Tilted Dirac Cones Research Articles

Tilted Dirac cones in two-dimensional materials: Impact on electron transmission and pseudospin dynamics

Tilted Dirac cones in two-dimensional materials: Impact on electron transmission and pseudospin dynamics

Dirac fermions and spin transport in the SrVO3/SrTiO3 quantum well

The type-II Dirac fermions are characterized by a tilted Dirac cone and sustain exotic quantum transport phenomena. Here, we show the emergence of a type-II Dirac nodal loop in the SrVO3/SrTiO3 quantum well structure by density functional theory calculations and symmetry arguments. When the spin–orbit coupling (SOC) is neglected, the unavoidable crossing between two t2g bands gives rise to a nodal loop in the Brillouin zone, which is protected by the mirror symmetry. Such a nodal loop is fully gapped by including SOC, which results in a large spin Hall effect due to large spin Berry curvatures. Our findings add the unexplored functionality to oxide quantum wells and offer a practical platform to explore the interplay between topological fermions and spin transport phenomena.

Kinetic theory of tilted Dirac cone materials

We formulate the Boltzmann kinetic equations for interacting electrons with tilted Dirac cones in two space dimensions characterized by a tilt parameter 0≤ζ<1. By solving the linearized Boltzmann equation, we find that the broadening of the Drude pole is enhanced by κ(ζ)×(1−ζ2)−1/2, where the κ is interaction-induced enhancement factor. The intensity of the Drude pole is also anisotropically enhanced by (1−ζ2)−1. The ubiquitous “redshift” factors (1−ζ2)1/2 can be regarded as a manifestation of an underlying spacetime structure in such solids. The additional broadening κ that arises from the interactions cannot be obtained from a simple coordinate change and are more pronounced for electrons in a ζ-deformed Minkowski spacetime of tilted Dirac fermions.

Dirac fermions collimation in heterostructures based on tilted Dirac cone materials

This paper aims to theoretically analyze the behavior of Dirac fermions in a tilted Dirac cone material, particularly those interacting with a barrier potential. Our results show that the degree of tilt in the y-direction can lead to different collimations of Dirac fermion beams relative to the Fermi and confinement surfaces. We have highlighted a range of results, including the conical geometry by illustrating the active surfaces and their geometric parameters in reciprocal space. To study the transmission probability, we have conducted numerical analyses, considering various system configurations and different external and internal physical parameters to characterize the fermionic transport behavior in a proposed heterostructure. Additionally, we examined the transmission of Dirac fermions in relation to the refractive indices and refraction between the different media constituting the system, discussing the tunneling effect and the Klein paradox in relation to various physical parameters. Our findings lay the groundwork for the development of controllable electronic devices using Dirac fermion collimation, governed by the tilt parameter, enabling precise manipulation and enhanced functionality.

Asymmetric Tilt-Induced Quantum Beating of Conductance Oscillation in Magnetically Modulated Dirac Matter Systems.

Herein, we investigate the effect of tilt mismatch on the quantum oscillations of spin transport properties in two-dimensional asymmetrically tilted Dirac cone systems. This study involves the examination of conductance oscillation in two distinct junction types: transverse- and longitudinal-tilted Dirac cones (TTDCs and LTDCs). Our findings reveal an unusual quantum oscillation of spin-polarized conductance within the TTDC system, characterized by two distinct anomaly patterns within a single period, labeled as the linear conductance phase and the oscillatory conductance phase. Interestingly, these phases emerge in association with tilt-induced orbital pseudo-magnetization and exchange interaction. Our study also demonstrates that the structure of the LTDC can modify the frequency of spin conductance oscillation, and the asymmetric effect within this structure results in a quantum beating pattern in oscillatory spin conductance. We note that an enhancement in the asymmetric longitudinal tilt velocity ratio within the structure correspondingly amplifies the beating frequency. Our research potentially contributes valuable insights for detecting the asymmetry of tilted Dirac fermions in type-I Dirac semimetal-based spintronics and quantum devices.

Bipolar electron waveguides in two-dimensional materials with tilted Dirac cones

We show that the (2+1)-dimensional massless Dirac equation, which includes a tilt term, can be reduced to the biconfluent Heun equation for a broad range of scalar confining potentials, including the well-known Morse potential. Applying these solutions, we investigate a bipolar electron waveguide in 8–Pmmn borophene, formed by a well and barrier, both described by the Morse potential. We demonstrate that the ability of two-dimensional materials with tilted Dirac cones to localize electrons in both a barrier and a well can be harnessed to create pseudogaps in their electronic spectrum. These pseudogaps can be tuned through varying the applied top-gate voltage. Potential opto-valleytronic and terahertz applications are discussed.

Quantum oscillations of pseudomagnetoresistance in tunable tilt-mismatch Dirac-cone junction

This paper presents research on the quantum oscillation of pseudomagnetoresistance (PMR) in tilted Dirac cone material junctions. Dirac cones are linear energy dispersions that arise in materials like graphene, which is a two-dimensional material with unique electronic properties. The presence of a tilted Dirac cone in the energy spectrum of these materials introduces interesting phenomena such as pseudomagnetism and anisotropic quantum transport. By applying strain, we can control the direction of the tilted Dirac cone in graphene and investigate the pseudomagnetotransport properties of this system. Magnetoresistance is a real effect that arises from the Lorentz force acting on the charge carriers, while PMR is a geometric effect that arises from the tilted Dirac cone and the crystal lattice structure of the material. Using computational methods for finite-superlattice materials and the transfer-matrix method, our results show that the quantum beating pattern of PMR is more pronounced with an increased number of barriers. Additionally, we observe that the amplitude and period of the modulation depend on the strength and orientation of the tilted-induced pseudomagnetic field. We demonstrate that the PMR behavior can be tuned and optimized for specific applications, potentially leading to improvements in the design and optimization of graphene-based devices such as sensors, transistors, and quantum computers, which rely on the PMR behavior of graphene.

Quantum transport in double tilted Dirac cone junction

We investigate quantum transport in tilt-inhomogeneous Dirac cone system, which partially mimic the behaviours of a double-pseudomagnetic-barrier structure. Exploring the effects of Dirac cone tilt helps us understand electron transmission probabilities through the barriers. Our results demonstrate significant enhancement of tunnelling transport properties by adjusting barrier parameters and the Dirac cone’s tilt angle. This study has important implications for optimizing resonant-tunnelling quantum devices based on the heterostructure, paving the way for novel quantum device development.

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.

Strain-induced topological transitions and tilted Dirac cones in kagome lattices

We study effects of strain on the electronic properties of the kagome lattice in a tight-binding formalism with spin–orbit coupling (SOC). The degeneracy at the Γ point evolves into a pair of emergent tilted Dirac cones under uniaxial strain, where the anisotropy and tilting of the bands depend on the magnitude and direction of the strain field. SOC opens gaps at the emergent Dirac points, making the flatband topological, characterized by a nontrivial index. Strains of a few percent drive the system into trivial or topological phases. This confirms that moderate strain can be used to engineer anisotropic Dirac bands with tunable properties to study new phases in kagome lattices.

Holographic hydrodynamics of tilted Dirac materials

We present a gravity dual to a quantum material with tilted Dirac cone in 2+1 dimensional spacetime. In this many-body system the electronics degrees of freedom are strongly-coupled, constitute a Dirac fluid and admit an effective hydrodynamic description. The holographic techniques are applied to compute the thermodynamic variables and hydrodynamic transports of a fluid on the boundary of an asymptotically anti de Sitter spacetime with a boosted black hole in the bulk. We find that these materials exhibit deviations from the normal Dirac fluid which rely on the tilt of the Dirac cone. In particular, the shear viscosity to entropy density ratio is reduced and the KSS bound is violated in this system. This prediction can be experimentally verified in two-dimensional quantum materials (e.g. organic α-(BEDT-TTF)2I3 and 8Pmmn borophene) with tilted Dirac cone.

Localized magnetic states in a tilted Dirac cone system

We investigate the localized magnetic state in the tilted Dirac cone system, wherein a lattice staggered potential (LSP) is introduced to create a gap between the conduction and valence bands. Our findings reveal that the breaking of symmetry between the sublattices results in depletion of the magnetic region of the impurity for positive LSP values, while a sharp strip is formed for negative LSP values with an increase in the tilt of the Dirac cone. Interestingly, within the magnetic region, the magnetic moment of the impurity remains constant at 0.8 Bohr magneton irrespective of the sign of LSP. However, the magnetic susceptibility at the edge of the magnetic region displays inconsistent behavior for positive and negative LSP values. We also analyze in detail the variations in the magnetic region, magnetic moment, and magnetic susceptibility with LSP strength at a fixed tilt.

Fluctuations in Planar Magnetotransport Due to Tilted Dirac Cones in Topological Materials.

Fluctuations in planar magnetotransport are ubiquitous in topological HgTe structures, in both tensile (topological insulator) and compressively strained layers (Weyl semimetal phase). We show that the common reason for the fluctuations is the presence of tilted Dirac cones combined with the formation of charge puddles. The origin of the tilted Dirac cones is the mix of the Zeeman term due to the in-plane magnetic field and quadratic contributions to the dispersion relation. We develop a network model that mimics the transport of tilted Dirac fermions in the landscape of charge puddles. The model captures the essential features of the experimental data. It should be relevant for the interpretation of planar magnetotransport in a variety of topological and small band gap materials.

Robust three-dimensional type-II Dirac semimetal state in SrAgBi

Topological semimetals such as Dirac, Weyl or nodal line semimetals are widely studied for their peculiar properties including high Fermi velocities, small effective masses and high magnetoresistance. When the Dirac cone is tilted, exotic phenomena could emerge whereas materials hosting such states are promising for photonics and plasmonics applications. Here we present evidence that SrAgBi is a spin-orbit coupling-induced type-II three-dimensional Dirac semimetal featuring tilted Dirac cone at the Fermi energy. Near charge compensation and Fermi surface characteristics are not much perturbed by 7% of vacancy defects on the Ag atomic site, suggesting that SrAgBi could be a material of interest for observation of robust optical and spintronic topological quantum phenomena.

Fermi velocity and effective mass of quasiparticles in bilayer phosphorene nanoribbons

Based on the Green’s function approach in combination with the tight-binding approximation, we have investigated the electronic properties of zigzag bilayer phosphorene nanoribbons (ZBLPNRs). A complete and fully reversible metal-to-semiconductor or insulator phase transition has been observed via tuning a perpendicular electric field. We explain the effect of the interlayer hopping parameter on the electronic characterizations, namely, the energy band-gap, Fermi velocity, and effective mass of carriers in biased ZBLPNRs. In the presence of the interlayer hopping term, the band structure of a ZBLPNR in the vicinity of the Fermi level has the form of two tilted Dirac cones, while, in the absence of it, the created cones are not tilted. Besides, the bands above and below the Fermi level are not symmetric, i.e., there is no electron–hole symmetry for both limits of the interlayer coupling. A remarkable tuning of both the Fermi velocity and the reciprocal effective mass can be observed by adjusting the external bias voltage. At certain critical bias voltages, the band edge reciprocal masses and carrier velocities become zero, i.e., the electrons exhibit localization behaviour. This phenomenon is indeed a transition from massive to massless Dirac fermions and vice versa. The possibility of simultaneous control of the thermal and magnetic properties using an electric agent, which can be realized experimentally by using a perpendicular potential difference, opens up possibilities for low-power-consuming thermomagnetic devices based on ZBLPNRs.

Topological Langmuir-cyclotron wave.

A theory is developed to describe the topological Langmuir-cyclotron wave (TLCW), a topological excitation in magnetized plasmas recently identified by numerical simulations. As a topological wave in a continuous medium, the TLCW propagates unidirectionally without scattering in complex boundaries and can be explored as an effective mechanism to energize particles. We show that, because momentum space in continuous media is contractible in general, the topology of the wave bundles is trivial over momentum space that contains no degeneracy points. This is in stark contrast to condensed matters with periodic lattice structures that impose nontrivial topology on momentum space. In continuous media without lattice structures, nontrivial topology of the eigenmode bundles manifests over phase space, and it is the nontrivial topology over phase space that underpins the topological excitations, such as the TLCW. It is shown that the TLCW can be faithfully modeled by a generic tilted Dirac cone in phase space, whose entire spectrum, including the spectral flow, is given.

Analysis of Dirac exceptional points and their isospectral Hermitian counterparts

Recently, a Dirac exceptional point (EP) was reported in a non-Hermitian system. Unlike a Dirac point in Hermitian systems, this Dirac EP has coalesced eigenstates in addition to the degenerate energy. Also different from a typical EP, the two energy levels connected at this Dirac EP remain real in its vicinity and display a linear instead of square root dispersion, forming a tilted Dirac cone in the hybrid space consisting of a momentum dimension and a synthetic dimension for the strength of non-Hermiticity. In this report, we first present simple three-band and two-band matrix models with a Dirac EP, where the linear dispersion of the tilted Dirac cone can be expressed analytically. Importantly, our analysis also reveals that there exist Hermitian and non-Hermitian systems that have the same (real-valued) energy spectrum in their entire parameter space, with the exception that one or more degeneracies in the former are replaced by Dirac EPs in the later. Finally, we show the existence of an imaginary Dirac cone with an EP at its center.

Electron currents from gradual heating in tilted Dirac cone materials

Materials hosting tilted Dirac/Weyl fermions provide an emergent spacetime structure for the solid state physics. They admit a geometric description in terms of an effective spacetime metric. Using this metric that is rooted in the long-distance behavior of the underlying lattice, we formulate the hydrodynamic theory for tilted Dirac/Weyl materials in 2+12+1 spacetime dimensions. We find that the mingling of space and time through the off-diagonal components of the metric gives rise to: (i) heat and electric currents proportional to the temporal gradient of temperature, \partial_t T∂tT and (ii) a non-zero Hall-like conductance \sigma^{ij}\propto \zeta^i\zeta^jσij∝ζiζj where \zeta^jζj parameterize the tilt in jj’th space direction. The finding (i) above that can be demonstrated in the laboratory, implies that the non-trivial emergent spacetime geometry in these materials empowers them with a fascinating capability to harness naturally available sources of \partial_t T∂tT of hot deserts to produce electric current. We further find a tilt-induced non-Drude contribution to conductivity which can be experimentally disentangled from the usual Drude pole.

Effective medium model for graphene superlattices with electrostatic and magnetic vector potentials

In this article we develop an effective medium model to characterize the electron wave propagation in graphene based nanostructures with electrostatic and magnetic vector potentials imposed on their surface. We use a numerical algorithm to determine the effective medium parameters of the heterostructure and calculate the electronic band structure of the system. We apply our formalism to analyze superlattices with solely a magnetic potential and reveal that the response of the structure remains reciprocal and is characterized by a decrease in the velocity of the charge carriers. We also study the response of superlattices with both potentials superimposed on graphene and show that the response of the system becomes nonreciprocal with a dispersion characterized by a tilted Dirac cone. We demonstrate that it is possible to alternate between type-I, type-II, or type-III Dirac cones by properly tuning the amplitude of the potentials.

Tilted Dirac cones and asymmetric conical diffraction in photonic Lieb-kagome lattices

The Lieb lattice and the kagome lattice, which are both well known for their Dirac cones and flat bands, can be continuously converted into each other by a shearing transformation. During this transformation, the flat band is destroyed, but the Dirac cones remain and become tilted, with types I, II, and III occurring for different parameters. In this work, we first study these tilted Dirac cones using a tight-binding model, revealing how they can be engineered into the different types. We then demonstrate conical diffraction in a photonic lattice realization of the Lieb-kagome lattice using split-step beam propagation simulations, obtaining evidence of the presence of Dirac cones tilted in different directions. Finally, we performed experiments with photonic lattices laser-written in fused silica (SiO$_2$) to validate the results of the simulations. These studies advance the understanding of the Lieb-kagome lattice and tilted Dirac cones in general and provide a basis for further research into this interesting tunable lattice system.