Evidence for relativistic quantum criticality of antiferromagnetism and superconductivity in two-dimensional Dirac fermion systems has been found in large-scale quantum Monte Carlo simulations. However, the corresponding ($2+1$)-dimensional Gross–Neveu–Yukawa field theory with $N_f=2$ four-component Dirac fermions coupled to two triplets of order parameters does not exhibit a renormalization group fixed point at one-loop order. Instead, the theory only features a critical point for a large or very small fractional number of fermion flavors $N_f$, which disappears for a broad range of flavor numbers around the physical case, $N_f=2$, due to fixed-point annihilation. This raises the question on how to explain the observed scaling collapse in the quantum Monte Carlo data. Here, we extend previous renormalization-group analyses by studying a generalized model at two-loop order in $4-\epsilon$ spacetime dimensions. We determine the $\epsilon$ correction to the upper and lower critical flavor numbers for the fixed-point annihilation and find that they both go towards the physical case $N_f=2$. However, this only happens very slowly, such that an extrapolation to $\epsilon =1$ still suggests the absence of criticality in $2+1$ dimensions. Thereby, we consolidate the finding that the continuum field theory does not feature a stable renormalization-group fixed point and no true quantum criticality would be expected for the considered system. We briefly discuss a possible reconciliation in terms of a complex conformal field theory. Further, we also explore the fixed-point structure in an enlarged theory space and identify a candidate stable fixed-point solution.

Higher-order topological insulators are a novel type of topological phase that supports $d$-dimensional topological boundary states in D-dimensional systems with $D-d>1$. In this work, we theoretically predict that interlayer couplings in AB-stacked bilayer transition metal dichalcogenides (TMDs) lead to the emergence of extrinsic second-order topological phases, where corner states are induced by the band inversion of zigzag edge bands. We find that the systems feature a quantized multiband Berry phase defined for a zigzag nanoribbon geometry, unveiling the nontrivial topological properties of its two zigzag edges. With a detailed investigation into the bilayer TMDs under different geometries, we find two types of boundary-obstructed corner states arising from different corner terminations of either the same type or heterogeneous zigzag edges. The topological nature of these corner states and their degeneracy is further analyzed with both the crystalline symmetries of different geometries and a topological phase transition of the Berry phase induced by layer-dependent on-site energy.

In this series of papers, we study a Hamiltonian model for (3+1)-dimensional topological phases introduced in [Bullivant et al., Phys. Rev. B 95, 155118 (2017)], based on a generalization of lattice gauge theory known as “higher-lattice gauge theory.” Higher-lattice gauge theory has so-called “2-gauge fields” describing the parallel transport of lines, in addition to ordinary 1-gauge fields which describe the parallel transport of points. In this series we explicitly construct the creation operators for the pointlike and looplike excitations supported by the model. We use these creation operators to examine the properties of the excitations, including their braiding statistics. These creation operators also reveal that some of the excitations are confined, costing energy to separate that grows linearly with the length of the creation operator used. This is discussed in the context of condensation-confinement transitions between different cases of this model. We also discuss the topological charges of the model and use explicit measurement operators to rederive a relationship between the number of charges measured by a 2-torus and the ground-state degeneracy of the model on the 3-torus. From these measurement operators, we can see that the ground-state degeneracy on the 3-torus is related to the number of types of linked looplike excitations. This first paper provides an accessible summary of our findings, with more detailed results and proofs to be presented in the other papers in the series.

In this work, the second paper of this series, we study the $(2+1)$-dimensional version of a Hamiltonian model for topological phases based on higher-lattice gauge theory. We construct the ribbon operators that produce the pointlike excitations. These ribbon operators are used to find the braiding properties and topological charge carried by the pointlike excitations. The model also hosts looplike excitations, which are produced by membrane operators. By considering a change of basis, we show that, in certain cases, some looplike excitations represent domain walls between patches corresponding to different symmetry-related ground states, and we find this symmetry. We also map the higher-lattice gauge theory Hamiltonian to the symmetry-enriched string-net model for symmetry-enriched topological phases described by Heinrich, Burnell, Fidkowski, and Levin [Phys. Rev. B 94, 235136 (2016)], again in a subset of cases.

We present numerical evidence for a paradigm in one-dimensional interacting fermion systems, whose phenomenology has traits of both Luttinger liquids and Fermi liquids. This state, dubbed a quasi-Fermi liquid, possesses a discontinuity in its fermion occupation number at the Fermi momentum. The excitation spectrum presents particlelike quasiparticles and absence of holelike quasiparticles, giving rise instead to edge singularities. Such a state is realized in a one-dimensional spinless fermion lattice Hamiltonian by fine-tuning the interactions to a regime where they become irrelevant in the renormalization group sense. We show, using uniform infinite matrix products states and finite-entanglement scaling analysis, that the system ground state is characterized by a Luttinger parameter $K=1$ and a discontinuous jump in the fermion occupation number. We support the characterization with calculations of the spectral function that show a particle-hole asymmetry reflected in the existence of well-defined Landau quasiparticles above the Fermi level and edge singularities without the associated quasiparticles below. These results indicate that the quasi-Fermi liquid paradigm can be realized beyond the low-energy perturbative realm.

The π phase shift of quantum oscillations is generally believed to be a smoking gun evidence for nontrivial Berry phase. However, the spin-zero effect, a sign reversal of quantum oscillations at different magnetic field directions, adds an additional π phase shift. Thus, the nontrivial Berry curvature can be concealed by the spin-zero effect, resulting in an apparent trivial phase in quantum oscillation measurements. In this work, we report a hidden Berry phase in Weyl semiconductor Te nanowires. A trivial-like Berry phase is observed in the quantum oscillations in Te nanowires. However, a large $g$ factor, together with the band evolution under magnetic fields, leads to a spin-zero effect in Te nanowires. We further derive the nontrivial nature of Te nanowires from quantum transport.

The Mott insulating state is the progenitor of many interesting quantum phases of matter including the famous high-temperature superconductors and quantum spin liquids. A recent candidate for novel spin liquid phenomena is $\alpha \text{−}{\mathrm{RuCl}}_3$, a layered honeycomb Mott insulator whose electronic structure has been a source of mystery. In particular, scanning tunneling spectroscopy has indicated a Mott gap in $\alpha \text{−}{\mathrm{RuCl}}_3$ that is much lower than the 2-eV value observed in photoemission measurements. Here, we show that the origin of this discrepancy is a spreading resistance artifact associated with tunneling into highly resistive materials by comparing with prior experiments and numerical modeling. A similar phenomenon is also observed in a substitutional alloy, ${\mathrm{Ir}}_{0.5}{\mathrm{Ru}}_{0.5}{\mathrm{Cl}}_3$, that has a higher resistivity than the parent compound. While the tunneling measurements cannot be used to accurately measure the sample density of states for these materials, we can take advantage of the spreading resistance sensitivity to quantify the anisotropic resistivity of these layered materials and connect to previous macroscopic transport observations.

The sine-Gordon model is a paradigmatic quantum field theory that provides the low-energy effective description of many gapped one-dimensional systems. Despite this fact, its complete thermodynamic description in all its regimes has been lacking. Here, we fill this gap and derive the framework that captures its thermodynamics and serves as the basis of its hydrodynamic description. As a first application, we compute the Drude weight characterizing the ballistic transport of topological charge and demonstrate that its dependence on the value of the coupling shows a fractal structure, similar to the gapless phase of the XXZ spin chain. The thermodynamic framework can be applied to study other features of nonequilibrium dynamics in the sine-Gordon model using generalized hydrodynamics, opening the way to a wide array of theoretical studies and potential novel experimental predictions.

Quenched disorder slows down the scrambling of quantum information. Using a bottom-up approach, we formulate a kinetic theory of scrambling in a correlated metal near a superconducting transition, following the scrambling dynamics as the impurity scattering rate is increased. Within this framework, we rigorously show that the butterfly velocity $v$ is bounded by the light-cone velocity $v_{\mathrm{lc}}$ set by the Fermi velocity. We analytically identify a disorder-driven dynamical transition occurring at small but finite disorder strength between a spreading of information characterized at late times by a discontinuous shock wave propagating at the maximum velocity $v_{\mathrm{lc}}$, and a smooth traveling wave belonging to the Fisher or Kolmogorov-Petrovsky-Piskunov (FKPP) class and propagating at a slower, if not considerably slower, velocity $v$. In the diffusive regime, we establish the relation $v^2/{\lambda }_{\mathrm{FKPP}}\sim D_{\mathrm{el}}$, where ${\lambda }_{\mathrm{FKPP}}$ is the Lyapunov exponent set by the inelastic scattering rate and $D_{\mathrm{el}}$ is the elastic diffusion constant.

The spontaneous breaking of time-reversal symmetry due to purely orbital mechanisms (i.e., not involving spin degrees of freedom) yields extremely exotic phases of matter such as Chern insulators and chiral superconductors. In this Letter, we show that excitonic insulators, by exploiting the transition from the excitonic ground state to a purely orbital time-reversal symmetry broken hidden state, can realize another notable example of this class. The transition to the hidden state is controlled by engineered geometrical constraints, which enable the coupling between the excitonic order parameter and the free-space electromagnetic field. These results pave the way towards exotic orbital magnetic order in quantum materials and are also relevant for disentangling excitonic phase transitions from trivial structural ones.

We present a framework for analyzing Mott insulators using a material-based tight-binding model. We start with a realistic multiorbital Hubbard model and derive an effective model for the localized electrons through the second-order perturbation theory with respect to intersite hopping. This effective model, known as the Kugel-Khomskii model, is described by $\mathrm{SU}\left(N\right)$ generators, where $N$ is the number of localized states. We solve this model by the mean-field theory that takes local correlations into account and reveal spin-orbital ordered states. To include spatial correlations, we apply the classical Monte Carlo based on the path-integral approach with $\mathrm{SU}(N$) coherent states, and also derive the equation of motion for spin-orbital degrees of freedom. Our approach enables quantitative analysis of Mott insulator materials with a small intersite quantum correlation. The $5d$-pyrochlore oxide is used here as a demonstration.

Several decades of debate have centered around the nature of the enigmatic pseudogap state in high-temperature superconducting copper oxides. Recently, we reported polarized neutron diffraction measurements that suggested the existence of a magnetic texture bound to the pseudogap phase [Bounoua et al. Commun. Phys. 5, 268 (2022)]. Such a magnetic texture is likely to involve the spontaneous appearance of loop currents within the ${\mathrm{CuO}}_2$ unit cells, which give birth to complex correlated patterns. In the underdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.6}$, the magnetic structure factor of such an orbital magnetic texture gives rise to two distinct magnetic responses at $\mathbf{q}=0$ and $\mathbf{q}=1/2$. As this pattern alters the lattice translation invariance, such a state of matter could contribute to an instability of the Fermi surface. Here, we report polarized neutron scattering measurements on a nearly optimally doped high-quality single crystal of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.9}$ that exhibits the same $\mathbf{q}=1/2$ magnetism and a weakly overdoped ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$ sample where this signal is no longer sizable. The in-plane and out-of-plane magnetic neutron scattering intensities in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.9}$ (at $\mathbf{q}=1/2$) and ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.85}$ (at $\mathbf{q}=0$), reported previously, display the same temperature-dependent hallmarks. The magnitudes of both $\mathbf{q}=0$ and $\mathbf{q}=1/2$ magnetic signals further exhibit the same trends upon doping in ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+\mathrm{x}}$, confirming that they are likely intertwined.

Strong spin-lattice coupling makes external pressure ($P$) an important parameter across a first-order magnetostructural phase transition. Here, we have studied the effect of $P$ under different magnetic fields on the phase coexistence and kinetics of nucleation and growth around such transitions in two prototype systems ${\mathrm{Pr}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{Mn}}_{0.975}{\mathrm{Al}}_{0.025}{\mathrm{O}}_3$ and ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$, where the ferromagnetic-metal and antiferromagnetic-insulator phases compete in real space. We have determined the $H-P$ phase diagram of supercooling and superheating temperatures. The change in supercooling and superheating temperatures and the nucleation and growth control the phase coexistence. Surprisingly, despite having contrasting ground states, in both ${\mathrm{Pr}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{Mn}}_{0.975}{\mathrm{Al}}_{0.025}{\mathrm{O}}_3$ and ${\mathrm{La}}_{0.5}{\mathrm{Ca}}_{0.5}{\mathrm{MnO}}_3$ the transformation rate between the two states is suppressed at higher pressure. This proves that there must be some universal phenomena controlling the dynamics. Different spin and structural order at the interface of the two phases appear to be responsible for giving rise to strong frustration and eventually hindering the kinetics, resulting in the stabilization of glasslike behavior.

We consider the possibility of superfluid behavior in a coherently driven, dissipative microcavity polariton system in gapless spectrum regimes. Previous work demonstrated the absence of such behavior for gapped spectra via a linear response analysis. The system can, however, be tuned to possess a gapless spectrum in special cases, leaving open the possibility of superfluid behavior. Here we show the absence of superfluidity in all regimes; we find a divergent linear response in the system's gapless regimes, which may be linked to phase-transition behavior. This indicates that the gapless spectrum is related to phase instability and not superfluid-enabling massless modes.

Monolayer ${\mathrm{FeTe}}_{1-x}{\mathrm{Se}}_x$ films grown on a ${\mathrm{SrTiO}}_3\left(001\right)$ substrate is a promising platform to explore both high-temperature and topological superconductivity. Using molecular beam epitaxy, we successfully synthesized monolayer ${\mathrm{FeTe}}_{1-x}{\mathrm{Se}}_x$ films ($0\le x\le 1$) on a $\mathrm{Nb}$-doped ${\mathrm{SrTiO}}_3\left(001\right)$ substrate. The as-grown films with $0.30\le x\le 1$ show superconductivity. By spatially mapping the superconducting gap distribution, we found a large gap variation of $\sim 3–7\mathrm{meV}$. Our analysis shows that impurities/defects and local chemical composition variation play a minor role in the superconducting gap inhomogeneity. The large gap variation is possibly attributed to the joint effects of the interface inhomogeneity and inhomogeneous superfluid. Our study sheds light on the fundamental properties of two-dimensional iron-based superconductors.

Structural and physical properties of the ${\mathrm{Yb}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ Remeika phase are investigated on large single crystals grown from Sn-flux. It crystallizes with disordered ${\mathrm{Y}}_3{\mathrm{Co}}_4{\mathrm{Ge}}_{13}$ structure type [space group $Pm\overline{3}n, a=9.6709\left(2\right)$ Å], where the $24k$ crystallographic site occupied by Sn atoms is split. ${\mathrm{Yb}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ is a superconductor (SC) with the critical temperature $T_{\mathrm{c}}=7.63\left(5\right)$ K, lower [$B_{\mathrm{c}1}=14.5\left(5\right)$ mT] and upper [$B_{\mathrm{c}2}\left(0\right)=2.89\left(5\right)$ T] critical fields, as well as a clear peak effect with $B^{*}\left(0\right)=1.96\left(9\right)$ T observed in the $M\left(H\right)$ loops. $B_{\mathrm{c}2}\left(T_{\mathrm{c}}\right)$ can be described by the sum of two Werthamer-Helfand-Hohenberg equations. A $\gamma \left(B\right)\propto B^{0.75}$ dependency is found. The electronic specific heat below $T_{\mathrm{c}}$ follows an exponential function including 87% of a strongly coupled [${\mathrm{\Delta }}_1/k_B{T}_{\mathrm{c}}=3.52\left(1\right)$] and 13% of a conventional $s$-wave-like [${\mathrm{\Delta }}_2/k_{\mathrm{B}}{T}_{\mathrm{c}}=1.32\left(1\right)$] gap. The observations are in line with ${\mathrm{Yb}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ being a two-gap SC. The Remeika phase reveals a complex electronic band structure studied by Hall coefficient ($R_{\mathrm{H}}$) measurements and calculations performed within the density functional theory. A “rattling” effect in ${\mathrm{Yb}}_3{\mathrm{Rh}}_4{\mathrm{Sn}}_{13}$ is discussed based on structural refinements and phononic contributions to its specific heat capacity.

The superconducting state with the usual $2e$ flux quantization formed from a normal state with $3Q$ charge density or loop-current order is a linear combination of 3 different paired states with an overall gauge-invariant phase and two internal phases such that the phases in equilibrium are at $2\pi /3$ with respect to each other. In the fluctuation regime of such a 3-component superconductor, internal phase fluctuations are of the same class as for frustrated classical $\mathit{XY}$ spins on a triangular lattice. The fluctuation region is known therefore to be abnormally extended below the mean-field or the Kosterlitz-Thouless transition temperature. A $6e$ flux and a $4e$ flux quantized state can be constructed which are also eigenstates of the BCS Hamiltonian and stationary points of the Ginzburg-Landau free energy with a transition temperature above that of the renormalized $2e$ flux quantized state. Such states have no internal phases and so no frustrating internal phase fluctuations. These states however cannot acquire long-range order because their free energy is higher than the co-existing fluctuating state of $2e$ flux quantization. $6e$ as well as $4e$ flux quantized Little-Parks oscillations however occur in which the resistivity increases periodically with field above that of the $2e$ fluctuating state in its extended fluctuation regime, as is observed, followed at low temperatures to a condensation of the time-reversal odd $2e$ quantized state.