arXiv subjects

D. Belitz

Publications and source records attributed to D. Belitz.

At least 109 records · Page 6Linked to original sources

arXiv2000

Anderson-Mott Transition in a Magnetic Field: Corrections to Scaling

It is shown that the Anderson-Mott metal-insulator transition of paramagnetic, interacting disordered electrons in an external magnetic field is in the same universality class as the transition from a ferromagnetic metal to a ferromagnetic insulator discussed recently. As a consequence, large corrections to scaling exist in the magnetic-field universality class, which have been neglected in previous theoretical descriptions. The nature and consequences of these corrections to scaling are discussed.

cond-mat.stat-mech↗

arXiv2000

Theory of Disordered Itinerant Ferromagnets I: Metallic Phase

A comprehensive theory for electronic transport in itinerant ferromagnets is developed. We first show that the Q-field theory used previously to describe a disordered Fermi liquid also has a saddle-point solution that describes a ferromagnet in a disordered Stoner approximation. We calculate transport coefficients and thermodynamic susceptibilities by expanding about the saddle point to Gaussian order. At this level, the theory generalizes previous RPA-type theories by including quenched disorder. We then study soft-mode effects in the ferromagnetic state in a one-loop approximation. In three-dimensions, we find that the spin waves induce a square-root frequency dependence of the conductivity, but not of the density of states, that is qualitatively the same as the usual weak-localization effect induced by the diffusive soft modes. In contrast to the weak-localization anomaly, this effect persists also at nonzero temperatures. In two-dimensions, however, the spin waves do not lead to a logarithmic frequency dependence. This explains experimental observations in thin ferromagnetic films, and it provides a basis for the construction of a simple effective field theory for the transition from a ferromagnetic metal to a ferromagnetic insulator.

cond-mat.stat-mech↗

arXiv2000

Theory of Disordered Itinerant Ferromagnets II: Metal-Insulator Transition

The theory for disordered itinerant ferromagnets developed in a previous paper is used to construct a simple effective field theory that is capable of describing the quantum phase transition from a ferromagnetic metal to a ferromagnetic insulator. It is shown that this transition is in the same universality class as the one from a paramagnetic metal to a paramagnetic insulator in the presence of an external magnetic field, and that strong corrections to scaling exist in this universality class. The experimental consequences of these results are discussed.

cond-mat.stat-mech↗

arXiv2000

Annealed disorder, rare regions, and local moments: A novel mechanism for metal-insulator transitions

Local magnetic moments in disordered sytems can be described in terms of annealed magnetic disorder, in addition to the underlying quenched disorder. It is shown that for noninteracting electron systems at zero temperature, the annealed disorder leads to a new mechanism, and a new universality class, for a metal-insulator transition. The transition is driven by a vanishing of the thermodynamic density susceptibility rather than by localization effects. The critical behavior near two-dimensions is determined, and the underlying physics is discussed.

cond-mat.stat-mech↗

arXiv1999

Quantum critical behavior of itinerant ferromagnets

We investigate the quantum phase transition of itinerant ferromagnets. It is shown that correlation effects in the underlying itinerant electron system lead to singularities in the order parameter field theory that result in an effective long-range interaction between the spin fluctuations. This interaction turns out to be generically {\em antiferromagnetic} for clean systems. In disordered systems analogous correlation effects lead to even stronger singularities. The resulting long-range interaction is, however, generically ferromagnetic. We discuss two possibilities for the ferromagnetic quantum phase transition. In clean systems, the transition is generically of first order, as is experimentally observed in MnSi. However, under certain conditions the transition may be continuous with non-mean field critical behavior. In disordered systems, one finds a very rich phase diagram showing first order and continuous phase transitions and several multicritical points.

cond-mat.stat-mech↗

arXiv1999

Rare regions and annealed disorder in quantum phase transitions

The Griffiths region that is due to rare regions and the resulting local moments in disordered itinerant quantum magnets, and its influence on the critical behavior, is considered within the framework of an effective field theory. It is shown that the local moments can be described in terms of static, annealed disorder, and the physical consequences of this description are discussed.

cond-mat.stat-mech↗

arXiv1999

The disordered Fermi-liquid fixed point and its instabilities

The concept of a disordered Fermi-liquid fixed point is introduced and used to understand various properties of disordered metals within a unifying framework. Corrections to scaling near this fixed point give what are commonly called weak-localization effects. Various instabilities of the disordered Fermi-liquid phase are discussed. These include two distinct types of superconducting-to-normal-metal quantum phase transitions. First, the quantum phase transition from a disordered metal to a conventional superconductor in bulk materials is considered. Second, a quantum phase transition in two dimensions from metallic-like behavior to a novel type of disorder induced, spin-triplet, even parity, superconductivity is treated. The paper is concluded with a discussion of the nature of the ground state of two-dimensional, disordered electron systems.

cond-mat.stat-mech↗

arXiv1999

A metal-insulator transition as a quantum glass problem

We discuss a recent mapping of the Anderson-Mott metal-insulator transition onto a random field magnet problem. The most important new idea introduced is to describe the metal-insulator transition in terms of an order parameter expansion rather than in terms of soft modes via a nonlinear sigma model. For spatial dimensions d>6 a mean field theory gives the exact critical exponents. In an epsilon expansion about d=6 the critical exponents are identical to those for a random field Ising model. Dangerous irrelevant quantum fluctuations modify Wegner's scaling law relating the conductivity exponent to the correlation or localization length exponent. This invalidates the bound s>2/3 for the conductivity exponent s in d=3. We also argue that activated scaling might be relevant for describing the AMT in three-dimensional systems.

cond-mat.stat-mech↗

arXiv1999

Nonanalytic Magnetization Dependence of the Magnon Effective Mass in Itinerant Quantum Ferromagnets

The spin wave dispersion relation in both clean and disordered itinerant quantum ferromagnets is calculated. It is found that effects akin to weak-localization physics cause the frequency of the spin-waves to be a nonanalytic function of the magnetization m. For low frequencies Ω, small wavevectors k, and small m, the dispersion relation is found to be of the form Ω~ m^{1-α} k^2, with α= (4-d)/2 (2<d<4) for disordered systems, and α= (3-d) (1<d<3) for clean ones. In d=4 (disordered) and d=3 (clean), Ω~ m ln(1/m) k^2. Experiments to test these predictions are proposed.

cond-mat.str-el↗

arXiv1999

On the critical behavior of disordered quantum magnets: The relevance of rare regions

The effects of quenched disorder on the critical properties of itinerant quantum antiferromagnets and ferromagnets are considered. Particular attention is paid to locally ordered spatial regions that are formed in the presence of quenched disorder even when the bulk system is still in the paramagnetic phase. These rare regions or local moments are reflected in the existence of spatially inhomogeneous saddle points of the Landau-Ginzburg-Wilson functional. We derive an effective theory that takes into account small fluctuations around all of these saddle points. The resulting free energy functional contains a new term in addition to those obtained within the conventional perturbative approach, and it comprises what would be considered non-perturbative effects within the latter. A renormalization group analysis shows that in the case of antiferromagnets, the previously found critical fixed point is unstable with respect to this new term, and that no stable critical fixed point exists at one-loop order. This is contrasted with the case of itinerant ferromagnets, where we find that the previously found critical behavior is unaffected by the rare regions due to an effective long-ranged interaction between the order parameter fluctuations.

cond-mat.stat-mech↗

arXiv1999

Theory of many-fermion systems II: The case of Coulomb interactions

In a recent paper (cond-mat/9703164) a general field-theoretical description of many-fermion systems with short-ranged interactions has been developed. Here we extend this theory to the case of disordered electrons interacting via a Coulomb potential. A detailed discussion is given of the Ward identity that controls the soft modes in the system, and the generalized nonlinear sigma model for the Coulombic case is derived and discussed.

cond-mat.str-el↗

arXiv1999

Properties of spin-triplet, even-parity superconductors

The physical consequences of the spin-triplet, even-parity pairing that has been predicted to exist in disordered two-dimensional electron systems are considered in detail. We show that the presence of an attractive interaction in the particle-particle spin-triplet channel leads to an instability of the normal metal that competes with the localizing effects of the disorder. The instability is characterized by a diverging length scale, and has all of the characteristics of a continuous phase transition. The transition and the properties of the ordered phase are studied in mean-field theory, and by taking into account Gaussian fluctuations. We find that the ordered phase is indeed a superconductor with an ordinary Meissner effect and a free energy that is lower than that of the normal metal. Various technical points that have given rise to confusion in connection with this and other manifestations of odd-gap superconductivity are also discussed.

cond-mat.supr-con↗

arXiv1999

First order transitions and multicritical points in weak itinerant ferromagnets

It is shown that the phase transition in low-T_c clean itinerant ferromagnets is generically of first order, due to correlation effects that lead to a nonanalytic term in the free energy. A tricritical point separates the line of first order transitions from Heisenberg critical behavior at higher temperatures. Sufficiently strong quenched disorder suppresses the first order transition via the appearance of a critical endpoint. A semi-quantitative discussion is given in terms of recent experiments on MnSi, and predictions for other experiments are made.

cond-mat.stat-mech↗

arXiv1999

Influence of rare regions on magnetic quantum phase transitions

The effects of quenched disorder on the critical properties of itinerant quantum magnets are considered. Particular attention is paid to locally ordered rare regions that are formed in the presence of quenched disorder even when the bulk system is still in the nonmagnetic phase. It is shown that these local moments or instantons destroy the previously found critical fixed point in the case of antiferromagnets. In the case of itinerant ferromagnets, the critical behavior is unaffected by the rare regions due to an effective long-range interaction between the order parameter fluctuations.

cond-mat.stat-mech↗

arXiv1998

Quantum kinetic theory: The disordered electron problem

These are notes for lectures delivered at the NATO ASI on Dynamics in Leiden, The Netherlands, in July 1998. The quantum kinetic theory for noninteracting electrons in a disordered solid is introduced and discussed. We first use many-body theory to derive the quantum Boltzmann equation that describes transport and time correlation functions in this system. Particular attention is paid to the calculation of the electrical conductivity and the density response function. We then consider corrections to the Boltzmann equation due to wave interference effects. The disorder expansion of the conductivity is addressed, and the so-called weak localization or long-time tail contribution to the conductivity is discussed. We conclude with a brief discussion of the influence of electron-electron interactions on the properties of disordered electronic systems.

cond-mat.stat-mech↗

arXiv1998

Quantum phase transitions

These are notes for lectures delivered at the NATO ASI on Dynamics in Leiden, The Netherlands, in July 1998. The main concepts relating to quantum phase transitions are explained, using the paramagnet-to-ferromagnet transition of itinerant electrons as the primary example. Some aspects of metal-insulator transitions are also briefly discussed. The exposition is strictly pedagogical in nature, with no ambitions with respect to completeness or going into technical details. The goal of the lectures is to provide a bridge between textbooks on classical critical phenomena and the current literature on quantum phase transitions. Some familiarity with the concepts of classical phase transitions is helpful, but not absolutely necessary.

cond-mat.stat-mech↗

arXiv1998

Possible triplet superconductivity in MOSFETs

A theory that predicts a spin-triplet, even-parity superconducting ground state in two-dimensional electron systems is re-analyzed in the light of recent experiments showing a possible insulator-to-conductor transition in such systems. It is shown that the observations are consistent with such an exotic superconductivity mechanism, and predictions are made for experiments that would further corroborate or refute this proposal.

cond-mat.str-el↗

arXiv1997

Theory of many-fermion systems

A general field-theoretical description of many-fermion systems, with or without quenched disorder, is developed. Starting from the Grassmannian action for interacting fermions, we first bosonize the theory by introducing composite matrix variables that correspond to two-fermion excitations and integrating out the fermion degrees of freedom. The saddle point solution of the resulting matrix field theory reproduces a disordered Hartree-Fock approximation and an expansion to Gaussian order about the saddle point corresponds to a disordered RPA-like theory. In the clean limit they reduce to the ordinary Hartree-Fock and random-phase approximations. We first concentrate on disordered systems, and perform a symmetry analysis that allows for a systematic separation of the massless modes from the massive ones. By treating the massive modes in a simple approximation, one obtains a technically satisfactory derivation of the generalized nonlinear sigma-model that has been used in the theory of metal-insulator transitions. The theory also allows for the treatment of other phase transitions in the disordered Fermi liquid. We further use renormalization group techniques to establish the existence of a disordered Fermi-liquid fixed point, and show that it is stable for all dimensions d>2. The so-called weak-localization effects can be understood as corrections to scaling near this fixed point. The general theory also allows for studying the clean limit. For that case we develop a loop expansion that corresponds to an expansion in powers of the screened Coulomb interaction, and that represents a systematic improvement over RPA. We corroborate the existence of a Fermi-liquid fixed point that is stable for all dimensions d>1, in agreement with other recent field-theoretical treatments of clean Fermi liquids.

cond-mat.str-el↗