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Many seemingly contradictory experimental findings concerning the superconducting state in Sr2RuO4 can be accounted for on the basis of a conjectured accidental degeneracy between two patterns of pairing that are unrelated to each other under the (D4h) symmetry of the crystal: a dx2-y2-wave (B1g) and a gxy(x2-y2)-wave (A2g) superconducting state. In this paper, we propose a generic multiband model in which the g-wave pairing involving the xz and yz orbitals arises from second-nearest-neighbor BCS channel effective interactions. Even if timereversal symmetry is broken in a d + ig state, such a superconductor remains gapless with a Bogoliubov Fermi surface that approximates a (vertical) line node. The model gives rise to a strain-dependent splitting between the critical temperature Tc and the time-reversal symmetry-breaking temperature TTRSB that is qualitatively similar to some of the experimental observations in Sr2RuO4. 

We study multi-valley electron gases in the low density (rs ≫ 1) limit. Here the ground-state is always a Wigner crystal (WC), with additional pseudo-spin order where the pseudo-spins are related to valley occupancies. Depending on the symmetries of the host semiconductor and the values of the parameters such as the anisotropy of the effective mass tensors, we find a striped or chiral pseudo-spin antiferromagnet, or a time-reversal symmetry breaking orbital loop-current ordered pseudo-spin ferromagnet. Our theory applies to the recently-discovered WC states in AlAs and in mono and bilayer transition metal dichalcogenides. We identify a set of interesting electronic liquid crystalline phases that could arise by continuous quantum melting of such WCs. 

An electronic solid with itinerant carriers and localized magnetic moments represents a paradigmatic strongly correlated system. The electrical transport properties associated with the itinerant carriers, as they scatter off these local moments, have been scrutinized across a number of materials. Here, we analyze the transport characteristics associated with ultraclean PdCrO ${}_2$—a quasi-two-dimensional material consisting of alternating layers of itinerant Pd-electrons and Mott-insulating CrO ${}_2$layers—which shows a pronounced regime ofT-linear resistivity over a wide range of intermediate temperatures. By contrasting these observations to the transport properties in a closely related material PdCoO ${}_2$, where the CoO ${}_2$layers are band-insulators, we can rule out the traditional electron–phonon interactions as being responsible for this interesting regime. We propose a previously ignored electron-magneto-elastic interaction between the Pd-electrons, the Cr local moments and an out-of-plane phonon as the main scattering mechanism that leads to the significant enhancement of resistivity and aT-linear regime in PdCrO ${}_2$at temperatures far in excess of the magnetic ordering temperature. We suggest a number of future experiments to confirm this picture in PdCrO ${}_2$as well as other layered metallic/Mott-insulating materials. 

Abstract What limits the value of the superconducting transition temperature ( T c ) is a question of great fundamental and practical importance. Various heuristic upper bounds on T c have been proposed, expressed as fractions of the Fermi temperature, T F , the zero-temperature superfluid stiffness, ρ s (0), or a characteristic Debye frequency, ω 0 . We show that while these bounds are physically motivated and are certainly useful in many relevant situations, none of them serve as a fundamental bound on T c . To demonstrate this, we provide explicit models where T c / T F (with an appropriately defined T F ), T c / ρ s (0), and T c / ω 0 are unbounded. 

The repulsive Hubbard model has been immensely useful in understanding strongly correlated electron systems and serves as the paradigmatic model of the field. Despite its simplicity, it exhibits a strikingly rich phenomenology reminiscent of that observed in quantum materials. Nevertheless, much of its phase diagram remains controversial. Here, we review a subset of what is known about the Hubbard model based on exact results or controlled approximate solutions in various limits, for which there is a suitable small parameter. Our primary focus is on the ground state properties of the system on various lattices in two spatial dimensions, although both lower and higher dimensions are discussed as well. Finally, we highlight some of the important outstanding open questions.