Abstract
Magnetic fluctuations and electrons couple in intriguing ways in the vicinity of zero-temperature phase transitions—quantum critical points—in conducting materials. Quantum criticality is implicated in non-Fermi liquid behavior of diverse materials and in the formation of unconventional superconductors. Here, we uncover an entirely new type of quantum critical point describing the onset of antiferromagnetism in a nodal semimetal engendered by the combination of strong spin-orbit coupling and electron correlations, and which is predicted to occur in the iridium oxide pyrochlores. We formulate and solve a field theory for this quantum critical point by renormalization group techniques and show that electrons and antiferromagnetic fluctuations are strongly coupled and that both these excitations are modified in an essential way. This quantum critical point has many novel features, including strong emergent spatial anisotropy, a vital role for Coulomb interactions, and highly unconventional critical exponents. Our theory motivates and informs experiments on pyrochlore iridates and constitutes a singular realistic example of a nontrivial quantum critical point with gapless fermions in three dimensions.
- Received 6 May 2014
DOI:https://doi.org/10.1103/PhysRevX.4.041027
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Published by the American Physical Society
Popular Summary
Much like water can take various forms, electrons in solids exist in a wide variety of phases. The change from one form to another is called a phase transition, and for electrons, phase transitions may occur at zero temperature. In this situation, the phase transition is inherently quantum mechanical, and quantum zero-point fluctuations are particularly pronounced and exist at all length scales. Such “quantum criticality” in conducting materials—first pioneered by Hertz in the 1970s—has profound experimental consequences and has challenged the physics community for many decades. The key issue in quantum criticality is the strong coupling of electrons and the fluctuating “order parameter” that describes the change of phase. This tight coupling is known to occur in planar materials where electrons behave almost two dimensionally, such as high-temperature cuprate superconductors, but is usually thought to be absent in fully three-dimensional metals. We show that electrons and order-parameter fluctuations are inextricably intertwined at some three-dimensional quantum critical points, and we fully solve the theory for this phenomenon analytically.
Another area of intense modern research is that of materials where interactions are strong both between electrons and between internal “spin” and “orbital” degrees of freedom of single electrons. Many new phases have been predicted in such compounds. We argue that a new critical point occurs in a family of iridium pyrochlores characterized by the chemical formula , where A is a rare-earth element. We examine quadratic band-touching electrons interacting with an Ising order parameter—two ingredients for which there is strong experimental evidence in the pyrochlore iridates. We formulate a field theory for this quantum critical point and solve it using renormalization group methods (including the associated logarithmic corrections), uncovering a novel theoretical structure. This field theory is compelling not only for its relevance to this frontier of materials physics but also as a unique theoretical example of a quantum critical point with strong coupling between electrons and collective modes in three dimensions.
Our calculations reveal intimate connections between this quantum critical point and topological insulators and related phases of matter.
