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We theoretically study the nonlinear optical response of ABC trilayer graphene with inversion symmetry broken by the application of a displacement field perpendicular to the trilayer. We show that rhombohedral trilayer graphene exhibits a large bulk photovoltaic effect arising from a DC shift current response. The conductivity of the trilayer contains features similar to AB bilayer graphene as well as features distinct from AB bilayer graphene. The new features of ABC trilayer graphene relative to AB bilayer graphene arise from the quantum geometric features of the electronic band structure and can be tuned by varying the displacement field. We focus on a regime of displacement field where certain band gaps close and reopen away from the charge neutrality point leading to drastic changes in the quantum geometric structure in momentum space, a feature characteristic of the trilayer graphene band structure. These features manifest as a sign change in shift current conductivity in a certain frequency window and can thus serve as a probe of quantum geometry., Comment: 15 pages, 12 figures

Moir\'e materials represent strongly interacting electron systems bridging topological and correlated physics. Despite significant advances, decoding wavefunction properties underlying the quantum geometry remains challenging. Here, we utilize polarization-resolved photocurrent measurements to probe magic-angle twisted bilayer graphene, leveraging its sensitivity to the Berry connection that encompasses quantum "textures" of electron wavefunctions. Using terahertz light resonant with optical transitions of its flat bands, we observe bulk photocurrents driven by broken symmetries and reveal the interplay between electron interactions and quantum geometry. We observe inversion-breaking gapped states undetectable through quantum transport, sharp changes in the polarization axes caused by interaction-induced band renormalization, and recurring photocurrent patterns at integer fillings of the moir\'e unit cell that track the evolution of quantum geometry through the cascade of phase transitions. The large and tunable terahertz response intrinsic to flat-band systems offers direct insights into the quantum geometry of interacting electrons and paves the way for innovative terahertz quantum technologies.

Finding materials exhibiting substantial shift current holds the potential for designing shift current-based photovoltaics that outperform conventional solar cells. However, the myriad of factors governing shift current response poses significant challenges in designing devices that showcase large shift current. Here, we propose a general design principle that exploits inter-orbital mixing to excite virtual multiband transitions in materials with multiple flat bands to achieve enhanced shift current response. We further explicitly relate this design principle to maximizing Wannier function spread as expressed through the formalism of quantum geometry. We demonstrate the viability of our design using a 1D stacked Rice-Mele model. Then, we consider a concrete material realization - alternating angle twisted multilayer graphene (TMG) - a natural platform to experimentally realize such an effect. We identify a new set of twist angles at which the shift current response is maximized via virtual transitions for each multilayer graphene and highlight the importance of TMG as a promising material to achieve an enhanced shift current response at terahertz frequencies. Our proposed mechanism also applies to other 2D systems and can serve as a guiding principle for designing multiband systems that exhibit enhanced shift current response., Comment: 9 figures, 20 pages

We theoretically study first and second-order optical responses in a transition metal dichalcogenide monolayer with distinct trivial, nodal, and time-reversal invariant topological superconducting (TRITOPS) phases. We show that the second-order DC response, also known as the photogalvanic response, contains signatures for differentiating these phases while the first-order optical response does not. We find that the high-frequency photogalvanic response is insensitive to the phase of the system, while the low-frequency response exhibits features distinguishing the three phases. At zero doping, corresponding to an electron filling in which the Fermi level lies at nodal points, there are opposite sign zero-frequency divergences in the response when approaching the nodal phase boundaries from the trivial and the TRITOPS phases. In the trivial phase, both the high-frequency and low-frequency response of the system are negative, but in the TRITOPS phase, the low-frequency response becomes positive while the high-frequency response remains negative. Furthermore, since phase transitions are controlled by the Rashba spin-orbit coupling and the ratio of intra-orbital and inter-orbital paring amplitudes, our results not only help distinguish the phases but can also provide an estimate of the pairing amplitudes based on the photogalvanic response of the system., Comment: 13 pages, 9 figures

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 propose a novel analog memory device utilizing the gigantic magnetic Weyl semimetal (MWSM) domain wall (DW) magnetoresistance. We predict that the nucleation of domain walls between contacts will strongly modulate the conductance and allow for multiple memory states, which has been long sought-after for use in magnetic random access memories or memristive neuromorphic computing platforms. We motivate this conductance modulation by analyzing the electronic structure of the helically-magnetized MWSM Hamiltonian, and report tunable flat bands in the direction of transport in a helically-magnetized region of the sample for Bloch and Neel-type domain walls via the onset of a local axial Landau level spectrum within the bulk of the superlattice. We show that Bloch devices also provide means for the generation of chirality-polarized currents, which provides a path towards nanoelectronic utilization of chirality as a new degree of freedom in spintronics., Comment: 11 pages, 6 figures. Originally presented at NVMTS 2022, updated at APS March Meeting 2023

We have studied the terahertz response of a bulk single crystal of La$_{0.875}$Sr$_{0.125}$MnO$_3$ at around its Curie temperature, observing large changes in the real and imaginary parts of the optical conductivity as a function of magnetic field. The terahertz resistance and capacitance extracted from the optical conductivity rapidly increased with increasing magnetic field and did not show any sign of saturation up to 6 T, reaching 60% and 15%, respectively, at 180 K. The observed terahertz colossal magnetoresistance and magnetocapacitance effects can be qualitatively explained by using a two-component model that assumes the coexistence of two phases with vastly different conductivities. These results demonstrate the potential use of perovskite manganites for developing efficient terahertz devices based on magnetic modulations of the amplitude and phase of terahertz waves., Comment: 7 pages, 6 figures

We investigate the dependence of the photogalvanic response of a multi-Weyl semimetal on its topological charge, tilt, and chemical potential. We derive analytical expressions for the shift and injection conductivities for tilted charge-$n$ Weyl points $(n=1,2,3)$ using a low energy two-band effective Hamiltonian. For double-Weyl semimetals, we also compute the response from two-band and four-band tight-binding models with broken time-reversal symmetry to study the effect of band bending and the contributions from higher bands. We find a significant deviation in the responses obtained from the effective low-energy continuum model and more realistic four-band continuum and tight-binding models. We analyze several different limits of these models. We describe the nature of the deviations and provide estimates of their dependence on the frequency and other model parameters. Our analysis provides a simple explanation for the first-principle calculation based frequency dependence of the injection current in SrSi$_2$. Additionally, we find interesting parameter regimes where the frequency dependence of the non-linear optical response can be directly used to probe the type-I/type-II nature of the Weyl cone. We obtain analytical results for the charge-4 Weyl semimetal by reducing the original problem involving a triple $k$-space integral to one with only a double integral. This simplification allows us to extract all relevant information about the nature of its second-order dc response and the precise condition for observing circular photogalvanic effect quantization. The semi-analytical approach presented here can also be extended to a systematic study of second harmonic generation and first-order optical conductivity in charge-4 Weyl semimetals., Comment: 16 pages, 7 figures, references added, typos corrected

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

Motivated by the recent excitement around the physics of twisted transition metal dichalcogenide (TMD) multilayer systems, we study strongly correlated phases of TMD heterobilayers under the influence of light. We consider both waveguide light and circularly polarized light. The former allows for longitudinally polarized light, which in the high frequency limit can be used to selectively modify interlayer hoppings in a tight-binding model. We argue based on quasi-degenerate perturbation theory that changes to the interlayer hoppings can be captured as a modulation to the strength of the moir\'e potential in a continuum model. As a consequence, waveguide light can be used to drive transitions between a myriad of different magnetic phases, including a transition from a $120^\circ$ Neel phase to a stripe ordered magnetic phase, or from a spin density wave phase to a paramagnetic phase, among others. When the system is subjected to circularly polarized light we find that the effective mass of the active TMD layer is modified by an applied electromagnetic field. By simultaneously applying waveguide light and circularly polarized light to a system, one has a high level of control in moving through the phase diagram in-situ. Lastly, we comment on the experimental feasibility of Floquet state preparation and argue that it is within reach of available techniques when the system is coupled to a judiciously chosen bath., Comment: J. Phys.: Condens. Matter 2022

Moir\'e materials, and in particular twisted bilayer graphene (TBG), exhibit a range of fascinating phenomena, that emerge from the interplay of band topology and interactions. We show that the non-linear second-order photoresponse is an appealing probe of this rich interplay. A dominant part of the photoresponse is the shift-current, which is determined by the geometry of the electronic wavefunctions and carrier properties, and thus becomes strongly modified by electron-electron interactions. We analyze its dependence on the twist angle and doping, and investigate the role of interactions. In the absence of interactions, the response of the system is dictated by two energy scales: the mean energy of direct transitions between the hole and electron flat bands, and the gap between flat and dispersive bands. Including electron-electron interactions, both enhance the response at the non-interacting characteristic frequencies as well as produce new resonances. We attribute these changes to the filling-dependent band renormalization in TBG. Our results highlight the connection between non-trivial geometric properties of TBG and its optical response, as well as demonstrate how optical probes can access the role of interactions in moi\'re materials.

Excitons are neutral objects, that, naively, should have no response to a uniform, electric field. Could the Berry curvature of the underlying electronic bands alter this conclusion? In this work, we show that Berry curvature can indeed lead to anomalous transport for excitons in 2D materials subject to a uniform, in-plane electric field. By considering the constituent electron and hole dynamics, we demonstrate that there exists a regime for which the corresponding anomalous velocities are in the same direction. We establish the resulting center of mass motion of the exciton through both a semiclassical and fully quantum mechanical analysis, and elucidate the critical role of Bloch oscillations in achieving this effect. We identify transition metal dichalcogenide heterobilayers as candidate materials to observe the effect., Comment: 9+9 pages, 6+6 figures. Comments welcome!

A periodic drive could alter the effective exchange interactions in magnetic materials. Here, we explore how exchange pathways affect the effective interactions of periodically driven magnetic materials. Aiming to apply Floquet engineering methods to two-dimensional magnetic materials, we consider realistic models and discuss the effect of a periodic drive on ligand-mediated exchange interactions. We show that depending on bond angles and the number of ligand ions involved in the exchange process, drive-induced changes can be very different from those calculated from direct-hopping models considered earlier. We study these effects and find that the presence of ligand ions must be taken into account, especially for TMTCs where ligand ion mediated next-neighbor interactions play a crucial role in determining the magnetic ground state of the system.

The breaking of time-reversal symmetry is a crucial ingredient to topological bands. It can occur intrisically in materials with magnetic order, or be induced by external fields, such as magnetic fields in quantum Hall systems, or circularly polarized light fields in Floquet Chern insulators. Apart from polarization, photons can carry another degree of freedom, orbital angular momentum, through which time-reversal symmetry can be broken. In this Letter, we pose the question whether this property allows for inducing topological bands via a linearly polarized but twisted light beam. To this end, we study a graphene-like model of electrons on a honeycomb lattice interacting with a twisted light field. To identify topological behavior of the electrons, we calculate their local markers of Chern number, and monitor the presence of in-gap edge states. Our results are shown to be fully analogous to the behavior found in paradigmatic models for static and driven Chern insulators, and realizing the state is experimentally straightforward. With this, our work establishes a new mechanism for generating Fermionic topological phases of matter that can harness the central phase singularity of an optical vortex beam., Comment: 8 pages, 4 figures

The co-existence of spatial and non-spatial symmetries together with appropriate commutation/anticommutation relations between them can give rise to static higher-order topological phases, which host gapless boundary modes of co-dimension higher than one. Alternatively, space-time symmetries in a Floquet system can also lead to anomalous Floquet boundary modes of higher co-dimensions, presumably with alterations in the commutation/anticommutation relations with respect to non-spatial symmetries. We show how a coherently excited phonon mode can be used to promote a spatial symmetry with which the static system is always trivial, to a space-time symmetry which supports non-trivial Floquet higher-order topological phase. We present two examples -- one in class D and another in class AIII where a coherently excited phonon mode promotes the reflection symmetry to a time-glide symmetry such that the commutation/anticommutation relations between spatial and non-spatial symmetries are modified. These altered relations allow the previously trivial system to host gapless modes of co-dimension two at reflection-symmetric boundaries., Comment: 5 pages+Supplemental Material

We present a new scheme to control the spin exchange interactions between two magnetic ions by manipulating the orbital degrees of freedom using a periodic drive. We discuss two different protocols for orbital Floquet engineering. In one case, we modify the properties of the ligand orbitals which mediate magnetic interactions between two transition metal ions. While in the other case, we mix the d orbitals on each magnetic ion. In contrast to previous works on Floquet engineering of magnetic properties, the present scheme makes use of the AC Stark shift of the states involved in the exchange process.

The Berry curvature of a Bloch band can be interpreted as a local magnetic field in reciprocal space. This analogy can be extended by defining an electric field analog in reciprocal space which arises from the time-dependent Berry connection. We explore the term in the semi-classical equation of motion that gives rise to this phenomenon, and show that it can lead to anomalous drift in wave packet motion. A similar effect arises from changes in the band population due to periodic driving, where the resulting drift depends on the nature of the drive and can be expressed in terms of a shift vector. Finally, these effects can be combined to build a pump with a net anomalous drift during a cyclic evolution in momentum space.

We propose a single phase-only optical element that transforms different orbital angular momentum (OAM) modes into localized spots at separated angular positions on a transverse plane. We refer to this element as an angular lens since it separates out OAM modes in a manner analogous to how a converging lens separates out transverse wave-vector modes at the focal plane. We also simulate the proposed angular lens using a spatial light modulator and experimentally demonstrate its working. Our work can have important implications for OAM-based classical and quantum communication applications., Comment: 5 pages, 5 figures