We analyze the free energy and the specific heat for fermions interacting with a gapless boson at a quantum-critical point (QCP) in a metal. We use the Luttinger-Ward-Eliashberg formula for the free energy in the normal state, which includes contributions from bosons, fermions, and their interaction, all expressed via fully dressed fermionic and bosonic propagators. The sum of the last two contributions is the free energy $F_{\gamma }$ of an effective low-energy model of fermions with boson-mediated dynamical 4-fermion interaction $V\left({\mathrm{\Omega }}_m\right)\propto 1/{\left|{\mathrm{\Omega }}_m\right|}^{\gamma }$ (the $\gamma$ model). This purely electronic model has been used to analyze the interplay between non-Fermi liquid behavior and pairing near a QCP, which are both independent of the upper energy cutoff $\mathrm{\Lambda }$. However, the specific heat $C_{\gamma }\left(T\right)$, obtained from $F_{\gamma }$, does depend on $\mathrm{\Lambda }$. We argue that this dependence is spurious and cancels out, once we include the contribution from bosons. We further argue that the full $C\left(T\right)$ is the sum of the contribution from free fermions and the one from a critical boson, with the fully dressed propagator, other terms cancel out. We compare the full $C\left(T\right)$ with the $C_{\gamma }\left(T\right)$, obtained using recently proposed regularization of $F_{\gamma }$ [Phys. Rev. B 106, 054518 (2022)]. We argue that for $\gamma <1$, the full $C\left(T\right)$ and the regularized $C_{\gamma }\left(T\right)$ differ by a $\gamma$-dependent prefactor, while for $\gamma >1$, the full $C\left(T\right)$ and $C_{\gamma }\left(T\right)$ differ by the positive contribution from free massless fermions (a positive constant for the electron-phonon case $\gamma =2$). For these $\gamma , C_{\gamma }\left(T\right)$ is negative, but the full $C\left(T\right)$ is positive. We argue that only the full $C\left(T\right)$ matters as the positive and the negative contributions originate from the term in $C\left(T\right)$ which contains the fully dressed bosonic propagator. We then argue that the normal state remains stable until the pairing instability develops.

${\mathrm{MnSb}}_2{\mathrm{O}}_6$ is based on the noncentrosymmetric $P321$ space group with magnetic ${\mathrm{Mn}}^{2+}$ ($S=5/2$, $L\approx 0$) spins ordering below $T_{\mathrm{N}}=12\mathrm{K}$ in a cycloidal structure. The spin rotation plane was found to be tilted away from the $c$ axis [Kinoshita et al., Phys. Rev. Lett. 117, 047201 (2016)] resulting as a helicoidal ground state, which we refer as the tilted structure. In our previous diffraction study [Chan et al., Phys. Rev. B 106, 064403 (2022)] we found no evidence that this tilted structure is favored over the pure cycloidal order (referred as the untilted structure). The ground-state magnetic structure, expected to be built and originate from seven nearest-neighbor Heisenberg exchange constants, has been shown to be coupled to the underlying crystallographic chirality with polar domain switching being reported. We apply neutron spectroscopy to extract these symmetric exchange constants. Given the high complexity of the magnetic exchange network, crystallographic structure and complications fitting many parameter linear spin-wave models, we take advantage of multiplexed neutron instrumentation to use the first moment sum rule of neutron scattering to estimate these symmetric exchange constants. The first moment of neutron scattering provides a way of deriving the Heisenberg exchange constant between two neighboring spins if the relative angle and distance of the two ordered spins is known. We show that the first moment sum rule combined with the known magnetic ordering wavevector fixes six of the seven exchange constants. The remaining exchange constant is not determined by this analysis because of the equal spatial bond distances present for different chiral exchange interactions. However, we find this parameter is fixed by the magnon dispersion near the magnetic zone boundary, which is not sensitive to the tilting of the global magnetic structure. We then use these parameters to calculate the low-energy spin-waves in the Néel state to reproduce the neutron response without strong antisymmetric coupling. Using Green's response functions, the stability of long-wavelength excitations in the context of our proposed untilted magnetic structures is then discussed. The results show the presence of strong symmetric exchange constants for the chiral exchange pathways and illustrate an underlying coupling between crystallographic and magnetic “chirality” through predominantly symmetric exchange. We further argue that the excitations can be consistently modelled in terms of an untilted magnetic structure in the presence of symmetric-only exchange constants.

We discuss a Kohn-Luttinger-like mechanism for superconductivity in Bernal bilayer graphene and rhombohedral trilayer graphene. Working within the continuum model description without free parameters, we find that the screened long-range Coulomb interaction alone gives rise to superconductivity with critical temperatures that agree with experiments. We observe that the order parameter changes sign between valleys, which implies that both materials are valley-singlet, spin-triplet superconductors. Adding Ising spin-orbit coupling leads to a significant enhancement in the critical temperature, also in line with experiment, and the superconducting order parameter shows locking between the spin and valley degrees of freedom.

Recent experiments on multilayer graphene materials have discovered a plethora of correlated phases, including ferromagnetism and superconductivity, in the absence of a moiré potential. These findings pose an intriguing question of whether an underlying moiré potential plays a key role in determining the phases realizable in tunable two-dimensional quantum materials, or whether it merely acts as a weak periodic potential that perturbs an underlying correlated many body state. In this work, employing a Hartree-Fock mean field analysis, we examine this question theoretically by quantitatively studying the effects of a hexagonal boron nitride (h-BN) substrate on ABC-stacked trilayer graphene (ABC-TLG). For the topologically trivial regime, we find that the moiré potential leads to a strong suppression of the ferromagnetism of the underlying metal. Further, band insulators appear solely at full filling of the moiré unit cell, with a moiré potential stronger than is conventionally assumed. Thus the observed correlated insulating phases in ABC-TLG aligned with h-BN cannot be understood through band folding of the ferromagnetic metal found without the moiré potential. For the topologically nontrivial regime, we discover the appearance of prominent incompressible states when fractional hole fillings (of the moiré unit cell) coincide with the occurrence of fractional-metallic states in the moiré-less setting, as well as a slight weakening of the ferromagnetic nature of the phases; however, this once again requires a moiré potential stronger than is conventionally assumed. Our findings highlight the importance of interactions in renormalizing the electronic band structure and emphasize the key role played by the moiré potential in determining the strong correlation physics.

$\mathrm{RbMn}{\mathrm{F}}_3$ is an insulating antiferromagnet with a perovskite crystal structure and Néel temperature $T_N=83\mathrm{K}$. Having magnetic ions with a S electronic ground state in a cubic arrangement, its magnetic anisotropy vanishes so that it is a nearly perfect three-dimensional Heisenberg antiferromagnet. Here, we report measurements of the spin Seebeck effect (SSE) in bulk samples of $\mathrm{RbMn}{\mathrm{F}}_3$ with the shape of a slab onto which a thin Pt film strip is deposited. By applying a thermal gradient perpendicular to the slab plane, we detect an electric voltage along the Pt strip due to the charge current resulting from the conversion of the thermally generated spin current by means of the inverse spin Hall effect. By varying the magnetic field applied on the plane of the slab, we observe the antisymmetric step variation typical of the SSE both in the spin-flop and paramagnetic phases. Surprisingly the SSE increases with temperature in the paramagnetic phase and becomes comparable to the one in the ordered phase. This enhancement is attributed to a combination of the free spin fluctuations of paramagnetic insulators with the thermal conduction of long-lived paramagnons made possible by the short-range order that persists above $T_N$.

We show that while an orbital magnetic field and disorder, acting individually, weaken superconductivity, acting together they produce an intriguing evolution of a two-dimensional type-II $s$-wave superconductor. For weak disorder, the critical field $H_c$ at which the superfluid density collapses is coincident with the field at which the superconducting energy gap gets suppressed. However, with increasing disorder these two fields diverge from each other, creating a pseudogap region with insulating vortex cores. Our results naturally explain two outstanding puzzles: the gigantic magnetoresistance peak observed as a function of magnetic field in thin disordered superconducting films and the disappearance of the celebrated zero-bias Caroli–de Gennes–Matricon peak in the local density of states at the vortex core in disordered superconductors.

We investigate the ultrafast carrier dynamics in a ZnO crystal irradiated by a strong, linearly polarized midinfrared laser pulse. Depending on the laser intensity, there exist two dominant light wave-driven processes, i.e., the electron-hole collision recombination and the electron-electron impact excitation. The corresponding optical signatures are high-order harmonic generation and stimulated emission, respectively. By adding a weak infrared or telecom wavelength laser pulse with an orthogonal polarization, we show that these two carrier dynamic processes can be effectively controlled by tuning the time delay between the two laser pulses. This all-optical control has an ultrafast speed, a low threshold, and a broad spectral responsiveness, which have implications in understanding the ultrafast carrier dynamics in the condensed matter and the design of next-generation optoelectronic switches.

The electronic and optical properties of layered materials, such as transition metal dichalcogenides, can be strongly affected by their dielectric environment—this phenomenon is also known as the image charge effect. In multilayers, the stacked crystal structure implies a layer-dependent variation of the image charge effect. However, this variation and its implications on the interlayer coupling are heretofore not well understood. Here, we show that the variation of dielectric screening effects in layered materials can be described by a macroscopic dielectric continuum model within classical electrostatics. We present an efficient method that incorporates this effect in electronic structure calculations. The present method is based on semi-empirical tight-binding and amenable to use for large-scale systems. By applying this method to multilayer ${\mathrm{MoS}}_2$, we find an energetic decoupling of the surface layer—at the K point of the Brillouin zone—which leads to the formation of a surface-layer band gap. More generally, our calculations reveal that the image charge effect can cause spatial modulation of the interlayer coupling by changing the band alignment between the layers.

A variety of compounds, for example, doped paraelectrics and polar metals, exhibit both ferroelectricity and correlated electronic phenomena such as low-density superconductivity and anomalous transport. Characterizing such properties is tied to understanding the quantum dynamics of inversion symmetry breaking in the presence of itinerant electrons. Here, we present a comprehensive analysis of the properties of a metal near a quantum critical transition to a ferroelectric state, in both two and three dimensions. Starting from a minimal model of electrons coupled to a transverse polar phonon via a Rashba-type spin-orbit interaction, we compute the dynamical response of both electrons and phonons. We find that the system can evince both Fermi and non-Fermi liquid phases, as well as enhanced pairing in both singlet and triplet channels. Furthermore, we systematically compute corrections to one-loop theory and find a tendency to quantum order-by-disorder, leading to a phase diagram that can include second-order, first-order, and finite-momentum phase transitions. Finally, we show that the entire phase diagram can be controlled via application of external strain, either compressive or volume-preserving. Our results provide a map of the dynamical and thermodynamical phase space of quantum ferroelectic metals, which can serve in characterizing existing materials and in seeking applications for quantum technologies.

The realization of chiral Majorana modes using heterostructures is a challenging task. A significant reason is that the previous theoretical models are simple and cannot capture the real physics among the interplay of superconductivity, magnetism, and the electrostatic environment. Beyond the well-known minimal models, we develop a self-consistent Schrödinger-Poisson method to include a key focus—the electrostatic effects induced by the gate control. We show that the electrostatic environment imposes constraints on both induced superconductivity and the effective magnetization, and therefore significantly changes the topological region compared to previous work. However, within our theory we identify the topological regimes supporting the chiral Majorana mode with practical tunability. Importantly, the induced superconductivity in the topological regime, contrary to traditional beliefs, will not be reduced by the presence of the magnetization. Our results deeply comprehend the real phase diagrams and parameter tunability of the actual devices in a chiral Majorana search.

The polariton-polariton interaction strength is an important parameter for all kinds of applications using the nonlinear properties of polaritons, such as optical switching and single-photon blockade devices. In this paper, we review and compare the results of a series of experiments on polariton-polariton interactions in $\mathrm{GaAs}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}$ microcavity polariton structures and present an updated analysis of these experiments. We show that not just the energy shift of the spectral lines but also the results of measurements sensitive to the polariton scattering rate are important for the calibration of the interaction parameter at low excitation density. We find that when adjustments are made to correct for recent understanding of the experiments, the value of the interaction parameter at low density is lower than previous reported, but still significantly higher than theoretically predicted.

Highly oriented pyrolytic graphite may be the only known monatomic crystal with the ability to host naturally formed moiré patterns on its cleaved surfaces, which are coherent over micrometer scales and with discrete sets of twist angles of fixed periodicity. Such an aspect is in marked contrast to twisted bilayer graphene and other multilayered systems, where the long-range coherence of the moiré is not easily maintained due to twist angle disorder. We investigate the electronic and mechanical response of coherent graphite moiré patterns through inducing external strain from scanning tunneling microscopy tip-induced deformation. Consequently, unique anisotropic mechanical characteristics are revealed. For example, a lateral widening of one-dimensional domain walls (DWs) bridging Bernal (ABA) and rhombohedral (ABC) stacking domains (A, B, and C refer to the atomic layer positioning), was indicated. Further, in situ tunneling spectroscopy as a function of the deformation indicated a tendency towards increased electrical conductance, which may be associated with a higher density of electronic states, and the consequent flattening of the electronic energy band dispersion. Such features were probed across the DWs, with implications for strain-induced electronic modulation of the moiré characteristics.

Recent theoretical studies showed that the electronic structure of $1T\text{−}{\mathrm{TaS}}_2$ in the low-temperature commensurate charge density wave phase exhibits a nontrivial interplay between band-insulating and Mott-insulating behavior. This has important implications for the interpretation of photodoping experiments. Here we use nonequilibrium dynamical mean-field theory simulations of a realistic multilayer structure to clarify the charge carrier dynamics induced by a laser pulse. The solution is propagated up to the picosecond timescale by employing a memory-truncation scheme. While long-lived doublons and holons only exist in the surface state of a specific structure, the disturbance of bonding states in the bilayers which make up the bulk of the system explain the almost instantaneous appearance of in-gap states. Our simulations consistently explain the coexistence of a doublon feature with a prominent “background” signal in previous time-resolved photoemission experiments, and they suggest strategies for the selective population of the in-gap and doublon states by exploiting the sensitivity to the pump polarization and pump frequency.

Structure in quantum entanglement entropy is often leveraged to focus on a small corner of the exponentially large Hilbert space and efficiently parametrize the problem of finding ground states. A typical example is the use of matrix product states for local and gapped Hamiltonians. We study the structure of entanglement entropy using persistent homology, a relatively new method from the field of topological data analysis. The inverse quantum mutual information between pairs of sites is used as a distance metric to form a filtered simplicial complex. Both ground states and excited states of common spin models are analyzed as an example. Furthermore, the effect of homology with different coefficients and boundary conditions is also explored. Beyond these basic examples, we also discuss the promising future applications of this modern computational approach, including its connection to the question of how space-time could emerge from entanglement.

We investigated the electronic structure of the enigmatic ${\mathrm{CeRh}}_3{\mathrm{B}}_2$ using resonant inelastic scattering and x-ray absorption spectroscopy in combination with ab initio density functional calculations. We find that the $\mathrm{Rh}4d$ states are irrelevant for the high-temperature ferromagnetism and the Kondo effect. We also find that the $\mathrm{Ce}4f$ crystal-field strength is too small to explain the strong reduction of the Ce magnetic moment. The data revealed instead the presence of two different active $\mathrm{Ce}4f$ orbitals, with each coupling selectively to different bands in ${\mathrm{CeRh}}_3{\mathrm{B}}_2$. The intersite hybridization of the $|J=\frac{5}{2},J_z=\pm \frac{1}{2}\rangle$ crystal-field state and $\mathrm{Ce}5d$ band combined with the intrasite $\mathrm{Ce}4f\text{–}5d$ exchange creates the strong ferromagnetism, while hybridization between the $|J=\frac{5}{2},J_z=\pm \frac{5}{2}\rangle$ and the B $sp$ in the $ab$-plane contributes to the Kondo interaction, which causes the moment reduction. This orbital selective coupling explains the unique and seemingly contradictory properties of ${\mathrm{CeRh}}_3{\mathrm{B}}_2$.

Stacking three monolayers of graphene with a twist generally produces two moiré patterns. A moiré of moiré structure then emerges at larger distance where the three layers periodically realign. We devise here an effective low-energy theory to describe the spectrum at distances larger than the moiré length scale. In each valley of the underlying graphene, the theory comprises one Dirac cone at the ${\mathrm{\Gamma }}_{\text{M}}$ point of the moiré Brillouin zone and two weakly gapped points at ${\mathbf{K}}_{\text{M}}$ and ${\mathbf{K}}_{\text{M}}^{\prime }$. The velocities and small gaps exhibit a spatial dependence in the moiré-of-moiré unit cell, entailing a non-Abelian connection potential which ensures gauge invariance. The resulting model is numerically solved and a fully connected spectrum is obtained, which is protected by the combination of time-reversal and twofold-rotation symmetries.

Magnetic rare-earth orthoferrites $R{\mathrm{FeO}}_3$ host a variety of functional properties from multiferroicity and strong magnetostriction to spin-reorientation transitions and ultrafast light-driven manipulation of magnetism, which can be exploited in spintronics and next-generation devices. Among these systems, ${\mathrm{SmFeO}}_3$ is attracting particular interest for its rich phase diagram and the high temperature Fe-spin magnetic transitions, which combines with a very low temperature and as yet unclear Sm-spin ordering. Various experiments suggest that the interaction between the Sm and Fe magnetic moments (further supported by the magnetic anisotropy), is at the origin of the complex cascade of transitions, but a conclusive and clear picture has not yet been reached. In this paper, by means of comprehensive first-principles calculations, we unravel the role of the magnetic Sm ions in the Fe-spin reorientation transition and in the detected anomalies in the lattice vibrational spectrum, which are a signature of a relevant spin-phonon coupling. By including both Sm-$f$ electrons and noncollinear magnetism, we find frustrated and anisotropic Sm interactions, and a large magnetocrystalline anisotropy mediated by the SOC of the Sm-$4f$ electrons, which drive the complex magnetic properties and phase diagram of ${\mathrm{SmFeO}}_3$.

We introduce a time-reversal-symmetric analog of the Hopf insulator that we call a spin Hopf insulator. The spin Hopf insulator harbors nontrivial Kane-Mele ${\mathbb{Z}}_2$ invariants on its surfaces, and is the first example of a nonmagnetic delicate topological insulator with spin-orbit coupling. We show that the Kane-Mele ${\mathbb{Z}}_2$ topology on the surface is generically unstable, but can be stabilized by the addition of a composition of the particle hole and spatial inversion symmetry. Such a symmetry not only protects the surface ${\mathbb{Z}}_2$ invariant, but also protects gapless helical hinge states on the spin Hopf insulator. Furthermore, we show that, in the presence of fourfold rotational symmetry, the spin Hopf insulator exhibits a returning Thouless pump, as well as surface states on sharp boundary terminations.

${\mathrm{Y}}_3{\mathrm{Cu}}_9{\left(\mathrm{OH}\right)}_{19}{\mathrm{Cl}}_8$ realizes an original anisotropic kagome model hosting a rich magnetic phase diagram [Hering et al., npj Comput. Mater. 8, 10 (2022)]. We present an improved synthesis of large phase-pure single crystals via an external gradient method. These crystals were investigated in detail by susceptibility, specific heat, thermal expansion, neutron scattering, and local $\mu \mathrm{SR}$ and NMR techniques. At variance with polycrystalline samples, the study of single crystals gives evidence for subtle structural instabilities at 33 and 13 K which preserve the global symmetry of the system and thus the magnetic model. At 2.1 K the compound shows a magnetic transition to a coplanar (1/3,1/3) long-range order as predicted theoretically. However, our analysis of the spin-wave excitations yields magnetic interactions which locate the compound closer to the phase boundary to a classical jammed spin-liquid phase. Enhanced quantum fluctuations at this boundary may be responsible for the strongly reduced ordered moment of the ${\mathrm{Cu}}^{2+}$.

Recent spectroscopic measurements in a number of strongly correlated metals that exhibit non-Fermi-liquid-like properties have observed evidence of anomalous frequency and momentum-dependent charge-density fluctuations. Specifically, in the strange metallic regime of the cuprate superconductors, there is a featureless particle-hole continuum exhibiting unusual power laws, and experiments suggest that the plasmon mode decays into this continuum in a manner that is distinct from the expectations of conventional Fermi liquid theory. Inspired by these experimental developments, we address the nature of low-energy collective modes and the particle-hole continua for different solvable lattice models of non-Fermi liquids that host a critical Fermi surface—a sharp electronic Fermi surface without any low-energy electronic quasiparticles. We scrutinize theoretically the possible existence of a long-lived zero-sound mode, which is renormalized to the plasma frequency in the presence of long-ranged Coulomb interactions, and its decay into the continuum over a wide range of frequencies and momenta. Quite remarkably, some of the models analyzed here can account for certain aspects of the universal experimental observations, that clearly lie beyond the purview of standard Fermi liquid theory.