Dirac Dispersion Research Articles

Screening of the Coulomb interaction in C3N: Reduced dimensionality and electronic structure effects

Coulomb interactions in two-dimensional semimetals like graphene are not screened in the usual way, and sizable long-range interaction has been found. With the aim of achieving new materials with nonconventional screening, as well as, in order to investigate various effects such as reduced dimensionality and electronic band dispersion, we calculate the strength of the effective Coulomb interaction $U$ between ${p}_{z}$ electrons in recently developed hexagonal ${\mathrm{C}}_{3}\mathrm{N}$ materials from the first principles using the constrained random-phase approximation. We find that the calculated parameters in the monolayer of the ${\mathrm{C}}_{3}\mathrm{N}$ are larger than the ones in graphene and remain sizable even in metallic bilayers. Nonlocal Coulomb interactions $U(r)$ in nonmetallic ${\mathrm{C}}_{3}\mathrm{N}$ nanoribbons are almost 1 eV smaller than the ones for ${\mathrm{C}}_{3}\mathrm{N}$ monolayer. Our results show that similar to graphene, screening in hexagonal ${\mathrm{C}}_{3}\mathrm{N}$ is also nonconventional. This controversial screening of Coulomb interaction stems from the electronic structure and massless Dirac dispersion below Fermi energy, which has to be preserved for symmetry reasons in hexagonal ${\mathrm{C}}_{3}\mathrm{N}$ layers.

Fermiology of the Dirac type-II semimetal candidates (Ni,Zr) Te2 using de Haas–van Alphen oscillations

We have investigated the Fermi surface properties of the Dirac type-II semimetal candidates (Ni,Zr)${\mathrm{Te}}_{2}$ using torque magnetometry with applied fields up to 35 T. Magnetization shows clear de Haas--van Alphen (dHvA) oscillations above 20 T. The dHvA oscillations are smooth and well defined and consist of one distinct frequency (${F}_{\ensuremath{\alpha}}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}530$ T) in $\mathrm{Zr}{\mathrm{Te}}_{2}$ and three (${\overline{F}}_{\ensuremath{\alpha}}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}72$ T, ${\overline{F}}_{\ensuremath{\beta}}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}425$ T, and ${\overline{F}}_{\ensuremath{\gamma}}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}630$ T) in $\mathrm{Ni}{\mathrm{Te}}_{2}$. The Berry phase $\ensuremath{\phi}$ was determined by constructing the Landau level fan diagram. It is found that $\ensuremath{\phi}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}$ 0 and $\ensuremath{\pi}$ for ${F}_{\ensuremath{\alpha}}$ and ${\overline{F}}_{\ensuremath{\beta}}$, respectively, for $\mathrm{Zr}{\mathrm{Te}}_{2}$ and $\mathrm{Ni}{\mathrm{Te}}_{2}$. This strongly suggests that the Dirac fermions make a dominant contribution to the transport properties of $\mathrm{Ni}{\mathrm{Te}}_{2}$, whereas topologically trivial fermions dominate those in $\mathrm{Zr}{\mathrm{Te}}_{2}$. The presence of lighter effective mass ${m}^{*}=0.13{m}_{e}$ in $\mathrm{Ni}{\mathrm{Te}}_{2}$ compared to ${m}^{*}=0.26{m}_{e}$ in $\mathrm{Zr}{\mathrm{Te}}_{2}$, where ${m}_{e}$ is an electron's rest mass, further confirms the presence of Dirac fermions in $\mathrm{Ni}{\mathrm{Te}}_{2}$. Our density functional theory calculations find that while both systems host type-II Dirac dispersions along the out-of-plane direction, their relative positions and the natures of the dispersions are different. The Dirac cone is closer to the Fermi energy ${E}_{F}$ ($\ensuremath{\sim}100$ meV above) in $\mathrm{Ni}{\mathrm{Te}}_{2}$, whereas it is far ($\ensuremath{\sim}500$ meV) above ${E}_{F}$ for $\mathrm{Zr}{\mathrm{Te}}_{2}$. This is consistent with our experimental finding of a nontrivial Berry phase and dominant contribution from lighter electrons in the quantum oscillation signal for only $\mathrm{Ni}{\mathrm{Te}}_{2}$. These findings suggest that the proximity of the Dirac cone to ${E}_{F}$ in topological compounds is crucial for observing the effect from Dirac quasiparticles in their electrical transport or magnetic properties.

Topological flat bands in a kagome lattice multiorbital system

Flat bands and dispersive Dirac bands are known to coexist in the electronic bands in a two-dimensional kagome lattice. Including the relativistic spin-orbit coupling, such systems often exhibit nontrivial band topology, allowing for gapless edge modes between flat bands at several locations in the band structure, and dispersive bands or at the Dirac band crossing. Here, we theoretically demonstrate that a multiorbital system on a kagome lattice is a versatile platform to explore the interplay between nontrivial band topology and electronic interaction. Specifically, here we report that the multiorbital kagome model with the atomic spin–orbit coupling naturally supports topological bands characterized by nonzero Chern numbers {{{{{{{mathcal{C}}}}}}}}, including a flat band with | {{{{{{{mathcal{C}}}}}}}}| =1. When such a flat band is 1/3 filled, the non-local repulsive interactions induce a fractional Chern insulating state. We also discuss the possible realization of our findings in real kagome materials.

Proximity effects in graphene on monolayers of transition-metal phosphorus trichalcogenides MPX3 (M:Mn, Fe, Ni, Co, and X: S, Se)

We investigate the electronic band structure of graphene on a series of two-dimensional magnetic transition-metal phosphorus trichalcogenide monolayers, ${M\text{P}X}_{3}$ with $M={\mathrm{Mn},\mathrm{Fe},\mathrm{Ni},\mathrm{Co}}$ and $X={\mathrm{S},\mathrm{Se}}$, with first-principles calculations. A symmetry-based model Hamiltonian is employed to extract orbital parameters and sublattice resolved proximity-induced exchange couplings (${\ensuremath{\lambda}}_{\text{ex}}^{\text{A}}$ and ${\ensuremath{\lambda}}_{\text{ex}}^{\text{B}}$) from the low-energy Dirac bands of the proximitized graphene. Depending on the magnetic phase of the ${M\text{P}X}_{3}$ layer (ferromagnetic and three antiferromagnetic ones), completely different Dirac dispersions can be realized with exchange splittings ranging from 0 to 10 meV. Remarkably, not only the magnitude of the exchange couplings depends on the magnetic phase, but also the global sign and the type. Important, one can realize uniform $({\ensuremath{\lambda}}_{\text{ex}}^{\text{A}}\ensuremath{\approx}{\ensuremath{\lambda}}_{\text{ex}}^{\text{B}})$ and staggered $({\ensuremath{\lambda}}_{\text{ex}}^{\text{A}}\ensuremath{\approx}\ensuremath{-}{\ensuremath{\lambda}}_{\text{ex}}^{\text{B}})$ exchange couplings in graphene. From selected cases we find that the interlayer distance, as well as a transverse electric field, are efficient tuning knobs for the exchange splittings of the Dirac bands. More specifically, decreasing the interlayer distance by only about 10%, a giant fivefold enhancement of proximity exchange is found, while applying few V/nm of electric field, provides tunability of proximity exchange by tens of percent. We have also studied the dependence on the Hubbard $U$ parameter and find it to be weak. Moreover, we find that the effect of SOC on the proximitized Dirac dispersion is negligible compared to the exchange coupling.

Tuning the competition between superconductivity and charge order in the kagome superconductor Cs(V1−xNbx)3Sb5

The recently discovered coexistence of superconductivity and charge density wave order in the kagome systems AV3Sb5 (A = K, Rb, Cs) has stimulated enormous interest. According to theory, a vanadium-based kagome system may host a flat band, nontrivial linear dispersive Dirac surface states and electronic correlation. Despite intensive investigations, it remains controversial about the origin of the charge density wave (CDW) order, how does the superconductivity relate to the CDW, and whether the anomalous Hall effect (AHE) arises primarily from the kagome lattice or the CDW order. We report an extensive investigation on Cs(V1-xNbx)3Sb5 samples with systematic Nb doping. Our results show that the Nb doping induces apparent suppression of CDW order and promotes superconductivity; meanwhile, the AHE and magnetoresistance (MR) will be significantly weakened together with the CDW order. Combining with our density functional calculations, we interpret these effects by an antiphase shift of the Fermi energy with respect to the saddle points near M and the Fermi surface centered around {\Gamma}. It is found that the former depletes the filled states for the CDW instability and worsens the nesting condition for CDW order; while the latter lifts the Fermi level upward and enlarges the Fermi surface surrounding the {\Gamma} point, and thus promotes superconductivity. Our results uncover a delicate but unusual competition between the CDW order and superconductivity.

Correlated Insulators, Semimetals, and Superconductivity in Twisted Trilayer Graphene

Motivated by recent experiments indicating strong superconductivity and intricate correlated insulating and flavor-polarized physics in mirror-symmetric twisted trilayer graphene, we study the effects of interactions in this system close to the magic angle, using a combination of analytical and numerical methods. We identify asymptotically exact correlated many-body ground states at all integer filling fractions $\nu$ of the flat bands. To determine their fate when moving away from these fine-tuned points, we apply self-consistent Hartree-Fock numerics and analytic perturbation theory, with good agreement between the two approaches. This allows us to construct a phase diagram for the system as a function of $\nu$ and the displacement field, the crucial experimental tuning parameter of the system, and study the spectra of the different phases. The phase diagram is dominated by a correlated semimetallic intervalley coherent state and an insulating sublattice-polarized phase around charge neutrality, $\nu=0$, with additional spin-polarization being present at quarter ($\nu=-2$) or three quarter ($\nu=+2$) fillings of the quasi-flat bands. We further study the superconducting instabilities emerging from these correlated states, both in the absence and in the additional presence of electron-phonon coupling, also taking into account possible Wess-Zumino-Witten terms. In the experimentally relevant regime, we find triplet pairing to dominate, possibly explaining the observed violation of the Pauli limit. Our results have several consequences for experiments as well as future theoretical work and illustrate the rich physics resulting from the interplay of almost flat bands and dispersive Dirac cones in twisted trilayer graphene.

Topological band transition between hexagonal and triangular lattices with (p x , p y ) orbitals

By combining tight-binding modelling with density functional theory based first-principles calculations, we investigate the band evolution of two-dimensional (2D) hexagonal lattices with (p x , p y ) orbitals, focusing on the electronic structures and topological phase transitions. The (p x , p y )-orbital hexagonal lattice model possesses two flat bands encompassing two linearly dispersive Dirac bands. Breaking the A/B sublattice symmetry could transform the model into two triangular lattices, each featuring a flat band and a dispersive band. Inclusion of the spin–orbit coupling and magnetization may give rise to quantum spin Hall and quantum anomalous Hall (QAH) states. As a proof of concept, we demonstrate that half-hydrogenated stanene is encoded by a triangular lattice with (p x , p y ) orbitals, which exhibits ferromagnetism and QAH effect with a topological gap of ∼0.15 eV, feasible for experimental observation. These results provide insights into the structure-property relationships involving the orbital degree of freedom, which may shed light on future design and preparation of 2D topological materials for novel electronic/spintronic and quantum computing devices.

Engineering Proximity Exchange by Twisting: Reversal of Ferromagnetic and Emergence of Antiferromagnetic Dirac Bands in Graphene/Cr_{2}Ge_{2}Te_{6}.

We investigate the twist-angle and gate dependence of the proximity exchange coupling in twisted graphene on monolayer Cr_{2}Ge_{2}Te_{6} from first principles. The proximitized Dirac band dispersions of graphene are fitted to a model Hamiltonian, yielding effective sublattice-resolved proximity-induced exchange parameters (λ_{ex}^{A} and λ_{ex}^{B}) for a series of twist angles between 0° and 30°. For aligned layers (0° twist angle), the exchange coupling of graphene is the same on both sublattices, λ_{ex}^{A}≈λ_{ex}^{B}≈4 meV, while the coupling is reversed at 30° (with λ_{ex}^{A}≈λ_{ex}^{B}≈-4 meV). Remarkably, at 19.1° the induced exchange coupling becomes antiferromagnetic: λ_{ex}^{A}<0, λ_{ex}^{B}>0. Further tuning is provided by a transverse electric field and the interlayer distance. The predicted proximity magnetization reversal and emergence of an antiferromagnetic Dirac dispersion make twisted graphene/Cr_{2}Ge_{2}Te_{6} bilayers a versatile platform for realizing topological phases and for spintronics applications.

Experimental signature of the parity anomaly in a semi-magnetic topological insulator

A three-dimensional (3D) topological insulator features a 2D surface state consisting of a single linearly dispersive Dirac cone1–3. Under broken time-reversal symmetry, the single Dirac cone is predicted to cause half-integer quantization of Hall conductance, which is a manifestation of the parity anomaly in quantum field theory1–9. However, despite various observations of quantization phenomena10–15, the half-integer quantization has not been observed because most experiments simultaneously measure a pair of equivalent Dirac cones16 on two opposing surfaces. Here we demonstrate the half-integer quantization of Hall conductance in a synthetic heterostructure termed a semi-magnetic topological insulator, where only one surface state is gapped by magnetic doping and the opposite one is non-magnetic and gapless. We observe half-quantized Faraday and Kerr rotations with terahertz magneto-optical spectroscopy and half-quantized Hall conductance in transport at zero magnetic field. Our results suggest a condensed-matter realization of the parity anomaly4–9 and open a way for studying the physics enabled by a single Dirac fermion. An electron with a linear dispersion relation should contribute half of a quantum of Hall conductance and thereby manifest the parity anomaly. This is demonstrated in a heterostructure of topological insulator materials.

Synthesizing dispersion relations in a modulated tilted optical lattice

Dispersion relations are fundamental characteristics of the dynamics of quantum and wave systems. In this work we introduce a simple technique to generate arbitrary dispersion relations in a modulated tilted lattice. The technique is illustrated by important examples: the Dirac, Bogoliubov and Landau dispersion relations (the latter exhibiting the roton and the maxon). We show that adding a slow chirp to the lattice modulation allows one to reconstruct the dispersion relation from dynamical quantities. Finally, we generalize the technique to higher dimensions, and generate graphene-like Dirac points and flat bands in two dimensions.

Charge-Density-Wave-Induced Peak-Dip-Hump Structure and the Multiband Superconductivity in a Kagome Superconductor CsV_{3}Sb_{5}.

The entanglement of charge density wave (CDW), superconductivity, and topologically nontrivial electronic structure has recently been discovered in the kagome metal AV_{3}Sb_{5} (A=K, Rb, Cs) family. With high-resolution angle-resolved photoemission spectroscopy, we study the electronic properties of CDW and superconductivity in CsV_{3}Sb_{5}. The spectra around K[over ¯] is found to exhibit a peak-dip-hump structure associated with two separate branches of dispersion, demonstrating the isotropic CDW gap opening below E_{F}. The peak-dip-hump line shape is contributed by linearly dispersive Dirac bands in the lower branch and a dispersionless flat band close to E_{F} in the upper branch. The electronic instability via Fermi surface nesting could play a role in determining these CDW-related features. The superconducting gap of ∼0.4 meV is observed on both the electron band around Γ[over ¯] and the flat band around K[over ¯], implying the multiband superconductivity. The finite density of states at E_{F} in the CDW phase is most likely in favor of the emergence of multiband superconductivity, particularly the enhanced density of states associated with the flat band. Our results not only shed light on the controversial origin of the CDW, but also offer insights into the relationship between CDW and superconductivity.

Analytical Study of Dirac Type Dispersion in Simple Periodic Waveguide Structures for Leaky-Wave Applications

In this work, we present a study on the existence of Dirac type dispersion in the simplest of periodic metallic waveguide structures. It is shown that periodic repetitions of two dissimilar waveguides (WGs) can be properly designed to lead to a Dirac type dispersion. A simple theory using circuit modeling is presented to find the condition for Dirac point operation. In addition, mode-matching followed by full-wave simulations validate that the band structure matches that of the theory and shows that a Dirac dispersion can be realized. A Dirac Leaky-Wave Antenna (DLWA) is then implemented using this simple arrangement in substrate-integrated-waveguide (SIW) technology. This DLWA has the closed broadside stopband feature, leading to continuous frequency beam scanning through broadside and a simple feeding network. Phase and leakage constants are adjusted to yield a directive fan-beam featuring continuous scanning in a wide range of angles. The presented DLWA has a wide impedance bandwidth with high efficiency and operates with peak gains of about 12.5 dBi without any significant gain variation throughout the frequency range from 13.5 GHz to 16.5 GHz. Measured results show excellent agreement with the simulated results, validating the proposed concepts.

Zak phase induced interface states in two-dimensional phononic crystals

Interface states have great practical applications, therefore, searching for the existence of interface states has both scientific significance and application prospects. In this work, we tilt the structure unite of two-dimensional phononic crystal with a square lattice to construct an oblique lattice possessing linear Dirac dispersion. The Dirac dispersion gives rise to a π jump of the Zak phases of the bulk bands, so that the projected band gaps at both sides of the Dirac cone have opposite signs of surface impedance, resulting in deterministic interface states at the interface formed by the phononic crystal with a square lattice and its tilted oblique lattice system.

Infrared spectroscopic study of topological material BaMnSb&lt;sub&gt;2&lt;/sub&gt;

A detailed infrared optical spectrum of the new topological material BaMnSb&lt;sub&gt;2&lt;/sub&gt; has been measured at temperatures ranging from 7 K to 295 K. As the temperature decreases, the plasma minimum has a clear blue shift in reflectivity spectrum, indicating that the carrier density changes with temperature. In the real part of the optical conductivity &lt;inline-formula&gt;&lt;tex-math id="M1"&gt;\begin{document}$\sigma_{1}(\omega)$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220011_M1.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220011_M1.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;, two linearly-increased components can be identified, but neither of their extrapolation pass through the origin, which proves that BaMnSb&lt;sub&gt;2&lt;/sub&gt; has a gapped Dirac dispersion near the Fermi level. Comparing with the theoretical calculation by using first-principles methods, the onset of these two linearly-increased components are in good agreement with the band structures. In addition, a range of constant optical conductivity is found in &lt;inline-formula&gt;&lt;tex-math id="M2"&gt;\begin{document}$\sigma_{1}(\omega)$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220011_M2.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220011_M2.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;, which cannot be described well by the Drude-Lorentz model. Therefore, we introduce a frequency-independent component to fit &lt;inline-formula&gt;&lt;tex-math id="M3"&gt;\begin{document}$\sigma_{1}(\omega)$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220011_M3.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220011_M3.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt; successfully. However, different from the Dirac nodal-line semimetal YbMnSb&lt;sub&gt;2&lt;/sub&gt; which shares same fitting results as well as crystal structure, the constant component in BaMnSb&lt;sub&gt;2&lt;/sub&gt; has a small proportion of &lt;inline-formula&gt;&lt;tex-math id="M4"&gt;\begin{document}$\sigma_{1}(\omega)$\end{document}&lt;/tex-math&gt;&lt;alternatives&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220011_M4.jpg"/&gt;&lt;graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="10-20220011_M4.png"/&gt;&lt;/alternatives&gt;&lt;/inline-formula&gt;. Through calculation and analysis, we attribute the constant component to the surface state of BaMnSb&lt;sub&gt;2&lt;/sub&gt;.

Dirac cones with zero refractive indices in phoxonic crystals.

In this paper, simultaneous zero refractive indices (ZRIs) for both sound and light are realized on the basis of a 2D triangular lattice phoxonic crystal (PxC) with C6v symmetry. For the phononic mode, accidental phononic Dirac degeneracy at the center of Brillouin zone (BZ) occurs at a relatively high frequency which leads to the failure of the efficient medium theory; hence, it is no longer applicable to the realization of acoustic ZRI. We thus turn to a low-frequency phononic Dirac cone located at K point, the corner of the BZ, which shows in-phase pressure field oscillations in expanded unit cells. Using zone folding, we further reveal the cause for the characteristic of acoustic ZRI. For the photonic mode, a low-frequency photonic Dirac-like cone can be achieved by adjusting the geometric parameter due to the high contrast permittivity between scatterers and the matrix. When the phononic and photonic low-frequency Dirac dispersions coexist, the PxC can be mapped into a zero-index material for both sound and light at the same time. The new mechanism for simultaneously controlling sound and light helps to achieve acousto-optic synchronous cloaking and unidirectional transmission, which are numerically demonstrated.

Photoelectromagnetic Effect Induced by Terahertz Laser Radiation in Topological Crystalline Insulators Pb1-xSnxTe.

Topological crystalline insulators form a class of semiconductors for which surface electron states with the Dirac dispersion relation are formed on surfaces with a certain crystallographic orientation. Pb1−xSnxTe alloys belong to the topological crystalline phase when the SnTe content x exceeds 0.35, while they are in the trivial phase at x < 0.35. For the surface crystallographic orientation (111), the appearance of topologically nontrivial surface states is expected. We studied the photoelectromagnetic (PEM) effect induced by laser terahertz radiation in Pb1−xSnxTe films in the composition range x = (0.11–0.44), with the (111) surface crystallographic orientation. It was found that in the trivial phase, the amplitude of the PEM effect is determined by the power of the incident radiation, while in the topological phase, the amplitude is proportional to the flux of laser radiation quanta. A possible mechanism responsible for the effect observed presumes damping of the thermalization rate of photoexcited electrons in the topological phase and, consequently, prevailing of electron diffusion, compared with energy relaxation.

Floquet graphene antidot lattices

We establish the theoretical foundation of the Floquet graphene antidot lattice, whereby massless Dirac fermions are driven periodically by a circularly polarized electromagnetic field, while having their motion excluded from an array of nanoholes. The properties of interest are encoded in the quasienergy spectra, which are computed non-perturbatively within the Floquet formalism. We find that a rich Floquet phase diagram emerges as the amplitude of the drive field is varied. Notably, the Dirac dispersion can be restored in real time relative to the gapped equilibrium state, which may enable the creation of an optoelectronic switch or a dynamically tunable electronic waveguide. As the amplitude is increased, the ability to shift the quasienergy gap between high-symmetry points can change which crystal momenta dominate in the scattering processes relevant to electronic transport and optical emission. Furthermore, the bands can be flattened near the $\Gamma$ point, which is indicative of selective dynamical localization. Lastly, quadratic and linear dispersions emerge in orthogonal directions at the $M$ point, signaling a Floquet semi-Dirac material. Importantly, all our predictions are valid for experimentally accessible near-IR radiation, which corresponds to the above bandwidth limit for the graphene antidot lattice. Cycling between engineered Floquet electronic phases may play a key role in the development of next-generation on-chip devices for optoelectronic applications.

Coulomb Drag by Injected Ballistic Carriers in Graphene n+−i−n−n+ Structures: Doping and Temperature Effects

Carrier Drags Dirac dispersion law in graphene enables the Coulomb drag of quasi equilibrium electrons by injected ballistic electrons. The drag effect determines the shape of the current–voltage characteristics (monotonous or S-shaped). The S-shaped characteristics enable switching, current filamentation and negative differential resistance at terahertz frequencies. The applications of these new effects include voltage limiting, switching, terahertz detection, amplification and generation, and novel circuit solutions integrating the S-type graphene switches with conventional graphene transistors and diodes. More details can be found in article number 2100535 by Victor Ryzhii and co-workers.

Coulomb bound states and atomic collapse in tilted Dirac materials

Searching for new states of matter and unusual quasi-particles in Dirac materials attracts a significant interest in condensed matter physics. Here we investigate the bound state formation in tilted Dirac materials in the presence of the one- and two-dimensional Coulomb potentials. Based on the exact solution of the Dirac equation, we obtain the energy spectrum of the bound states and the corresponding wave functions in the one-dimensional case. It is shown that the lower-energy bound states dive into the continuum below the band gap with the increase of the tilted parameter. The atomic collapse appears when the strength of the Coulomb potential exceeds the critical value. We show that the tilt of Dirac cone facilitates lowing the critical Coulomb potential strength where atomic collapse happens. Most notably, it is found that the bound states are absent for an overtilted Dirac dispersion. For the two-dimensional Coulomb potential, we perform the second-order perturbation theory to study the effect of band tilting on the bound state formation with a single point-like Coulomb impurity. The result indicates that the ground state becomes more unstable near the critical point for a stronger tilt parameter.

Carrier transport theory for twisted bilayer graphene in the metallic regime

Understanding the normal-metal state transport in twisted bilayer graphene near magic angle is of fundamental importance as it provides insights into the mechanisms responsible for the observed strongly correlated insulating and superconducting phases. Here we provide a rigorous theory for phonon-dominated transport in twisted bilayer graphene describing its unusual signatures in the resistivity (including the variation with electron density, temperature, and twist angle) showing good quantitative agreement with recent experiments. We contrast this with the alternative Planckian dissipation mechanism that we show is incompatible with available experimental data. An accurate treatment of the electron-phonon scattering requires us to go well beyond the usual treatment, including both intraband and interband processes, considering the finite-temperature dynamical screening of the electron-phonon matrix element, and going beyond the linear Dirac dispersion. In addition to explaining the observations in currently available experimental data, we make concrete predictions that can be tested in ongoing experiments.