffuse γ-rays discovered by EGRET and the γ-ray flux is dominated by the contribution from subhaloes of dark matter, we calculate the expected number of dark matter subhaloes that Fermi may detect.We show that Fermi may detect a few tens to several hundred subhaloes in a 1-year all-sky survey.Since EGRET observation is taken as a normalization, this prediction is independent of the particle physics property of dark matter.The uncertainties of the prediction are discussed in detail.We find that the major uncertainty comes from the mass function of subhaloes, i.e., whether the subhaloes are "point like" (high-mass rich) or "diffuse like" (low-mass rich).Other uncertainties like the background estimation and the observational errors will contribute a factor of 2-3.     

Fermi-surface truncation from thermal nematic fluctuations

We analyze how thermal fluctuations near a finite temperature nematic phase transition affect the spectral function A(k,ω) for single-electron excitations in a two-dimensional metal. Perturbation theory yields a splitting of the quasiparticle peak with a d-wave form factor, reminiscent of a pseudogap. We present a resummation of contributions to all orders in the Gaussian fluctuation regime. Instead of a splitting, the resulting spectral function exhibits a pronounced broadening of the quasiparticle peak, which varies strongly around the Fermi surface and vanishes upon approaching the Brillouin-zone diagonal. The Fermi surface obtained from a Brillouin-zone plot of A(k,0) seems truncated to Fermi arcs.