We theoretically predict a new working principle for optical amplification, based on Weyl semimetals: when a Weyl semimetal is suitably irradiated at two frequencies, electrons close to the Weyl points convert energy between the frequencies through the mechanism of topological frequency conversion from [Martin et al, PRX 7 041008 (2017)]. Each electron converts energy at a quantized rate given by an integer multiple of Planck's constant multiplied by the product of the two frequencies. In simulations, we show that optimal, but feasible band structures can support topological frequency conversion in the "THz gap" at intensities down to $ 2{\rm W}/{\rm mm^2}$; the gain from the effect can exceed the dissipative loss when the frequencies are larger than the relaxation time of the system. Topological frequency conversion provides a new paradigm for optical amplification, and further extends Weyl semimetals' promise for technological applications. less

We develop a length-gauge formalism for treating one-dimensional periodic lattice systems in the presence of a photon cavity inducing light-matter interaction. The purpose of the formalism is to remove mathematical ambiguities that occur when defining the position operator in the context of the Power-Zienau-Woolley Hamiltonian. We then use a diagrammatic approach to analyze perturbatively the interaction between an electronic quantum system and a photonic cavity mode of long wavelength. We illustrate the versatility of the formalism by studying the cavity-induced electric charge imbalance and polarization in the Rice-Mele model with broken inversion symmetry. less

Magnon eigenmodes in easy-plane antiferromagnetic insulators are linearly polarized and are not expected to carry any net spin angular momentum. Motivated by recent nonlocal spin transport experiments in the easy-plane phase of hematite, we perform a series of micromagnetic simulations in a nonlocal geometry at finite temperatures. We show that by tuning an external magnetic field, we can control the magnon eigenmodes and the polarization of the spin transport signal in these systems. We argue that a coherent beating oscillation between two orthogonal linearly polarized magnon eigenmodes is the mechanism responsible for finite spin transport in easy-plane antiferromagnetic insulators. The sign of the detected spin signal is also naturally explained by the proposed coherent beating mechanism. Our finding opens a path for on-demand control of the spin signal in a large class of easy-plane antiferromagnetic insulators. less

Lowest Landau level wavefunctions are eigenstates of the Hamiltonian of a charged particle in two dimensions under a uniform magnetic field. They are known to be holomorphic both in real and momentum spaces, and also exhibit uniform, translationally invariant, geometrical properties in momentum space. In this paper, using the Stone-von Neumann theorem, we show that lowest Landau level wavefunctions are indeed the only possible states with unit Chern number satisfying these conditions. We also prove the uniqueness of their direct analogs with higher Chern numbers and provide their expressions. less

The recent observed anomalous Hall effect in magic angle twisted bilayer graphene (TBG) aligned to hexagonal boron nitride (hBN) and unconventional ferroelectricity in Bernal bilayer graphene sandwiched by hBN present a new platform to tune the correlated properties in graphene systems. In these graphene-based moir\'e superlattices, the aligned hBN substrate plays an important role. In this paper, we analyze the effects of hBN substrate on the band structure of the TBG. By means of an atomistic tight-binding model we calculate the electronic properties of TBG suspended and encapsulated with hBN. Interestingly, we found that the physical properties of TBG are extremely sensitive to the presence of hBN and they may be completely different if TBG is suspended or encapsulated. We quantify these differences by analysing their electronic properties, optical conductivity and band topology. We found that the narrow bandwidth, band gap, local density of states and optical conductivity are significantly modified by the aligned hBN substrates. Interestingly, these electronic properties can be used as a signature of the alignment in experiment. Moreover, the TBG/hBN superlattices in the presence or absence of the two-fold rotation symmetry response differently to the external electric field. For the TBG suspended in the hBN, application of an electric field results in the charge unevenly distributed between graphene layers, which can be used to tune the strength of the valley Hall effect or the anomalous Hall effect. Such rich topological phase diagram in these systems may be useful for experiments. less

Control of quantum matter through resonant electromagnetic cavities is a promising route towards establishing control over material phases and functionalities. Quantum paraelectric insulators -- materials which are nearly ferroelectric -- are particularly promising candidate systems for this purpose since they have strongly fluctuating collective modes which directly couple to the electric field. In this work we explore this possibility in a system comprised of a quantum paraelectric sandwiched between two high-quality metal mirrors, realizing a Fabry-Perot type cavity. By developing a full multimode, continuum description we are able to study the effect of the cavity in a spatially resolved way for a variety of system sizes and temperatures. Surprisingly, we find that once a continuum of transverse modes are included the cavity ends up suppressing ferroelectric correlations. This effect arises from the screening out of transverse photons at the cavity boundaries and as a result is confined to the surface of the paraelectric sample. We also explore the temperature dependence of this effect and find it vanishes at high temperatures, indicating it is a purely quantum mechanical effect. We connect our result to calculations of Casimir and Van der Waals forces, which we argue are closely related to the dipolar fluctuations in the quantum paraelectric. Our results are based on a general formalism and are expected to be widely applicable, paving the way towards studies of the quantum electrodynamics of heterostructures featuring multiple materials and phases. less

We analyze the effects of the long-range Coulomb interaction on the distribution of Berry curvature among the bands near charge neutrality of twisted bilayer graphene (TBG) closely aligned with hexagonal boron nitride (hBN). Due to the suppressed dispersion of the narrow bands, the band structure is strongly renormalized by electron-electron interactions, and thus, the associated topological properties of the bands are sensitive to filling. Using a Hartree formalism, we calculate the linear and nonlinear Hall conductivities, and find that for certain fillings, the remote bands contribute substantially to the Hall currents while the contribution from the central bands is suppressed. In particular, we find that these currents are generically substantial near regions of energies where the bands are highly entangled with each other, often featuring doping-induced band inversions. Our results demonstrate that topological transport in TBG/hBN is substantially modified by electron-electron interactions, which offer a simple explanation to recent experimental results. less

We present theoretically the thermal Hall effect of magnons in a ferromagnetic lattice with a Kekulé-O coupling (KOC) modulation and a Dzyaloshinskii-Moriya interaction (DMI). Through a strain-based mechanism for inducing the KOC modulation, we identify four topological phases in terms of the KOC parameter and DMI strength. We calculate the thermal magnon Hall conductivity ${\kappa^{xy}}$ at low temperature in each of these phases. We predict an unconventional conductivity due to a non-zero Berry curvature emerging from band proximity effects in the topologically trivial phase. We find sign changes of ${\kappa^{xy}}$ as a function of the model parameters, associated with the local Berry curvature and occupation probability of the bulk bands. Throughout, ${\kappa^{xy}}$ can be easily tuned with external parameters such as the magnetic field and temperature. less

The formation of a superlattice in graphene can serve as a way to modify its electronic bandstructure and thus to engineer its electronic transport properties. Recent experiments have discovered a Kekul\'e bond ordering in graphene deposited on top of a Copper substrate, leading to the breaking of the valley degeneracy while preserving the highly desirable feature of linearity and gapless character of its band dispersion. In this paper we study the effects of a Kekul\'e distortion in zigzag graphene nanoribbons in both, the subband spectrum and on its electronic transport properties. We extend our study to investigate also the electronic conductance in graphene nanoribbons composed of sequentially ordered Kek-Y superlattice. We find interesting resonances in the conductance response emerging in the otherwise energy gap regions, which scales with the number of Kek-Y interfaces minus one. Such features resembles the physics of resonant tunneling behavior observed in semiconductors heterostructures. Our findings provide a possible way to measure the strenght of Kekul\'e parameter in graphene nanoribbons. less

Twisted bilayer graphene has a rich phase diagram, including superconductivity. Recently, an unexpected discovery has been the observation of superconductivity in non-twisted graphene bilayers and trilayers. In this Perspective, we give an overview of the search for uncommon phases in non-twisted graphene systems. We first contextualise these recent results within earlier work in the field, before examining the new experimental findings. Finally, we analyse the numerous theoretical models which study the underlying physical processes in these systems. less

We discuss a Kohn-Luttinger-like mechanism for superconductivity in Bernal bilayer graphene and rhombohedral trilayer graphene. Working within the continuum model description, 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. less

The difference between the edge on-site potential and the bulk values in a magnonic topological honeycomb lattice leads to the formation of edge states in a bearded boundary, and the same difference is found to be the responsible for the absence of edge states in a zig-zag termination. In a finite lattice, the intrinsic on-site interactions along the boundary sites generate an effective defect and Tamm-like edge states appear for both zig-zag and bearded terminations. If a non-trivial gap is induced, Tamm-like and topologically protected edge states appear in the band structure. The effective defect can be strengthened by an external on-site potential and the dispersion relation, velocity and magnon-density of the edge states become tunable. less

Spin currents driven by spin-orbit coupling are key to spin torque devices, but determining the proper spin current is highly non-trivial. Here we derive a general quantum-mechanical formula for the intrinsic proper spin current showing that it is a topological quantity, and can be finite even in the gap. We determine the spin-Hall current due to the bulk states of topological insulators both deep in the bulk, where the system is unmagnetized, and near the interface, where a proximity-induced magnetization is present, as well as for low-dimensional spin-3/2 hole systems. less

We investigate the properties of magnon edge states in a ferromagnetic honeycomb lattice with armchair boundaries. In contrast with fermionic graphene, we find novel edge states due to the missing bonds along the boundary sites. After introducing an external on-site potential at the outermost sites we find that the energy spectra of the edge states are tunable. Additionally, when a non-trivial gap is induced, we find that some of the edge states are topologically protected and also tunable. Our results may explain the origin of the novel edge states recently observed in photonic lattices. We also discuss the behavior of these edge states for further experimental confirmations less

We discuss the effect of long-range interactions within the self-consistent Hartree-Fock (HF) approximation in comparison to short-range atomic Hubbard interactions on the band structure of twisted bilayer graphene (TBG) at charge neutrality for various twist angles. Starting from atomistic calculations, we determine the quasi-particle band structure of TBG with Hubbard interactions for various magnetic orderings: modulated anti-ferromagnetic (MAFM), nodal anti-ferromagnetic (NAFM) and hexagonal anti-ferromagnetic (HAFM). Then, we develop an approach to incorporate these magnetic orderings along with the HF potential in the continuum approximation. Away from the magic angle, we observe a drastic effect of the magnetic order on the band structure of TBG compared to the influence of the HF potential. Near the magic angle, however, the HF potential seems to play a major role on the band structure compared to the magnetic order. These findings suggest that the spin-valley degenerate broken symmetry state often found in HF calculations of charge neutral TBG near the magic angle should favour magnetic order, since the atomistic Hubbard interaction will break this symmetry in favour of spin polarization. less

In spin torque magnetic memories, electrically actuated spin currents are used to switch a magnetic bit. Typically, these require a multilayer geometry including both a free ferromagnetic layer and a second layer providing spin injection. For example, spin may be injected by a nonmagnetic layer exhibiting a large spin Hall effect, a phenomenon known as spin-orbit torque. Here, we demonstrate a spin-orbit torque magnetic bit in a single two-dimensional system with intrinsic magnetism and strong Berry curvature. We study AB-stacked MoTe2/WSe2, which hosts a magnetic Chern insulator at a carrier density of one hole per moire superlattice site. We observe hysteretic switching of the resistivity as a function of applied current. Magnetic imaging using a superconducting quantum interference device reveals that current switches correspond to reversals of individual magnetic domains. The real space pattern of domain reversals aligns precisely with spin accumulation measured near the high-Berry curvature Hubbard band edges. This suggests that intrinsic spin- or valley-Hall torques drive the observed current-driven magnetic switching in both MoTe2/WSe2 and other moire materials. The switching current density of 10^3 Amps per square centimeter is significantly less than reported in other platforms paving the way for efficient control of magnetic order. less

We examine the combined effects of a Kekule coupling texture (KC) and a Dzyaloshinskii-Moriya interaction (DMI) in a two-dimensional ferromagnetic honeycomb lattice. By analyzing the gap closing conditions and the inversions of the bulk bands, we identify the parameter range in which the system behaves as a trivial or a nontrivial topological magnon insulator. We find four topological phases in terms of the KC parameter and the DMI strength. We present the bulk-edge correspondence for the magnons in a honeycomb lattice with an armchair or a zigzag boundary. Furthermore, we find Tamm-like edge states due to the intrinsic on-site interactions along the boundary sites. Our results may have significant implications to magnon transport properties in the 2D magnets at low temperatures. less

A chain of magnetic impurities deposited on the surface of a superconductor can form a topological Shiba band that supports Majorana zero modes and hold a promise for topological quantum computing. Yet, most experiments scrutinizing these zero modes rely on transport measurements, which only capture local properties. Here we propose to leverage the intrinsic dynamics of the magnetic impurities to access their non-local character. We use linear response theory to determine the dynamics of the uniform magnonic mode in the presence of external $ac$ magnetic fields and the coupling to the Shiba electrons. We demonstrate that this mode, which spreads over the entire chain of atoms, becomes imprinted with the parity of the ground state and, moreover, can discriminate between Majorana and trivial zero modes located at the ends of the chain. Our approach offers a non-invasive alternative to the scanning tunnelling microscopy techniques used to probe Majorana zero modes. Conversely, the magnons could facilitate the manipulation of Majorana zero modes in topological Shiba chains. less