Infrared spectroscopy of Landau levels of graphene

Table-top laser-based terahertz high harmonic generation spectroscopy under magnetic fields and low temperatures

We have developed a terahertz (THz) nonlinear spectrometer at low temperatures (1.5-300 K) and under high magnetic fields (up to 10 T) by combining the laser-driven table-top intense THz source with a superconducting magnet. The strong-field THz pump pulse was generated from LiNbO3 crystal using the tilted-pulse-front technique and tightly focused into the center of the magnet by an off-axis parabolic mirror and a THz lens. The electric fields at the focus can achieve 500 kV/cm with a monocycle waveform and 30 kV/cm with a multicycle waveform at 0.5 THz. The sample was mounted on a low-temperature motorized rotation stage, which enables performing the polarization dependent measurements of the third harmonic generation (THG) intensity without rotating the incident THz pulses. The magnetic field direction can be rotated using a mechanical rotator, allowing for a convenient switch between Faraday and Voigt geometry. We demonstrate the excellent performance of our instrument by conducting THG measurements in the two-band superconductor MgB2 as a function of temperature, sample azimuth angle, as well as in-plane and out-of-plane magnetic fields. The successful combination of the strong field THz source with magnetic fields enables us to study a variety of materials with magnetic-field-dependent properties of interest.

Nonlinear parametric generation and optical vortex transfer in graphene ensemble under Landau quantization

We explore the dynamics of nonlinear parametric generation and light beam propagation in a Landau-quantized graphene structure with three energy levels interacting with two laser pulses, utilizing the Maxwell-Bloch equations. By applying a laser field to one transition of the graphene sample while keeping the second beam initially absent, the distinctive preparation of the graphene sample, coupled with its weak interaction with laser radiation, results in the parametric generation of a new laser beam in a different transition. We investigate the influence of diverse system parameters on both the efficiency of the generated beam and the propagation dynamics of both beams. Our findings reveal that manipulating these parameters can induce oscillations in the intensity of propagated beams, mitigate absorption losses during propagation allowing for earlier relaxation, and enhance the efficiency of energy transfer from the initial to the generated beam. Additionally, we demonstrate the transfer of optical vortices within the graphene ensemble by introducing an optical vortex to the initial beam. This scheme holds promise for applications in high-dimensional quantum information processing.

Landau-phonon polaritons in Dirac heterostructures

Polaritons are light-matter quasiparticles that govern the optical response of quantum materials at the nanoscale, enabling on-chip communication and local sensing. Here, we report Landau-phonon polaritons (LPPs) in magnetized charge-neutral graphene encapsulated in hexagonal boron nitride (hBN). These quasiparticles emerge from the interaction of Dirac magnetoexciton modes in graphene with the hyperbolic phonon polariton modes in hBN. Using infrared magneto-nanoscopy, we reveal the ability to completely halt the LPP propagation in real space at quantized magnetic fields, defying the conventional optical selection rules. The LPP-based nanoscopy also tells apart two fundamental many-body phenomena: the Fermi velocity renormalization and field-dependent magnetoexciton binding energies. Our results highlight the potential of magnetically tuned Dirac heterostructures for precise nanoscale control and sensing of light-matter interaction.

Carbon Nanomaterial Fluorescent Probes and Their Biological Applications

Fluorescent carbon nanomaterials have broadly useful chemical and photophysical attributes that are conducive to applications in biology. In this review, we focus on materials whose photophysics allow for the use of these materials in biomedical and environmental applications, with emphasis on imaging, biosensing, and cargo delivery. The review focuses primarily on graphitic carbon nanomaterials including graphene and its derivatives, carbon nanotubes, as well as carbon dots and carbon nanohoops. Recent advances in and future prospects of these fields are discussed at depth, and where appropriate, references to reviews pertaining to older literature are provided.

Infrared nano-imaging of Dirac magnetoexcitons in graphene

Magnetic fields can have profound effects on the motion of electrons in quantum materials. Two-dimensional electron systems subject to strong magnetic fields are expected to exhibit quantized Hall conductivity, chiral edge currents and distinctive collective modes referred to as magnetoplasmons and magnetoexcitons. Generating these propagating collective modes in charge-neutral samples and imaging them at their native nanometre length scales have thus far been experimentally elusive. Here we visualize propagating magnetoexciton polaritons at their native length scales and report their magnetic-field-tunable dispersion in near-charge-neutral graphene. Imaging these collective modes and their associated nano-electro-optical responses allows us to identify polariton-modulated optical and photo-thermal electric effects at the sample edges, which are the most pronounced near charge neutrality. Our work is enabled by innovations in cryogenic near-field optical microscopy techniques that allow for the nano-imaging of the near-field responses of two-dimensional materials under magnetic fields up to 7 T. This nano-magneto-optics approach allows us to explore and manipulate magnetopolaritons in specimens with low carrier doping via harnessing high magnetic fields.

Theoretical method for the analysis and design of tunable terahertz graphene-based Faraday polarization rotators

A theoretical method is presented that facilitates the analysis and design of graphene-based tunable terahertz polarization rotators. Most previous designs are based on a three-dimensional (3-D) full-wave electromagnetic simulation; thus, it is time-consuming to get well-tuned structural parameters. Using the proposed method, the transmission response of the polarization rotator is directly calculated for a given set of structural parameters. Hence, the need of the electromagnetic simulation is lifted. The accuracy of the proposed method is rigorously validated, as excellent agreement between the theoretical and simulation results is observed. Using the method, a rotator of 12 THz central frequency with a small magnetic bias field of 0.5 T and a small unit cell of 0.5 by 0.5(µm)2 is designed. It is shown that the center frequency can be increased to any desired frequency, without the need of a large magnetic bias, by reducing the unit cell size. The method presented in this work can be extended for the analysis and design of other tunable terahertz nonreciprocal devices, such as isolators, circulators, phase shifters, and switches.

Topological Lifshitz transition and one-dimensional Weyl mode in HfTe5

Landau band crossings typically stem from the intra-band evolution of electronic states in magnetic fields and enhance the interaction effect in their vicinity. Here in the extreme quantum limit of topological insulator HfTe₅, we report the observation of a topological Lifshitz transition from inter-band Landau level crossings using magneto-infrared spectroscopy. By tracking the Landau level transitions, we demonstrate that band inversion drives the zeroth Landau bands to cross with each other after 4.5 T and forms a one-dimensional Weyl mode with the fundamental gap persistently closed. The unusual reduction of the zeroth Landau level transition activity suggests a topological Lifshitz transition at 21 T, which shifts the Weyl mode close to the Fermi level. As a result, a broad and asymmetric absorption feature emerges due to the Pauli blocking effect in one dimension, along with a distinctive negative magneto-resistivity. Our results provide a strategy for realizing one-dimensional Weyl quasiparticles in bulk crystals.

Azimuthal and radial modulation of double-four-wave mixing in a coherently driven graphene ensemble

We investigate in detail the azimuthal and radial modulation (i.e., the azimuthal order l_j and radial order p_j with j = 1, 2) of double-four-wave mixing (double-FWM) by use of two higher-order Laguerre-Gaussian (LG) beams in a Landau quantized graphene ensemble. A pair of weak probe pulses in the graphene ensemble interacts with two LG beams and thus two vortex FWM fields with the opposite vorticity are subsequently generated. In combination with numerical simulations, we reveal that (i) there appear l₁ + l₂ periods of phase jumps in the phase profiles under any conditions; (ii) p + 1 concentric rings emerge in the intensity profile and the strength is mainly concentrated on the inner ring when the two LG beams have the same radial orders (i.e., p₁ = p₂ = p); (iii) there are p raised narrow rings occurring in the phase profile in the case of p₁ = p₂ = p and l₁ ≠ l₂, and the raised narrow rings would disappear when p₁ = p₂ and l₁ = l₂; (iv) p_max + 1 concentric rings appear in the intensity profile, meanwhile, |p₁ - p₂| convex discs and p_min raised narrow rings emerge in the phase diagram in the case of p₁ ≠ p₂, here p_max = max(p₁, p₂) and p_min = min(p₁, p₂). Moreover, the two generated FWM fields have the same results, and the difference is that the phase jumps are completely opposite. These findings may have potential application in graphene-based nonlinear optical device by using LG beams with adjustable mode orders.

Magneto-Optical Transport Properties of Type-II Nodal Line Semimetals

We investigate the magneto-optical transport properties and Landau levels of type-II nodal line semimetals. The tilted liner dispersion in type-II nodal line semimetals makes the conduction band and valence band asymmetric, and Landau levels are coupling in the presence of a magnetic field. We find the background of absorption peaks is curved. The oscillation peaks are tailless with the change of magnetic field. Through tuning tilt term, we find the absorption peaks of optical conductivity change from incomplete degenerate structure to splitting double peaks structure. We also find interband absorption peaks is no longer zero in the imaginary part of Hall conductivity. With the change of the tilt term, the contribution of the absorption peak has two forms, one is that the negative peak only appears at high frequencies, and the other is two adjacent peaks with opposite signs. In addition, the resistivity, circularly polarized light and magnetic oscillation of Hall conductivity are studied.

Magnetic-Field-Driven Electron Dynamics in Graphene

Graphene exhibits unique optoelectronic properties originating from the band structure at the Dirac points. It is an ideal model structure to study the electronic and optical properties under the influence of the applied magnetic field. In graphene, electric field, laser pulse, and voltage can create electron dynamics which is influenced by momentum dispersion. However, computational modeling of momentum-influenced electron dynamics under the applied magnetic field remains challenging. Here, we perform computational modeling of the photoexcited electron dynamics achieved in graphene under an applied magnetic field. Our results show that magnetic field leads to local deviation from momentum conservation for charge carriers. With the increasing magnetic field, the delocalization of electron probability distribution increases and forms a cyclotron-like trajectory. Our work facilitates understanding of momentum resolved magnetic field effect on non-equilibrium properties of graphene, which is critical for optoelectronic and photovoltaic applications.

Electronic spectrum of Kekulé patterned graphene considering second neighbor-interactions

The effects of second-neighbor interactions in Kekulé-Y patterned graphene electronic properties are studied starting from a tight-binding Hamiltonian. Thereafter, a low-energy effective Hamiltonian is obtained by projecting the high energy bands at the Γ point into the subspace defined by the Kekulé wave vector. The spectrum of the low energy Hamiltonian is in excellent agreement with the one obtained from a numerical diagonalization of the full tight-binding Hamiltonian. The main effect of the second-neighbour interaction is that a set of bands gains an effective mass and a shift in energy, thus lifting the degeneracy of the conduction bands at the Dirac point. This band structure is akin to a 'pseudo spin-one Dirac cone', a result expected for honeycomb lattices with a distinction between one third of the atoms in one sublattice. Finally, we present a study of Kekulé patterned graphene nanoribbons. This shows that the previous effects are enhanced as the width decreases. Moreover, edge states become dispersive, as expected due to second neighbors interaction, but here the Kek-Y bond texture results in an hybridization of both edge states. The present study shows the importance of second neighbors in realistic models of Kekulé patterned graphene, specially at surfaces.

Novel electric field effects on magneto-optical conductivity in eight-Pmmnborophene

We theoretically study the Landau levels and the magneto-optical conductivity of eight-Pmmnborophene in the presence of a perpendicular magnetic field and an inplane electric field. We find that in the absence of the inplane electric field, the magneto-optical conductivity of eight-Pmmnborophene presents a series of striking single resonance peaks as functions of the frequencyω, and the longitudinal conductivities are found to be anisotropic due to its anisotropic tilted Dirac cones. In the presence of the inplane electric field, some novel effects are predicted on the Landau levels and the magneto-optical conductivity. The Landau level spacings in the two tilted Dirac cones are different, which lifts the degeneracy of the twofold valley, and the magneto-optical conductivity appears a double peak structure. We also discuss the influence of the chemical potential between different Landau levels on the double peak of the magneto-optical response. The valley related magneto-optical properties in the anisotropic structure may make eight-Pmmnborophene a candidate for the new optical devices.

Interacting chiral electrons at the 2D Dirac points: a review

The pseudo-relativistic chiral electrons in 2D graphene and 3D topological semimetals, known as the massless Dirac or Weyl fermions, constitute various intriguing issues in modern condensed-matter physics. In particular, the issues linked to the Coulomb interaction between the chiral electrons attract great attentions due to their unusual features, namely, the interaction is not screened and has a long-ranged property near the charge-neutrality point, in clear contrast to its screened and short-ranged properties in the conventional correlated materials. In graphene, this long-range interaction induces an anomalous logarithmic renormalization of the Fermi velocity, which causes a nonlinear reshaping of its Dirac cone. In addition, for strong interactions, it even leads to the predictions of an excitonic condensation with a spontaneous mass generation. The interaction, however, would seem to be not that large in graphene, so that the latter phenomenon appears to have not yet been observed. Contrastingly, the interaction is probably large in the pressurized organic materialα-(BEDT-TTF)₂I₃, where a 2D massless-Dirac-fermion phase emerges next to a correlated insulating phase. Therefore, an excellent testing ground would appear in this material for the studies of both the velocity renormalization and the mass generation, as well as for those of the short-range electronic correlations. In this review, we give an overview of the recent progress on the understanding of such interacting chiral electrons in 2D, by placing particular emphasis on the studies in graphene andα-(BEDT-TTF)₂I₃. In the first half, we briefly summarize our current experimental and theoretical knowledge about the interaction effects in graphene, then turn attentions to the understanding inα-(BEDT-TTF)₂I₃, and highlight its relevance to and difference from graphene. The second half of this review focusses on the studies linked to the nuclear magnetic resonance experiments and the associated model calculations inα-(BEDT-TTF)₂I₃. These studies allow us to discuss the anisotropic reshaping of a tilted Dirac cone together with various electronic correlations, and the precursor excitonic dynamics growing prior to a condensation. We see these provide unique opportunities to resolve the momentum dependence of the spin excitations and fluctuations that are strongly influenced by the long-range interaction near the Dirac points.

Magnetoplasmon-surface phonon polaritons' coupling effects in radiative heat transfer

In this work, the coupling of magnetoplasmon polaritons (MPP) to surface phonon polaritons (SPhPs) in near-field radiative heat transfer is theoretically investigated. The system is composed of two parallel graphene-coated SiO₂ substrates. By applying an external magnetic field, the separated branches of MPPs can couple with SPhPs to form tunable modes. The behavior remolds the energy transport of the system. The relative thermal magnetoresistance ratio can reach values of up to 160% for a magnetic field of 8 T. In addition, the thermal stealthy for the coated graphene is realized by tuning the intensity of fields. This work has substantial importance to graphene-based magneto-optical devices.

Observation of Terahertz-Induced Magnetooscillations in Graphene

When high-frequency radiation is incident upon graphene subjected to a perpendicular magnetic field, graphene absorbs incident photons by allowing transitions between nearest Landau levels that follow strict selection rules dictated by angular momentum conservation. Here, we show a qualitative deviation from this behavior in high-quality graphene devices exposed to terahertz (THz) radiation. We demonstrate the emergence of a pronounced THz-driven photoresponse, which exhibits low-field magnetooscillations governed by the ratio of the frequency of the incoming radiation and the quasiclassical cyclotron frequency. We analyze the modifications of generated photovoltage with the radiation frequency and carrier density and demonstrate that the observed photoresponse shares a common origin with microwave-induced resistance oscillations discovered in GaAs-based heterostructures; however, in graphene it appears at much higher frequencies and persists above liquid nitrogen temperatures. Our observations expand the family of radiation-driven phenomena in graphene, paving the way for future studies of nonequilibrium electron transport.

Transient lensing from a photoemitted electron gas imaged by ultrafast electron microscopy

Understanding and controlling ultrafast charge carrier dynamics is of fundamental importance in diverse fields of (quantum) science and technology. Here, we create a three-dimensional hot electron gas through two-photon photoemission from a copper surface in vacuum. We employ an ultrafast electron microscope to record movies of the subsequent electron dynamics on the picosecond-nanosecond time scale. After a prompt Coulomb explosion, the subsequent dynamics is characterized by a rapid oblate-to-prolate shape transformation of the electron gas, and periodic and long-lived electron cyclotron oscillations inside the magnetic field of the objective lens. In this regime, the collective behavior of the oscillating electrons causes a transient, mean-field lensing effect and pronounced distortions in the images. We derive an analytical expression for the time-dependent focal length of the electron-gas lens, and perform numerical electron dynamics and probe image simulations to determine the role of Coulomb self-fields and image charges. This work inspires the visualization of cyclotron dynamics inside two-dimensional electron-gas materials and enables the elucidation of electron/plasma dynamics and properties that could benefit the development of high-brightness electron and X-ray sources.

Cyclotron Resonance Study of Monolayer Graphene under Double Moiré Potentials

We report the first cyclotron resonance study of monolayer graphene under double-moiré potentials in which the crystal axis of graphene is nearly aligned to those of both the top and bottom hexagonal boron nitride (h-BN) layers. Under mid-infrared light irradiation, we observe cyclotron resonance absorption with the following unique features: (1) cyclotron resonance magnetic field B_CR is entirely different from that of nonaligned monolayer graphene, (2) B_CR exhibits strong electron-hole asymmetry, and (3) splitting of B_CR is observed for |ν| < 1, with the split maximum at |ν| = 1, resulting in eyeglass-shaped trajectories. These features are well explained by considering the large bandgap induced by the double moiré potentials, the electron-hole asymmetry in the Fermi velocity, and the Fermi-level-dependent enhancement of spin gaps, which suggests a large electron-electron correlation contribution in this system.

Unconventional valley-dependent optical selection rules and landau level mixing in bilayer graphene

Selection rules are of vital importance in determining the basic optical properties of atoms, molecules and semiconductors. They provide general insights into the symmetry of the system and the nature of relevant electronic states. A two-dimensional electron gas in a magnetic field is a model system where optical transitions between Landau levels (LLs) are described by simple selection rules associated with the LL index N. Here we examine the inter-LL optical transitions of high-quality bilayer graphene by photocurrent spectroscopy measurement. We observed valley-dependent optical transitions that violate the conventional selection rules Δ|N| = ± 1. Moreover, we can tune the relative oscillator strength by tuning the bilayer graphene bandgap. Our findings provide insights into the interplay between magnetic field, band structure and many-body interactions in tunable semiconductor systems, and the experimental technique can be generalized to study symmetry-broken states and low energy magneto-optical properties of other nano and quantum materials.

THz white light cavity with nonlinear dispersion in graphene

A white light cavity (WLC) scheme is proposed to achieve broadband response in the terahertz (THz) region by enhanced nonlinear dispersion in a magnetized graphene system. In the weak probe field limit, the cavity linewidth is narrowed due to electromagnetically induced transparency, and then it becomes nearly as broad as the empty-cavity linewidth under the condition of Autler-Towns splitting. It is interesting to find that the cavity linewidth can be further broadened by enhanced nonlinear dispersion. The simulation result shows that the response range of the cavity is from 6.273 THz to 6.308 THz under the given condition, which is nearly 11 times larger than the empty-cavity linewidth. Furthermore, the improvement in cavity transmission and the response of WLC at different frequencies are investigated.

The discovery of dynamic chiral anomaly in a Weyl semimetal NbAs

The experimental discovery of Weyl semimetals offers unprecedented opportunities to study Weyl physics in condensed matters. Unique electromagnetic response of Weyl semimetals such as chiral magnetic effect has been observed and presented by the axial θ E · B term in electromagnetic Lagrangian (E and B are the electric and magnetic field, respectively). But till now, the experimental progress in this direction in Weyl semimetals is restricted to the DC regime. Here we report experimental access to the dynamic regime in Weyl semimetal NbAs by combining the internal deformation potential of coupled phonons with applied static magnetic field. While the dynamic E · B field is realized, it produces an anomalous phonon activity with a characteristic angle-dependence. Our results provide an effective approach to achieve the dynamic regime beyond the widely-investigated DC limit which enables the coupling between the Weyl fermions and the electromagnetic wave for further study of novel light-matter interactions in Weyl semimetals.

Unique electronmagnetic response of Weyl semimetals have only been reported in static field regime. Here, the authors report evidence of a dynamical chiral anomaly response realized by internal collective lattice deformation with an external static magnetic field in a Weyl semimetal NbAs.

Electromagnetically induced holographic imaging using monolayer graphene

Graphene exhibits remarkable optical and electronic properties when interacts with electromagnetic field. These properties play a vital role in a broad range of applications, such as, optical communication, optical storage, biomedical imaging and security purposes. Based on electromagnetically induced grating (EIG), we study lensless holographic imaging via quantized energy levels of two-dimensional (2D) monolayer graphene model. We observe that by exploiting electromagnetically induced grating (EIG), holographic interference patterns via electromagnetically induced classical holographic imaging (EICHI) and, non locally, electromagnetically induced quantum holographic imaging (EIQHI) can be obtained in the infrared range (THz) of the spectrum. We notice that for EIQHI one can obtain image magnification using monolayer graphene via manipulation of certain controllable parameters. The scheme provides an experimentally viable option for the classical and quantum mechanical holographic imaging and possibilities for the design of graphene-based quantum mechanical devices which can have many applications.

Valley and Zeeman Splittings in Multilayer Epitaxial Graphene Revealed by Circular Polarization Resolved Magneto-infrared Spectroscopy

Circular-polarization-resolved magneto-infrared studies of multilayer epitaxial graphene (MEG) are performed using tunable quantum cascade lasers in high magnetic fields up to 17.5 T. Landau level (LL) transitions in the monolayer and bilayer graphene inclusions of MEG are resolved, and considerable electron-hole asymmetry is observed in the extracted electronic band structure. For monolayer graphene, a four-fold splitting of the n = 0 to n = 1 LL transition is evidenced and attributed to the lifting of the valley and spin degeneracy of the zeroth LL and the broken electron-hole symmetry. The magnetic field dependence of the splitting further reveals its possible mechanisms. The best fit to experimental data yields effective g-factors, g_VS^* = 6.7 and g_ZS^* = 4.8, for the valley and Zeeman splittings, respectively.

Colossal infrared and terahertz magneto-optical activity in a two-dimensional Dirac material

When two-dimensional electron gases (2DEGs) are exposed to a magnetic field, they resonantly absorb electromagnetic radiation via electronic transitions between Landau levels¹. In 2DEGs with a Dirac spectrum, such as graphene, theory predicts an exceptionally high infrared magneto-absorption, even at zero doping^2-5. However, the measured Landau-level magneto-optical effects in graphene have been much weaker than expected^2,6-12 because of imperfections in the samples available for such experiments. Here, we measure magneto-transmission and Faraday rotation in high-mobility encapsulated monolayer graphene using a custom-designed set-up for magneto-infrared microspectroscopy. Our results show strongly enhanced magneto-optical activity in the infrared and terahertz ranges, characterized by absorption of light near to the 50% maximum allowed, 100% magnetic circular dichroism and high Faraday rotation. Considering that sizeable effects have been already observed at routinely achievable magnetic fields, our findings demonstrate the potential of magnetic tuning in 2D Dirac materials for long-wavelength optoelectronics and plasmonics.

Peculiar optical properties of bilayer silicene under the influence of external electric and magnetic fields

We conduct a comprehensive investigation of the effect of an applied electric field on the optical and magneto-optical absorption spectra for AB-bt (bottom-top) bilayer silicene. The generalized tight-binding model in conjunction with the Kubo formula is efficiently employed in the numerical calculations. The electronic and optical properties are greatly diversified by the buckled lattice structure, stacking configuration, intralayer and interlayer hopping interactions, spin-orbital couplings, as well as the electric and magnetic fields (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${E}_{z}\hat{z}$$\end{document}Ezzˆ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\& $$\end{document}&\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${B}_{z}\hat{z}$$\end{document}Bzzˆ). An electric field induces spin-split electronic states, a semiconductor-metal phase transitions and the Dirac cone formations in different valleys, leading to the special absorption features. The E_z-dependent low-lying Landau levels possess lower degeneracy, valley-created localization centers, peculiar distributions of quantum numbers, well-behaved and abnormal energy spectra in B_z-dependencies, and the absence of anti-crossing behavior. Consequently, the specific magneto-optical selection rules exist for diverse excitation categories under certain critical electric fields. The optical gaps are reduced as E_z is increased, but enhanced by B_z, in which the threshold channel might dramatically change in the former case. These characteristics are in sharp contrast with those for layered graphene.

Landau Quantization in Coupled Weyl Points: A Case Study of Semimetal NbP

Weyl semimetal (WSM) is a newly discovered quantum phase of matter that exhibits topologically protected states characterized by two separated Weyl points with linear dispersion in all directions. Here, via combining theoretical analysis and magneto-infrared spectroscopy of an archetypal Weyl semimetal, niobium phosphide, we demonstrate that the coupling between Weyl points can significantly modify the electronic structure of a WSM and provide a new twist to the protected states. These findings suggest that the coupled Weyl points should be considered as the basis for analysis of realistic WSMs.

Shifted Landau levels in curved graphene sheets

We study the Landau levels in curved graphene sheets by measuring the discrete energy spectrum in the presence of a magnetic field. We observe that in rippled graphene sheets, the Landau energy levels satisfy the same square root dependence on the energy quantum number as in flat sheets, [Formula: see text]. Though, we find that the Landau levels in curved sheets are shifted towards lower energies by an amount proportional to the average spatial deformation of the sheet. Our findings are relevant for the quantum Hall effect in curved graphene sheets, which is directly related to Landau quantization. For the purpose of this study, we develop a new numerical method, based on the quantum lattice Boltzmann method, to solve the Dirac equation on curved manifolds, describing the low-energetic states in strained graphene sheets.

Chiral Landau levels in Weyl semimetal NbAs with multiple topological carriers

Recently, Weyl semimetals have been experimentally discovered in both inversion-symmetry-breaking and time-reversal-symmetry-breaking crystals. The non-trivial topology in Weyl semimetals can manifest itself with exotic phenomena, which have been extensively investigated by photoemission and transport measurements. Despite the numerous experimental efforts on Fermi arcs and chiral anomaly, the existence of unconventional zeroth Landau levels, as a unique hallmark of Weyl fermions, which is highly related to chiral anomaly, remains elusive owing to the stringent experimental requirements. Here, we report the magneto-optical study of Landau quantization in Weyl semimetal NbAs. High magnetic fields drive the system toward the quantum limit, which leads to the observation of zeroth chiral Landau levels in two inequivalent Weyl nodes. As compared to other Landau levels, the zeroth chiral Landau level exhibits a distinct linear dispersion in magnetic field direction and allows the optical transitions without the limitation of zero z momentum or [Formula: see text] magnetic field evolution. The magnetic field dependence of the zeroth Landau levels further verifies the predicted particle-hole asymmetry of the Weyl cones. Meanwhile, the optical transitions from the normal Landau levels exhibit the coexistence of multiple carriers including an unexpected massive Dirac fermion, pointing to a more complex topological nature in inversion-symmetry-breaking Weyl semimetals. Our results provide insights into the Landau quantization of Weyl fermions and demonstrate an effective tool for studying complex topological systems.

Terahertz magneto-optical properties of bi- and tri-layer graphene

Magneto-optical (MO) properties of bi- and tri-layer graphene are investigated utilizing terahertz time-domain spectroscopy (THz TDS) in the presence of a strong magnetic field at room-temperature. In the Faraday configuration and applying optical polarization measurements, we measure the real and imaginary parts of the longitudinal and transverse MO conductivities of different graphene samples. The obtained experimental data fits very well with the classical MO Drude formula. Thus, we are able to obtain the key sample and material parameters of bi- and tri-layer graphene, such as the electron effective mass, the electronic relaxation time and the electron density. It is found that in high magnetic fields the electronic relaxation time τ for bi- and tri-layer graphene increases with magnetic field B roughly in a form [Formula: see text]. Most importantly, we obtain the electron effective mass for bi- and tri-layer graphene at room-temperature under non-resonant conditions. This work shows how the advanced THz MO techniques can be applied for the investigation into fundamental physics properties of atomically thin 2D electronic systems.

Ultrafast Terahertz Nonlinear Optics of Landau Level Transitions in a Monolayer Graphene

We investigated the ultrafast terahertz (THz) nonlinearity in a monolayer graphene under the strong magnetic field using THz pump-THz probe spectroscopy. An ultrafast suppression of the Faraday rotation associated with inter-Landau level (LL) transitions is observed, reflecting the Dirac electron character of nonequidistant LLs with large transition dipole moments. A drastic modulation of electron distribution in LLs is induced by far off-resonant THz pulse excitation in the transparent region. Numerical simulation based on the density matrix formalism without rotating-wave approximation reproduces the experimental results. Our results indicate that the strong light-matter coupling regime is realized in graphene, with the Rabi frequency exceeding the carrier wave frequency and even the relevant energy scale of the inter-LL transition.

Many-Particle Effects in the Cyclotron Resonance of Encapsulated Monolayer Graphene

We study the infrared cyclotron resonance of high-mobility monolayer graphene encapsulated in hexagonal boron nitride, and simultaneously observe several narrow resonance lines due to interband Landau-level transitions. By holding the magnetic field strength B constant while tuning the carrier density n, we find the transition energies show a pronounced nonmonotonic dependence on the Landau-level filling factor, ν∝n/B. This constitutes direct evidence that electron-electron interactions contribute to the Landau-level transition energies in graphene, beyond the single-particle picture. Additionally, a splitting occurs in transitions to or from the lowest Landau level, which is interpreted as a Dirac mass arising from coupling of the graphene and boron nitride lattices.

Controllable population dynamics in Landau-quantized graphene

In this paper, we carry out a theoretical investigation on the population dynamics of graphene system under continuous-wave (cw) laser and chirped pulse excitation. Results of our numerical simulations reveal that complete population transfer from an initially occupied ground state to the initially unoccupied excited states can be achieved by choosing appropriate values of the chirp rate, the laser field intensity and frequency, as well as other system parameters. Also, we observe coherent Rabi-like population oscillations between the initial ground state and the excited final state. It is induced by the combined effect of cw and chirped-pulse laser fields. These results will contribute to the understanding of carrier-carrier and carrier-phonon interactions in graphene system, and may find applications in graphene-based high-speed electronic and optoelectronic devices.

Light-Induced Fractional Quantum Hall Phases in Graphene

We show how to realize two-component fractional quantum Hall phases in monolayer graphene by optically driving the system. A laser is tuned into resonance between two Landau levels, giving rise to an effective tunneling between these two synthetic layers. Remarkably, because of this coupling, the interlayer interaction at nonzero relative angular momentum can become dominant, resembling a hollow-core pseudopotential. In the weak tunneling regime, this interaction favors the formation of singlet states, as we explicitly show by numerical diagonalization, at fillings ν=1/2 and ν=2/3. We discuss possible candidate phases, including the Haldane-Rezayi phase, the interlayer Pfaffian phase, and a Fibonacci phase. This demonstrates that our method may pave the way towards the realization of non-Abelian phases, as well as the control of topological phase transitions, in graphene quantum Hall systems using optical fields and integrated photonic structures.

Two-Dimensional Massless Dirac Fermions in Antiferromagnetic AFe_{2}As_{2} (A=Ba,Sr)

We report infrared studies of AFe_{2}As_{2} (A=Ba, Sr), two representative parent compounds of iron-arsenide superconductors, at magnetic fields (B) up to 17.5 T. Optical transitions between Landau levels (LLs) were observed in the antiferromagnetic states of these two parent compounds. Our observation of a sqrt[B] dependence of the LL transition energies, the zero-energy intercepts at B=0  T under the linear extrapolations of the transition energies and the energy ratio (∼2.4) between the observed LL transitions, combined with the linear band dispersions in two-dimensional (2D) momentum space obtained by theoretical calculations, demonstrates the existence of massless Dirac fermions in the antiferromagnet BaFe_{2}As_{2}. More importantly, the observed dominance of the zeroth-LL-related absorption features and the calculated bands with extremely weak dispersions along the momentum direction k_{z} indicate that massless Dirac fermions in BaFe_{2}As_{2} are 2D. Furthermore, we find that the total substitution of the barium atoms in BaFe_{2}As_{2} by strontium atoms not only maintains 2D massless Dirac fermions in this system, but also enhances their Fermi velocity, which supports that the Dirac points in iron-arsenide parent compounds are topologically protected.

Observation of ultrahigh mobility surface states in a topological crystalline insulator by infrared spectroscopy

Topological crystalline insulators possess metallic surface states protected by crystalline symmetry, which are a versatile platform for exploring topological phenomena and potential applications. However, progress in this field has been hindered by the challenge to probe optical and transport properties of the surface states owing to the presence of bulk carriers. Here, we report infrared reflectance measurements of a topological crystalline insulator, (001)-oriented Pb_1−xSn_xSe in zero and high magnetic fields. We demonstrate that the far-infrared conductivity is unexpectedly dominated by the surface states as a result of their unique band structure and the consequent small infrared penetration depth. Moreover, our experiments yield a surface mobility of 40,000 cm² V⁻¹ s⁻¹, which is one of the highest reported values in topological materials, suggesting the viability of surface-dominated conduction in thin topological crystalline insulator crystals. These findings pave the way for exploring many exotic transport and optical phenomena and applications predicted for topological crystalline insulators.

Probing optical and transport properties of the surface states in topological crystalline insulators remains a challenge. Here, Wang et al. demonstrate that the far-infrared conductivity of Pb_1−xSn_xSe (x = 0.23−0.25) single crystals is dominated by the surface states where carriers show a high surface mobility of 40,000 cm² V⁻¹ s⁻¹.

Dynamic control of coherent pulses via destructive interference in graphene under Landau quantization

We analyze the destructive interference in monolayer graphene under Landau quantization in a time-dependent way by using the Bloch-Maxwell formalism. Based on this analysis, we investigate the dynamics control of an infrared probe and a terahertz (THz) switch pulses in graphene. In presence of the THz switch pulse, the destructive interference take places and can be optimized so that the monolayer graphene is completely transparent to the infrared probe pulse. In absence of the THz switch pulse, however, the infrared probe pulse is absorbed due to such a interference does not take place. Furthermore, we provide a clear physics insight of this destructive interference by using the classical dressed-state theory. Conversely, the present model may be rendered either absorbing or transparent to the THz switch pulse. By choosing appropriate wave form of the probe and switch pulses, we show that both infrared probe and THz switch pulses exhibit the steplike transitions between absorption and transparency. Such steplike transitions can be used to devise a versatile quantum interference-based solid-state optical switching with distinct wave-lengths for optical communication devices.

Optical signatures of parity anomaly in a gapped graphene-like system

Parity anomaly refers to the violation of coordinate reflection symmetry induced by the quantum fluctuations. It is proposed to exist in a graphene-like system with a finite bare mass for Dirac fermions, and manifests itself as a parity-violating quantum correction to the current of each species of fermions. Coulomb interaction greatly increases the fermion mass, and produces various types of excitons. Of particular interest is the ρ-exciton, which is directly connected to parity anomaly and can be generated by absorbing a specific photon. The exciton is a particle-hole bound state, and can be regarded as condensed-matter analogue of meson composed of quark-anti-quark pair. By virtue of this correspondence, we analyze the optical conductivity and calculate the mass of ρ-exciton by employing the Shifman-Vainshtein-Zakharov sum rule method that is widely used in the studies of hadron phenomenology. We show that ρ-exciton leads to a sharp peak in the optical conductivity, which is observable in optical experiments. Moreover, we study the impact of scalar-like excitons on two-photon processes by computing the decay amplitude, and also find peaks in the Raman spectra.

Faraday Rotation Due to Surface States in the Topological Insulator (Bi1-xSbx)2Te3

Using magneto-infrared spectroscopy, we have explored the charge dynamics of (Bi,Sb)₂Te₃ thin films on InP substrates. From the magneto-transmission data we extracted three distinct cyclotron resonance (CR) energies that are all apparent in the broad band Faraday rotation (FR) spectra. This comprehensive FR-CR data set has allowed us to isolate the response of the bulk states from the intrinsic surface states associated with both the top and bottom surfaces of the film. The FR data uncovered that electron- and hole-type Dirac Fermions reside on opposite surfaces of our films, which paves the way for observing many exotic quantum phenomena in topological insulators.

Spectroscopic evidence for bulk-band inversion and three-dimensional massive Dirac fermions in ZrTe5

Three-dimensional topological insulators (3D TIs) represent states of quantum matters in which surface states are protected by time-reversal symmetry and an inversion occurs between bulk conduction and valence bands. However, the bulk-band inversion, which is intimately tied to the topologically nontrivial nature of 3D Tis, has rarely been investigated by experiments. Besides, 3D massive Dirac fermions with nearly linear band dispersions were seldom observed in TIs. Recently, a van der Waals crystal, ZrTe₅, was theoretically predicted to be a TI. Here, we report an infrared transmission study of a high-mobility [∼33,000 cm²/(V ⋅ s)] multilayer ZrTe₅ flake at magnetic fields (B) up to 35 T. Our observation of a linear relationship between the zero-magnetic-field optical absorption and the photon energy, a bandgap of ∼10 meV and a [Formula: see text] dependence of the Landau level (LL) transition energies at low magnetic fields demonstrates 3D massive Dirac fermions with nearly linear band dispersions in this system. More importantly, the reemergence of the intra-LL transitions at magnetic fields higher than 17 T reveals the energy cross between the two zeroth LLs, which reflects the inversion between the bulk conduction and valence bands. Our results not only provide spectroscopic evidence for the TI state in ZrTe₅ but also open up a new avenue for fundamental studies of Dirac fermions in van der Waals materials.

Coulomb excitations of monolayer germanene

The feature-rich electronic excitations of monolayer germanene lie in the significant spin-orbit coupling and the buckled structure. The collective and single-particle excitations are diversified by the magnitude and direction of transferred momentum, the Fermi energy and the gate voltage. There are four kinds of plasmon modes, according to the unique frequency- and momentum-dependent phase diagrams. They behave as two-dimensional acoustic modes at long wavelength. However, for the larger momenta, they might change into another kind of undamped plasmons, become the seriously suppressed modes in the heavy intraband e-h excitations, keep the same undamped plasmons, or decline and then vanish in the strong interband e-h excitations. Germanene, silicene and graphene are quite different from one another in the main features of the diverse plasmon modes.

Layer-number dependent and structural defect related optical properties of InSe

We present systematic investigations on the layer-dependent optical properties of InSe and modify its excitonic states by electron beam irradiation.

Electronic and optical properties of graphene nanoribbons in external fields

A review work is done for the electronic and optical properties of graphene nanoribbons in magnetic, electric, composite, and modulated fields. Effects due to the lateral confinement, curvature, stacking, non-uniform subsystems and hybrid structures are taken into account. The special electronic properties, induced by complex competitions between external fields and geometric structures, include many one-dimensional parabolic subbands, standing waves, peculiar edge-localized states, width- and field-dependent energy gaps, magnetic-quantized quasi-Landau levels, curvature-induced oscillating Landau subbands, crossings and anti-crossings of quasi-Landau levels, coexistence and combination of energy spectra in layered structures, and various peak structures in the density of states. There exist diverse absorption spectra and different selection rules, covering edge-dependent selection rules, magneto-optical selection rule, splitting of the Landau absorption peaks, intragroup and intergroup Landau transitions, as well as coexistence of monolayer-like and bilayer-like Landau absorption spectra. Detailed comparisons are made between the theoretical calculations and experimental measurements. The predicted results, the parabolic subbands, edge-localized states, gap opening and modulation, and spatial distribution of Landau subbands, have been identified by various experimental measurements.

Observation of an anisotropic Dirac cone reshaping and ferrimagnetic spin polarization in an organic conductor

The Coulomb interaction among massless Dirac fermions in graphene is unscreened around the isotropic Dirac points, causing a logarithmic velocity renormalization and a cone reshaping. In less symmetric Dirac materials possessing anisotropic cones with tilted axes, the Coulomb interaction can provide still more exotic phenomena, which have not been experimentally unveiled yet. Here, using site-selective nuclear magnetic resonance, we find a non-uniform cone reshaping accompanied by a bandwidth reduction and an emergent ferrimagnetism in tilted Dirac cones that appear on the verge of charge ordering in an organic compound. Our theoretical analyses based on the renormalization-group approach and the Hubbard model show that these observations are the direct consequences of the long-range and short-range parts of the Coulomb interaction, respectively. The cone reshaping and the bandwidth renormalization, as well as the magnetic behaviour revealed here, can be ubiquitous and vital for many Dirac materials.

Temperature-driven massless Kane fermions in HgCdTe crystals

It has recently been shown that electronic states in bulk gapless HgCdTe offer another realization of pseudo-relativistic three-dimensional particles in condensed matter systems. These single valley relativistic states, massless Kane fermions, cannot be described by any other relativistic particles. Furthermore, the HgCdTe band structure can be continuously tailored by modifying cadmium content or temperature. At critical concentration or temperature, the bandgap collapses as the system undergoes a semimetal-to-semiconductor topological phase transition between the inverted and normal alignments. Here, using far-infrared magneto-spectroscopy we explore the continuous evolution of band structure of bulk HgCdTe as temperature is tuned across the topological phase transition. We demonstrate that the rest mass of Kane fermions changes sign at critical temperature, whereas their velocity remains constant. The velocity universal value of (1.07±0.05) × 10⁶ m s⁻¹ remains valid in a broad range of temperatures and Cd concentrations, indicating a striking universality of the pseudo-relativistic description of the Kane fermions in HgCdTe.

Kane fermions are predicted to be tunable with external parameters such as temperature. Here, Teppe et al. show a band structure evolution of bulk HgCdTe as temperature is tuned across topological phase transition, demonstrating that Kane fermions change sign in rest-mass and remain constant in velocity.

Rich magneto-absorption spectra of AAB-stacked trilayer graphene

A generalized tight-binding model is developed to investigate the feature-rich magneto-optical properties of AAB-stacked trilayer graphene. Three intragroup and six intergroup inter-Landau-level (inter-LL) optical excitations largely enrich magneto-absorption peaks. In general, the former are much higher than the latter, depending on the phases and amplitudes of LL wavefunctions. The absorption spectra exhibit single- or twin-peak structures which are determined by quantum modes, LL energy spectra and Fermion distribution. The splitting LLs, with different localization centers (2/6 and 4/6 positions in a unit cell), can generate very distinct absorption spectra. There exist extra single peaks because of LL anti-crossings. AAB, AAA, ABA, and ABC stackings considerably differ from one another in terms of the inter-LL category, frequency, intensity, and structure of absorption peaks. The main characteristics of LL wavefunctions and energy spectra and the Fermi-Dirac function are responsible for the configuration-enriched magneto-optical spectra.

Effective hyper-Raman scattering via inhibiting electromagnetically induced transparency in monolayer graphene under an external magnetic field

We propose and analyze an effective scheme to generate hyper-Raman scattering via inhibiting electromagnetically induced transparency (EIT) in a monolayer graphene under a magnetic field. By solving the Schrödinger-Maxwell formalism, we derive explicitly analytical expressions for linear susceptibility, nonlinear susceptibility, and generated Raman electric field under the steady-state condition. Based on dressed-state theory, our results show a competition between EIT and hyper-Raman scattering, and the hyper-Raman process is totally dominant when multiphoton destructive interference is completely suppressed.

Gate-Dependent Electronic Raman Scattering in Graphene

We report the direct observation of polarization resolved electronic Raman scattering in a gated monolayer graphene device. The evolution of the electronic Raman scattering spectra with gate voltage and its polarization dependence are in full agreement with theoretical expectations for nonresonant Raman processes involving interband electron-hole excitations across the Dirac cone. We further show that the spectral dependence of the electronic Raman scattering signal can be simply described by the dynamical polarizability of graphene in the long wavelength limit. The possibility to directly observe Dirac fermion excitations in graphene opens the way to promising Raman investigations of electronic properties of graphene and other 2D crystals.

Faraday rotation in bilayer graphene-based integrated microcavity

Bernal-stacked bilayer graphene has rich ground states with various broken symmetries, allowing the existence of magneto-optical (MO) effects even in the absence of an external magnetic field. Here we report controllable Faraday rotation (FR) of bilayer graphene induced by electrostatic gate voltage, whose value is 10 times smaller than the case of single layer graphene with a magnetic field. A proposed bilayer graphene-based microcavity configuration enables the enhanced FR angle due to the large localized electromagnetic field. Our results offer unique opportunities to apply bilayer graphene for MO devices.