arXiv subjects

D. Belitz

Publications and source records attributed to D. Belitz.

At least 127 records · Page 7Linked to original sources

arXiv1997

Metal-superconductor transition at zero temperature: A case of unusual scaling

An effective field theory is derived for the normal metal-to-superconductor quantum phase transition at T=0. The critical behavior is determined exactly for all dimensions d>2. Although the critical exponents βand νdo not exist, the usual scaling relations, properly reinterpreted, still hold. A complete scaling description of the transition is given, and the physics underlying the unusual critical behavior is discussed. Quenched disorder leads to anomalously strong T_c-fluctuations which are shown to explain the experimentally observed broadening of the transition in low-T_c thin films.

cond-mat.supr-con↗

arXiv1997

Quantum critical behavior of clean itinerant ferromagnets

We consider the quantum ferromagnetic transition at zero temperature in clean itinerant electron systems. We find that the Landau-Ginzburg-Wilson order parameter field theory breaks down since the electron-electron interaction leads to singular coupling constants in the Landau-Ginzburg-Wilson functional. These couplings generate an effective long-range interaction between the spin or order parameter fluctuations of the form 1/r^{2d-1}, with d the spatial dimension. This leads to unusual scaling behavior at the quantum critical point in 1 < d\leq 3, which we determine exactly. We also discuss the quantum-to-classical crossover at small but finite temperatures, which is characterized by the appearance of multiple temperature scales. A comparison with recent results on disordered itinerant ferromagnets is given.

cond-mat.stat-mech↗

arXiv1997

Long-range correlations and generic scale invariance in classical fluids and disordered electron systems

Long-ranged, or power-law, behavior of correlation functions in both space and time is discussed for classical systems and for quantum systems at finite temperature, and is compared with the corresponding behavior in quantum systems at zero temperature. The origin of the long-ranged correlations is explained in terms of soft modes. In general, correlations at zero temperature are of longer range than their finite temperature or classical counterparts. This phenomenon is due to additional soft modes that exist at zero temperature.

cond-mat.stat-mech↗

arXiv1997

Nonanalytic behavior of the spin susceptibility in clean Fermi systems

The wavevector and temperature dependent static spin susceptibility, χ_s(Q,T), of clean interacting Fermi systems is considered in dimensions 1\leq d \leq 3. We show that at zero temperature χ_s is a nonanalytic function of |Q|, with the leading nonanalyticity being |Q|^{d-1} for 1<d<3, and Q^2\ln|Q| for d=3. For the homogeneous spin susceptibility we find a nonanalytic temperature dependence T^{d-1} for 1<d<3. We give qualitative mode-mode coupling arguments to that effect, and corroborate these arguments by a perturbative calculation to second order in the electron-electron interaction amplitude. The implications of this, in particular for itinerant ferromagnetism, are discussed. We also point out the relation between our findings and established perturbative results for 1-d systems, as well as for the temperature dependence of χ_s(Q=0) in d=3.

cond-mat.stat-mech↗

arXiv1997

Long-range order versus random-singlet phases in quantum antiferromagnetic systems with quenched disorder

The stability of antiferromagnetic long-range order against quenched disorder is considered. A simple model of an antiferromagnet with a spatially varying Neel temperature is shown to possess a nontrivial fixed point corresponding to long-range order that is stable unless either the order parameter or the spatial dimensionality exceeds a critical value. The instability of this fixed point corresponds to the system entering a random-singlet phase. The stabilization of long-range order is due to quantum fluctuations, whose role in determining the phase diagram is discussed.

cond-mat.stat-mech↗

arXiv1997

Breakdown of Landau-Ginzburg-Wilson theory for certain quantum phase transitions

The quantum ferromagnetic transition of itinerant electrons is considered. It is shown that the Landau-Ginzburg-Wilson theory described by Hertz and others breaks down due to a singular coupling between fluctuations of the conserved order parameter. This coupling induces an effective long-range interaction between the spins of the form 1/r^{2d-1}. It leads to unusual scaling behavior at the quantum critical point in $1<d\leq 3$ dimensions, which is determined exactly.

cond-mat.stat-mech↗

arXiv1997

Magnetic pair breaking in disordered superconducting films

A theory for the effects of nonmagnetic disorder on the magnetic pair breaking rate $α$ induced by paramagnetic impurities in quasi two-dimensional superconductors is presented. Within the framework of a strong-coupling theory for disordered superconductors, we find that the disorder dependence of $α$ is determined by the disorder enhancements of both the electron-phonon coupling and the spin-flip scattering rate. These two effects have a tendency to cancel each other. With parameter values appropriate for Pb_{0.9} Bi_{0.1}, we find a pair breaking rate that is very weakly dependent on disorder for sheet resistances 0 < R < 2.5 kOhm, in agreement with a recent experiment by Chervenak and Valles.

cond-mat.supr-con↗

arXiv1997

Density expansion for transport coefficients: Long-wavelength versus Fermi surface nonanalyticities

The expansion of the conductivity in 2-d quantum Lorentz models in terms of the scatterer density n is considered. We show that nonanalyticities in the density expansion due to scattering processes with small and large momentum transfers, respectively, have different functional forms. Some of the latter are not logarithmic, but rather of power-law nature, in sharp contrast to the 3-d case. In a 2-d model with point-like scatterers we find that the leading nonanalytic correction to the Boltzmann conductivity, apart from the frequency dependent weak-localization term, is of order n^{3/2}.

cond-mat.stat-mech↗

arXiv1997

Quantum critical behavior of disordered itinerant ferromagnets

The quantum ferromagnetic transition at zero temperature in disordered itinerant electron systems is considered. Nonmagnetic quenched disorder leads to diffusive electron dynamics that induces an effective long-range interaction between the spin or order parameter fluctuations of the form r^{2-2d}, with d the spatial dimension. This leads to unusual scaling behavior at the quantum critical point, which is determined exactly. In three-dimensional systems the quantum critical exponents are substantially different from their finite temperature counterparts, a difference that should be easily observable. Experiments to check these predictions are proposed.

cond-mat.stat-mech↗

arXiv1997

Quantum critical behavior of itinerant ferromagnets

The quantum ferromagnetic transition of itinerant electrons is considered. We give a pedagogical review of recent results which show that zero-temperature soft modes that are commonly neglected, invalidate the standard Landau-Ginzburg-Wilson description of this transition. If these modes are taken into account, then the resulting order parameter field theory is nonlocal in space and time. Nevertheless, for both disordered and clean systems the critical behavior has been exactly determined for spatial dimensions d>2 and d>1, respectively. The critical exponents characterizing the paramagnetic-to-ferromagnetic transition are dimensionality dependent, and substantially different from both mean-field critical exponents, and from the classical Heisenberg exponents that characterize the transition at finite temperatures. Our results should be easily observable, particularly those for the disordered case, and experiments to check our predictions are proposed.

cond-mat.stat-mech↗

arXiv1997

Anderson-Mott transition as a quantum glass problem

We combine a recent mapping of the Anderson-Mott metal-insulator transition on a random-field problem with scaling concepts for random-field magnets to argue that disordered electrons near an Anderson-Mott transition show glass-like behavior. We first discuss attempts to interpret experimental results in terms of a conventional scaling picture, and argue that some of the difficulties encountered point towards a glassy nature of the electrons. We then develop a general scaling theory for a quantum glass, and discuss critical properties of both thermodynamic and transport variables in terms of it. Our most important conclusions are that for a correct interpretation of experiments one must distinguish between self-averaging and non-self averaging observables, and that dynamical or temperature scaling is not of power-law type but rather activated, i.e. given by a generalized Vogel-Fulcher law. Recent mutually contradicting experimental results on Si:P are discussed in the light of this, and new experiments are proposed to test the predictions of our quantum glass scaling theory.

cond-mat.stat-mech↗

arXiv1997

Quantum ferromagnetic transition in disordered itinerant electron systems

An effective field theory is derived for the ferromagnetic transition of diffusive electrons at T=0. The static disorder which leads to diffusive electron dynamics induces an effective long-range interaction between the spins of the form 1/r^(2d-2). This leads to unusual scaling behavior at the quantum critical point, which is determined exactly. The crossover from this quantum fixed point to the classical Heisenberg fixed point should be observable in ferromagnetic materials with low Curie temperatures.

cond-mat.stat-mech↗

arXiv1996

Mean-field limit of the random flux model

The problem of non--interacting electrons on a square lattice subject to a random magnetic flux is mapped onto a one--dimensional model with infinitely many orbitals per site. Linking each orbital with $N(\gg1)$ other orbitals maps the problem onto Wegner's $N$-orbital model in the same limit, while the original problem corresponds to $N=1$. The exact solution for $N=\infty$, the mean--field limit, is discussed and compared with numerical results. An outline of a $1/N$-expansion is given.

cond-mat↗

arXiv1995

The Eliashberg Function of Amorphous Metals

A connection is proposed between the anomalous thermal transport properties of amorphous solids and the low-frequency behavior of the Eliashberg function. By means of a model calculation we show that the size and frequency dependence of the phonon mean-free-path that has been extracted from measurements of the thermal conductivity in amorphous solids leads to a sizeable linear region in the Eliashberg function at small frequencies. Quantitative comparison with recent experiments gives very good agreement.

cond-mat↗

arXiv1994

Equations of State for Nonlinear Sigma-Models II: Relations between Resummation Schemes, and Crossover Phenomena

It is shown how a recent method to systematically extrapolate and resum the loop expansion for nonlinear sigma-models is related to solutions of the renormalization group equation. This relation is used to generalize the explicit equations of state obtained previously to models which display crossover phenomena. As an example we discuss Wegner's localization model and consider the crossover from symplectic to unitary symmetry.

cond-mat↗

arXiv1994

Order Parameter Description of the Anderson-Mott Transition

An order parameter description of the Anderson-Mott transition (AMT) is given. We first derive an order parameter field theory for the AMT, and then present a mean-field solution. It is shown that the mean-field critical exponents are exact above the upper critical dimension. Renormalization group methods are then used to show that a random-field like term is generated under renormalization. This leads to similarities between the AMT and random-field magnets, and to an upper critical dimension $d_{c}^{+}=6$ for the AMT. For $d<6$, an $ε= 6-d$ expansion is used to calculate the critical exponents. To first order in $ε$ they are found to coincide with the exponents for the random-field Ising model. We then discuss a general scaling theory for the AMT. Some well established scaling relations, such as Wegner's scaling law, are found to be modified due to random-field effects. New experiments are proposed to test for random-field aspects of the AMT.

cond-mat↗

arXiv1994

Density Expansion for the Mobility in a Quantum Lorentz Model

We consider the mobility of electrons in an environment of static hard-sphere scatterers, which provides a realistic description of electrons in Helium gas. A systematic expansion in the scatterer density is carried to second order relative to the Boltzmann result, and the analytic contribution at this order is derived, together with the known logarithmic term in the density expansion. It is shown that existing experimental data are consistent with the existence of the logarithmic term in the density expansion, but more precise experiments are needed in order to unambiguously detect it. We show that our calculations provide the necessary theoretical information for such an experiment, and give a detailed discussion of a suitable parameter range.

cond-mat↗

arXiv1994

The Anderson-Mott Transition as a Random-Field Problem

The Anderson-Mott transition of disordered interacting electrons is shown to share many physical and technical features with classical random-field systems. A renormalization group study of an order parameter field theory for the Anderson-Mott transition shows that random-field terms appear at one-loop order. They lead to an upper critical dimension $d_{c}^{+}=6$ for this model. For $d>6$ the critical behavior is mean-field like. For $d<6$ an $ε$-expansion yields exponents that coincide with those for the random-field Ising model. Implications of these results are discussed.

cond-mat↗