Optical conductivity and resistivity in a four-band model for ZrTe5 from ab initio calculations

Abstract

ZrTe 5 is considered a potential candidate for either a Dirac semimetal or a topological insulator in close proximity to a topological phase transition. Recent optical conductivity results motivated a two-band model with a conical dispersion in 2D, in contrast to density-functional-theory calculations. Here, we reconcile the two by deriving a four-band model for ZrTe 5 using k • p theory, and fitting its parameters to the ab initio band structure. The optical conductivity with an adjusted electronic structure matches the key features of experimental data. The chemical potential varies strongly with temperature, to the point that it may cross the gap entirely between zero and room temperature. The temperature-dependent resistivity displays a broad peak and confirms theoretically the conclusions of recent experiments attributing the origin of the resistivity peak to the large shift of the chemical potential with temperature.

Gap-Opening Transition in Dirac Semimetal ZrTe5

“…Thus, we model this system in a three-band approximation, including the Dirac electrons and holes, and quadratic CB pocket. For the Dirac-cone dispersion, magneto-optic measurements [5] are consistent with approximately quadratic dispersion along k b , and linear in other directions, while other recent work [6,41] also points to a non-Dirac dispersion along k b . To include the effect of a flatter k b dispersion, we compare the limiting cases of a 3D linear Dirac cone, and the quasi-2D case with no dispersion along k b .…”

“…From the Hamiltonian parameters quoted in Ref. [23], we calculate an energy dispersion of about 10 meV over the range of the filled N ¼ 0 þ states, and the proposed flatter k b dispersion [5,6,41] implies a situation closer to quasi-2D discrete Landau levels. Thus, our sample is within the quantum limit in the 9 T measuring field, with only the N ¼ 0 þ level occupied at low temperatures in the absence of interactions.…”

Gap-opening transition in Dirac semimetal ZrTe$_5$

“…Thus, we model this system in a 3-band approximation, including the Dirac electrons and holes, and quadratic CB pocket. For the Dirac-cone dispersion, magneto-optic measurements [10] are consistent with approximately quadratic dispersion along k b , and linear in other directions, while other recent work [11,27] also points to a non-Dirac dispersion along k b . To include the effect of a flatter k b dispersion, we compare the limiting cases of a 3D linear Dirac cone, and the quasi-2D case with no dispersion along k b .…”

“…From the Hamiltonian parameters quoted in Ref. [28], we calculate an energy dispersion of about 10 meV over the range of the filled N = 0 + states, and the proposed flatter k b dispersion [10,11,27] implies a situation closer to quasi-2D discrete Landau levels. Thus, our sample is within the quantum limit in the 9 T measuring field, with only the N = 0 + level occupied at low temperatures in absence of interactions.…”

Strain-tuned topological phase transition and unconventional Zeeman effect in ZrTe5 microcrystals

“…Its electronic properties of is largely dominated by the Fermi surface centered around the Γ point with a Dirac dispersion, but can also have contribution from the parabolic side bands with Fermi surfaces centered between the R and E points in the Brillouin zone (see Supplementary Note 2). ZrTe 5 hosts intriguing properties such as a resistance peak (Lifshitz transition) [27][28][29] , chiral magnetic effect 30 , and 3D quantum Hall effect 31 . In its 3D bulk form, ZrTe 5 has a Dirac-like low energy band structure, with sampledependent mass gap rendering the material from Dirac semimetal to topological insulator 30,[32][33][34][35][36] , suggesting extreme sensitivity to lattice deformations.…”