Revealing the band structure of ${\mathrm{ZrTe}}_{5}$ using multicarrier transport

Revealing the band structure of ${ZrTe}_{5}$ using multicarrier transport

Zoltán Kovács-Krausz, Endre Tóvári, Dániel Nagy, Albin Márffy, Bogdan Karpiak, Zoltán Tajkov, László Oroszlány, János Koltai, Péter Nemes-Incze, Saroj P. Dash, Péter Makk, and Szabolcs Csonka

Phys. Rev. B 107, 075152 – Published 27 February 2023

Abstract

The layered material ${ZrTe}_{5}$ appears to exhibit several exotic behaviors, which resulted in significant interest recently, although the exact properties are still highly debated. Among these we find a Dirac/Weyl semimetallic behavior, nontrivial spin textures revealed by low-temperature transport, and a potential weak or strong topological phase. The anomalous behavior of resistivity has been recently elucidated as originating from band shifting in the electronic structure. Our work examines magnetotransport behavior in ${ZrTe}_{5}$ samples in the context of multicarrier transport. The results, in conjunction with ab initio band structure calculations, indicate that many of the transport features of ${ZrTe}_{5}$ across the majority of the temperature range can be adequately explained by the semiclassical multicarrier transport model originating from a complex Fermi surface.

Received 12 September 2022
Revised 15 December 2022
Accepted 23 December 2022

DOI:https://doi.org/10.1103/PhysRevB.107.075152

Physics Subject Headings (PhySH)

Electronic structure Magnetotransport Shubnikov-de Haas effect

Dirac semimetal Topological materials

Density functional theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Zoltán Kovács-Krausz ^1,2, Endre Tóvári ^1,3,*, Dániel Nagy ^4,5, Albin Márffy ^1,2, Bogdan Karpiak ⁶, Zoltán Tajkov ^7,8, László Oroszlány ^4,9, János Koltai ⁵, Péter Nemes-Incze ⁷, Saroj P. Dash ⁶, Péter Makk ^1,3, and Szabolcs Csonka ^1,2

¹Department of Physics, Institute of Physics, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
²MTA-BME Superconducting Nanoelectronics Momentum Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
³MTA-BME Correlated van der Waals Structures Momentum Research Group, Műegyetem rkp. 3., H-1111 Budapest, Hungary
⁴Department of Physics of Complex Systems, ELTE Eötvös Loránd University, 1117 Budapest, Hungary
⁵Department of Biological Physics, ELTE Eötvös Loránd University, 1117 Budapest, Hungary
⁶Department of Microtechnology and Nanoscience, Chalmers University of Technology, SE-41296, Göteborg, Sweden
⁷Centre for Energy Research, Institute of Technical Physics and Materials Science, 1121 Budapest, Hungary
⁸Centre of Low Temperature Physics, Institute of Experimental Physics, Slovak Academy of Sciences, Košice SK-04001, Slovakia
⁹MTA-BME Lendület Topology and Correlation Research Group, Budapest University of Technology and Economics, 1521 Budapest, Hungary

^*tovari.endre@ttk.bme.hu

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Vol. 107, Iss. 7 — 15 February 2023

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Figure 1
(a) Crystal structure of ${ZrTe}_{5}$ . The coordinate system is defined such that $z$ is the vdW stacking direction. Components of the unit cell are highlighted with red lines. (b) Exfoliated ${ZrTe}_{5}$ crystal on ${SiO}_{2}$ . The $x$ axis is along the horizontal direction. The experimental measurement setup is depicted on the Cr/Au electrical contacts deposited on the device. The scale bar is 5 $µ m$ . (c) Temperature dependence of longitudinal resistivity, exhibiting characteristic peak at $T_{p} = 152 K$ . This behavior is attributed to the Dirac-like bands of ${ZrTe}_{5}$ shifting with respect to the chemical potential as the temperature changes. (d) A visual representation of this shift on a model (gapped) Dirac band with the dotted lines representing the points in temperature shown in (c).
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Figure 2
Full temperature range magnetotransport in ${ZrTe}_{5}$ . (a) Transverse magnetoresistivity and (b) longitudinal magnetoresistivity. The measurements were taken simultaneously at each temperature while sweeping the magnetic field, using the experimental setup in Fig. 1.
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Figure 3
Fitting of multiple carriers on magnetotransport data. Simultaneous fitting of (a) transverse and (b) longitudinal sheet conductivity, with the inset in (a) being magnified detail around the 0 T region of (a). The fitting is repeated for different carrier counts (NC) from 2–6. The inset in (b) shows the mean-square error of the fits. As can be seen on all panels, the fit approaches the experimental curves as NC increases, but reaches an optimal fit at $N C = 5$ and does not improve by further increasing NC (the $N C = 6$ curve is almost completely hidden behind $N C = 5$ ). The shown example is the fitting of the $T = 140 K$ data of the device; the procedure is repeated for all temperatures independently.
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Figure 4
Combined results of the multicarrier fitting. (a) Signed sheet conductivity contributions of the various obtained sub-bands as a function of temperature. Their corresponding mobilities are shown in (b). Vertical bars representing the errors of the fits are included. There are a total of five sub-bands identified, although not all play significant roles at every temperature. The sub-band represented in black ( $i = 1$ ) is assumed to be an edge state, as illustrated by black lines in the inset of (a) [hence the lack of $μ_{1}$ in (b)].
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Figure 5
(a) Signed carrier densities of the various carriers in the MCT model (discrete data points) and fit results (dotted lines) for each carrier (parabolic dispersion for $i = 2, 3$ and Dirac for $i = 4, 5$ ). The color notations are identical to Fig. 4, and error bars are included. (b) DFT results of the first conduction and valence bands of ${ZrTe}_{5}$ . Color notations on the band structure show the best guess correspondence to the carriers from (a). (c)–(e) Energy isosurfaces at $E_{F} =$ 20, 80, and 148 meV, corresponding to orange dashed lines of (b). The path in black follows the $x$ axis in (b) along high symmetry points of the BZ. The isosurface color is blue for the valence band and red for the conduction band. The colored arrows denote the features of the band structure in (b) depicted in the same colors.
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Physical Review B

covering condensed matter and materials physics

Revealing the band structure of ${ZrTe}_{5}$ using multicarrier transport

Zoltán Kovács-Krausz, Endre Tóvári, Dániel Nagy, Albin Márffy, Bogdan Karpiak, Zoltán Tajkov, László Oroszlány, János Koltai, Péter Nemes-Incze, Saroj P. Dash, Péter Makk, and Szabolcs Csonka

Phys. Rev. B 107, 075152 – Published 27 February 2023

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Physical Review B

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Revealing the band structure of ZrTe5 using multicarrier transport

Zoltán Kovács-Krausz, Endre Tóvári, Dániel Nagy, Albin Márffy, Bogdan Karpiak, Zoltán Tajkov, László Oroszlány, János Koltai, Péter Nemes-Incze, Saroj P. Dash, Péter Makk, and Szabolcs Csonka

Phys. Rev. B 107, 075152 – Published 27 February 2023

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Revealing the band structure of ${ZrTe}_{5}$ using multicarrier transport