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The manganese pnictide CaMn$_2$Bi$_2$, with Mn atoms arranged in a puckered honeycomb structure, exhibits narrow-gap antiferromagnetism, and it is currently a promising candidate for the study of complex electronic and magnetic phenomena, such as magnetotransport effects and potential spin spirals under high pressure. In this paper, we perform a detailed research of the magnetic properties of CaMn$_2$Bi$_2$ using density functional theory (DFT) combined with the Hubbard U correction and spin-orbit coupling, which accurately describe the magnetic interactions. Our results obtained for a large number of magnetic configurations are accurately captured by a modified Heisenberg model that includes on-site magnetization terms to describe magnetic energy excitations. We further investigate the role of the spin-orbit coupling, and find that the magnetic anisotropy of CaMn$_2$Bi$_2$ shows an easy plane, with the preferred magnetization direction being exchanged between axes in the plane by applying small strain values. This strain-tunable magnetization, driven by the interplay between spin-orbit interactions and lattice distortions, highlights the potential for controlling magnetic states in Mn-pnictides for future applications in spintronic and magnetoelectric devices.

We theoretically study the impact of light-driven structural changes via nonlinear phononics on the magnetic order of untwisted bilayer van der Waals materials. We consider an illustrative example of the AA-stacked bilayer honeycomb lattice and show that high-intensity light in resonance with selected phonons induces large amplitude phonon displacements that modify the magnetic Hamiltonian of the system. We performed a group theory analysis to identify the vibrational modes of the honeycomb bilayer and the nonlinear couplings among them in the strongly driven regime. We find that the structural changes in the strongly driven regime lower the symmetry relative to the equilibrium lattice and produce changes in the magnetic interactions between the local moments. In particular, the lattice symmetry changes permit a non-zero interlayer Dzyaloshinskii-Moriya interaction that induces a magnetic state with canted local moments. Using a spin-wave analysis about the new magnetic configuration we study the corresponding changes in the magnon spectrum and identify a protocol for engineering topological band transitions using a combination of nonlinear phononics and an external magnetic field. Our work suggests a strategy to induce interlayer Dyzaloshinskii-Moriya interactions in a class of layered van der Waals materials, the effect of which is to modify the magnetic ground state, magnon dispersions, and related band geometric properties, including topological invariants.

We theoretically study the conditions under which a spin Nernst effect - a transverse spin current induced by an applied temperature gradient - can occur in a canted antiferromagnetic insulator, such as ${\rm LaFeO_3}$ and other materials of the same family. The spin Nernst effect may provide a microscopic mechanism for an experimentally observed anomalous thermovoltage in ${\rm LaFeO_3}$/Pt heterostructures, where spin is transferred across the insulator/metal interface when a temperature gradient is applied to ${\rm LaFeO_3}$ parallel to the interface [W. Lin ${\it et \; al}$, Nat. Phys. ${\bf 18}$, 800 (2022)]. We find that ${\rm LaFeO_3}$ exhibits a topological spin Nernst effect when inversion symmetry is broken on the axes parallel to both the applied temperature gradient and the direction of spin transport, which can result in a spin injection across the insulator/metal interface. Our work provides a general derivation of a symmetry-breaking-induced spin Nernst effect, which may open a path to engineering a finite spin Nernst effect in systems where it would otherwise not arise.

Circularly polarized lattice vibrations carry angular momentum and lead to magnetic responses in applied magnetic fields or when resonantly driven with ultrashort laser pulses. Recent measurements have found responses that are orders of magnitude larger than those calculated in prior theoretical studies. Here, we present a microscopic model for the effective magnetic moments of chiral phonons in magnetic materials that is able to reproduce the experimentally measured magnitudes and that allows us to make quantitative predictions for materials with giant magnetic responses using microscopic parameters. Our model is based on orbit-lattice couplings that hybridize optical phonons with orbital electronic transitions. We apply our model to two types of materials: $4f$ rare-earth halide paramagnets and $3d$ transition-metal oxide magnets. In both cases, we find that chiral phonons can carry giant effective magnetic moments of the order of a Bohr magneton, orders of magnitude larger than previous predictions.

We have studied the magnetic response of transverse optical phonons in Pb$_{1-x}$Sn$_{x}$Te films. Polarization-dependent terahertz magnetospectroscopy measurements revealed Zeeman splittings and diamagnetic shifts, demonstrating that these phonon modes become chiral in magnetic fields. Films in the topological crystalline insulator phase ($x > 0.32$) exhibited magnetic moment values that are larger than those for topologically trivial films ($x < 0.32$) by two orders of magnitude. Furthermore, the sign of the effective $g$-factor was opposite in the two phases, which can be explained by our theoretical model. These results strongly indicate the existence of interplay between the magnetic properties of chiral phonons and the topology of electronic band structure., Comment: 6 pages, 3 figures, see Supplemental Material in the Ancillary directory

In this work, we study the real-time evolution of periodically driven (Floquet) systems on a quantum computer using IBM quantum devices. We consider a driven Landau-Zener model and compute the transition probability between the Floquet steady states as a function of time. We find that for this simple one-qubit model, Floquet states can develop in real-time, as indicated by the transition probability between Floquet states. Next, we model light-driven spin chains and compute the time-dependent antiferromagnetic order parameter. We consider models arising from light coupling to the underlying electrons as well as those arising from light coupling to phonons. For the two-spin chains, the quantum devices yield time evolutions that match the effective Floquet Hamiltonian evolution for both models once readout error mitigation is included. For three-spin chains, zero-noise extrapolation yields a time dependence that follows the effective Floquet time evolution. Therefore, the current IBM quantum devices can provide information on the dynamics of small Floquet systems arising from light drives once error mitigation procedures are implemented., Comment: 19 pages, 16 figures

We theoretically study the effect of low-frequency light pulses in resonance with phonons in the topological and magnetically ordered two septuple-layer (2-SL) MnBi2Te4 (MBT) and MnSb2Te4 (MST). These materials share symmetry properties and an antiferromagnetic ground state in pristine form but present different magnetic exchange interactions. In both materials, shear and breathing Raman phonons can be excited via non-linear interactions with photo-excited infrared phonons using intense laser pulses attainable in current experimental setups. The light-induced transient lattice distortions lead to a change in the sign of the effective interlayer exchange interaction and magnetic order accompanied by a topological band transition. Furthermore, we show that moderate anti-site disorder, typically present in MBT and MST samples, can facilitate such an effect. Therefore, our work establishes 2-SL MBT and MST as candidate platforms to achieve non-equilibrium magneto-topological phase transitions., Comment: 23 pages, 6 figures

PbTe crystals have a soft transverse optical phonon mode in the terahertz frequency range, which is known to efficiently decay into heat-carrying acoustic phonons, resulting in anomalously low thermal conductivity. Here, we studied this phonon via polarization-dependent terahertz spectroscopy. We observed softening of this mode with decreasing temperature, indicative of incipient ferroelectricity, which we explain through a model including strong anharmonicity with a quartic displacement term. In magnetic fields up to 25T, the phonon mode split into two modes with opposite handedness, exhibiting circular dichroism. Their frequencies displayed Zeeman splitting together with an overall diamagnetic shift with increasing magnetic field. Using a group-theoretical approach, we demonstrate that these observations are results of magnetic field-induced morphic changes in the crystal symmetries through the Lorentz force exerted on the lattice ions. This study thus reveals a novel process of controlling phonon properties in a soft ionic lattice by a strong magnetic field.

Motivated by the recent experimental realization of twisted trilayer graphene and the observed superconductivity that is associated with its flat bands at specific angles, we study trilayer graphene under the influence of different forms of light in the non-interacting limit. Specifically, we study four different types of stacking configurations with a single twisted layer. In all four cases, we study the impact of circularly polarized light and longitudinal light coming from a waveguide. We derive effective time-independent Floquet Hamiltonians and review light-induced changes to the band structure. For circularly polarized light, we find band flattening effects as well as band gap openings. We emphasize that there is a rich band topology, which we summarize in Chern number maps that are different for all four studied lattice configurations. The case of a so-called ABC stacking with top layer twist is especially rich and shows a different phase diagram depending on the handedness of the circularly polarized light. Consequently, we propose an experiment where this difference in typologies could be captured via optical conductivity measurements. In contrast for the case of longitudinal light that is coming from a waveguide, we find that the band structure is very closely related to the equilibrium one but the magic angles can be tuned in-situ by varying the intensity of the incident beam of light.

Spin-phonon interaction is an important channel for spin and energy relaxation in magnetic insulators. Understanding this interaction is critical for developing magnetic insulator-based spintronic devices. Quantifying this interaction in yttrium iron garnet (YIG), one of the most extensively investigated magnetic insulators, remains challenging because of the large number of atoms in a unit cell. Here, we report temperature-dependent and polarization-resolved Raman measurements in a YIG bulk crystal. We first classify the phonon modes based on their symmetry. We then develop a modified mean-field theory and define a symmetry-adapted parameter to quantify spin-phonon interaction in a phonon-mode specific way for the first time in YIG. Based on this improved mean-field theory, we discover a positive correlation between the spin-phonon interaction strength and the phonon frequency., Comment: 12 pages, 4 figures, 1 table; (Supp. Info. 10 pages, 5 figures, 2 tables)

We review recent work on low-frequency Floquet engineering and its application to quantum materials driven by light, emphasizing van der Waals systems hosting Moir\'e superlattices. These non-equilibrium systems combine the twist-angle sensitivity of the band structures with the flexibility of light drives. The frequency, amplitude, and polarization of light can be easily tuned in experimental setups, leading to platforms with on-demand properties. First, we review recent theoretical developments to derive effective Floquet Hamiltonians in different frequency regimes. We apply some of these theories to study twisted graphene and twisted transition metal dichalcogenide systems irradiated by light in free space and inside a waveguide. We study the changes induced in the quasienergies and steady-states, which can lead to topological transitions. Next, we consider van der Waals magnetic materials driven by low-frequency light pulses in resonance with the phonons. We discuss the phonon dynamics induced by the light and resulting magnetic transitions from a Floquet perspective. We finish by outlining new directions for Moir\'e-Floquet engineering in the low-frequency regime and their relevance for technological applications., Comment: 66 pages, 13 figures

Motivated by the recent experimental realization of twisted transition metal dichalcogenide bilayers, we study a simplified model driven by different forms of monochromatic light. As a concrete and representative example we use parameters that correspond to a twisted MoTe$_2$ homobilayer. First, we consider irradiation with circularly polarized light in free space and demonstrate that the corresponding Floquet Hamiltonian takes the same form as the static Hamiltonian, only with a constant overall shift in quasi-energy. This is in stark contrast to twisted bilayer graphene, where new terms are typically generated under an analagous drive. Longitudinal light, on the other hand, which can be generated from the transverse magnetic mode in a waveguide, has a much more dramatic effect--it renormalizes the tunneling strength between the layers, which effectively permits the tuning of the twist angle {\em in-situ}. We find that, by varying the frequency and amplitude of the drive, one can induce a topological transition that cannot be obtained with the traditional form of the Floquet drive in free space. Furthermore, we find that strong drives can have a profound effect on the layer pseudospin texture of the twisted system, which coincides with multiple simultaneous band gap closings in the infinite-frequency limit. Surprisingly, these bandgap closings are not associated with topological transitions. For high but finite drive frequencies near $0.7$eV, the infinite-frequency band crossings become band gap minima of the order of $10^{-6}$ eV or smaller.

We study theoretically AB-stacked honeycomb bilayers driven by light in resonance with an infrared phonon within a tight-binding description. We characterize the phonon properties of honeycomb bilayers with group theory and construct an electronic time-dependent tight-binding model for the system following photo-excitation in resonance with an infrared phonon. We adopt an "atomically adiabatic" approximation, introduced by Mohantya and Heller PNAS 116, 18316 (2019) to describe classically vibrating nuclei, but obtain the Floquet quasienergy spectrum associated with the time-dependent model exactly. We introduce a general scheme to disentangle the complex low-frequency Floquet spectrum to elucidate the relevant Floquet bands. As a prototypical example, we consider bilayer graphene. We find that light in the low-frequency regime can induce a bandgap in the quasienergy spectrum in the vicinity of the K points even if it is linearly polarized, in contrast with the expectations within the Born-Oppenheimer approximation and the high-frequency regime. Finally, we analyze the diabaticity of the driven electron and driven phonon processes and found contrasting effects on the autocorrelation functions at the same driving frequency: driven phonons preserve the character of the initial state while driven electrons exhibit strong deviations within a few drive cycles. The procedure outlined here can be applied to other materials to describe the combined effects of low-frequency light on phonons and electrons., Comment: 12 pages, 11 figures

We employ group theory to study the properties of the lattice vibrations and magnetic order in the antiferromagnetic topological insulator MnBi$_2$Te$_4$, both in bulk and few-layer form. In the paramagnetic phase, we obtain the degeneracies, the selection rules, and real-space displacements for the lattice vibrational modes for different stacking configurations. We discuss how magnetism influences these results. As a representative example, we consider a double septuple layer system and obtain the form of the magnetic order allowed by the symmetries of the crystal. We derive the allowed coupling terms that describe the paramagnetic to antiferromagnetic transition. Finally, we discuss the implications of our results for Raman scattering and other optical measurements. Our work sets the stage for a deeper understanding of the interplay of lattice modes, band topology, and magnetic order in MnBi$_2$Te$_4$ and other symmetry-related materials., Comment: 11 pages, 8 figures

Motivated by the recent experimental realization of twisted double bilayer graphene (TDBG) samples we study, both analytically and numerically, the effects of circularly polarized light propagating in free space and confined into a waveguide on the band structure and topological properties of these systems. These two complementary Floquet protocols allow us to selectively tune different parameters of the system by varying the intensity and the frequency of the light. For the drive protocol in free space, in the high-frequency regime, we find that in TDBG with AB/BA stacking, we can selectively close the zone-center quasienergy gaps around one valley while increasing the gaps near the opposite valley by tuning the parameters of the drive. In TDBG with AB/AB stacking, a similar effect can be obtained upon the application of a perpendicular static electric field. Furthermore, we study the topological properties of the driven system in different settings, provide accurate effective Floquet Hamiltonians, and show that relatively strong drives can generate flat bands. On the other hand, longitudinal light confined into a waveguide couples to the components of the interlayer hopping that are perpendicular to the TDBG sheet, allowing for selective engineering of the bandwidth of Floquet zone center quasienergy bands without breaking the symmetries of the static system., Comment: 12 pages, 12 figures

We derive effective Floquet Hamiltonians for twisted bilayer graphene driven by circularly polarized light in two different regimes beyond the weak-drive, high frequency regime. First, we consider a driving protocol relevant for experiments with frequencies smaller than the bandwidth and weak amplitudes and derive an effective Hamiltonian, which through a symmetry analysis, provides analytical insight into the rich effects of the drive. We find that circularly polarized light at low frequencies can selectively decrease the strength of AA-type interlayer hopping while leaving the AB-type unaffected. Then, we consider the intermediate frequency, and intermediate-strength drive regime. We provide a compact and accurate effective Hamiltonian which we compare with the Van Vleck expansion and demonstrate that it provides a significantly improved representation of the exact quasienergies. Finally, we discuss the effect of the drive on the symmetries, Fermi velocity and the gap of the Floquet flat bands.

The Verwey transition in magnetite (Fe$_3$O$_4$) is the first metal-insulator transition ever observed and involves a concomitant structural rearrangement and charge-orbital ordering. Due to the complex interplay of these intertwined degrees of freedom, a complete characterization of the low-temperature phase of magnetite and the mechanism driving the transition have long remained elusive. It was demonstrated in recent years that the fundamental building blocks of the charge-ordered structure are three-site small polarons called trimerons. However, electronic collective modes of this trimeron order have not been detected to date, and thus an understanding of the dynamics of the Verwey transition from an electronic point of view is still lacking. Here, we discover spectroscopic signatures of the low-energy electronic excitations of the trimeron network using terahertz light. By driving these modes coherently with an ultrashort laser pulse, we reveal their critical softening and hence demonstrate their direct involvement in the Verwey transition. These findings represent the first observation of soft modes in magnetite and shed new light on the cooperative mechanism at the origin of its exotic ground state., Comment: 20 pages, 18 figures

We introduce a new approach that allows one complete control over the modulation of the effective twist angle change in few-layer van der Waals heterostructures by irradiating them with longitudinal waves of light at the end of a waveguide. As a specific application, we consider twisted bilayer graphene and show that one can tune the magic angles to be either larger or smaller, allowing in-situ experimental control of the phase diagram of this and other related materials. A waveguide allows one to circumvent the free-space constraints on the absence of longitudinal electric field components of light. We propose to place twisted bilayer graphene at a specific location at the exit of a waveguide, such that it is subjected to purely longitudinal components of a transverse magnetic modes (TM) wave.

We develop a theory to derive effective Floquet Hamiltonians in the weak drive and low-frequency regime. We construct the theory in analogy with band theory for electrons in a spatially-periodic and weak potential, such as occurs in some crystalline materials. As a prototypical example, we apply this theory to graphene driven by circularly polarized light of low intensity. We find an analytic expression for the effective Floquet Hamiltonian in the low-frequency regime which accurately predicts the quasienergy spectrum and the Floquet states. Furthermore, we identify self-consistency as the crucial feature effective Hamiltonians in this regime need to satisfy to achieve a high accuracy. The method is useful in providing a realistic description of off-resonant drives for multi-band solid state systems where light-induced topological band structure changes are sought.

We report the theoretical discovery and characterization of higher-order Floquet topological phases dynamically generated in a periodically driven system with mirror symmetries. We demonstrate numerically and analytically that these phases support lower-dimensional Floquet bound states, such as corner Floquet bound states at the intersection of edges of a two-dimensional system, protected by the nonequilibrium higher-order topology induced by the periodic drive. We characterize higher-order Floquet topologies of the bulk Floquet Hamiltonian using mirror-graded Floquet topological invariants. This allows for the characterization of a new class of higher-order "anomalous" Floquet topological phase, where the corners of the open system host Floquet bound states with the same as well as with double the period of the drive. Moreover, we show that bulk vortex structures can be dynamically generated by a drive that is spatially inhomogeneous. We show these bulk vortices can host multiple Floquet bound states. This "stirring drive protocol" leverages a connection between higher-order topologies and previously studied fractionally charged, bulk topological defects. Our work establishes Floquet engineering of higher-order topological phases and bulk defects beyond equilibrium classification and offers a versatile tool for dynamical generation and control of topologically protected Floquet corner and bulk bound states., Comment: v2: 13 pages, 8 figures, 3 appendices; new references, and new analytical and numerical work showing the robustness of Z invariant without diagonal mirror symmetries

One-atom thick crystalline layers and their vertical heterostructures carry the promise of designer electronic materials that are unattainable by standard growth techniques. In order to realize their potential it is necessary to isolate them from environmental disturbances in particular those introduced by the substrate. But finding and characterizing suitable substrates, and minimizing the random potential fluctuations they introduce, has been a persistent challenge in this emerging field. Here we show that Landau-level (LL) spectroscopy is exquisitely sensitive to potential fluctuations on both local and global length scales. Harnessing this technique we demonstrate that the insertion of an intermediate graphene layer provides superior screening of substrate induced disturbances, more than doubling the electronic mean free path. Furthermore, we find that the proximity of hBN acts as a nano-scale vacuum cleaner, dramatically suppressing the global potential fluctuations. This makes it possible to fabricate high quality devices on standard SiO2 substrates., Comment: 16 pages, 4 figures

We study the effect of long-range disorder created by charge impurities on the carrier density distribution of graphene-based heterostructures. We consider heterostructures formed by two graphenic sheets (either single layer graphene, SLG, or bilayer graphene, BLG) separated by a dielectric film. We present results for symmetric heterostructures, SLG-SLG and BLG-BLG, and hybrid ones, BLG-SLG. As for isolated layers, we find that the presence of charged impurities induces strong carrier density inhomogeneities, especially at low dopings where the density landscape breaks up in electron-hole puddles. We provide quantitative results for the strength of the carrier density inhomogeneities and for the screened disorder potential for a large range of experimentally relevant conditions. For heterostructures in which BLG is present we also present results for the band-gap induced by the perpendicular electric field generated self-consistently by the disorder potential and by the distribution of charges in the heterostructure. For SLG-SLG heterostructures we discuss the relevance of our results for the understanding of the recently observed metal-insulator transition in each of the graphene layers forming the heterostructure. Moreover, we calculate the correlation between the density profiles in the two graphenic layers and show that for standard experimental conditions the two profiles are well correlated., Comment: 21 pages, 29 figures