Effects of spatial dimensionality and band tilting on the longitudinal optical conductivities in Dirac bands

Abstract

We report a unified theory based on linear response, for analyzing the longitudinal optical conductivity (LOC) of materials with tilted Dirac cones. Depending on the tilt parameter $t$, the Dirac electrons have four phases: untilted, type-I, type-II, and type-III; the Dirac dispersion can be isotropic or anisotropic; the spatial dimension of the material can be one-, two-, or three-dimensions (1D, 2D and 3D). The interband LOCs and intraband LOCs in $d$ dimension (with $d\ge 2$) are found to scale as ${\sigma }_0{\omega }^{d-2}$ and ${\sigma }_0{\mu }^{d-1}\delta (\omega )$, respectively, where $\omega$ is the frequency and $\mu$ the chemical potential. The interband LOC vanishes in 1D due to lack of extra spatial dimension. In contrast, the interband LOCs in 2D and 3D are nonvanishing and share many similar properties. A universal and robust fixed point of interband LOCs appears at $\omega =2\mu$ no matter $d=2$ or $d=3$, which can be intuitively understood by the geometric structures of Fermi surface and energy resonance contour. The intraband LOCs and the carrier density for 2D and 3D tilted Dirac bands are both closely related to the geometric structure of Fermi surface and the cutoff of integration. The angular dependence of LOCs is found to characterize both spatial dimensionality and band tilting and the constant asymptotic background values of LOC reflect features of Dirac bands. The LOCs in the anisotropic tilted Dirac cone can be connected to its isotropic counterpart by a ratio that consists of Fermi velocities for both 2D and 3D. Most of the findings are universal for tilted Dirac materials and hence valid for a great many Dirac materials in the spatial dimensions of physical interest.

arXiv comment22 pages, 7 figures

References in corpus (34)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Type-II Weyl Semimetals
• Measurement of the Optical Conductivity of Graphene
• Universal dynamical conductance in graphite
• The optical conductivity of graphene in the visible region of the spectrum
• A new electromagnetic mode in graphene
• Semimetallic Two-Dimensional Boron Allotrope with Massless Dirac Fermions
• Unusual Microwave Response of Dirac Quasiparticles in Graphene
• Pressure-Induced Zero-Gap Semiconducting State in Organic Conductor $\alpha$-(BEDT-TTF)${}_2$I${}_3$ Salt
• Sum Rules for the Optical and Hall Conductivity in Graphene
• Chiral anomaly and optical absorption in Weyl semimetals
• Intrinsic Anomalous Hall Effect in Type-II Weyl Semimetals
• Optical Signatures of the Tunable Band Gap and Valley-Spin Coupling in Silicene
• Exotic Lifshitz transitions in topological materials
• Effect of electron-hole asymmetry on optical conductivity in 8-Pmmn borophene
• Lifshitz transitions, type-II Dirac and Weyl fermions, event horizon and all that
• Optical properties of massive anisotropic tilted Dirac systems
• Collective modes in two- and three-dimensional electron systems with Rashba spin-orbit coupling
• Anisotropic longitudinal optical conductivities of tilted Dirac bands in 1T${}^{\prime }$-MoS${}_2$
• Absorption of circular polarized light in tilted Type-I and II Weyl semimetals
• Observation of band crossings protected by nonsymmorphic symmetry in the layered ternary telluride Ta3SiTe6
• Tilted-Cone Induced Cusps and Nonmonotonic Structures in Dynamical Polarization Function of Massless Dirac Fermions
• Directional massless Dirac fermions in a layered van der Waals material with one-dimensional long-range order
• Optical absorption in two-dimensional materials with tilted Dirac cones
• Large enhancement of conductivity in Weyl semimetals with tilted cones: Pseudorelativity and linear response
• Kubo conductivity for anisotropic tilted Dirac semimetals and its application to 8-Pmmn borophene: The role of different frequency, temperature and scattering limits
• Observation of one-dimensional Dirac fermions in silicon nanoribbons
• Hyperbolic plasmons in massive tilted 2D Dirac materials
• Signatures of Lifshitz transition in the optical conductivity of two-dimensional tilted Dirac materials
• Realistic tight-binding model for monolayer transition metal dichalcogenides in 1T' structure
• Dynamical polarization and plasmons in noncentrosymmetric metals
• Optical conductivity of a 2DEG with anisotropic Rashba interaction at the interface of LaAlO${}_3$/SrTiO${}_3$

Cited by in corpus (4)

• Highly anisotropic optical conductivities in two-dimensional tilted semi-Dirac bands
• Optical conductivity of tilted higher pseudospin Dirac-Weyl cones
• Spin-polarized scanning tunneling microscopy measurement scheme for determining the quantum geometric tensor
• Current response to axial gauge fields in noncentrosymmetric magnetic Weyl semimetals