Jan Zaanen

String Theory, Quantum Phase Transitions, and the Emergent Fermi Liquid

String Theory and Condensed Matter The complex interactions involving highly correlated electron systems can give rise to “exotic behavior” in electronic systems, such as quantum criticality and superconductivity. The usual theoretical tools, however, are limited when describing these states. String theory is a highly mathematical approach initially developed to describe gravity and high-energy particle physics. Certain aspects of string theory may be relevant to describe condensed matter systems. Čubrović et al. (p. 439; published online 25 June) take one such approach, and show that the characteristic properties of a Fermi liquid can emerge from string theory. The formulation may provide an approach to describing the exotic states of matter that arise in condensed matter systems. Mathematical methods developed in string theory to describe gravity are applied to complex condensed matter systems. A central problem in quantum condensed matter physics is the critical theory governing the zero-temperature quantum phase transition between strongly renormalized Fermi liquids as found in heavy fermion intermetallics and possibly in high–critical temperature superconductors. We found that the mathematics of string theory is capable of describing such fermionic quantum critical states. Using the anti–de Sitter/conformal field theory correspondence to relate fermionic quantum critical fields to a gravitational problem, we computed the spectral functions of fermions in the field theory. By increasing the fermion density away from the relativistic quantum critical point, a state emerges with all the features of the Fermi liquid.

Superconductivity in the Fullerenes

Intramolecular vibrations strongly scatter electrons near the Fermi-surface in doped fullerenes. A simple expression for the electron-phonon coupling parameters for this case is derived and evaluated by quantum-chemical calculations. The observed superconducting transition temperatures and their variation with lattice constants can be understood on this basis. To test the ideas and calculations presented here, we predict that high frequency H2 modes acquire a width of about 20% of their frequency in superconductive fullerenes, and soften by about 5% compared to the insulating fullerenes.

From quantum matter to high-temperature superconductivity in copper oxides

The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the ‘normal’ state at elevated temperatures.

Quantum critical behaviour in a high-Tc superconductor

Quantum criticality is associated with a system composed of a nearly infinite number of interacting quantum degrees of freedom at zero temperature, and it implies that the system looks on average the same regardless of the time- and length scale on which it is observed. Electrons on the atomic scale do not exhibit such symmetry, which can only be generated as a collective phenomenon through the interactions between a large number of electrons. In materials with strong electron correlations a quantum phase transition at zero temperature can occur, and a quantum critical state has been predicted, which manifests itself through universal power-law behaviours of the response functions. Candidates have been found both in heavy-fermion systems and in the high-transition temperature (high-Tc) copper oxide superconductors, but the reality and the physical nature of such a phase transition are still debated. Here we report a universal behaviour that is characteristic of the quantum critical region. We demonstrate that the experimentally measured phase angle agrees precisely with the exponent of the optical conductivity. This points towards a quantum phase transition of an unconventional kind in the high-Tc superconductors.In certain materials with strong electron correlations a quantum phase transition (QPT) at zero temperature can occur, in the proximity of which a quantum critical state of matter has been anticipated. This possibility has recently attracted much attention because the response of such a state of matter is expected to follow universal patterns defined by the quantum mechanical nature of the fluctuations. Forementioned universality manifests itself through power-law behaviours of the response functions. Candidates are found both in heavy fermion systems and in the cuprate high Tc superconductors. Although there are indications for quantum criticality in the cuprate superconductors, the reality and the physical nature of such a QPT are still under debate. Here we identify a universal behaviour of the phase angle of the frequency dependent conductivity that is characteristic of the quantum critical region. We demonstrate that the experimentally measured phase angle agrees precisely with the exponent of the optical conductivity. This points towards a QPT in the cuprates close to optimal doping, although of an unconventional kind.

Holographic duality and the resistivity of strange metals

Department of Physics, Harvard University, Cambridge MA 02138, USA(Dated: December 16, 2013)We present a strange metal, described by a holographic duality, which reproduces the famouslinear resistivity of the normal state of the copper oxides, in addition to the linear specific heat.This holographic metal reveals a simple and general mechanism for producing such a resistivity,which requires only quenched disorder and a strongly interacting quantum critical state. The key isthe minimal viscosity of the latter: unlike in a Fermi-liquid, the viscosity is very small and thereforeis important for the electrical transport. This mechanism produces a resistivity proportional to theelectronic entropy.

SYSTEMATICS IN BAND-GAPS AND OPTICAL-SPECTRA OF 3D TRANSITION-METAL COMPOUNDS

In this paper we discuss the systematics in the transition metal d-d Coulomb interactions and the anion to cation charge transfer energies, and relate these to systematics in observed band gaps. In addition, we discuss the nature of the optical thresholds and their dependence on the cation and anion electronegativity.

Nodal quasiparticle in pseudogapped colossal magnetoresistive manganites

A characteristic feature of the copper oxide high-temperature superconductors is the dichotomy between the electronic excitations along the nodal (diagonal) and antinodal (parallel to the Cu–O bonds) directions in momentum space, generally assumed to be linked to the ‘d-wave’ symmetry of the superconducting state. Angle-resolved photoemission measurements in the superconducting state have revealed a quasiparticle spectrum with a d-wave gap structure that exhibits a maximum along the antinodal direction and vanishes along the nodal direction. Subsequent measurements have shown that, at low doping levels, this gap structure persists even in the high-temperature metallic state, although the nodal points of the superconducting state spread out in finite ‘Fermi arcs’. This is the so-called pseudogap phase, and it has been assumed that it is closely linked to the superconducting state, either by assigning it to fluctuating superconductivity or by invoking orders which are natural competitors of d-wave superconductors. Here we report experimental evidence that a very similar pseudogap state with a nodal–antinodal dichotomous character exists in a system that is markedly different from a superconductor: the ferromagnetic metallic groundstate of the colossal magnetoresistive bilayer manganite La1.2Sr1.8Mn2O7. Our findings therefore cast doubt on the assumption that the pseudogap state in the copper oxides and the nodal-antinodal dichotomy are hallmarks of the superconductivity state.

Quantum melting of magnetic order due to orbital fluctuations

We have studied the phase diagram and excitations of the spin-orbital model derived for a three dimensional perovskite lattice, as in KCuF_3. The results demonstrate that the orbital degeneracy drastically increases quantum fluctuations and suppresses the classical long-range order near the multicritical point in the mean-field phase diagram. This generates a qualitatively new spin liquid, providing the first example of a valence bond ground state in three dimensions.

Topological Defects Coupling Smectic Modulations to Intra–Unit-Cell Nematicity in Cuprates

A theoretical model explains how electronic states with different symmetries coexist and interact. We study the coexisting smectic modulations and intra–unit-cell nematicity in the pseudogap states of underdoped Bi2Sr2CaCu2O8+δ. By visualizing their spatial components separately, we identified 2π topological defects throughout the phase-fluctuating smectic states. Imaging the locations of large numbers of these topological defects simultaneously with the fluctuations in the intra–unit-cell nematicity revealed strong empirical evidence for a coupling between them. From these observations, we propose a Ginzburg-Landau functional describing this coupling and demonstrate how it can explain the coexistence of the smectic and intra–unit-cell broken symmetries and also correctly predict their interplay at the atomic scale. This theoretical perspective can lead to unraveling the complexities of the phase diagram of cuprate high-critical-temperature superconductors.

The space group classification of topological band-insulators

Topological insulators are now shown to be protected not only by time-reversal symmetry, but also by crystal lattice symmetry. By accounting for the crystalline symmetries, additional topological insulators can be predicted.