We report a homotopic analysis of quantum states in two-dimensional (2D) polymorphs. Two typical models, namely the honeycomb-type and Shastry-Sutherland-type models, are continuously connected through a deformable herringbone lattice model having a nonsymmorphic group symmetry. The evolution of Dirac fermions is characterized within the phase space spanned by the deformation parameters. Our tight-binding models, based on single orbitals for each site with and without spin-orbit coupling (SOC), reveal how the SOC convolutes, the manner being important in facilitating the search and design of 2D topological insulators focused on the homotopic feature of symmetry-protected properties independent of specific materials.

We generalize the iterative diagonalization procedure adopted in the method of numerical renormalization group to analyze the Kondo effect in strong magnetic fields, where the density of states for itinerary electrons at the chemical potential varies discontinuously as the magnetic field changes. We first examine phases of many-body ground states in the presence of a single impurity. By investigating the change of the $z$ component of total spin, $\mathrm{\Delta }{S}_z$, and spin-spin correlation between the impurity and conduction electrons, we find that there are three states competing for the ground state when Zeeman splitting is present. One of the states is a doublet in which the impurity spin is unscreened. The other two states are Kondo screening states with $\mathrm{\Delta }{S}_z=\frac{1}{2}$ and 1, in which the impurity spin is partially screened and completely screened, respectively. For Kondo systems with two impurities in strong magnetic fields, we find that the interplay between the Kondo screening effect, Rudermann-Kittel-Kasuya-Yoshida interaction, and quantum oscillations due to Landau levels determines the ground state of the system. A combination of these three factors results in different screening scenarios for different phases in which spins of two impurities can form spin-0 or spin-1 states, while impurity spins in these phases can be either screened, partially screened, or unscreened by conduction electrons. The emergence of the ground state from these competing states oscillates with the change of magnetic field, chemical potential or inter-impurity distance. This leads to quantum oscillations in magnetization and conductivity. In particular, we find extra peak structures in longitudinal conductivity that reflect changes of Kondo screening phases and are important features to be observed in experiments. Our results provide a complete characterization of phases for Kondo effect in strong magnetic fields.

We compute the electric spin susceptibility of Bloch electrons with spin-orbit coupling to second order. We find that it is possible to generate a nonequilibrium spin polarization in the bulk of nonmagnetic inversion-symmetric materials using linearly polarized electric fields, but the process depends on interband coherence and produces heating. It may be possible to avoid heating with circular polarization in certain scenarios. The standard Edelstein effect and spin orientation effects are recovered in appropriate limits within the formalism. Finally, the electric spin susceptibility of metals has contributions proportional to spin multipole moments of the Fermi sea that dominate the low frequency spin response.

We study how polariton condensation modifies charge transport in organic materials. In typical organic materials, charge transport proceeds via incoherent hopping. We therefore provide an approach to determine how the rate and final state of this hopping process is affected by strong matter-light coupling and polariton condensation. We show how the hopping process may create excitations when starting from a state with a finite excitation density. That is, how hopping can change the state of a lower polariton condensate by creating upper polaritons, optically inactive excitonic dark states, or by exciting vibrational sidebands. While the matrix elements for these processes can be large, for typical materials at room temperature, such excitations are suppressed by thermal factors, and ground-state processes dominate. We thus study how the ground-state hopping rate depends on condensate density, matter-light coupling, and cavity photon detuning. All these factors change the vibrational configuration associated with the optically active molecules, which can enhance or suppress hopping by increasing or decreasing the vibrational overlap with the state of a charged molecule. We show that hopping rates can be exponentially sensitive to detuning and condensate density, allowing an increase or decrease of hopping rate by two orders of magnitude.

Maxwell's boundary conditions (MBCs) were long known to be insufficient to determine the optical responses of spatially dispersive medium. Supplementing MBCs with additional boundary conditions (ABCs) has become a normal yet controversial practice. Here, the problem of ABCs is solved by analyzing some subtle aspects of a physical surface. A generic theory is presented for handling the interaction of light with the surfaces of an arbitrary medium and applied to study the traditional problem of exciton polaritons. We show that ABCs can always be adjusted to fit the theory in the examples studied here but they can by no means be construed as intrinsic surface characteristics, which are instead captured by a surface scattering amplitude. Methods for experimentally extracting the spatial profile of this quantity are proposed.

NMR techniques have been used to investigate the dynamics of highly degenerate ${}^3\mathrm{He}$ confined to the interior of ${}^4\mathrm{He}$ plated nanotubes of MCM-41 (Mobil Composition Matter No. 41). The ${}^3\mathrm{He}$ line density was $0.93\pm 0.10{\mathrm{nm}}^{-1}$, corresponding to a Fermi degeneracy temperature of $T_F\approx 0.1$ K. Experiments conducted down to 10 mK reveal a linear temperature dependence of the nuclear spin-lattice relaxation for $T<T_F$, following a peak at $2T_F$, which are hallmarks of Luttinger liquid physics.

We study the dynamics of multimode polariton lasing in organic microcavities by using a second-order cumulant equation approach. By inspecting the time evolution of the photon mode occupations, we show that if multiple lasing peaks are observed in time-integrated mode occupations, the reason can be either bimodal lasing or temporal switching between several modes. The former takes place within a narrow range of parameters while the latter occurs more widely. We find that the origin of the temporal switching is different in the weak- and strong-coupling regimes. At weak coupling the different gradients of mode occupation vs pump power is the determining factor, while for strong coupling it is changes in the eigenmodes and gain spectrum upon pumping. This difference is revealed by investigating the photoluminescence and momentum-resolved gain spectra. Our results underscore the importance of understanding the time evolution of the populations when characterizing the lasing behavior of a multimode polariton system, and show how these features differ between weak and strong coupling.

The Landauer formula provides a general scattering formulation of electrical conduction. Despite its utility, it has been mainly applied to the linear-response regime, and a scattering theory of nonlinear response has yet to be fully developed. Here, we extend the Landauer formula to the nonlinear-response regime. We show that while the linear conductance is directly related to the transmission probability, the nonlinear conductance is given by its derivatives with respect to energy. This sensitivity to the energy derivatives is shown to produce unique nonlinear transport phenomena of mesoscopic systems including disordered and topological materials. By way of illustration, we investigate nonlinear conductance of disordered chains and identify their universal behavior according to symmetry. In particular, we find large singular nonlinear conductance for zero modes, including Majorana zero modes in topological superconductors. We also show the critical behavior of nonlinear response around the mobility edges due to the Anderson transitions. Moreover, we study nonlinear response of graphene as a prime example of topological materials featuring quantum anomaly. Furthermore, considering the geometry of electronic wave functions, we develop a scattering theory of the nonlinear Hall effect. We establish a new connection between the nonlinear Hall response and the nonequilibrium quantum fluctuations. We also discuss the influence of disorder and Anderson localization on the nonlinear Hall effect. Our work opens a new avenue in quantum physics beyond the linear-response regime.

The interaction-driven quantum anomalous Hall (QAH) insulator has been sought for a long time in a Dirac semimetal with linear band touching points at the Fermi level. By combining exact diagonalization, density matrix renormalization group, and analytical methods, we study a spinless fermion system on the checkerboard lattice with twofold rotational symmetry, which realizes two Dirac band touching points in the absence of interaction. At weak coupling, the Dirac semimetal is stable. At a finite density-density repulsive interaction, we analyze possible symmetry broken states, and find that an QAH state is stabilized when the interaction strength exceeds the energy scale controlling the separation between the Dirac points. Through numerical simulations, we verify the existence of the QAH phase with spontaneous time-reversal symmetry breaking and quantized Chern number $C=1$.

We propose a method to compute spectral functions of generic Hamiltonians using the density matrix renormalization group (DMRG) algorithm directly in the frequency domain, based on a modified Krylov-space decomposition to compute the correction vectors. Our approach entails the calculation of the root-$N$ ($N=2$ is the standard square root) of the Hamiltonian propagator using Krylov-space decomposition and repeating this procedure $N$ times to obtain the actual correction vector. We show that our method greatly alleviates the burden of keeping a large bond dimension at large target frequencies, a problem found with conventional correction-vector DMRG, whereas achieving better computational performance at large $N$. We apply our method to spin and charge spectral functions of $t\text{−}J$ and Hubbard models in the challenging two-leg ladder geometry and provide evidence that the root-$N$ approach reaches a much improved spectral resolution compared to the conventional correction vector.

Presently, the unusual quantum phenomena recently discovered in intrinsic antiferromagnetic topological insulators are far from being fully understood. Motivated by recent controversial ARPES results on the ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ family compounds, we theoretically study the underlying physics of spectral properties of such materials. By using a continual model, we address the issue of the topological surface fermions which simultaneously experience an exchange field of a regular antiferromagnetic alignment and a surface electrostatic potential. The emergent net exchange field acting on the surface state is shown to depend on the surface potential strength, of which variation could be associated with concentration fluctuations of antisite and other defects that are inevitably present in ${\mathrm{MnBi}}_2{\mathrm{Te}}_4$ material. In this scenario, we discuss the possible microscopic mechanism for change of both size and sign of the surface exchange gap from sample to sample. Furthermore, we provide a natural explanation for the appearance of a finite density of states inside the exchange gap in the case of strong fluctuations in the surface potential. Thus, our results allow for a unified interpretation of various spectroscopic measurements on intrinsic antiferromagnetic topological insulators.

We investigate the electronic dispersion and transport properties of graphene/${\mathrm{WSe}}_2$ heterostructures in the presence of a proximity-induced spin-orbit coupling ${\lambda }_v$, sublattice potential $\mathrm{\Delta }$, and an off-resonant circularly polarized light of frequency $\mathrm{\Omega }$ that renormalizes $\mathrm{\Delta }$ to ${\overline{\mathrm{\Delta }}}_{\eta p}=\mathrm{\Delta }+\eta p{\mathrm{\Delta }}_{\mathrm{\Omega }}$ with $\eta$ and $p$ the valley and polarization indices, respectively, and ${\mathrm{\Delta }}_{\mathrm{\Omega }}$ the gap due to the off-resonant circularly polarized light. Using a low-energy Hamiltonian we find that the interplay between different perturbation terms leads to inverted spin-orbit coupled bands. At high $\mathrm{\Omega }$ we study the band structure and dc transport using the Floquet theory and linear response formalism, respectively. We find that the inverted band structure transfers into the direct band one when the off-resonant light is present. The valley-Hall conductivity behaves as an even function of the Fermi energy in the presence and absence of this light. At ${\mathrm{\Delta }}_{\mathrm{\Omega }}$ = ${\lambda }_v$ – $\mathrm{\Delta }$, a transition occurs from the valley-Hall phase to the anomalous Hall phase. In addition, the valley-Hall conductivity switches sign when the polarization of the off-resonant light changes. The valley polarization vanishes for ${\mathrm{\Delta }}_{\mathrm{\Omega }}$ = 0 but it is finite for ${\mathrm{\Delta }}_{\mathrm{\Omega }}\ne$ 0 and reflects the lifting of the valley degeneracy of the energy levels, for ${\mathrm{\Delta }}_{\mathrm{\Omega }}\ne 0$, when the off-resonant light is present. The corresponding spin polarization, present for ${\mathrm{\Delta }}_{\mathrm{\Omega }}$ = 0, increases for ${\mathrm{\Delta }}_{\mathrm{\Omega }}\ne$ 0. Further, pure $K$ or $K^{\prime }$ valley polarization is generated when ${\mathrm{\Delta }}_{\mathrm{\Omega }}$ changes sign. Also, the charge Hall conductivity is finite for ${\mathrm{\Delta }}_{\mathrm{\Omega }}\ne 0$ and changes sign when the handedness of the light polarization changes.

Motivated by a recent experiment (Y. Zhang et al., arXiv:2205.05087), we investigate a possible mechanism that enhances superconductivity in hole-doped Bernal bilayer graphene due to a proximate ${\mathrm{WSe}}_2$ monolayer. We show that the virtual tunneling between ${\mathrm{WSe}}_2$ and Bernal bilayer graphene, which is known to induce Ising spin-orbit coupling, can generate an additional attraction between two holes, providing a potential explanation for enhancing superconductivity in Bernal bilayer graphene. Using microscopic interlayer tunneling, we derive the Ising spin-orbit coupling and the effective attraction as functions of the twist angle between Bernal bilayer graphene and the ${\mathrm{WSe}}_2$ monolayer. Our theory provides an intuitive and physical explanation for the intertwined relation between Ising spin-orbit coupling and superconductivity enhancement, which should motivate future studies.

Layered ruthenates are a unique class of systems which manifest a variety of electronic and magnetic features from competing energy scales. At the heart of such features lies multi-orbital physics, especially orbital-selective behavior. Here, we propose that the ${\mathrm{SrRuO}}_3-{\mathrm{SrTiO}}_3$ heterostructure is a highly tunable platform to obtain the various emergent properties. Employing the density functional theory plus dynamical mean-field theory, we thoroughly investigate the orbital-dependent physics of the system and identify the competing magnetic fluctuations. We show that the epitaxial strain drives the system towards multi-orbital or orbital selective Mott phases from the Hund metal regime. At the same time, the two different types of static magnetism, ferromagnetism and checkerboard antiferromagnetism, are stabilized from the competition with the spin-density wave instability.

Voltage/electric-field control of ultrafast magnetization dynamics in magnetoelectrics provides a novel avenue for electronic tuning with orders of magnitude less power consumption, improved tuning response time, and more compact form factor, compared with conventional magnetic field control of magnetization dynamics. Magnetoelectrically tuned laser-driven magnetization dynamics has the potential to enable the next generation of optomagnetic devices from THz communication to optical magnetic recording. In this study, we fabricated a magnetoelectric heterostructure, specifically ferromagnetic ${\left({\mathrm{Fe}}_{81}{\mathrm{Ga}}_{19}\right)}_{88}{\mathrm{B}}_{12}$ (FeGaB) thin film deposited on a $\mathrm{Pb}\left({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}\right){\mathrm{O}}_3\text{−}\mathrm{PbTi}{\mathrm{O}}_3$ ferroelectric substrate, to explore the electric field tuning of ultrafast demagnetization and to understand how magnetic anisotropy changes postdemagnetization. We characterized the magnetoelectric coupling of our heterostructure to demonstrate the static and dynamic magnetization tunability with an applied electric field. We utilized the time-resolved magneto-optic Kerr effect to understand the ultrafast demagnetization process under different applied electric fields and magnetic fields. The typically observed strain-induced magnetic easy-axis rotation in a ferromagnetic/ferroelectric heterostructure was also observed to tune the ultrafast demagnetization of FeGaB in our experiment. Additionally, we found that the magnetization rotation can be achieved with a lower electric field compared with static tuning without laser heating. Furthermore, we observed the hysteresis loops postultrafast demagnetization and found that the magnetoelectric heterostructure exhibits a mixture of volatile and nonvolatile behaviors. These findings shed light on the potential of our magnetoelectric heterostructure for ultrafast optomagnetic devices and electric field tuning of spintronic THz emitters.

The effect of the cationic redistribution on the complex spinel structure and magnetic properties were investigated in ${\mathrm{Zn}}_{0.7}{\mathrm{Cu}}_{0.3}{\mathrm{Fe}}_2{\mathrm{O}}_4$ ferrite. X-ray photoelectron spectroscopy and x-ray diffraction studies revealed that the system exhibits a mixed spinel structure with ${\mathrm{Fe}}^{3+}, {\mathrm{Zn}}^{2+}$, and ${\mathrm{Cu}}^{2+}$ occupying both tetrahedral and octahedral sublattices. The DC magnetization results revealed the absence of long-range magnetic order in the system. Furthermore, the AC susceptibility data analysis using dynamic scaling laws suggests that the system exhibits magnetic relaxation below two different temperatures: (i) a spin-glass–like transition at low temperature ($\sim 49.2\mathrm{K}$) with critical exponent 10.3 and spin-flip time $\sim {10}^{-11}\mathrm{s}$, and (ii) a cluster-glass–like transition at higher temperature ($\sim 317\mathrm{K}$) with critical exponent 4.6 and spin-flip time $\sim {10}^{-10}\mathrm{s}$. The existence of glassy behavior and magnetic memory effects below the spin-glass transition temperature proves that the system is in nonequilibrium dynamical state. The coexistence of spin-glass and cluster-glass along with the thermal hysteresis between these two transitions could widen the technological applications of these systems.

Motivated by dipolar-coupled artificial spin systems, we present a theoretical study of the classical $J_1\text{−}{J}_2\text{−}{J}_3$ Ising antiferromagnet on the kagome lattice. We establish the ground-state phase diagram of this model for $J_1>|J_2|,|J_3|$ based on exact results for the ground-state energies. When all the couplings are antiferromagnetic, the model has three macroscopically degenerate ground-state phases, and using tensor networks, we can calculate the entropies of these phases and of their boundaries very accurately. In two cases, the entropy appears to be a fraction of that of the triangular lattice Ising antiferromagnet, and we provide analytical arguments to support this observation. We also notice that, surprisingly enough, the dipolar ground state is not a ground state of the truncated model, but of the model with smaller $J_3$ interactions, an indication of a very strong competition between low-energy states in this model.