arXiv subjects

Peter Kopietz

Publications and source records attributed to Peter Kopietz.

At least 127 records · Page 7Linked to original sources

arXiv1998

Coulomb Gap in the Density of States of Disordered Metals in Two Dimensions

We calculate the effect of Coulomb interactions on the average density of states nu (omega) of two-dimensional disordered electrons. It is shown that for weak disorder the most singular terms in the perturbative expansion of nu (omega) can be summed by means of a simple gauge transformation, which also establishes a relation between the low-frequency behavior of nu (omega) and the average conductivity sigma (omega). Using this relation, we show that if lim_{omega rightarrow 0} sigma (omega) is finite, then nu (omega) approaches C | omega | / e^4 for omega rightarrow 0, where C is a dimensionless constant and e is the charge of the electron. This implies that a normal metallic state of disordered electrons in two dimensions is not a Fermi liquid.

cond-mat.str-el↗

arXiv1998

Vertex corrections in gauge theories for two-dimensional condensed matter systems

We calculate the self-energy of two-dimensional fermions that are coupled to transverse gauge fields, taking two-loop corrections into account. Given a bare gauge field propagator that diverges for small momentum transfers q as 1 / q^{eta}, 1 < eta < 2, the fermionic self-energy without vertex corrections vanishes for small frequencies omega as Sigma (omega) propto omega^{gamma with gamma = {frac{2}{1 + eta}} < 1. We show that inclusion of the leading radiative correction to the fermion - gauge field vertex leads to Sigma (omega) propto omega^{gamma} [ 1 - a_{eta} ln (omega_0 / omega) ], where a_η is a positive numerical constant and omega_0 is some finite energy scale. The negative logarithmic correction is consistent with the scenario that higher order vertex corrections push the exponent gamma to larger values.

cond-mat.str-el↗

arXiv1997

Spin conductance, dynamic spin stiffness and spin diffusion in itinerant magnets

We discuss analogies between the charge- and spin response functions of itinerant magnets. We show that the spin-analog of the charge stiffness is not given by the usual spin stiffness rho_s, but by the dynamic spin stiffness D_s, which is obtained from the dynamic spin conductance G_s (omega) in the limit of vanishing frequency omega. The low-frequency behavior of G_s (omega) is used to define ideal spin conductors, normal spin conductors, and spin insulators. Assuming diffusive spin dynamics, we show that the spin diffusion coefficient is proportional to lim_{omega rightarrow 0} {Re} {G}_s (omega). We exploit this fact to develop a new extrapolation scheme for the spin diffusion coefficient in the paramagnetic phase of the Hubbard model.

cond-mat.str-el↗

arXiv1997

Non-linear response and electron-electron interactions in mesoscopic metal rings

A time-dependent electric field gives rise to a stationary non-equilibrium current I^{(2)} around a mesoscopic metal ring threaded by a magnetic flux. We show that this current, which is proportional to the intensity of the field, is closely related to the exchange part of the interaction contribution to the equilibrium persistent current, and that the corresponding non-linear conductivity directly measures the weak localization correction to the polarization. We explicitly calculate the disorder average of I^{(2)} in the diffusive regime as function of the frequency of the electric field and the static flux piercing the ring, and suggest an experiment to test our theory.

cond-mat.mes-hall↗

arXiv1997

The weak localization correction to the polarization and persistent currents in mesoscopic metal rings

We re-examine the effect of electron-electron interactions on the persistent current in mesoscopic metal rings threaded by an Aharonov-Bohm flux. The exchange contribution to the current is shown to be determined by the weak localization correction to the polarization. We explicitly calculate the contribution from exchange interactions with momentum transfers smaller than the inverse elastic mean free path to the average current, and find that it has the same order of magnitude as the {\it{canonical}} current without interactions. \\

cond-mat.mes-hall↗

arXiv1997

The NMR relaxation rate of O in undoped Sr_2CuO_2Cl_2: Probing two-dimensional magnons at short distances

We calculate the nuclear relaxation rate of oxygen in the undoped quasi two-dimensional quantum Heisenberg antiferromagnet Sr_2CuO_2Cl_2 above the Neel temperature. The calculation is performed at two-loop order with the help of the Dyson-Maleev formulation of the spin-wave expansion, taking all scattering processes involving two and three magnons into account. At low temperatures T we find 1 / T_1 = c_1 T^3 + c_2 T^4 + O (T^5), and give explicit expressions for the coefficients c_1 (two-magnon scattering) and c_2 (three magnon scattering). We compare our result with a recent experiment by Thurber et al. and show that this experiment directly probes the existence of short-wavelength magnons in a two-dimensional antiferromagnet.

cond-mat.str-el↗

arXiv1997

An Exactly Solvable Model of N Coupled Luttinger Chains

We calculate the exact Green function of a special model of N coupled Luttinger chains with arbitrary interchain hopping t_{perp}. The model is exactly solvable via bosonization if the interchain interaction does not fall off in the direction perpendicular to the chains. For any finite N we find Luttinger liquid behavior and explicitly calculate the anomalous dimension gamma^(N). However, the Luttinger liquid state does not preclude coherent interchain hopping. We also show that gamma^(N) -> 0 for N -> infinity, so that in the limit of infinitely many chains we obtain a Fermi liquid.

cond-mat.str-el↗

arXiv1997

Crossover between Luttinger and Fermi liquid behavior in weakly coupled metallic chains

We use higher-dimensional bosonization to study the normal state of electrons in weakly coupled metallic chains interacting with long-range Coulomb forces. Particular attention is paid to the crossover between Luttinger and Fermi liquid behavior as the interchain hopping is varied. Although in the physically interesting case of finite but small interchain hopping the quasi-particle residue does not vanish, the single-particle Green's function exhibits the signature of Luttinger liquid behavior (i.e. anomalous scaling and spin-charge separation) in a large intermediate parameter regime. Using realistic parameters, we find that the scaling behavior in this regime is characterized by an anomalous dimension of the order of unity, as suggested by recent experiments on quasi-one-dimensional conductors. Our calculation gives new insights into the approximations inherent in higher-dimensional bosonization. We also compare our approach with other methods.

cond-mat.str-el↗

arXiv1996

Spectral correlations in disordered mesoscopic metals and their relevance for persistent currents

We use the Lanczos method to calculate the variance of the number of energy levels in an energy window of width E below the Fermi energy for non-interacting disordered electrons on a thin three-dimensional ring threaded by an Aharonov-Bohm flux . We find that for small E the flux-dependent part of the variance is well described by a well-known Feynman diagram involving two Cooperons. However, this result cannot be extrapolated to energies E where the energy-dependence of the average density of states becomes significant. We discuss consequences for persistent currents.

cond-mat.mes-hall↗

arXiv1996

Screening of persistent currents in mesoscopic metal rings

The effect of the Coulomb-interaction on persistent currents in disordered mesoscopic metal rings threaded by a magnetic flux $ϕ$ is studied numerically. We use the simplest form of ``self-consistent'' Hartree theory, where the spatial variations of the self-consistent Hartree potential are ignored. In this approximation the self-consistent Hartree energies are simply obtained by diagonalizing the non-interacting system via the Lanczos method and then calculating the (disorder-dependent) particle number on the ring self-consistently. In the diffusive regime we find that the variance of the total particle number is strongly reduced, in agreement with the prediction of the random-phase approximation. On the other hand, the variance of the number of energy levels in a small interval below the Fermi energy is not affected by the Coulomb interaction.

cond-mat.mes-hall↗

arXiv1996

Quasi-particle behavior of composite fermions in the half-filled Landau level

We calculate the effect of infrared fluctuations of the Chern-Simons gauge field on the single-particle Green's function of composite fermions in the half-filled Landau level via higher-dimensional bosonization on a curved Fermi surface. We find that composite fermions remain well-defined quasi-particles, with an effective mass given by the mean-field value, but with anomalously large damping and a spectral function that contains considerable weight away from the quasi-particle peak.

cond-mat.mes-hall↗

arXiv1996

How to bosonize fermions with non-linear energy dispersion

We develop a systematic method to treat the effect of non-linearity in the energy dispersion on the usual bosonization result for the single-particle Green's function of fermions in arbitrary dimension. The leading corrections due to the quadratic term in the energy dispersion are explicitly calculated. In the Chern-Simons theory for half-filled quantum Hall systems curvature is shown to be essential.

cond-mat↗

arXiv1996

Bosonization and the eikonal expansion: similarities and differences

We compare two non-perturbative techniques for calculating the single-particle Green's function of interacting Fermi systems with dominant forward scattering: our recently developed functional integral approach to bosonization in arbitrary dimensions, and the eikonal expansion. In both methods the Green's function is first calculated for a fixed configuration of a background field, and then averaged with respect to a suitably defined effective action. We show that, after linearization of the energy dispersion at the Fermi surface, both methods yield for Fermi liquids exactly the same non-perturbative expression for the quasi-particle residue. However, in the case of non-Fermi liquid behavior the low-energy behavior of the Green's function predicted by the eikonal method can be erroneous. In particular, for the Tomonaga-Luttinger model the eikonal method neither reproduces the correct scaling behavior of the spectral function, nor predicts the correct location of its singularities.

cond-mat↗

arXiv1996

Calculation of the average Green's function of electrons in a stochastic medium via higher-dimensional bosonization

The disorder averaged single-particle Green's function of electrons subject to a time-dependent random potential with long-range spatial correlations is calculated by means of bosonization in arbitrary dimensions. For static disorder our method is equivalent with conventional perturbation theory based on the lowest order Born approximation. For dynamic disorder, however, we obtain a new non-perturbative expression for the average Green's function. Bosonization also provides a solid microscopic basis for the description of the quantum dynamics of an interacting many-body system via an effective stochastic model with Gaussian probability distribution.

cond-mat↗

arXiv1995

Bosonization of coupled electron-phonon systems

We calculate the single-particle Green's function of electrons that are coupled to acoustic phonons by means of higher dimensional bosonization. This non-perturbative method is {\it{not}} based on the assumption that the electronic system is a Fermi liquid. For isotropic three-dimensional phonons we find that the long-range part of the Coulomb interaction cannot destabilize the Fermi liquid state, although for strong electron-phonon coupling the quasi-particle residue is small. We also show that Luttinger liquid behavior in three dimensions can be due to quasi-one-dimensional anisotropy in the electronic band structure {\it{or in the phonon frequencies}}.

cond-mat↗

arXiv1995

Why normal electrons with sufficiently singular interactions do not have a sharp Fermi surface

We use a bosonization approach to show that the momentum distribution $n_{\bf{k}}$ of normal Fermi systems with sufficiently singular interactions is analytic in the vicinity of the non-interacting Fermi surface. These include singular density-density interactions that diverge in $d$ dimensions stronger than $ | {\bf{q}} |^{- 2 (d -1)}$ for vanishing momentum transfer ${\bf{q}}$, but also fermions that are coupled to transverse gauge fields in $ d < 3$.

cond-mat↗

arXiv1995

Calculation of the single-particle Green's function of interacting fermions in arbitrary dimension via functional bosonization

The single-particle Green's function of an interacting Fermi system with dominant forward scattering is calculated by decoupling the interaction by means of a Hubbard-Stratonowich transformation involving a bosonic auxiliary field $ϕ^α$. We obtain a higher dimensional generalization of the well-known one-dimensional bosonization result for the Green's function by first calculating the Green's function for a fixed configuration of the $ϕ^α$-field and then averaging the resulting expression with respect to the probability distribution ${\cal{P}} \{ ϕ^α \} \propto \exp [ - S_{eff} \{ ϕ^α \} ]$, where $S_{eff} \{ ϕ^α \}$ is the effective action of the $ϕ^α$-field. We emphasize the approximations inherent in the higher-dimensional bosonization approach and clarify its relation with diagrammatic perturbation theory.

cond-mat↗

arXiv1995

Non-Relativistic Fermions Coupled to Transverse Gauge-Fields: The Single-Particle Green's Function in Arbitrary Dimension

We use a bosonization approach to calculate the single-particle Green's function $G ( {\bf{r}} , τ)$ of non-relativistic fermions coupled to transverse gauge-fields in arbitrary dimension $d$. We find that in $d>3$ transverse gauge-fields do not destroy the Fermi liquid, although for $d < 6$ the quasi-particle damping is anomalously large. For $d \rightarrow 3$ the quasi-particle residue vanishes as $Z \propto \exp [ - \frac{1}{2 π( d-3)} (\frac{ κ}{mc } )^2 ]$, where $κ$ is the Thomas-Fermi wave-vector, $m$ is the mass of the electrons, and $c$ is the velocity of the gauge-particle. In $d=3$ the system is a Luttinger liquid, with anomalous dimension $γ_{\bot} = \frac{1}{6 π} ( \frac{ κ}{mc} )^2$. For $d < 3$ we find that $G ({\bf{r}} , 0 )$ decays exponentially at large distances.

cond-mat↗