Functional renormalization group for multi-orbital Fermi surface instabilities
By Christian Platt, Werner Hanke, R. Thomale. 2013
156 citations recorded by the source corpus.
Technological progress in material synthesis, as well as artificial realization of condensed matter scenarios via ultra-cold atomic gases in optical lattices or epitaxial growth of thin films, is opening the gate to investigate a plethora of unprecedented strongly correlated electron systems. In a large subclass thereof, a metallic state of layered electrons undergoes an ordering transition below some temperature into unconventional states of matter driven by electronic correlations, such as magnetism, superconductivity (SC), or other Fermi surface (FS) instabilities. While these phenomena have been a well-established direction of research in condensed matter for decades, the variety of today's accessible scenarios pose fundamental new challenges to describe them. A core complication is the multi-orbital nature of the low-energy electronic structure of these systems, such as the multi-d orbital nature of electrons in iron-pnictides and transition-metal oxides in general, but also electronic states of matter on lattices with multiple sites per unit cell such as the honeycomb or kagome lattice. In this review, we propagate the functional renormalization group (FRG) as a suited approach to investigate multi-orbital FS instabilities. The primary goal of the review is to describe the FRG in explicit detail and render it accessible to everyone both at a technical and intuitive level. Summarizing recent progress in the field of multi-orbital FS instabilities, we illustrate how the unbiased fashion by which the FRG treats all kinds of ordering tendencies guarantees an adequate description of electronic phase diagrams and often allows to obtain parameter trends of sufficient accuracy to make qualitative predictions for experiments. This review includes detailed and illustrative examples of magnetism and, in particular, SC for the iron-pnictides from the viewpoint of FRG. Furthermore, it discusses candidate scenarios for topological bulk singlet SC and exotic particle–hole condensates on hexagonal lattices such as sodium-doped cobaltates, graphene doped to van-Hove filling, and the kagome Hubbard model. In total, the FRG promises to be one of the most versatile and revealing numerical approaches to address unconventional FS instabilities in future fields of condensed matter research.
Subfields: Condensed Matter Physics, Electronic, Optical and Magnetic Materials
View Paper: https://www.semanticscholar.org/paper/810096ce5444980fa27f04ca55b4f2fa8363b484
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In Condensed Matter Physics
In Electronic, Optical and Magnetic Materials
Citations in the corpus
- Physical realization of a quantum spin liquid based on a complex frustration mechanism (2016, background): “[39, 40]) then formulates an infinite hierarchy of coupled differential equations for the evolution of all m-particle”
- Magnetism, Superconductivity, and Spontaneous Orbital Order in Iron-Based Superconductors: Which Comes First and Why? (2016, result): “The phenomenon in which the SDW interaction creates an attraction in the SC channel and eventually SC wins had already been found in earlier numerical and analytical RG studies in multiband FeSCs [33,38] and in doped graphene 041045-8 [50,51].”
- An Asymptotically Safe Guide to Quantum Gravity and Matter (2018, methodology): “The method is well-suited to models with dimensionful couplings, and therefore widely-used in condensed-matter physics and statistical physics (Kopietz et al., 2010; Metzner et al., 2012; Platt et al., 2013).”
- The nonperturbative functional renormalization group and its applications (2020, unknown): “[576].”