The interplay between strong correlations and nontrivial topology in twisted moiré systems can give rise to a rich landscape of ordered states that intertwine the spin, valley, and charge degrees of freedom. In this paper, we investigate the properties of a system that displays long-range valley-polarized nematic order. Besides breaking the threefold rotational symmetry of the triangular moiré superlattice, this type of order also breaks twofold rotational and time-reversal symmetries, which leads to interesting properties. First, we develop a phenomenological model to describe the onset of this ordered state in twisted moiré systems, and to explore its signatures in their thermodynamic and electronic properties. Its main manifestation is that it triggers the emergence of in-plane orbital magnetic moments oriented along high-symmetry lattice directions. We also investigate the properties of the valley-polarized nematic state at zero temperature. Due to the existence of a dangerously irrelevant coupling λ in the six-state clock model that describes the putative valley-polarized nematic quantum critical point, the ordered state displays a pseudo-Goldstone mode. Using a two-patch model, we compute the fermionic self-energy to show that down to very low energies, the Yukawa-like coupling between the pseudo-Goldstone mode and the electronic degrees of freedom promotes the emergence of non-Fermi liquid behavior. Below a crossover energy scale Ω∗∼λ3/2, however, Fermi liquid behavior is recovered. Finally, we discuss the applicability of these results to other nontrivial nematic states, such as the spin-polarized nematic phase.

Higher-pseudospin fermions, associated with multiple band crossings in topological semimetals, are condensed matter analogs of higher-spin fermions in high-energy physics. In this paper, we demonstrate that analyzing the response of a circular drive is an effective way to detect the topology of the lowest-energy Bloch band, as it can be connected to a frequency-dependent probe. The response exhibits circular dichroism due to the differential excitation rates by the left- and right-circular orientations of a time-periodic drive, induced on a filled band, because of the geometrical properties of the Bloch bands. Our analytical approximation reveals that the dichroic response is quantized for isotropic systems, when the frequency of the drive is above a critical value, and thus correctly infers the ground-state Chern number. We demonstrate this through explicit numerical computations by considering three kinds of semimetals with pseudospin values of 1/2, 1, and 3/2, respectively, and all having linear dispersions. Furthermore, we investigate the effects of tilt and anisotropy on the systems, and find that although tilt does not have any effect on the response, the presence of anisotropy can drastically hamper the quantization. Our scheme thus provides an important methodology for designing future experiments to detect the topology of band structures.

We consider tunneling of quasiparticles through a rectangular quantum well, subject to periodic driving. The quasiparticles are the itinerant charges in two-dimensional and three-dimensional semimetals having a quadratic bandtouching (QBT) point in the Brillouin zone. To analyze the time-periodic Hamiltonian, we assume a non-adiabatic limit where the Floquet theorem is applicable. By deriving the Floquet scattering matrices, we chalk out the transmission and shot noise spectra of the QBT semimetals. The spectra show Fano resonances, which we identify with the (quasi)bound states of the systems.

We investigate the interplay of Coulomb interactions and correlated disorder in pseudospin-3/2 semimetals, which exhibit birefringent spectra in the absence of interactions. Coulomb interactions drive the system to a marginal Fermi liquid, both for the two-dimensional (2d) and three-dimensional (3d) cases. Short-ranged correlated disorder in 2d, or a power-law correlated disorder 3d, has the same engineering dimension as the Coulomb term, in a renormalization group (RG) sense. In order to analyze the combined effects of these two kinds of interactions, we apply a dimensional regularization scheme and derive the RG flow equations. The results show that the marginal Fermi liquid phase is robust against disorder.

We study quantum transport in disordered systems with particle-hole symmetric Hamiltonians. The particle-hole symmetry is spontaneously broken after averaging with respect to disorder, and the resulting massless mode is treated in a random-phase representation of the invariant measure of the symmetry group. We compute the resulting fermionic functional integral of the average two-particle Green's function in a perturbation theory around the diffusive limit. The results up to two-loop order show that the corrections vanish, indicating that the diffusive quantum transport is robust. On the other hand, the diffusion coefficient depends strongly on the particle-hole symmetric Hamiltonian we choose to study. This reveals a connection between the underlying microscopic theory and the classical long-scale metallic behaviour of these systems.

Exceptional points (EPs), at which both eigenvalues and eigenvectors coalesce, are ubiquitous and unique features of non-Hermitian systems. Second-order EPs are by far the most studied due to their abundance, requiring only the tuning of two real parameters, which is less than the three parameters needed to generically find ordinary Hermitian eigenvalue degeneracies. Higher-order EPs generically require more fine-tuning, and are thus assumed to play a much less prominent role. Here, however, we illuminate how physically relevant symmetries make higher-order EPs dramatically more abundant and conceptually richer. More saliently, third-order EPs generically require only two real tuning parameters in the presence of either a parity-time (PT) symmetry or a generalized chiral symmetry. Remarkably, we find that these different symmetries yield topologically distinct types of EPs. We illustrate our findings in simple models, and show how third-order EPs with a generic ∼k1/3 dispersion are protected by PT symmetry, while third-order EPs with a ∼k1/2 dispersion are protected by the chiral symmetry emerging in non-Hermitian Lieb lattice models. More generally, we identify stable, weak, and fragile aspects of symmetry-protected higher-order EPs, and tease out their concomitant phenomenology.

We compute the thermoelectric and thermal transport coefficients in the weakly disordered non-Fermi liquid phase of the Luttinger semimetals at zero doping, where the decay rate associated with the (strong) Coulomb interactions is much larger than the electron-impurity scattering rate. To this end, we implement the Mori-Zwanzig memory matrix method, that does not rely on the existence of long-lived quasiparticles in the system. We find that the thermal conductivity at zero electric field scales as (kappa) over bar similar to T-n (with 0 less than or similar to n less than or similar to 1) at low temperatures, whereas the thermoelectric coefficient has the temperature dependence given by alpha similar to T-p (with 1/2 less than or similar to p less than or similar to 3/2). These unconventional properties turn out to be key signatures of this long sought-after non-Fermi liquid state in the Luttinger semimetals, which is expected to emerge in strongly correlated spin-orbit coupled materials like the pyrochlore iridates. Finally, our results indicate that these materials might be good candidates for achieving high figure-of-merit for thermoelectric applications.