Large enhancement of conductivity in Weyl semimetals with tilted cones: Pseudorelativity and linear response

Abstract

We study the conductivity of two-dimensional graphene-type materials with tilted cones as well as their three-dimensional Weyl counterparts and show that a covariant quantum Boltzmann equation is capable of providing an accurate description of these materials' transport properties. The validity of the covariant Boltzmann approach is corroborated by calculations within the Kubo formula. We find a strong anisotropy in the conductivities parallel and perpendicular to the tilt direction upon an increase of the tilt parameter η, which can be interpreted as the boost parameter of a Lorentz transformation. While the ratio between the two conductivities is 1 − η 2 in the twodimensional case where only the conductivity perpendicular to the tilt direction diverges for η → 1, both conductivities diverge in three-dimensional Weyl semimetals, where η = 1 separates a type-I (for η < 1) from a type-II Weyl semimetal (for η > 1).

Kubo conductivity for anisotropic tilted Dirac semimetals and its application to 8-Pmmnborophene: Role of frequency, temperature, and scattering limits

“…We notice that both σ min xx,1 and σ min yy,1 increase with the tilt parameter γ, while σ min xx,1 > σ min yy,1 and only σ min xx,1 diverges as γ → 1 [39,41]. This limit coincides with recent calculations of the static conductivity using the covariant Boltzmann equation [41].…”

“…We notice that both σ min xx,1 and σ min yy,1 increase with the tilt parameter γ, while σ min xx,1 > σ min yy,1 and only σ min xx,1 diverges as γ → 1 [39,41]. This limit coincides with recent calculations of the static conductivity using the covariant Boltzmann equation [41]. The fact that both σ min xx,1 and σ min yy,1 grow with the tilt of the dispersion can be attributed to the increase in the density of states with the tilt parameter γ,…”

“…To account for the anisotropy we point out that the constant-energy cross sections of the dispersion cone describe ellipses in momentum space given by (v x k x ) 2 /A 2 + (v y k y − h) 2 /B 2 = 1 with h = ±γE/(1 − γ 2 ), A = E/ 1 − γ 2 and B = E/(1 − γ 2 ). As the tilt increases, the eccentricity of the isoenergetic ellipses becomes more pronounced and scattering events across the shorter axis (here the x-axis) become more probable [39,41] than along the tilt axis (here the y-axis). We further note that in the purely tilted case (v x = v y ) the ratio between the lengths of the ellipse's semi-axes B/A is precisely equal to the ratio between these conductivities σ min xx,1 σ min…”

“…These distortions of the dispersion cones of 8-Pmmn borophene are found to produce direction dependent terms and scaling factors in the conductivity, both absent in graphene. Although there are now some works in which the zero-temperature conductivity in anisotropic tilted Dirac Hamiltonians is calculated through the Kubo formula [31,[39][40][41], not so much attention has been drawn to the role of a non-zero temperature, or to the fact that different results depend upon different physical and mathematical limits. This is well known in graphene's optical [2,42,43] and electronic properties [2,[42][43][44].…”

Photonic spin Hall effect on the surfaces of type-I and type-II Weyl semimetals

“…Nevertheless, most of the experimentally observed WSMs are oppositely tilted so far [11]. Attempt to search for more type-II WSMs with various tilts is ongoing from both the theoretical and experimental communities [17,22].…”