Extremely large magnetoresistance from electron-hole compensation in the nodal-loop semimetal ${\mathrm{ZrP}}_{2}$

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Extremely large magnetoresistance from electron-hole compensation in the nodal-loop semimetal ${ZrP}_{2}$

J. Bannies, E. Razzoli, M. Michiardi, H.-H. Kung, I. S. Elfimov, M. Yao, A. Fedorov, J. Fink, C. Jozwiak, A. Bostwick, E. Rotenberg, A. Damascelli, and C. Felser

Phys. Rev. B 103, 155144 – Published 22 April 2021

Abstract

Several early transition metal dipnictides (TMDPs) have been found to host topological semimetal states and exhibit large magnetoresistance (MR). In this paper, we use angle-resolved photoemission spectroscopy (ARPES) and magnetotransport to study the electronic properties of a TMDP ${ZrP}_{2}$ . We find that ${ZrP}_{2}$ exhibits an extremely large and unsaturated MR of up to 40 000% at 2 K, which originates from an almost perfect electron-hole (e-h) compensation. Our band structure calculations further show that ${ZrP}_{2}$ hosts a topological nodal loop in proximity to the Fermi level. Based on the ARPES measurements, we confirm the results of our calculations and determine the surface band structure. This paper establishes ${ZrP}_{2}$ as a platform to investigate near-perfect e-h compensation and its interplay with topological band structures.

Received 20 October 2020
Accepted 22 March 2021

DOI:https://doi.org/10.1103/PhysRevB.103.155144

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Magnetoresistance Symmetry protected topological states

Node-line semimetals

Angle-resolved photoemission spectroscopy Density functional theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

J. Bannies ^1,2,*, E. Razzoli^2,3, M. Michiardi^2,3,1, H.-H. Kung ^2,3,1, I. S. Elfimov^2,3, M. Yao¹, A. Fedorov^4,5, J. Fink ^1,4,6, C. Jozwiak ⁷, A. Bostwick⁷, E. Rotenberg⁷, A. Damascelli ^2,3, and C. Felser^1,†

¹Max Planck Institute for Chemical Physics of Solids, 01187 Dresden, Germany
²Quantum Matter Institute, University of British Columbia, Vancouver, British Columbia, V6T 1Z4, Canada
³Department of Physics & Astronomy, University of British Columbia, Vancouver, British Columbia, V6T 1Z1, Canada
⁴Leibniz Institute for Solid State and Materials Research Dresden, 01069 Dresden, Germany
⁵Helmholtz-Zentrum Berlin für Materialien und Energie, 12489 Berlin, Germany
⁶Institut für Festkörperphysik, Technische Universität Dresden, 01062 Dresden, Germany
⁷Advanced Light Source (ALS), Berkeley, California 94720, USA

^*jbannies@chem.ubc.ca
^†claudia.felser@cpfs.mpg.de

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Vol. 103, Iss. 15 — 15 April 2021

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Figure 1
Occurrence of extremely large magnetoresistance (XMR) in early transition metal dipnictides (TMDPs). (a) Excerpt of the periodic table. Elements for which at least one TMDP was found to show XMR are marked in red. (b) and (c) Common crystal structure types of early TMDPs: ${OsGe}_{2}$ type and ${MoP}_{2}$ type, both containing glide planes and two formula units per primitive unit cell. Covalent bonding motifs of anions are encircled. (d) Schematic of a trivial semiclassical two-band model (left). Simulated magnetoresistance (MR) for different carrier density ratios (right). Mobilities: $μ_{h} = μ_{e} = 1$ $m^{2}$ /Vs. (e) Schematic of a nontrivial compensated two-band system. (f) Distorted ${PbCl}_{2}$ -type crystal structure as found in ${ZrP}_{2}$ . One of the nonsymmorphic symmetry elements, the $n$ glide plane, is shown.
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Figure 2
Electrical transport behavior of ${ZrP}_{2}$ evidencing a semimetallic state. (a) Temperature dependence of $ρ_{x x}$ in different magnetic fields with $I ∥ b$ . (b) and (c) Magnetic field dependence of magnetoresistance (MR) and $ρ_{xy}$ at selected temperatures. (d) Charge carrier densities and mobilities obtained by simultaneously fitting MR and $ρ_{x y}$ to the two-band model [34]. Note that the large uncertainties of $n_{h}$ compared with $n_{e} / n_{h}$ below 50 K originate from the fits. Depending on the initial values for the fit, values of $n_{h}$ converged only to the window given by the uncertainties. In contrast, independent of the final value of $n_{h}, n_{e} / n_{h}$ is always $\sim 1$ .
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Figure 3
Electronic structure of ${ZrP}_{2}$ from density functional theory calculations without spin-orbit coupling. (a) Band structure with the three bands crossing $E_{F}$ colored. (b) and (c) Three-dimensional (3D) Fermi surface of ${ZrP}_{2}$ exhibiting two hole pockets ( $α$ and $β$ ) and an electron pocket ( $γ$ ). Color coding according to panel (a). (d) Close-up of the low-energy band structure in the $k_{x} = 0$ plane. Eigenvalues $η_{\pm}$ with respect to the $n$ glide plane are indicated (closed line $η_{+}$ , dashed $η_{-}$ ). (e) 3D visualization $E (k_{y}, k_{z})$ of the $β$ and $γ$ bands forming the nodal loop (black line) in the $k_{x} = 0$ plane. Only one quadrant of the $k_{x} = 0$ plane is shown.
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Figure 4
Bulk and surface band structure of ${ZrP}_{2}$ measured by angle-resolved photoemission spectroscopy (ARPES; both $h ν = 40$ eV, linear horizontal polarization) and comparison with density functional theory calculations. (a) Bulk Fermi surface from ARPES (left) and calculations (right) both at $k_{z} = 0$ . (b) and (c) Cuts along $\bar{Y} − \bar{Γ} − \bar{Y}$ and $\bar{M} − \bar{X} − \bar{M}$ showing bulk bands, respectively. Calculations show the projected band structures for $k_{z} \in [0, 0.6 π / c]$ , where bands with $k_{z} = 0$ are highlighted in black. (d)–(f) Data acquired at Advanced Light Source, where the small spot size allowed us to focus on an area with a single termination, emphasizing the surface band structures [36]. Note that the calculated surface band structure was shifted by 50 meV with respect to the theoretical Fermi level to match the experimental dispersion. Experimental Fermi surfaces were integrated within $\pm 10$ meV of the Fermi level.
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Figure 5
Gap opening along the nodal loop through increased spin-orbit coupling (SOC). Band structures along Y- $Γ$ -Z for (a) ${ZrP}_{2}$ , (b) ${ZrAs}_{2}$ , (c) ${HfP}_{2}$ , and (d) ${HfAs}_{2}$ . Black lines: without SOC, red lines: with SOC. Experimentally determined crystal structures were used for calculations on ${ZrP}_{2}$ [40] and ${ZrAs}_{2}$ [51]. For ${HfP}_{2}$ and ${HfAs}_{2}$ , the crystal structures of ${ZrP}_{2}$ and ${ZrAs}_{2}$ were used, respectively.
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Physical Review B

covering condensed matter and materials physics

Extremely large magnetoresistance from electron-hole compensation in the nodal-loop semimetal ${ZrP}_{2}$

J. Bannies, E. Razzoli, M. Michiardi, H.-H. Kung, I. S. Elfimov, M. Yao, A. Fedorov, J. Fink, C. Jozwiak, A. Bostwick, E. Rotenberg, A. Damascelli, and C. Felser

Phys. Rev. B 103, 155144 – Published 22 April 2021

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Physical Review B

covering condensed matter and materials physics

Extremely large magnetoresistance from electron-hole compensation in the nodal-loop semimetal ZrP2

J. Bannies, E. Razzoli, M. Michiardi, H.-H. Kung, I. S. Elfimov, M. Yao, A. Fedorov, J. Fink, C. Jozwiak, A. Bostwick, E. Rotenberg, A. Damascelli, and C. Felser

Phys. Rev. B 103, 155144 – Published 22 April 2021

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Extremely large magnetoresistance from electron-hole compensation in the nodal-loop semimetal ${ZrP}_{2}$