Johannes Zaanen (1957-2024).

Oracle of condensed matter physics.

Failure of Topological Invariants in Strongly Correlated Matter.

We show exactly that standard "invariants" advocated to define topology for noninteracting systems deviate strongly from the Hall conductance whenever the excitation spectrum contains zeros of the single-particle Green's function, G, as in general strongly correlated systems. Namely, we show that if the chemical potential sits atop the valence band, the "invariant" changes without even accessing the conduction band but by simply traversing the band of zeros that might lie between the two bands. Since such a process does not change the many-body ground state, the Hall conductance remains fixed. This disconnect with the Hall conductance arises from the replacement of the Hamiltonian, h(k), with G^{-1} in the current operator, thereby laying plain why perturbative arguments fail.

1/4 is the new 1/2 when topology is intertwined with Mottness.

In non-interacting systems, bands from non-trivial topology emerge strictly at half-filling and exhibit either the quantum anomalous Hall or spin Hall effects. Here we show using determinantal quantum Monte Carlo and an exactly solvable strongly interacting model that these topological states now shift to quarter filling. A topological Mott insulator is the underlying cause. The peak in the spin susceptibility is consistent with a possible ferromagnetic state at T = 0. The onset of such magnetism would convert the quantum spin Hall to a quantum anomalous Hall effect. While such a symmetry-broken phase typically is accompanied by a gap, we find that the interaction strength must exceed a critical value for this to occur. Hence, we predict that topology can obtain in a gapless phase but only in the presence of interactions in dispersive bands. These results explain the recent quarter-filled quantum anomalous Hall effects seen in moiré systems.

Pines' demon observed as a 3D acoustic plasmon in Sr2RuO4.

The characteristic excitation of a metal is its plasmon, which is a quantized collective oscillation of its electron density. In 1956, David Pines predicted that a distinct type of plasmon, dubbed a 'demon', could exist in three-dimensional (3D) metals containing more than one species of charge carrier1. Consisting of out-of-phase movement of electrons in different bands, demons are acoustic, electrically neutral and do not couple to light, so have never been detected in an equilibrium, 3D metal. Nevertheless, demons are believed to be critical for diverse phenomena including phase transitions in mixed-valence semimetals2, optical properties of metal nanoparticles3, soundarons in Weyl semimetals4 and high-temperature superconductivity in, for example, metal hydrides3,5-7. Here, we present evidence for a demon in Sr2RuO4 from momentum-resolved electron energy-loss spectroscopy. Formed of electrons in the ß and γ bands, the demon is gapless with critical momentum qc = 0.08 reciprocal lattice units and room-temperature velocity v = (1.065 ± 0.12) × 105 m s-1 that undergoes a 31% renormalization upon cooling to 30 K because of coupling to the particle-hole continuum. The momentum dependence of the intensity of the demon confirms its neutral character. Our study confirms a 67-year old prediction and indicates that demons may be a pervasive feature of multiband metals.

Stranger than metals.

In traditional metals, the temperature (T) dependence of electrical resistivity vanishes at low or high T, albeit for different reasons. Here, we review a class of materials, known as "strange" metals, that can violate both of these principles. In strange metals, the change in slope of the resistivity as the mean free path drops below the lattice constant, or as T → 0, can be imperceptible, suggesting continuity between the charge carriers at low and high T. We focus on transport and spectroscopic data on candidate strange metals in an effort to isolate and identify a unifying physical principle. Special attention is paid to quantum criticality, Planckian dissipation, Mottness, and whether a new gauge principle is needed to account for the nonlocal transport seen in these materials.

Anomalous diffusion and Noether's second theorem.

Despite the fact that conserved currents have dimensions that are determined solely by dimensional analysis (and hence no anomalous dimensions), Nature abounds in examples of anomalous diffusion in which L∝t^{γ}, with γ≠1/2, and heat transport in which the thermal conductivity diverges as L^{α}. Aside from breaking of Lorentz invariance, the true common link in such problems is an anomalous dimension for the underlying conserved current, thereby violating the basic tenet of field theory. We show here that the phenomenological nonlocal equations of motion that are used to describe such anomalies all follow from Lorentz-violating gauge transformations arising from Noether's second theorem. The generalizations lead to a family of diffusion and heat transport equations that systematize how nonlocal gauge transformations generate more general forms of Fick's and Fourier's laws for diffusive and heat transport, respectively. In particular, the associated Goldstone modes of the form ω∝k^{α}, α∈R are direct consequences of fractional equations of motion.

Doped Twisted Bilayer Graphene near Magic Angles: Proximity to Wigner Crystallization, Not Mott Insulation.

We devise a model to explain why twisted bilayer graphene exhibits insulating behavior when ν = 2 or 3 charges occupy a unit moiré cell, a feature attributed to Mottness per previous work but not for ν = 1, clearly inconsistent with Mott insulation. We compute rs = EU/ EK, where EU and EK are the potential and kinetic energies, respectively, and show that (i) the Mott criterion lies at a density larger than experimental values by a factor of 104 and (ii) a transition to a series of Wigner crystalline states exists as a function of ν. We find that, for ν = 1, rs fails to cross the threshold ( rs = 37) for the triangular lattice, and metallic transport ensues. However, for ν = 2 and ν = 3, the thresholds rs = 22 and rs = 17, respectively, are satisfied for a transition to Wigner crystals (WCs) with a honeycomb (ν = 2) and a kagome (ν = 3) structure. We posit that such crystalline states form the correct starting point for analyzing superconductivity.

Theory of point contact spectroscopy in correlated materials.

We developed a microscopic theory for the point-contact conductance between a metallic electrode and a strongly correlated material using the nonequilibrium Schwinger-Kadanoff-Baym-Keldysh formalism. We explicitly show that, in the classical limit, contact size shorter than the scattering length of the system, the microscopic model can be reduced to an effective model with transfer matrix elements that conserve in-plane momentum. We found that the conductance dI/dV is proportional to the effective density of states, that is, the integrated single-particle spectral function A(ω = eV) over the whole Brillouin zone. From this conclusion, we are able to establish the conditions under which a non-Fermi liquid metal exhibits a zero-bias peak in the conductance. This finding is discussed in the context of recent point-contact spectroscopy on the iron pnictides and chalcogenides, which has exhibited a zero-bias conductance peak.

Divergent thermopower without a quantum phase transition.

A general principle of modern statistical physics is that divergences of either thermodynamic or transport properties are only possible if the correlation length diverges. We show by explicit calculation that the thermopower in the quantum XY model d = 1 + 1 and the Kitaev model in d = 2 + 1 can (i) diverge even when the correlation length is finite and (ii) remain finite even when the correlation length diverges, thereby providing a counterexample to the standard paradigm. Two conditions are necessary: (i) the sign of the charge carriers and that of the group velocity must be uncorrelated and (ii) the current operator defined formally as the derivative of the Hamiltonian with respect to the gauge field does not describe a set of excitations that have a particle interpretation, as in strongly correlated electron matter. Recent experimental and theoretical findings on the divergent thermopower of a 2D electron gas are discussed in this context.

Absence of Luttinger's theorem due to zeros in the single-particle Green function.

We show exactly with an SU(N) interacting model that even if the ambiguity associated with the placement of the chemical potential, µ, for a T=0 gapped system is removed by using the unique value µ(T→0), Luttinger's sum rule is violated even if the ground-state degeneracy is lifted by an infinitesimal hopping. The failure stems from the nonexistence of the Luttinger-Ward functional for a system in which the self-energy diverges. Since it is the existence of the Luttinger-Ward functional that is the basis for Luttinger's theorem which relates the charge density to sign changes of the single-particle Green function, no such theorem exists. Experimental data on the cuprates are presented which show a systematic deviation from the Luttinger count, implying a breakdown of the electron quasiparticle picture in strongly correlated electron matter.

Dynamically generated Mott gap from holography.

In the fermionic sector of top-down approaches to holographic systems, one generically finds that the fermions are coupled to gravity and gauge fields in a variety of ways, beyond minimal coupling. In this Letter, we take one such interaction-a Pauli, or dipole, interaction-and study its effects on fermion correlators. We find that this interaction modifies the fermion spectral density in a remarkable way. As we change the strength of the interaction, we find that spectral weight is transferred between bands, and beyond a critical value, a gap emerges in the fermion density of states. A possible interpretation of this bulk interaction then is that it drives the dynamical formation of a (Mott) gap, in the absence of continuous symmetry breaking.

Mottness collapse and T-linear resistivity in cuprate superconductors.

Central to the normal state of cuprate high-temperature superconductors is the collapse of the pseudo-gap, briefly reviewed here, at a critical point and the subsequent onset of the strange metal characterized by a resistivity that scales linearly with temperature. A possible clue to the resolution of this problem is the inter-relation between two facts: (i) a robust theory of T-linear resistivity resulting from quantum criticality requires an additional length scale outside the standard one-parameter scaling scenario and (ii) breaking the Landau correspondence between the Fermi gas and an interacting system with short-range repulsions requires non-fermionic degrees. We show that a low-energy theory of the Hubbard model that correctly incorporates dynamical spectral weight transfer has the extra degrees of freedom needed to describe this physics. The degrees of freedom that mix into the lower band as a result of dynamical spectral weight transfer are shown to either decouple beyond a critical doping, thereby signalling Mottness collapse, or unbind above a critical temperature, yielding strange metal behaviour characterized by T-linear resistivity.

Magnon-mediated pairing and isotope effect in iron-based superconductors.

Within a minimal model for the iron-based superconductors in which itinerant electrons interact with a band of local moments, we derive a general conclusion for multiband superconductivity. In a multiband superconductor, due to the Adler theorem, the interband scattering dominates the intraband scattering at the long wavelength limit as long as both interactions are induced by the Goldstone boson (which is the magnon in our case) and the transferred momentum is non-zero. Such an interaction leads to a well known sign-reversing superconductivity even if the interband and intraband interaction are repulsive. This effect can be modeled as arising from an internal Josephson link between the Fermi surface sheets. Our model is also consistent with the recently discovered coexistence of superconductivity and magnetic order in iron-pnictides. Although the experimentally observed isotope effect is large, α = 0.4, we show that it is consistent with a non-phononic mechanism in which it is the isotope effects which result in a change in the lattice constant and, as a consequence, the zero-point motion of the Fe atoms.

Signatures of surface states in bismuth at high magnetic fields.

Electrons in a metal subject to a magnetic field commonly exhibit oscillatory behavior as the field strength varies, with a period set by the area of quantized electronic orbits. Recent experiments on elemental bismuth have revealed oscillations for fields above 9 T that do not follow this simple dependence and have been interpreted as a signature of electron fractionalization in the bulk. We argue instead that a simple explanation in terms of the surface states of bismuth exists when additional features of the experiment are included. These surface electrons are known to have significant spin-orbit interaction. We show the observed oscillations are in quantitative agreement with the surface theory, which we propose to test by studying the effect of the Zeeman coupling in higher fields, dependence on the field orientation, and the thickness of the samples.

Theory of the magnetic moment in iron pnictides.

We show that the combined effects of spin orbit, monoclinic distortion, and p-d hybridization in tetrahedrally coordinated Fe in LaFeAsO invalidate the naive Hund's rule filling of the Fe d levels. The two highest occupied levels have one electron each, but, as a result of differing p-d hybridizations, the upper level is more itinerant, while electrons in the lower level are more localized. The resulting magnetic moment is highly anisotropic with an in-plane value of 0.25 micro_B-0.35 micro_B per Fe and a z projection of 0.06 micro_B, both of which are in agreement with experiment.