Research ArticleCONDENSED MATTER PHYSICS

Evidence for a strain-tuned topological phase transition in ZrTe5

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Science Advances  09 Aug 2019:
Vol. 5, no. 8, eaav9771
DOI: 10.1126/sciadv.aav9771
  • Fig. 1 Topological phase diagram and band structures of ZrTe5.

    (A) Universal phase diagram of topological insulators proposed by Murakami for a 3D system (2, 3, 10). The control parameter 𝛿 describes the breaking of inversion symmetry. The control parameter ϵ does not break inversion symmetry. (B) Crystal structure of ZrTe5. Chains of ZrTe3 prisms (consisting of Tea and Ted atoms) extend along the a axis. These chains are connected by Tez atoms along the c axis to form layers. These layers are vdW bonded in the b axis direction. (C) Size of bandgap Eg at the Γ point as functions of strains in the a and c lattice directions. The dashed gray arrow indicates the anisotropic strain induced by a uniaxial stress along the a axis direction, as governed by the calculated Poisson’s ratio ϵaa = −4.0ϵcc. (D) Band structures for different strain states taken at points along the Poisson’s ratio path. These points (from left to right) correspond to STI, Dirac semimetal, and WTI, respectively. Fermi level is defined as the zero energy, and the k-point labeling is based on the primitive unit cell. A band inversion involving Ted and Tez p orbitals (shown as red and green colors, respectively) is seen in the STI phase.

  • Fig. 2 Temperature and strain dependence of resistivity of ZrTe5.

    (A) Strain dependence of resistivity of ZrTe5 at T = 2 K for five samples S1 to S5. A clear minimum in resistivity can be seen for each sample. The resistivity is normalized by its minimum value ρmin, which varies between 1 and 16 milli-Ohm⋅cm. The x axis is the strain along the a lattice direction, which is estimated on the basis of the method described in Materials and Methods. (B) Resistivity versus strain for temperatures between 2 and 100 K. A clear minimum can be seen for the entire temperature range. (C) Resistivity versus temperature for three ZrTe5 crystals S1 to S3, as measured before gluing onto the three-piezo strain apparatus. (D) Three-piezostack apparatus used to deliver strain. (E) Quadratic coefficient Q obtained from fitting ρρmin=1+Q(ϵaaϵmin)2. The sensitivity of the response to strain shows a nonmonotonic temperature dependence, as discussed in the main text. Inset: Coefficient Q computed using Boltzmann transport equations (Materials and Methods). The main calculated features agree with the experimental data: A local minimum then maximum is seen with increasing temperature. The relative strength and temperature of these features depend on the carrier density input into the model (see Materials and Methods for more information).

  • Fig. 3 Strain dependence of longitudinal magnetoresistance and magnetoconductance of ZrTe5 at T = 2 K.

    NLMR for negative strains (A) and positive strains (B) measured relative to ϵmin, corresponding to the STI and WTI phases, respectively. The negative magnetoresistance is strongest at ϵmin, at which ZrTe5 is a gapless Dirac semimetal. Straining the crystal away from ϵmin suppresses the negative magnetoresistance. (C) Weak field positive magnetoconductance for several strain set points close to ϵmin. The conductance is fitted to the equation σ(B) = σ0 + αB2 (black solid curves), where α is a positive coefficient proportional to the helicity relaxation time. (D) Quadratic coefficient α as a function of strain measured relative to ϵmin.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/8/eaav9771/DC1

    Fig. S1. Schematic and picture of piezo device.

    Fig. S2. Finite element analysis of strain transmission.

    Fig. S3. Sample aging and zero-strain tuning.

    Fig. S4. Comparison between three-piezo and single-piezo elastoresistivity measurement.

    Fig. S5. Additional longitudinal magneto-transport measurement as a function of strain.

    Fig. S6. Angle dependence of longitudinal magnetoresistance.

    Fig. S7. Fitting of positive longitudinal magnetoconductance.

    Fig. S8. DFT calculations of Z2 topological indices, Poisson ratio, and DOS.

    Fig. S9. DFT band structures for ZrTe5 in different strained states.

    Table S1. Dimensions, 2 K resistivity, and QC of each sample crystal.

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Schematic and picture of piezo device.
    • Fig. S2. Finite element analysis of strain transmission.
    • Fig. S3. Sample aging and zero-strain tuning.
    • Fig. S4. Comparison between three-piezo and single-piezo elastoresistivity measurement.
    • Fig. S5. Additional longitudinal magneto-transport measurement as a function of strain.
    • Fig. S6. Angle dependence of longitudinal magnetoresistance.
    • Fig. S7. Fitting of positive longitudinal magnetoconductance.
    • Fig. S8. DFT calculations of Z2 topological indices, Poisson ratio, and DOS.
    • Fig. S9. DFT band structures for ZrTe5 in different strained states.
    • Table S1. Dimensions, 2 K resistivity, and QC of each sample crystal.

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