In 1992, Dagotto, in collaboration with José Riera and Doug Scalapino, opened the field of ladder compounds, materials with atomic substructures containing two chains next to each other and with inter-ladder coupling (along rungs) of magnitude comparable to that in the long direction (along legs). This research was the first to demonstrate that the transition from one chain to a full two-dimensional plane was not a smooth process simply involving the addition of one chain to another. Instead, it was revealed that even and odd number of chains (called legs due to its ladder-like geometry) belong to classes with quite different behavior. The even-leg ladders, with two legs being the most dramatic case, were theoretically predicted by Dagotto to display a spin gap, spin liquid properties, and tendencies toward superconductivity upon hole doping, all properties confirmed experimentally in materials of the family of copper-based high critical superconductors. Even in the more recently discovered
iron-based high critical temperature superconductor, the "123" materials such as BaFe2S3 with ladder geometry also display superconductivity under high pressure. Dagotto employed computational techniques to study model Hamiltonians for high critical temperature superconductors based on copper, In 1990, he studied dynamical properties of the
Hubbard model and
t-J model computationally, addressing photoemission dispersions and
quasiparticle weights. In 1998, Dagotto developed the Monte Carlo techniques that allowed for the first computational studies of spin-fermion models for manganites, in collaboration with Seiji Yunoki and Adriana Moreo. Employing these techniques,
phase separation involving electronic degrees of freedom, dubbed "electronic phase separation" was discovered. More recently, similar Monte Carlo techniques have been employed by him and collaborators to study properties of iron-based superconductors, revealing the role of the lattice to stabilize the electronic nematic regime above the antiferromagnetic critical temperature. In a highly cited 2005 publication, Dagotto argued that the electronic degree of freedom in transition metal oxides and related materials displays characteristics similar to those of
soft matter, where complex patterns arise from deceptively simple interactions. He, along with Ivan Sergienko, Cengiz Sen,
Silvia Picozzi and collaborators also proposed magnetostriction as a mechanism for multiferroicity. Dagotto made several other contributions to theoretical
condensed matter physics. Together with
Pengcheng Dai and Jiangping Hu, in 2012 they were among the first to argue that the iron based high critical temperature superconductors are not located in the weak Hubbard coupling limit. Instead they are in the intermediate Hubbard coupling regime, thus requiring a combination of localized and itinerant degrees of freedom. In particular, iron selenides are an example of materials where electronic correlations and spin frustration cannot be ignored. With Julian Rincon, Jacek Herbrych and collaborators, employing the density matrix renormalization group, they computationally discovered "block" states in low-dimensional multi-orbital Hubbard models. Spin blocks are groups of spin that are aligned ferromagnetically, anti-ferro coupled among them, and they display exotic dynamical spin structure factors with a mixture of spin waves and optical modes. Among the related findings, Herbrych, Dagotto and collaborators revealed the existence of a spin spiral made out of blocks, a state never reported before. When this spiral one-dimensional state is placed over a two-dimensional superconducting plane,
Majorana fermions developed at the chain by proximity effect from the plane, and for this reason this chain-plane geometry has potential value in
topological quantum computing. He, together with Narayan Mohanta and Satoshi Okamoto, also reported Majoranas in a two-dimensional three-layer geometry with a skyrmion crystal at the bottom, an electron gas in the middle, and a standard superconductor at the top with a carved one-dimensional channel. Within topology in one dimension, he, Nirav Patel, and collaborators proposed a fermionic two-orbital electronic model that becomes the S=1 Haldane chain in strong Hubbard coupling, and has similarities with the
AKLT state of spin systems. The proposed fermionic model has a spin gap and spin liquid properties, as the Haldane chain, and it is quite different from the S=1/2 Heisenberg chain. Moreover, he and collaborators predicted superconductivity upon hole doping, similarly as it occurs in ladders due to the existence of preformed spin ½ singlets in the ground state as in a
resonant valence bond state. Together with Shuai Dong and collaborators, he showed that a superlattice made of insulating Mn-oxide components becomes globally metallic in the new geometry. He has also worked in skyrmions. In the early stages of his career, he made contributions: to particle physics in the context of lattice gauge theories, to the interface between particle physics and condensed matter, and to frustrated spin systems. ==Personal life==