The computation of determinants plays a central role in diagrammatic Monte Carlo algorithms for strongly correlated systems. The evaluation of large numbers of determinants can often be the limiting computational factor determining the number of attainable diagrammatic expansion orders. In this work we build on the algorithm presented in [K. Griffin and M. J. Tsatsomeros, Principal minors, part i: A method for computing all the principal minors of a matrix, Linear Algebra Appl. 419, 107 (2006)] which computes all principal minors of a matrix in $O\left(2^n\right)$ operations. We present multiple generalizations of the algorithm to the efficient evaluation of certain subsets of all principal minors with immediate applications to connected determinant diagrammatic Monte Carlo within the normal and symmetry-broken phases as well as continuous-time quantum Monte Carlo. Additionally, we improve the asymptotic scaling of diagrammatic Monte Carlo formulated in real time to $O\left(2^n\right)$ and report speedups of up to a factor 25 at computationally realistic expansion orders. We further show that all permanent principal minors, corresponding to sums of bosonic Feynman diagrams, can be computed in $O\left(3^n\right)$, thus encouraging the investigation of bosonic and mixed systems by means of diagrammatic Monte Carlo.

We theoretically study magnon-phonon hybrid excitations (magnon polarons) in two-dimensional antiferromagnets on a honeycomb lattice. With an in-plane Dzyaloshinskii-Moriya interaction (DMI) allowed from mirror symmetry breaking from phonons, we find nontrivial Berry curvature around the anticrossing rings among the magnon and both optical and acoustic phonon bands, which gives rise to finite Chern numbers. We show that the Chern numbers of the magnon-polaron bands can be manipulated by changing the magnetic field direction or strength. We evaluate the thermal Hall conductivity reflecting the nontrivial Berry curvatures of magnon polarons and propose a valley Hall effect resulting from spin-induced chiral phonons as a possible experimental signature. Our study complements prior work on magnon-phonon hybridized systems without optical phonons and suggests possible applications in spin caloritronics with topological magnons and chiral phonons.

Chiral phonons were initially proposed and further verified experimentally in two-dimensional (2D) hexagonal crystal lattices. Many intriguing features brought about by chiral phonons are attributed to the pseudoangular momenta which are associated with the threefold rotational symmetry of hexagonal lattices. Here, we go beyond the hexagonal crystals and investigate the chiral phonons in systems with fourfold rotational symmetry. We clarify the symmetry requirements for the emergence of chiral phonons in both 2D square lattices and three-dimensional tetragonal lattices. For two dimensions, the realization of $C_4$ chiral phonons requires the breaking of time-reversal symmetry; while for three dimensions, they can exist on the $C_4$-invariant path in a chiral tetragonal lattice. These phonons have the advantage that they can be more readily coupled with optical transitions, which facilitates their experimental detection. We demonstrate our idea via model analysis and first-principles calculations of concrete materials, including the MnAs monolayer and the $\alpha$-cristobalite. Our work reveals chiral phonons beyond the hexagonal lattices and paves the way for further exploration of chiral phonon physics in square/tetragonal materials and metamaterials.

Lateral heterostructures of atomic layered materials alter the electronic properties of pristine crystals and provide a possibility to produce useful monolayer materials. We reveal that metal-semiconductor-metal lateral heterojunctions of $1H$-transition-metal dichalcogenides intrinsically possess conducting channels of electrons with spin-valley locking without any extrinsic fabrication breaking the crystal symmetry, e.g., gate electrodes. We theoretically investigate the electronic structure and transport properties of lateral heterojunctions and show that the heterostructure produces conducting channels through the $K$ and $K^{\prime }$ valleys in the semiconducting transition-metal dichalcogenides and restricts the spin of the conducting electrons in each valley due to the valley-dependent charge transfer effect. Moreover, the theoretical investigation shows that the heterojunction of ${\mathrm{WSe}}_2$ realizes a high transmission probability for valley-spin locked electrons even in a long semiconducting region. The heterojunction also provides a useful electronic transport property, a steplike I-V characteristic.

The spin conductance of two-dimensional topological insulators (2D TIs) is not expected to be quantized in the presence of perturbations that break the spin-rotational symmetry. However, the deviation from the pristine-limit quantization has yet to be studied in detail. In this paper, we define the spin current operator for the helical edge modes of a 2D TI and introduce a four-terminal setup to measure spin conductances. Using the developed formalism, we consider the effects of disorder terms that break spin-rotational symmetry or give rise to edge-to-edge coupling. We identify a key role played by spin torque in an out-of-equilibrium edge. We then utilize a tight-binding model of topological monolayer ${\mathrm{WTe}}_2$ and scattering matrix formalism to numerically study spin transport in a four-terminal 2D TI device. In particular, we calculate the spin conductances and characteristic spin decay length in the presence of magnetic disorder. In addition, we study the effects of interedge scattering in a quantum point contact geometry. We find that the spin Hall conductance is surprisingly robust to spin symmetry-breaking perturbations, as long as time-reversal symmetry is preserved and interedge scattering is weak.

Discrete lattice models are a cornerstone of quantum many-body physics. They arise as effective descriptions of condensed-matter systems and lattice-regularized quantum field theories. Lieb-Robinson bounds imply that if the degrees of freedom at each lattice site only interact locally with each other, correlations can only propagate with a finite group velocity through the lattice, similarly to a light cone in relativistic systems. Here we show that Lieb-Robinson bounds are equivalent to the locality of the interactions: a system with $k$-body interactions fulfills Lieb-Robinson bounds in exponential form if and only if the underlying interactions decay exponentially in space. In particular, our result already follows from the behavior of two-point correlation functions for single-site observables and generalizes to different decay behaviors as well as fermionic lattice models. As a side result, we thus find that Lieb-Robinson bounds for single-site observables imply Lieb-Robinson bounds for bounded observables with arbitrary support.

The incommensurate ${30}^{\circ }$ twisted bilayer graphene (BG) possesses both relativistic Dirac fermions and quasiperiodicity with 12-fold rotational symmetry arising from the interlayer interaction [Ahn et al., Science 361, 782 (2018) and Yao et al., Proc. Natl. Acad. Sci. USA 115, 6928 (2018)]. Understanding how the interlayer states interact with each other is of vital importance for identifying and subsequently engineering the quasicrystalline order in the layered structure. Herein, via symmetry and group representation theory we unravel the interlayer hybridization selection rules governing the interlayer coupling in both untwisted and twisted BG systems. Compared with the only allowed equivalent hybridization in $D_{6h}$ untwisted BG, $D_6$ twisted BG permits equivalent and mixed hybridizations, and $D_{6d}$ graphene quasicrystal allows both equivalent and nonequivalent hybridizations. The energy-dependent hybridization strengths in graphene quasicrystal and $D_6$ twisted BG show two remarkable characteristics: (i) near the Fermi level the weak hybridization owing to the relatively large energy difference between Dirac bands from top and bottom layers, and (ii) in high-energy regions the electron-hole asymmetry of hybridization strength with stronger interlayer coupling for holes, which arises from the non-nearest-neighbor interlayer hoppings and the wave-function phase difference between pairing states. These hybridization-generated band structures and their hybridization strength characteristics are verified by the calculated optical conductivity spectra. Our theoretical study paves a way for revealing the interlayer hybridization in van der Waals layered systems.

Stoner and Heisenberg excitations in magnetic materials are inherently different. The first involves an effective reduction of the exchange splitting, whereas the second comprises excitation of spin waves. In this work, we test the impact of these two excitations in the hybrid Stoner-Heisenberg system of FePd. We present a microscopic picture of ultrafast demagnetization dynamics in this alloy, which represents both components of strong local exchange splitting in Fe and induced polarization in Pd. We identify the spin-orbit coupling (SOC) and the optical intersite spin transfer (OISTR) as the two dominant factors for demagnetization at ultrashort timescales. Remarkably, the drastic difference in the origin of the magnetic moment of the Fe and Pd species is not deciding the initial magnetization dynamics in this alloy. By tuning the external laser pulse, the extrinsic OISTR can be manipulated for site-selective demagnetization on femtosecond timescales providing the fastest way for optical and selective control of the magnetization dynamics in alloys. Saliently, our results signify why various experiments demonstrating OISTR might obtain conflicting results.

When the particle size of a metal is reduced, it is expected that an energy gap will open due to the quantum size effect. However, the energy gap in platinum (Pt) metal nanoparticles has not been observed directly by nuclear magnetic resonance (NMR). To investigate the particle size dependence of the electronic state of Pt nanoparticles, we performed ${}^{195}\mathrm{Pt}$ NMR experiments on thiol-capped Pt nanoparticles with three different average diameters of less than 3 nm. For the nanoparticles with a diameter of 2.8 nm, we observed usual metallic behavior with a smaller density of states than that of the bulk Pt. In contrast, the temperature dependence of $1/T_{1}T$ in nanoparticles less than 2.5 nm in diameter is an activation-energy form above 150 K, which is semiconducting behavior with an energy gap of the order of 2000 K. The significant decrease in $1/T_{1}T$ by more than two orders of magnitude in the smaller Pt nanoparticles compared to the bulk Pt is attributable to the disappearance of the density of states at the Fermi energy, which is consistent with the opening of an energy gap. These results indicate a metal-insulator transition below 2.5 nm in diameter is present in our thiol-capped Pt nanoparticle samples. The effect of the thiol capping on the electronic structure suggested by the experimental results is also discussed.

Couplings between different ferroics in two-dimensional (2D) materials, with atomic thickness and van der Waals surface, have been long sought but not yet realized. Here we show the first-principles evidence of unique triferroic couplings in recently synthesized ${\mathrm{CrI}}_2$ monolayer. Its ferroelasticity with a low switching barrier stems from the Jahn-Teller effect. When coupled with the interaction of a substrate, a type of interfacial ferroelectricity with direction determined by the ferroelastic states can emerge which can be switched following the same low-barrier pathway of ferroelastic switching. The direction of its striped antiferromagnetism is also governed by its ferroelastic states, leading to a coupling of ferroelasticity, ferroelectricity, and magnetism. Such mechanism of multiferroic couplings, denoted as interfacial Jahn-Teller triferroicity, can be applied to other 2D materials such as ${\mathrm{CuCl}}_2$ and their Janus monolayers, enabling electrical manipulation of spintronics for efficient nonvolatile random-access memories.

Bose-Einstein condensation (BEC) of triplet excitations triggered by a magnetic field, sometimes called magnon BEC, in dimerized antiferromagnets gives rise to a long-range antiferromagnetic order in the plane perpendicular to the applied magnetic field. To explore the effects of spin-orbit coupling on magnon condensation, we study a spin model on a distorted honeycomb lattice with dimerized Heisenberg exchange ($J$ terms) and uniform off-diagonal exchange (${\mathrm{\Gamma }}^{\prime }$ terms) interactions. Via variational Monte Carlo calculations and spin-wave theory, we find that an out-of-plane magnetic field can induce different types of long-range magnetic orders, no matter if the ground state is a nonmagnetic dimerized state or an ordered Néel state. Furthermore, the critical properties of field-driven phase transitions in the presence of spin-orbit couplings, as illustrated from the spin-wave spectrum and interpreted by the effective field theory, can be different from the conventional magnon BEC. Our study is helpful to understand the rich phases of spin-orbit coupled antiferromagnets induced by magnetic fields.

The Heisenberg pyrochlore antiferromagnet ${\mathrm{Gd}}_2{\mathrm{Pt}}_2{\mathrm{O}}_7$ is one of a series of gadolinium pyrochlore compounds with a variety of B-site cations. Despite the expected simplicity of a spin-only ${\mathrm{Gd}}^{3+}$ Heisenberg interaction model, the gadolinium pyrochlore series exhibits various complex magnetic ground states at low temperature. ${\mathrm{Gd}}_2{\mathrm{Pt}}_2{\mathrm{O}}_7$ displays the highest temperature magnetic order of the series with $T_N=1.6$ K, which has been attributed to enhanced superexchange pathways facilitated by empty $5d{e}_g$ Pt orbitals. In this study, we use various neutron scattering techniques on an isotopically enriched polycrystalline ${}^{160}\mathrm{Gd}{}_2{\mathrm{Pt}}_2{\mathrm{O}}_7$ sample to examine the magnetic structure and spin-wave excitation spectrum below $T_N$ in order to extract the dominant exchange interactions. We find that the ground-state magnetic structure is the Palmer-Chalker state previously seen in ${\mathrm{Gd}}_2{\mathrm{Sn}}_2{\mathrm{O}}_7$ with an associated gapped excitation spectrum consistent with enhanced exchange interactions between further near-neighbor ${\mathrm{Gd}}^{3+}$ ions. We confirm this exchange model with analysis of the magnetic diffuse scattering in the paramagnetic regime using polarized neutrons.

Strategies for tuning the thermal conductivity of crystals by means of external fields are rare. Here, we predict the existence of large magnetophononic effects in materials that undergo antiferromagnetic (AFM) $\leftrightarrow$ ferromagnetic (FM) phase transitions, which allow for the modulation of the lattice heat conductivity, ${\kappa }_L$, via the application of magnetic fields. Specifically, by using first-principles methods we predict a large and anomalous ${\kappa }_L$ increase of $\approx 40\%$ for the metamagnetic phase transition occurring in bulk FeRh near room temperature. The disclosed magnetophononic effects are caused by large anharmonic spin-phonon couplings, namely, significant differences in the phase space of allowed phonon-phonon collision processes taking place in the respective AFM and FM phases.

Under what conditions does a superconductor inherit topologically protected nodes from its parent normal state? In the context of inter-Fermi-surface pairing in three-dimensional Weyl semimetals with broken time-reversal symmetry, the pairing order parameter is classified by monopole harmonics and is necessarily nodal [Li and Haldane, Phys. Rev. Lett. 120, 067003 (2018)]. Here, we show that a similar conclusion could also be drawn for 2D Dirac semimetals, although the conditions for the existence of nodes are more complex, depending on the pairing matrix structure in the valley and sublattice space. We analytically and numerically analyze the Bogoliubov-de Gennes quasiparticle spectra for Dirac systems based on the monolayer as well as twisted bilayer graphene. We find that in the cases of intravalley intrasublattice and intervalley intersublattice pairings, the point nodes in the BdG spectra (which are inherited from the Dirac cone in the normal state) are protected by a 1D winding number. The nodal structure of the superconductivity is confirmed numerically using tight-binding models of monolayer and twisted bilayer graphene. Notably, the BdG spectrum is nodal even with a momentum-independent “bare” pairing, which, however, acquires a momentum dependence and point nodes upon projection to the Bloch states on the topologically nontrivial Fermi surface, similar in spirit to the Li-Haldane monopole superconductor and the Fu-Kane proximity-induced superconductor on the surface of a topological insulator.

We performed scanning tunneling microscopy/spectroscopy (STM/STS) measurements to investigate the superconducting properties of single-layer FeSe grown on ${\text{SrTiO}}_3$ (STO) $\left(001\right)\text{−}(\sqrt{13}\times \sqrt{13})$. We found “$+$” and “z” patterns arranged in $\sqrt{13}\times \sqrt{13}$ periodicity in the STM images. Surprisingly, they show $C_2$ symmetry, although free-standing FeSe itself has $C_4$ symmetry. STS spectra and quasiparticle interference patterns near the Fermi level also indicate the broken $C_4$ symmetry with the superconducting gap showing a local variation within the STO surface unit cell because of the short coherence length. This clearly shows the non-negligible role of the substrate surface in the superconductivity of the FeSe/STO system.

Measurements of the thermal Hall conductivity in hole-doped cuprates have shown that phonons acquire chirality in a magnetic field both in the pseudogap phase and in the Mott insulator state. The microscopic mechanism at play is still unclear. A number of theoretical proposals are being considered including skew scattering of phonons by various defects, the coupling of phonons to spins, and a state of loop-current order with the appropriate symmetries, but more experimental information is required to constrain theoretical scenarios. Here we present our study of the thermal Hall conductivity ${\kappa }_{\mathrm{xy}}$ in the electron-doped cuprates ${\mathrm{Nd}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$ and ${\mathrm{Pr}}_{2-x}{\mathrm{Ce}}_x{\mathrm{CuO}}_4$ for dopings across the phase diagram, from $x=0$ in the insulating antiferromagnetic phase up to $x=0.17$ in the metallic phase above optimal doping. We observe a large negative thermal Hall conductivity at all dopings in both materials. Since heat conduction perpendicular to the ${\mathrm{CuO}}_2$ planes is dominated by phonons, the large thermal Hall conductivity we observe in electron-doped cuprates for a heat current in that direction must also be due to phonons, as in hole-doped cuprates. However, the degree of chirality, measured as the ratio $|{\kappa }_{\mathrm{xy}}/{\kappa }_{\mathrm{xx}}|$ where ${\kappa }_{\mathrm{xx}}$ is the longitudinal thermal conductivity, is much larger in the electron-doped cuprates. We discuss various factors that may be involved in the mechanism that confers chirality to phonons in cuprates, including short-range spin correlations.