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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.

Papers
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TL;DR: In this article, it was shown that the critical temperature for spin-triplet, $p$-wave superconductivity mediated by spin fluctuations is generically higher in a Heisenberg ferromagnetic phase than in a paramagnetic one, due to the coupling of the magnons to the longitudinal magnetic susceptibility.
Abstract: It is 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 the magnons to the longitudinal magnetic susceptibility. Together with the tendency of the low-temperature ferromagnetic transition in very clean Heisenberg magnets to be of first order, this qualitatively explains the phase diagram recently observed in ${\mathrm{UGe}}_{2}$.

72 citations

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TL;DR: In this paper, the authors investigated the quantum phases of the frustrated spin on the square lattice with ferromagnetic and antiferromagnetic interactions and found an intermediate paramagnetic phase located between classically ordered spin phases and incommensurate spiral phases.
Abstract: We investigate the quantum phases of the frustrated spin-$\frac{1}{2}\phantom{\rule{0.16em}{0ex}}{J}_{1}\ensuremath{-}{J}_{2}\ensuremath{-}{J}_{3}$ Heisenberg model on the square lattice with ferromagnetic ${J}_{1}$ and antiferromagnetic ${J}_{2}$ and ${J}_{3}$ interactions. Using the pseudofermion functional renormalization group technique, we find an intermediate paramagnetic phase located between classically ordered ferromagnetic, stripy antiferromagnetic, and incommensurate spiral phases. We observe that quantum fluctuations lead to significant shifts of the spiral pitch angles compared to the classical limit. By computing the response of the system with respect to various spin rotation and lattice symmetry-breaking perturbations, we identify a complex interplay between different nematic spin states in the paramagnetic phase. While retaining time-reversal invariance, these phases either break spin-rotation symmetry, lattice-rotation symmetry, or a combination of both. We therefore propose the ${J}_{1}\ensuremath{-}{J}_{2}\ensuremath{-}{J}_{3}$ Heisenberg model on the square lattice as a paradigmatic example where different intimately connected types of nematic orders emerge in the same model.

45 citations

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TL;DR: In this article, the Coulomb interaction on a 1/3-filling fractional quantum Hall system was studied by using an exact diagonalization method on small systems in torus geometry.
Abstract: We study the anisotropic effect of the Coulomb interaction on a 1/3-filling fractional quantum Hall system by using an exact diagonalization method on small systems in torus geometry. For weak anisotropy the system remains to be an incompressible quantum liquid, although anisotropy manifests itself in density correlation functions and excitation spectra. When the strength of anisotropy increases, we find the system develops a Hall-smectic-like phase with a one-dimensional charge density wave order and is unstable towards the one-dimensional crystal in the strong anisotropy limit. In all three phases of the Laughlin liquid, Hall-smectic-like, and crystal phases the ground state of the anisotropic Coulomb system can be well described by a family of model wave functions generated by an anisotropic projection Hamiltonian. We discuss the relevance of the results to the geometrical description of fractional quantum Hall states proposed by Haldane [Phys. Rev. Lett. 107, 116801 (2011)].

39 citations

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TL;DR: Graphene with (effective) vacancy disorder is a physical representative of generic bipartite random hopping models that may also exhibit unconventional (strong-coupling) fixed points for certain kinds of randomly placed scatterers if these are strong enough.
Abstract: The density of states ϱ(E) of graphene is investigated numerically and within the self-consistent T-matrix approximation in the presence of vacancies within the tight binding model. The focus is on compensated disorder, where the concentration of vacancies n(A) and n(B) in both sublattices is the same. Formally, this model belongs to the chiral symmetry class BDI. The onlinear sigma model predicts for BDI a Gade-type singularity ϱ(E)∼|E|(-1)exp[-|log(E)|(-1/x)]. Our numerical data are comparable to this result in a preasymptotic regime that gives way, however, at even lower energies to ϱ(E)∼E(-1)|log(E)|(-x), 1≤x<2. We take this finding as evidence that, similar to the case of dirty d-wave superconductors, generic bipartite random hopping models may also exhibit unconventional (strong-coupling) fixed points for certain kinds of randomly placed scatterers if these are strong enough. Our research suggests that graphene with (effective) vacancy disorder is a physical representative of such systems.

34 citations

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TL;DR: In this paper, a phenomenological theory together with explicit calculations of the electronic ground-state energy, the surface contribution, and the elastic constants (Lam\'e parameters'' i.e., Poisson ratio, Young's modulus) of graphene flakes on the level of the density functional theory employing different standard functionals.
Abstract: We present a phenomenological theory together with explicit calculations of the electronic ground-state energy, the surface contribution, and the elastic constants (``Lam\'e parameters,'' i.e., Poisson ratio, Young's modulus) of graphene flakes on the level of the density-functional theory employing different standard functionals. We observe that the Lam\'e parameters in small flakes can differ from the bulk values by 30% for hydrogenated zigzag edges. The change results from the edge of the flake that compresses the interior. When including the vibrational zero-point motion, we detect a decrease in the bending rigidity, $\ensuremath{\kappa}$, by $\ensuremath{\sim}26\mathrm{%}$. The vibrational frequencies flow with growing $N$ due to the release of the edge-induced compression. We calculate the corresponding Gr\"uneisen parameters and find good agreement with previous authors.

32 citations


Cited by
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TL;DR: In this paper, the physics of Anderson transition between localized and metallic phases in disordered systems is reviewed, including both metal-insulator transitions and quantum-Hall-type transitions between phases with localized states.
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

1,505 citations

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TL;DR: In this article, the authors discuss the instabilities of the Fermi-liquid state of conduction electrons in metals with particular emphasis on magnetic quantum critical points, with the aim of assessing the validity of presently available theory.
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.

1,420 citations

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TL;DR: The experimental status of the study of the superconducting phases of $f$-electron compounds is reviewed in this paper, where superconductivity has been found at the border of magnetic order as well as deep within ferromagnetic and antiferromagnetically ordered states.
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.

529 citations

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TL;DR: A review of quantum phase transitions in condensed matter physics can be found in this article, where the authors introduce important concepts of phase transitions and discuss the interplay of quantum and classical fluctuations near criticality.
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.

508 citations