日本物理学会誌及びJournal of the Physical Society of Japanの月刊について

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

Anderson Transitions

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.

http://export.arxiv.org/pdf/cond-mat/0606317

Fermi-liquid instabilities at magnetic quantum phase transitions

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.

Superconducting phases of f -electron compounds

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.

https://iopscience.iop.org/article/10.1088/0034-4885/66/12/R01/pdf

Quantum phase transitions

We study the superconductor-insulator transition in the quasi-two-dimensional electron gas (q-2DEG) formed at the interface of LaScO 3 / SrTiO 3 heterostructures. Using various tuning parameters such as the gate voltage and the magnetic ﬁeld, we show an intervening anomalous metallic state apart from the usual superconducting and insulating ground states. Further, by studying the scaling of the magnetoresistivity data, we ﬁnd a highly unusual two-stage divergence of the dynamical critical exponent. The ﬁrst increase, at higher temperatures, demonstrates that the system hosts a quantum Gri ﬃ ths phase caused by disorder-induced rare puddles of superconductivity embedded in a non-superconducting matrix. The second, stronger, increase of the dynamical exponent at lower temperatures indicates that the quantum Gri ﬃ ths phase is cut-o ﬀ or cloaked below a crossover temperature scale. We elucidate possible mechanisms that account for the cloaking of the Gri ﬃ ths phase. Finally, we construct a phase diagram that encapsulates the various phases of the q-2DEG as a function of the applied magnetic ﬁeld and temperature. We further discuss the various cross-overs and phase transitions in the system by utilizing this phase diagram.

Temperature dependent cloaking of the Quantum Griffiths Singularity in LaScO$_3$/SrTiO$_3$ heterostructures

We study the ferromagnetic phase transition in a randomly layered Heisenberg model. A recent strong-disorder renormalization group approach [Phys. Rev. B 81, 144407 (2010)] predicted that the critical point in this system is of exotic infinite-randomness type and is accompanied by strong power-law Griffiths singularities. Here, we report results of Monte-Carlo simulations that provide numerical evidence in support of these predictions. Specifically, we investigate the finite-size scaling behavior of the magnetic susceptibility which is characterized by a non-universal power-law divergence in the Griffiths phase. In addition, we calculate the time autocorrelation function of the spins. It features a very slow decay in the Griffiths phase, following a non-universal power law in time.

Evidence for power-law Griffiths singularities in a layered Heisenberg magnet

The breached-pair state wherein superconductivity coexists with magnetic polarization is known to exist as a ground state of an imbalanced Fermi system only under very fine-tuned conditions. Here, we show that an s-wave superconductor that is well described by a spin-selectively disordered attractive Hubbard model away from half filling has the breached-pair state as a ground-state without the need for such fine-tuning. The existence of this breached-pair phase is established by laying recourse to a Monte Carlo technique called static path approximation (SPA). Further, by using the SPA, we map out the entire phase diagram of the spin-selectively disordered attractive Hubbard model and show that apart from the breached-pair phase, the many-body system hosts the putative s-wave superconducting state and a polarized Fermi-liquid state. 

Disorder stabilized breached-pair phase in an 
s
-wave superconductor

/pdf/evidence-for-power-law-griffiths-singularities-in-a-layered-27mvtudc7z.pdf

Rajesh Narayanan

Papers

Temperature dependent cloaking of the Quantum Griffiths Singularity in LaScO$_3$/SrTiO$_3$ heterostructures

Evidence for power-law Griffiths singularities in a layered Heisenberg magnet

Disorder stabilized breached-pair phase in an s -wave superconductor

Evidence for power-law Griffiths singularities in a layered Heisenberg magnet