Signatures of Lifshitz transition in the optical conductivity of tilted Dirac materials

Abstract

Lifshitz transition is a kind of topological phase transition in which the Fermi surface is reconstructed. It can occur in the two-dimensional (2D) tilted Dirac materials when the energy bands change between the type-I phase (0 < t < 1) and the type-II phase (t > 1) through the type-III phase (t = 1), where different tilts are parameterized by the values of t. In order to characterize the Lifshitz transition therein, we theoretically investigate the longitudinal optical conductivities (LOCs) in type-I, type-II, and type-III Dirac materials within linear response theory. In the undoped case, the LOCs are independent of the tilt parameter in both type-I and type-III phases, but is determined by the tilt parameter in the type-II phase. In the doped case, the LOCs are anisotropic and share two resonance peaks determined by ω = ω1(t) and ω = ω2(t). The tilt parameter and chemical potential can be extracted from optical experiments by measuring the positions of these two peaks and their separation ∆ω(t) = ω2(t) − ω1(t). With increasing the tilt, the separation goes larger in the type-I phase whereas smaller in the type-II phase. The LOCs in the asymptotical region are exactly the same as that in the undoped case. The type of 2D tilted Dirac bands can be determined by the asymptotic background values, resonance peaks and their separation in the LOCs. These can therefore be taken as signatures of Lifshitz transition therein. The results of this work are expected to be qualitatively valid for a large number of monolayer tilted Dirac materials such as 8-Pmmn borophene tuned by gate voltage and different compounds of T -phase transition metal dichalcogenides.

Floquet Modification of the Bandgaps and Energy Spectrum in Flat-Band Pseudospin-1 Dirac Materials

“…we apply canonical substitution (27) so that Hamiltonian (19) has an additional interaction term Ĥ(e)…”

“…[11] Floquet theory has been successfully applied to original, [12][13][14][15][16][17] gapped [13,18] and Kekulepatterned graphene. [19] It also enters into extensive studies of anisotropic [20] and tilted Dirac materials [21][22][23][24][25][26][27] as well as other structures. [12,[28][29][30][31][32].…”

Floquet engineering of tilted and gapped Dirac band structures in 1T'-MoS2

“…The zero-gap limit of 1T ′ -MoS 2 bands is found in 8-Pmmn borophene which was extensively explored over many years because of an observed strong anisotropy in all of its crucial physical properties. [66][67][68][69][70] Very recently, a plasmonic gain was reported in current-biased tilted Dirac nodes. 71 Their optical conductivity and other properties have also been investigated thoroughly.…”

Floquet engineering of titled and gapped Dirac materials

“…The zero-gap limit of 1T -MoS 2 bands is found in 8-Pmmn borophene which was intensively studied overt the recent years because of a strong anisotropy in all of its crucial physical properties. [59][60][61][62][63] Very recently, a plasmonic gain was reported in current-biased tilted Dirac nodes 64 Their optical properties and optical conductivity have been also thoroughly investigated. 53,65 Other monolayer materials with similar tilted band structure, such as TaIrTe 4 , TaCoTe 2 or α − SnS 2 have been recently synthesized.…”