The Hubbard Model

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. Expected final online publication date for the Annual Review of Condensed Matter Physics, Volume 13 is March 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Band-selective gap opening by a C4-symmetric order in a proximity-coupled heterostructure Sr2VO3FeAs

Complex electronic phases in strongly correlated electron systems are manifested by broken symmetries in the low-energy electronic states. Some mysterious phases, however, exhibit intriguing energy gap opening without an apparent signature of symmetry breaking (e.g., high-TC cuprates and heavy fermion superconductors). Here, we report an unconventional gap opening in a heterostructured, iron-based superconductor Sr2VO3FeAs across a phase transition at T0 ∼150 K. Using angle-resolved photoemission spectroscopy, we identify that a fully isotropic gap opens selectively on one of the Fermi surfaces with finite warping along the interlayer direction. This band selectivity is incompatible with conventional gap opening mechanisms associated with symmetry breaking. These findings, together with the unusual field-dependent magnetoresistance, suggest that the Kondo-type proximity coupling of itinerant Fe electrons to localized V spin plays a role in stabilizing the exotic phase, which may serve as a distinct precursor state for unconventional superconductivity.

Magnetoelectric phase transition driven by interfacial-engineered Dzyaloshinskii-Moriya interaction

Strongly correlated oxides with a broken symmetry could exhibit various phase transitions, such as superconductivity, magnetism and ferroelectricity. Construction of superlattices using these materials is effective to design crystal symmetries at atomic scale for emergent orderings and phases. Here, antiferromagnetic Ruddlesden-Popper Sr2IrO4 and perovskite paraelectric (ferroelectric) SrTiO3 (BaTiO3) are selected to epitaxially fabricate superlattices for symmetry engineering. An emergent magnetoelectric phase transition is achieved in Sr2IrO4/SrTiO3 superlattices with artificially designed ferroelectricity, where an observable interfacial Dzyaloshinskii-Moriya interaction driven by non-equivalent interface is considered as the microscopic origin. By further increasing the polarization namely interfacial Dzyaloshinskii-Moriya interaction via replacing SrTiO3 with BaTiO3, the transition temperature can be enhanced from 46 K to 203 K, accompanying a pronounced magnetoelectric coefficient of ~495 mV/cm·Oe. This interfacial engineering of Dzyaloshinskii-Moriya interaction provides a strategy to design quantum phases and orderings in correlated electron systems.

Interplay between Vortex Dynamics and Superconducting Gap Structure in Layered Organic Superconductors

Layered organic superconductors motivate intense investigations because they provide various unexpected issues associated with their low dimensionality and the strong electron correlation. Since layered organic superconductors possess simple Fermi surface geometry and they often share similarities to the high temperature oxide superconductors and heavy fermion compounds, research on layered organic superconductors is suitable for understanding the essence and nature of strongly correlated electron systems. In strongly correlated electron systems, one of the central problems concerning the superconducting (SC) state is the symmetry of the SC gap, which is closely related to the paring mechanism. Thus, experimental determination of the SC gap structure is of essential importance. In this review, we present the experimental results for the in-plane angular variation of the flux-flow resistance in layered organic superconductors k-(ET)2Cu(NCS)2, β″-(ET)2SF5CH2CF2SO3, and λ-(BETS)2GaCl4. The interplay between the vortex dynamics and nodal structures is discussed for these superconductors.

Pristine quantum criticality in a Kondo semimetal

The observation of quantum criticality in diverse classes of strongly correlated electron systems has been instrumental in establishing ordering principles, discovering new phases, and identifying the relevant degrees of freedom and interactions. At focus so far have been insulators and metals. Semimetals, which are of great current interest as candidate phases with nontrivial topology, are much less explored in experiments. Here, we study the Kondo semimetal CeRu4Sn6 by magnetic susceptibility, specific heat, and inelastic neutron scattering experiments. The power-law divergence of the magnetic Grünesien ratio reveals that, unexpectedly, this compound is quantum critical without tuning. The dynamical energy over temperature scaling in the neutron response throughout the Brillouin zone and the temperature dependence of the static uniform susceptibility, indicate that temperature is the only energy scale in the criticality. Such behavior, which has been associated with Kondo destruction quantum criticality in metallic systems, could be generic in the semimetal setting.

Propagation of shear stress in strongly interacting metallic Fermi liquids enhances transmission of terahertz radiation

A highlight of Fermi-liquid phenomenology, as explored in neutral $$^3$$ 3 He, is the observation that in the collisionless regime shear stress propagates as if one is dealing with the transverse phonon of a solid. The existence of this “transverse zero sound” requires that the quasiparticle mass enhancement exceeds a critical value. Could such a propagating shear stress also exist in strongly correlated electron systems? Despite some noticeable differences with the neutral case in the Galilean continuum, we arrive at the verdict that transverse zero sound should be generic for mass enhancement higher than 3. We present an experimental setup that should be exquisitely sensitive in this regard: the transmission of terahertz radiation through a thin slab of heavy-fermion material will be strongly enhanced at low temperature and accompanied by giant oscillations, which reflect the interference between light itself and the “material photon” being the actual manifestation of transverse zero sound in the charged Fermi liquid.