Faraday rotation and the Hall constant in strongly correlated Fermi systems

Observation of universal Hall response in strongly interacting Fermions

The Hall effect, which originates from the motion of charged particles in magnetic fields, has deep consequences for the description of materials, extending far beyond condensed matter. Understanding such an effect in interacting systems represents a fundamental challenge, even for small magnetic fields. In this work, we used an atomic quantum simulator in which we tracked the motion of ultracold fermions in two-leg ribbons threaded by artificial magnetic fields. Through controllable quench dynamics, we measured the Hall response for a range of synthetic tunneling and atomic interaction strengths. We unveil a universal interaction-independent behavior above an interaction threshold, in agreement with theoretical analyses. The ability to reach hard-to-compute regimes demonstrates the power of quantum simulation to describe strongly correlated topological states of matter.

Intrinsic Anomalous Hall Effect in a Bosonic Chiral Superfluid

The anomalous Hall effect has had a profound influence on the understanding of many electronic topological materials but is much less studied in their bosonic counterparts. We predict that an intrinsic anomalous Hall effect exists in a recently realized bosonic chiral superfluid, a p-orbital Bose-Einstein condensate in a 2D hexagonal boron nitride optical lattice [Wang et al., Nature (London) 596, 227 (2021)NATUAS0028-083610.1038/s41586-021-03702-0]. We evaluate the frequency-dependent Hall conductivity within a multi-orbital Bose-Hubbard model that accurately captures the real experimental system. We find that in the high frequency limit, the Hall conductivity is determined by finite loop current correlations on the s-orbital residing sublattice, the latter a defining feature of the system's chirality. In the opposite limit, the dc Hall conductivity can trace its origin back to the noninteracting band Berry curvature at the condensation momentum, although the contribution from atomic interactions can be significant. We discuss available experimental probes to observe this intrinsic anomalous Hall effect at both zero and finite frequencies.

Effect of nonequilibrium order parameter on the optical response of superconductor Sr2RuO4

The breaking of time reversal symmetry of the superconducting pairings is expected to manifest itself through characteristic transport properties such as a non-zero Kerr angle which provides fingerprint of the quantum anomalous Hall state. In this work, we theoretically study the Kerr effect or the Hall-type response and also consider how this response is modified by the nonequilibrium shape of order parameter of the superconducting state due to the influence of the electromagnetic radiation for the most favorable candidates of chiral superconducting order parameters and of the non-chiral states in strontium ruthenate (Sr₂RuO₄). The unique sensitivity of the Hall-type response introduced above to different types of pairings can be used to identify the most favored pairing which is a serious doubt on the superconducting state of this material.

Probing the Hall Voltage in Synthetic Quantum Systems

In the context of experimental advances in the realization of artificial magnetic fields in quantum gases, we discuss feasible schemes to extend measurements of the Hall polarization to a study of the Hall voltage, allowing for direct comparison with solid state systems. Specifically, for the paradigmatic example of interacting flux ladders, we report on characteristic zero crossings and a remarkable robustness of the Hall voltage with respect to interaction strengths, particle fillings, and ladder geometries, which is unobservable in the Hall polarization. Moreover, we investigate the site-resolved Hall response in spatially inhomogeneous quantum phases.

Universal Hall Response in Interacting Quantum Systems

We theoretically study the Hall effect on interacting M-leg ladder systems, comparing different measures and properties of the zero temperature Hall response in the limit of weak magnetic fields. Focusing on SU(M) symmetric interacting bosons and fermions, as relevant for, e.g., typical synthetic dimensional quantum gas experiments, we identify an extensive regime in which the Hall imbalance Δ_{H} is universal and corresponds to a classical Hall resistivity R_{H}=-1/n for a large class of quantum phases. Away from this high symmetry point we observe interaction driven phenomena such as sign reversal and divergence of the Hall response.

Hall Number of Strongly Correlated Metals

An exact formula for the temperature dependent Hall number of metals is derived. It is valid for nonrelativistic fermions or bosons, with an arbitrary potential and interaction. This dc transport coefficient is proven to (remarkably) depend solely on equilibrium susceptibilities, which are more amenable to numerical algorithms than the conductivity. An application to strongly correlated phases is demonstrated by calculating the Hall sign in the vicinity of Mott phases of lattice bosons.

Intrinsic Hall effect in a multiband chiral superconductor in the absence of an external magnetic field

We identify an intrinsic Hall effect in multiband chiral superconductors in the absence of a magnetic field (i.e., an anomalous Hall effect). This effect arises from interband transitions involving time-reversal symmetry-breaking chiral Cooper pairs. We discuss the implications of this effect for the putative chiral p-wave superconductor, Sr2RuO4, and show that it can contribute significantly to Kerr rotation experiments. Since the magnitude of the effect depends on the structure of the order parameter across the bands, this result may be used to distinguish between different models proposed for the superconducting state of Sr2RuO4.

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.

Transport properties of the layered Rh oxide K0.49RhO2

We report measurements and analyses of resistivity, thermopower and the Hall coefficient of single-crystalline samples of the layered Rh oxide K(0.49)RhO(2). The resistivity is proportional to the square of the temperature up to 300 K, and the thermopower is proportional to the temperature up to 140 K. The Hall coefficient increases linearly with the temperature above 100 K, which is ascribed to the triangular network of Rh in this compound. The different transport properties between Na(x)CoO(2) and K(0.49)RhO(2) are discussed on the basis of the different bandwidth between Co and Rh evaluated from the magnetotransport.

Numerical linked-cluster algorithms. II. t-J models on the square lattice

We discuss the application of a recently introduced numerical linked-cluster (NLC) algorithm to strongly correlated itinerant models. In particular, we present a study of thermodynamic observables: chemical potential, entropy, specific heat, and uniform susceptibility for the t-J model on the square lattice, with Jt=0.5 and 0.3. Our NLC results are compared with those obtained from high-temperature expansions (HTE) and the finite-temperature Lanczos method (FTLM). We show that there is a sizeable window in temperature where NLC results converge without extrapolations whereas HTE diverges. Upon extrapolations, the overall agreement between NLC, HTE, and FTLM is excellent in some cases down to 0.25t . At intermediate temperatures NLC results are better controlled than other methods, making it easier to judge the convergence and numerical accuracy of the method.

Strong correlations produce the Curie-Weiss phase of NaxCoO2

Within the t-J model we study several experimentally accessible properties of the 2D-triangular lattice system NaxCoO2, using a numerically exact canonical ensemble study of 12 to 18 site triangular toroidal clusters as well as the icosahedron. Focusing on the doping regime of x approximately 0.7, we study the temperature dependent specific heat, magnetic susceptibility, and the dynamic Hall coefficient R_{H}(T,omega) as well as the magnetic field dependent thermopower. We find a crossover between two phases near x approximately 0.75 in susceptibility and field suppression of the thermopower arising from strong correlations. An interesting connection is found between the temperature dependence of the diamagnetic susceptibility and the Hall coefficient. We predict a large thermopower enhancement, arising from transport corrections to the Heikes-Mott formula, in a model situation where the sign of hopping is reversed from that applicable to NaxCoO2.

Electronic state of a CoO2 layer with hexagonal structure: a Kagomé lattice structure in a triangular lattice

The electronic state in layered cobalt oxides with a hexagonal structure is examined. We find that the electronic structure reflects the nature of the Kagomé lattice hidden in the CoO2 layer which consists of stacked triangular lattices of oxygen ions and of cobalt ions. A fundamental model for the electron system is proposed, and the mechanism of the unique transport and magnetic properties of the cobalt oxides are discussed in light of the model.