Annual Review of Condensed Matter Physics - Volume 4, 2013

What is written below is, as requested by the editor of AR Condensed Matter Physics, a set of recollections and insights gained from my personal trajectory that starts from my earliest years and continues on until now. I have been a participant in the growth of solid state physics from its early quantum insights to the highly popular foci of today’s vibrant condensed matter science community, while working at three institutions that helped spearhead this growth—UC Berkeley, Bell Labs, and Stanford University. It is rare to be actively involved in any creative enterprise for more than six decades. I credit my good fortune to stimulating science; great students and colleagues; a happy home; warm friendships; and, evidently, to my having inherited good genes.

Nitrogen-vacancy (NV) centers in diamond have recently emerged as a unique platform for fundamental studies in quantum information and nanoscience. The special properties of these impurity centers allow robust, room-temperature operation of solid-state qubits and have enabled several remarkable demonstrations in quantum information processing and precision nanoscale sensing. This article reviews the recent advances in magnetic and optical manipulation of the NV center’s quantum spin and their importance for prospective applications. We discuss how quantum control of individual centers can be harnessed for the protection of NV-center spin coherence, for multiqubit quantum operations in the presence of decoherence, and for high-fidelity initialization and readout. We also discuss the progress in resonant optical control, which has led to interfaces between spin and photonic qubits and may lead to spin networks based on diamond photonics. Many of these recently developed diamond-based technologies constitute critical components for the future leap toward practical multiqubit devices.

Experimental and theoretical progress toward quantum computation with spins in quantum dots (QDs) is reviewed, with particular focus on QDs formed in GaAs heterostructures, on nanowire-based QDs, and on self-assembled QDs. We report on a remarkable evolution of the field, where decoherence—one of the main challenges for realizing quantum computers—no longer seems to be the stumbling block it had originally been considered. General concepts, relevant quantities, and basic requirements for spin-based quantum computing are explained; opportunities and challenges of spin-orbit interaction and nuclear spins are reviewed. We discuss recent achievements, present current theoretical proposals, and make several suggestions for further experiments.

We discuss interfacing trapped atomic systems with solid-state systems such as superconducting Josephson-junction devices or nanomechanical oscillators. Such hybrid quantum systems could ease scalable quantum information processing and yield novel and profound insight into the quantum mechanics of macroscopic quantum many-body systems. We review the relevant interactions and illuminate the role of the vastly differing impedance of atomic and solid-state systems. We give some basic guidelines toward combining quantum systems, and finally, discuss some concrete proposals to interface atomic with solid-state systems.

Majorana fermions (particles that are their own antiparticle) may or may not exist in nature as elementary building blocks, but in condensed matter they can be constructed out of electron and hole excitations. What is needed is a superconductor to hide the charge difference and a topological (Berry) phase to eliminate the energy difference from zero-point motion. A pair of widely separated Majorana fermions, bound to magnetic or electrostatic defects, has non-Abelian exchange statistics. A qubit encoded in this Majorana pair is expected to have an unusually long coherence time. I discuss strategies to detect Majorana fermions in a topological superconductor, as well as possible applications in a quantum computer. The status of the experimental search is reviewed.

Strong electronic correlations are often associated with the proximity of a Mott-insulating state. In recent years however, it has become increasingly clear that the Hund’s rule coupling (intra-atomic exchange) is responsible for strong correlations in multiorbital metallic materials that are not close to a Mott insulator. Hund’s coupling has two effects: It influences the energetics of the Mott gap and strongly suppresses the coherence scale for the formation of a Fermi liquid. A global picture has emerged recently, which emphasizes the importance of the average occupancy of the shell as a control parameter. The most dramatic effects occur away from half-filling or single occupancy. We review the theoretical understanding and physical properties of these Hund’s metals, together with the relevance of this concept to transition-metal oxides (TMOs) of the 3d, and especially 4d, series (such as ruthenates), as well as to the iron-based superconductors (iron pnictides and chalcogenides).

We discuss designer Hamiltonians—lattice models tailored to be free from sign problems (“de-signed”) when simulated with quantum Monte Carlo (QMC) methods but which still host complex many-body states and quantum phase transitions of interest in condensed matter physics. We focus on quantum spin systems in which competing interactions lead to nonmagnetic ground states. These states and the associated quantum phase transitions can be studied in great detail, enabling direct access to universal properties and connections with low-energy effective quantum field theories. As specific examples, we discuss the transition from a Néel antiferromagnet to either a uniform quantum paramagnet or a spontaneously symmetry-broken valence-bond solid (VBS) in SU(2) and SU(N) invariant spin models. We also discuss anisotropic (XXZ) systems harboring topological Z2 spin liquids and the XY* transition. We briefly review recent progress on QMC algorithms, including ground-state projection in the valence-bond basis and direct computation of the Renyi variants of the entanglement entropy.

Colloidal particles are microscopic solid particles suspended in a fluid. Colloids are small enough that thermal energy drives their dynamics and ensures equilibration with the suspending fluid; they are also large enough that their positions and motions can be measured precisely using optical methods, such as light scattering and laser-scanning confocal fluorescence microscopy. Colloidal suspensions are a powerful model system for the study of other phenomena in condensed matter physics, where the collective phase behavior of the solid particles mimics that of other condensed systems. We review three classes of interacting colloidal particles, crystals, glasses, and gels, each of which represents fascinating properties of colloidal particles as well as a model for more general types of materials and their behavior.

In this review we discuss, from an experimental point of view, several concepts of statistical mechanics for systems that are out of equilibrium either because they are driven by external forces or because they are slowly relaxing toward equilibrium. We focus on the case where the mean injected energy is of the order of thermal fluctuations, which therefore cannot be neglected. We first introduce the main concepts of fluctuation theorems (FTs) for work and heat using measurements of (a) a harmonic oscillator driven out of equilibrium by an external force and (b) a colloidal particle trapped in a time-dependent double-well potential. We use the example of the Brownian particle to analyze the problem of the fluctuation-dissipation relation (FDR) in out-of-equilibrium systems. We next study the fluctuations of the position of a Brownian particle inside an aging gelatin after a fast quench. Using the experimental data of this experiment, we show that the mean heat flux is quantitatively related to the violation of the equilibrium fluctuation-dissipation theorem or equivalently to the entropy production rate. Finally, we discuss briefly the problems and the new directions for the stochastic thermodynamics.

The remarkable kinetic slowdown experienced by liquids as they are cooled toward their glass transition is not accompanied by any obvious structural change. Understanding the origin of this behavior is a major scientific challenge. At present, this area of condensed matter theory is characterized by an abundance of divergent viewpoints that attempt to describe well-defined physical phenomena. We review representative theoretical views on the unusual kinetics of liquid supercooling, which fall into two broad competing categories: thermodynamic and kinetic. In the former, an apparent “ideal,” thermodynamic, glass transition caused by rapid loss of entropy in the supercooled liquid underlies kinetic slowdown; in the latter, purely kinetic constraints are responsible for loss of ergodicity. The possible existence of an ideal thermodynamic glass transition is discussed and placed in its proper statistical mechanical context.

Biological structure organizes over evolutionary timescales. This review discusses the spontaneous emergence of hierarchical structure in biology as a result of environmental change. A body of theoretical and experimental work on evolutionary dynamics is reviewed, and a theory for these results based on a principle of least action is discussed. The structure that has emerged in biology is complementary to a type of evolutionary dynamics known as horizontal gene transfer. How horizontal gene transfer ameliorates the difficulty that finite populations would otherwise have to evolve on rugged fitness landscapes is also discussed.

A normal heartbeat is orchestrated by the stable propagation of an excitation wave that produces an orderly contraction. In contrast, wave turbulence in the ventricles, clinically known as ventricular fibrillation (VF), stops the heart from pumping and is lethal without prompt defibrillation. I review experimental, computational, and theoretical studies that have shed light on complex dynamical phenomena linked to the initiation, maintenance, and control of wave turbulence. I first discuss advances made to understand the precursor state to a reentrant arrhythmia where the refractory period of cardiac tissue becomes spatiotemporally disordered; this is known as an arrhythmogenic tissue substrate. I describe observed patterns of transmembrane voltage and intracellular calcium signaling that can contribute to this substrate, and symmetry breaking instabilities to explain their formation. I then survey mechanisms of wave turbulence and discuss novel methods that exploit electrical pacing stimuli to control precursor patterns and low-energy pulsed electric fields to control turbulence.

In addition to an innate immune system that battles pathogens in a nonspecific fashion, higher organisms, such as humans, possess an adaptive immune system to combat diverse (and evolving) microbial pathogens. Remarkably, the adaptive immune system mounts pathogen-specific responses, which can be recalled upon reinfection with the same pathogen. It is difficult to see how the adaptive immune system can be preprogrammed to respond specifically to a vast and unknown set of pathogens. Although major advances have been made in understanding pertinent molecular and cellular phenomena, the precise principles that govern many aspects of an immune response are largely unknown. We discuss complementary approaches from statistical mechanics and cell biology that can shed light on how key components of the adaptive immune system, T cells, develop to enable pathogen-specific responses against many diverse pathogens. The mechanistic understanding that emerges has implications for how host genetics may influence the development of T cells with differing responses to the human immunodeficiency virus (HIV) infection.