Gapped Dirac Materials Research Articles

Gapped Dirac materials and quantum valley currents in dual-gated hBN/bilayer-graphene heterostructures

Gapped Dirac materials and quantum valley currents in dual-gated hBN/bilayer-graphene heterostructures

Optical valley separation in two-dimensional semimetals with tilted Dirac cones

Quasiparticles emerging in crystalline materials can possess a binary flavor known as the valley quantum number which can be used as a basis to encode information in an emerging class of valleytronic devices. Here we show that two-dimensional semimetals with tilted Dirac cones in the electronic band structure exhibit spatial separation of carriers belonging to different valleys under illumination. In stark contrast to gapped Dirac materials this optovalleytronic phenomenon occurs in systems with intact inversion and time-reversal symmetry that host gapless Dirac cones in the band structure, thereby retaining the exceptional graphene-like transport properties. We thus demonstrate that optical valley separation is possible at arbitrarily low photon frequencies including the deep infrared and terahertz regimes with full gate tunability via Pauli blocking. As a specific example of our theory, we predict tunable valley separation in the proposed two-dimensional tilted Dirac cone semimetal 8-Pmmn borophene for incident infrared photons at room temperature. This work highlights the potential of two-dimensional tilted Dirac cone materials as a platform for tunable broadband optovalleytronic applications.

Light-induced topological phases in two-dimensional gapped Dirac materials

We present a comparative study of light-induced topological phases in two-dimensional massive Dirac models with and without quadratic corrections, which depicts different inversion symmetry-breaking Dirac materials. We find that a light has two effects on the Floquet band topology: it not only inverts the massive bands near the Dirac points but also introduces pseudospin-orbital coupling around the resonant points of light-matter interaction. Depending on the presence or absence of the quadratic corrections, the interplay of these two effects of light results in versatile topological phases with dissipationless valley polarized edge currents. In particular, without quadratic correction as exemplified by gapped graphene, a circularly polarized light induces a pair of in-gap edge states at each valley, which propagate on the same direction at a fixed boundary. A linearly polarized light also induces a pair of in-gap edge states, while propagating on the opposite direction at a fixed boundary. When including the quadratic correction as exemplified by monolayer transition-metal dichalcogenides, a circularly polarized light can induce two pairs of in-gap edge states located at a single valley, while a linearly polarized light does not induce any in-gap edge state. These edge currents as controlled by switching on/off the applied light and its polarization nature suggest an optical way to engineer valleytronic devices.

Floquet-engineered half-valley-metal state in two-dimensional gapped Dirac materials

The half-valley-metal (HVM) states where the gap of one valley is closed while the other valley remains semiconducting are quite crucial for achieving 100% valley polarization and valley-Hall-effect. However, the symmetry of materials makes the HVM states scarce. In this work, using Floquet theory, we demonstrate the laser-dressed HVM states in two-dimensional (2D) gapped-Dirac materials. We show that as a circularly polarized laser is applied to a 2D gapped-Dirac material, the gaps of the two valleys (K and K') can be regulated by varying the photon energy, amplitude and chirality of the laser. At specific photon energies and laser amplitudes, the linear energy-momentum dispersion of Dirac materials is restituted in one valley while the gap in the other valley is preserved. On the basis of first-principles calculations, we also propose a promising candidate material, boron antimonide (BSb) monolayer to achieve the laser-dressed HVM states. More interestingly, the Berry curvature in the two valleys can be tuned by changing the laser parameters.

Optical valleytronics of impurity states in two-dimensional Dirac materials

We analyze the valley selection rules for optical transitions from impurity states to the conduction band in two-dimensional Dirac materials, taking a monolayer of ${\mathrm{MoS}}_{2}$ as an example. We employ the analytical model of a shallow impurity potential which localizes electrons described by a spinor wave function, and, first, find the system eigenstates taking into account the presence of two valleys in the Brillouin zone. Then, we find the spectrum of the absorbance and calculate the photon-drag electric current due to the impurity-band transitions, drawing the general conclusions regarding the valley optical selection rules for the impurity-band optical transitions in gapped Dirac materials.

Anisotropic longitudinal optical conductivities of tilted Dirac bands in 1T′−MoS2

1T$^\prime$-MoS$_2$ exhibits valley-spin-polarized tilted Dirac bands in the presence of external vertical electric field and undergoes a topological phase transition between the topological insulator and band insulator around the critical value of the electric field. Within the linear response theory, we theoretically investigate the anisotropic longitudinal optical conductivities of tilted Dirac bands in both undoped and doped 1T$^\prime$-MoS$_2$, including the effects of the vertical electric field. The influence of the spin-orbit coupling gap, band tilting, and vertical electric field on the optical conductivities of tilted Dirac bands is revealed. A theoretical scheme for probing the topological phase transition in 1T$^\prime$-MoS$_2$ via exotic behaviors of longitudinal optical conductivities is proposed. The results for 1T$^\prime$-MoS$_2$ are expected to be qualitatively valid for other monolayer tilted gapped Dirac materials, such as $\alpha$-SnS$_2$, TaCoTe$_2$, and TaIrTe$_4$, due to the similarity in their band structures.

Mass fluctuations and absorption rates in dark-matter sensors based on Dirac materials

We study the mass fluctuations in gapped Dirac materials by treating the mass-term as both a continuous and discrete random variable. Gapped Dirac materials were proposed to be used as materials for Dark matter sensors. One thus would need to estimate the role of disorder and fluctuations on the interband absorption of dark matter. We find that both continuous and discrete fluctuations across the sample introduce tails (e.g. Lifshitz tails) in the density of states and the interband absorption rate. We estimate the strength of the gap filling and discuss implications of these fluctuations on the performance as sensors for Dark matter detection. The approach used in this work provides a basic framework to model the disorder by any arbitrary mechanism on the interband absorption of Dirac material sensors.

Thermoelectric transport coefficients of a Dirac electron gas in high magnetic fields

We study the thermoelectric transport properties of a three-dimensional massive relativistic fermion gas with screened Coulomb impurities in high magnetic fields where only the lowest Landau levels contribute to the transport. Our results can be applied to experimental results of gapless and gapped Dirac materials. We focus on the effects of the mass term and we show the main differences that arise compared to the massless Dirac fermions. The different behavior is shown to be relevant at higher magnetic fields. The calculations are performed in the framework of the linear response theory using the exact quantum mechanical solution of the system in a constant magnetic field. We prove that the Mott formula and the Wiedemann-Franz law are valid at low temperatures and use them to calculate the thermoelectric transport coefficients. We show that the temperature range where the low temperature approximation is valid increases with increasing magnetic fields. The magnetic field dependence of measurable quantities (i.e. conductivity, Seebeck coefficient, Nernst coefficient and thermal conductivity) strongly depend on the magnetic field dependence of the scattering rate, thus the result relies on the proper treatment of the impurities. In this work they are included through the first Born approximation using screened charged impurities as impurity potential. We show that the electric conductivity does not change qualitatively in the case of finite mass term. On the other hand we find that the mass term causes significantly different behavior in the Seebeck and Nernst coefficients.

Topological valley currents in bilayer graphene/hexagonal boron nitride superlattices

Graphene superlattices have recently been attracting growing interest as an emergent class of quantum metamaterials. In this paper, we report the observation of nonlocal transport in bilayer graphene (BLG) superlattices encapsulated between two hexagonal boron nitride (hBN) layers, which formed hBN/BLG/hBN moiré superlattices. We then employed these superlattices to detect a long-range charge-neutral valley current using an all-electrical method. The moiré superlattice with broken inversion symmetry leads to a “hot spot” at the charge-neutral point (CNP), and it harbors satellites of the CNP. We observed nonlocal resistance on the order of 1 kΩ, which obeys a scaling relation. This nonlocal resistance evolves from an analog of the quantum Hall effect but without magnetic field/time-reversal symmetry breaking, which is associated with a hot-spot-induced topological valley current. This study should pave the way for developing a Berry-phase-sensitive probe to detect hot spots in gapped Dirac materials with inversion-symmetry breaking.

Magnetoresistance of a three-dimensional Dirac gas

We study the transversal magnetoconductivity and magnetoresistance of a massive Dirac fermion gas. This can be used as a simple model for gapped Dirac materials. In the zero-mass limit, the case of gapless Dirac semimetals is also studied. In the case of Weyl semimetals, to reproduce the nonsaturating linear magnetoresistance seen in experiments, the use of screened charged impurities is inevitable. In this paper, these are included using the first Born approximation for the self-energy. The screening wave number is calculated using the random phase approximation with the polarization function taking into account the electron-electron interaction. The Hall conductivity is calculated analytically in the case of no impurities and is shown to be perfectly inversely proportional to the magnetic field. Thus the magnetic field dependence of the magnetoresistance is mainly determined by $\sigma_{xx}$. We show that in the extreme quantum limit at very high magnetic fields the gapped Dirac materials are expected to have $\sigma_{xx}\propto B^{-3}$ leading to $\varrho_{xx}\propto B^{-1}$, in contrast with the gapless case where $\sigma_{xx}\propto B^{-1}$ and $\varrho_{xx}\propto B$. At lower fields, we find that the effect of the mass term is negligible and in the region of the Shubnikov-de Haas oscillations the two systems behave almost identically. We suggest a phenomenological scattering rate that is able to reproduce the linear behavior at the oscillating region. We show that in the case of the scattering rate calculated using the Born approximation, the strength of the relative permittivity and the density of impurities affects the magnetic field dependence of the conductivity significantly.

Entropy spikes as a signature of Lifshitz transitions in the Dirac materials

We demonstrate theoretically that the characteristic feature of a 2D system undergoing N consequent Lifshitz topological transitions is the occurrence of spikes of entropy per particle s of a magnitude ±ln2/(J − 1/2) with 2 ≤ J ≤ N at low temperatures. We derive a general expression for s as a function of chemical potential, temperature and gap magnitude for the gapped Dirac materials. Inside the smallest gap, the dependence of s on the chemical potential exhibits a dip-and-peak structure in the temperature vicinity of the Dirac point. The spikes of the entropy per particles can be considered as a signature of the Dirac materials. These distinctive characteristics of gapped Dirac materials can be detected in transport experiments where the temperature is modulated in gated structures.

Anisotropic transport of normal metal-barrier-normal metal junctions in monolayer phosphorene

We study transport properties of a phosphorene monolayer in the presence of single and multiple potential barriers of height U0 and width d, using both continuum and microscopic lattice models, and show that the nature of electron transport along its armchair edge (x direction) is qualitatively different from its counterpart in both conventional two-dimensional electron gas with Schrödinger-like quasiparticles and graphene or surfaces of topological insulators hosting massless Dirac quasiparticles. We show that the transport, mediated by massive Dirac electrons, allows one to achieve collimated quasiparticle motion along x and thus makes monolayer phosphorene an ideal experimental platform for studying Klein paradox in the context of gapped Dirac materials. We study the dependence of the tunneling conductance as a function of d and U0, and demonstrate that for a given applied voltage V its behavior changes from oscillatory to decaying function of d for a range of U0 with finite non-zero upper and lower bounds, and provide analytical expression for these bounds within which G decays with d. We contrast such behavior of G with that of massless Dirac electrons in graphene and also with that along the zigzag edge (y direction) in phosphorene where the quasiparticles obey an effective Schrödinger equation at low energy. We also study transport through multiple barriers along x and demonstrate that these properties hold for transport through multiple barriers as well. Finally, we suggest concrete experiments which may verify our theoretical predictions.

Rényi entropies and topological quantum numbers in 2D gapped Dirac materials

New topological quantum numbers are introduced by analyzing complexity measures and relative Rényi entropies in silicene in the presence of perpendicular electric and magnetic fields. These topological quantum numbers characterize the topological insulator and band insulator phases in silicene. In addition, we have found that, these information measures reach extremum values at the charge neutrality points. These results are valid for other 2D gapped Dirac materials analogous to silicene with a buckled honeycomb structure and a significant spin-orbit coupling.

All-optical band engineering of gapped Dirac materials

We demonstrate theoretically that the interaction of electrons in gapped Dirac materials (gapped graphene and transition-metal dichalchogenide monolayers) with a strong off-resonant electromagnetic field (dressing field) substantially renormalizes the band gaps and the spin-orbit splitting. Moreover, the renormalized electronic parameters drastically depend on the field polarization. Namely, a linearly polarized dressing field always decreases the band gap (and, particularly, can turn the gap into zero), whereas a circularly polarized field breaks the equivalence of valleys in different points of the Brillouin zone and can both increase and decrease corresponding band gaps. As a consequence, the dressing field can serve as an effective tool to control spin and valley properties of the materials and be potentially exploited in optoelectronic applications.

Giant Hall Photoconductivity in Narrow-Gapped Dirac Materials.

Carrier dynamics acquire a new character in the presence of Bloch-band Berry curvature, which naturally arises in gapped Dirac materials (GDMs). Here, we argue that photoresponse in GDMs with small band gaps is dramatically enhanced by Berry curvature. This manifests in a giant and saturable Hall photoconductivity when illuminated by circularly polarized light. Unlike Hall motion arising from a Lorentz force in a magnetic field, which impedes longitudinal carrier motion, Hall photoconductivity arising from Berry curvature can boost longitudinal carrier transport. In GDMs, this results in a helicity-dependent photoresponse in the Hall regime, where photoconductivity is dominated by its Hall component. We find that the induced Hall conductivity per incident irradiance is enhanced by up to 6 orders of magnitude when moving from the visible regime (with corresponding band gaps) to the far infrared. These results suggest that narrow-gap GDMs are an ideal test-bed for the unique physics that arise in the presence of Berry curvature and open a new avenue for infrared and terahertz optoelectronics.

Revivals of electron currents and topological-band insulator transitions in 2D gapped Dirac materials

We have studied the time evolution of electron wave packets in silicene under perpendicular magnetic and electric fields to characterize topological-band insulator transitions. We have found that at the charge neutrality points, the periodicities exhibited by the wave packet dynamics (classical and revival times) reach maximum values, and that the electron currents reflect the transition from a topological insulator to a band insulator. This provides a signature of topological phase transition in silicene that can be extended to other 2D Dirac materials isostructural to graphene and with a buckled structure and a significant spin-orbit coupling.

Chiral plasmons without magnetic field

Plasmons, the collective oscillations of interacting electrons, possess emergent properties that dramatically alter the optical response of metals. We predict the existence of a new class of plasmons-chiral Berry plasmons (CBPs)-for a wide range of 2D metallic systems including gapped Dirac materials. As we show, in these materials the interplay between Berry curvature and electron-electron interactions yields chiral plasmonic modes at zero magnetic field. The CBP modes are confined to system boundaries, even in the absence of topological edge states, with chirality manifested in split energy dispersions for oppositely directed plasmon waves. We unveil a rich CBP phenomenology and propose setups for realizing them, including in anomalous Hall metals and optically pumped 2D Dirac materials. Realization of CBPs will offer a powerful paradigm for magnetic field-free, subwavelength optical nonreciprocity, in the mid-IR to terahertz range, with tunable splittings as large as tens of THz, as well as sensitive all-optical diagnostics of topological bands.

Topological Valley Currents in Gapped Dirac Materials.

Gapped 2D Dirac materials, in which inversion symmetry is broken by a gap-opening perturbation, feature a unique valley transport regime. Topological valley currents in such materials are dominated by bulk currents produced by electronic states just beneath the gap rather than by edge modes. The system ground state hosts dissipationless persistent valley currents existing even when topologically protected edge modes are absent. Valley currents induced by an external bias are characterized by a quantized half-integer valley Hall conductivity. The undergap currents dominate magnetization and the charge Hall effect in a light-induced valley-polarized state.

Uncertainty relations and topological-band insulator transitions in 2D gapped Dirac materials

Uncertainty relations are studied for a characterization of topological-band insulator transitions in 2D gapped Dirac materials isostructural with graphene. We show that the relative or Kullback–Leibler entropy in position and momentum spaces, and the standard variance-based uncertainty relation give sharp signatures of topological phase transitions in these systems.

Identifying topological-band insulator transitions in silicene and other 2D gapped Dirac materials by means of Rényi-Wehrl entropy

We propose a new method to identify transitions from a topological insulator to a band insulator in silicene (the silicon equivalent of graphene) in the presence of perpendicular magnetic and electric fields, by using the Rényi-Wehrl entropy of the quantum state in phase space. Electron-hole entropies display an inversion/crossing behavior at the charge neutrality point for any Landau level, and the combined entropy of particles plus holes turns out to be maximum at this critical point. The result is interpreted in terms of delocalization of the quantum state in phase space. The entropic description presented in this work will be valid in general 2D gapped Dirac materials, with a strong intrinsic spin-orbit interaction, isostructural with silicene.