Rajesh Narayanan

Bio: Rajesh Narayanan is an academic researcher from Indian Institute of Technology Madras. The author has contributed to research in topics: Quantum phase transition & Phase transition. The author has an hindex of 15, co-authored 47 publications receiving 549 citations. Previous affiliations of Rajesh Narayanan include Asia Pacific Center for Theoretical Physics & University of Hong Kong.

Quantum critical behavior of itinerant ferromagnets

Abstract: 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.

Superconductivity and quantum phase transitions in weak itinerant ferromagnets

Abstract: It is argued that the phase transition in low Tc 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 UGe2. It is then shown that the critical temperature for spin-triplet, p-wave superconductivity mediated by spin fluctuations is generically much higher in a Heisenberg ferromagnetic phase than in a paramagnetic one, due to the coupling of magnons to the longitudinal magnetic susceptibility. This qualitatively explains the phase diagram recently observed in UGe2 and ZrZn2.

Influence of Local Moment Fluctuations on the Mott Transition

Abstract: The Mott metal to insulator transition is a remarkable phenomenon observed in strongly correlated materials, where the localization of electronic waves is driven by on-site electron–electron repulsion (see [7] for a review). Although the appearance of a Mott gap is clearly a charge-related effect, magnetism is expected to play a key role in elucidating the true nature of this phase transition. Indeed, since the Mott insulating state is purely paramagnetic, local moments are well-defined objects between their formation at high temperature (about the local Coulomb interaction ) and their ultimate ordering at the Neel temperature. This offers a window for the Mott transition to occur, in which the behavior of these local spin excitations is yet to be clearly understood. The simplest situation lies in case where the low-temperature magnetic ordering is first order, as in Cr-doped \({\textrm V}_2{\textrm O}_3\). Accordingly magnetic fluctuations should be expected to be weak, so that many predictions can be made from a single-site approach such as the Dynamical Mean Field Theory (DMFT) [4]. In particular, the fact that a low-temperature metallic state leads upon heating to an insulating phase can be understood as a Pomeranchuk effect , where the entropy gain benefits the state with magnetic degeneracy.

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

Abstract: 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

Superconductivity and Quantum Phase Transitions in Weak Itinerant Ferromagnets

Abstract: It is argued 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 UGe_2. It is then shown that the critical temperature for spin-triplet, p-wave superconductivity mediated by spin fluctuations is generically much higher in a Heisenberg ferromagnetic phase than in a paramagnetic one, due to the coupling of magnons to the longitudinal magnetic susceptibility. This qualitatively explains the phase diagram recently observed in UGe_2 and ZrZn_2.

Anderson Transitions

Abstract: The physics of Anderson transitions between localized and metallic phases in disordered systems is reviewed The term ``Anderson transition'' is understood in a broad sense, including both metal-insulator transitions and quantum-Hall-type transitions between phases with localized states The emphasis is put on recent developments, which include: multifractality of critical wave functions, criticality in the power-law random banded matrix model, symmetry classification of disordered electronic systems, mechanisms of criticality in quasi-one-dimensional and two-dimensional systems and survey of corresponding critical theories, network models, and random Dirac Hamiltonians Analytical approaches are complemented by advanced numerical simulations

Fermi-liquid instabilities at magnetic quantum phase transitions

Abstract: This review discusses instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points. Both the existing theoretical concepts and experimental data on selected materials are presented; with the aim of assessing the validity of presently available theory. After briefly recalling the fundamentals of Fermi-liquid theory, the local Fermi-liquid state in quantum impurity models and their lattice versions is described. Next, the scaling concepts applicable to quantum phase transitions are presented. The Hertz-Millis-Moriya theory of quantum phase transitions is described in detail. The breakdown of the latter is analyzed in several examples. In the final part experimental data on heavy-fermion materials and transition-metal alloys are reviewed and confronted with existing theory.

Superconducting phases of f -electron compounds

Abstract: Intermetallic compounds containing $f$-electron elements display a wealth of superconducting phases, which are prime candidates for unconventional pairing with complex order parameter symmetries. For instance, superconductivity has been found at the border of magnetic order as well as deep within ferromagnetically and antiferromagnetically ordered states, suggesting that magnetism may promote rather than destroy superconductivity. Superconducting phases near valence transitions or in the vicinity of magnetopolar order are candidates for new superconductive pairing interactions such as fluctuations of the conduction electron density or the crystal electric field, respectively. The experimental status of the study of the superconducting phases of $f$-electron compounds is reviewed.

Quantum phase transitions

Abstract: In recent years, quantum phase transitions have attracted the interest of both theorists and experimentalists in condensed matter physics. These transitions, which are accessed at zero temperature by variation of a non-thermal control parameter, can influence the behaviour of electronic systems over a wide range of the phase diagram. Quantum phase transitions occur as a result of competing ground state phases. The cuprate superconductors which can be tuned from a Mott insulating to a d-wave superconducting phase by carrier doping are a paradigmatic example. This review introduces important concepts of phase transitions and discusses the interplay of quantum and classical fluctuations near criticality. The main part of the article is devoted to bulk quantum phase transitions in condensed matter systems. Several classes of transitions will be briefly reviewed, pointing out, e.g., conceptual differences between ordering transitions in metallic and insulating systems. An interesting separate class of transitions is boundary phase transitions where only degrees of freedom of a subsystem become critical; this will be illustrated in a few examples. The article is aimed at bridging the gap between high-level theoretical presentations and research papers specialized in certain classes of materials. It will give an overview on a variety of different quantum transitions, critically discuss open theoretical questions, and frequently make contact with recent experiments in condensed matter physics.