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Nonsaturating Large Magnetoresistance in Semimetals This document is downloaded from DR‑NTU (https://dr.ntu.edu.sg) Nanyang Technological University, Singapore. Nonsaturating large magnetoresistance in semimetals Leahy, Ian A.; Lin, Yu‑Ping; Siegfried, Peter E.; Treglia, Andrew C.; Song, Justin Chien Wen; Nandkishore, Rahul M.; Lee, Minhyea 2018 Leahy, I. A., Lin, Y.‑P., Siegfried, P. E., Treglia, A. C., Song, J. C. W., Nandkishore, R. M., & Lee, M. (2018). Nonsaturating large magnetoresistance in semimeta. Proceedings of the National Academy of Sciences of the United States of America, 115 (42), 10570‑10575. doi:10.1073/pnas.1808747115 https://hdl.handle.net/10356/137998 https://doi.org/10.1073/pnas.1808747115 © 2018 The Author(s). All rights reserved. This paper was published by National Academy of Sciences in Proceedings of the National Academy of Sciences of the United States of America and is made available with permission of The Author(s). Downloaded on 01 Oct 2021 03:16:44 SGT Non-saturating large magnetoresistance in semimetals Ian A. Leahy,1 Yu-Ping Lin,1 Peter E. Siegfried,1 Andrew C. Treglia,1 Justin C. W. Song,2 Rahul M. Nandkishore,1, 3 and Minhyea Lee1, 4, ∗ 1Department of Physics, University of Colorado, Boulder, CO 80309, USA 2Division of Physics and Applied Physics, Nanyang Technological University, Singapore 637371 3Center for Theory of Quantum Matter, University of Colorado, Boulder, CO 80309, USA 4Center for Experiments on Quantum Materials, University of Colorado, Boulder, CO 80309, USA (Dated: September 6, 2018) The rapidly expanding class of quantum materials known as topological semimetals (TSM) dis- play unique transport properties, including a striking dependence of resistivity on applied magnetic field, that are of great interest for both scientific and technological reasons. So far many possible sources of extraordinarily large non-saturating magnetoresistance have been proposed. However, experimental signatures that can identify or discern the dominant mechanism and connect to avail- able theories are scarce. Here we present the magnetic susceptibility (χ), the tangent of the Hall angle (tan θH ) along with magnetoresistance in four different non-magnetic semimetals with high mobilities, NbP, TaP, NbSb2 and TaSb2, all of which exhibit non-saturating large MR. We find that the distinctly different temperature dependences, χ(T ) and the values of tan θH in phosphides and antimonates serve as empirical criteria to sort the MR from different origins: NbP and TaP being uncompensated semimetals with linear dispersion, in which the non-saturating magnetoresistance arises due to guiding center motion, while NbSb2 and TaSb2 being compensated semimetals, with a magnetoresistance emerging from nearly perfect charge compensation of two quadratic bands. Our results illustrate how a combination of magnetotransport and susceptibility measurements may be used to categorize the increasingly ubiquitous non-saturating large magnetoresistance in TSMs. PACS numbers: Introduction Magnetoresistance (MR) and the Hall non-saturating MR, known as extreme magnetoresis- effect are versatile experimental probes in exploring elec- tance (XMR) with unusually high mobilities for bulk tronic properties of materials, such as carrier density, mo- systems [12{18] and relatively low residual resistivity bility and the nature of scattering and disorder. In typi- ρ0. The proximity of the chemical potential to the cal non-magnetic and semiconducting materials, the MR charge neutrality point in semimetals allows the generic increases quadratically with applied transverse magnetic quadratic two band model to describe the MR and the field and saturates to a constant value when the product Hall effect in reasonable levels [19{23]. However, a two of the applied field and the mobility (ν) approaches unity. band model of this form generically predicts a magne- Non-saturating MR is commonly attributed to the semi- toresistance that is quadratic in applied fields, whereas classical two-band model, where electron-like and hole- the materials frequently exhibit a magnetoresistance lin- like carriers are nearly compensated [1], resulting in rich ear in applied field. While various theoretical propos- magnetotransport characteristics that are strongly tem- als for H linear magnetoresistance have been advanced perature (T ) and applied transverse magnetic field (H) (see e.g. [8, 24{26]) the origins of extreme magnetore- dependent in non-magnetic compounds. A flurry of in- sistance in topological semimetals remain unclear. As terest in non-saturating, H-linear MR [2{5] in narrow non-saturating, large MR becomes more ubiquitous, it gap semiconductors led to two main theoretical accounts: becomes particularly urgent to identify a set of distinct (i) a two-dimensional simple 4-terminal resistor network attributes that enable the delineation of their origins. model, where strong disorder or inhomogeneity of the In this article, we systematically examine the low field sample manifest as charge and mobility fluctuations [6, 7] diamagnetic susceptibility (χ), the transverse MR, and arXiv:1805.08797v2 [cond-mat.str-el] 5 Sep 2018 and (ii) the so-called `quantum linear MR' which emerges the Hall effect as a function of T and H in 4 different in systems with linear band crossings when the lowest semimetals with high mobility (ν ≥ 104 cm2/Vs) and Landau level is occupied [8]. The former approach has very large non-saturating MR { NbP, TaP (phosphides), provided a basis to engineer large magnetotransport re- NbSb2, and TaSb2(antimonates). Characteristic param- sponses via macroscopic inhomogeneities or disorder [9{ eters related to magnetic transport are summarized in 11]. Meanwhile, the latter has remained rather elusive Table I. until recently. We present two different types of non-saturating large Interest in non-saturating very large MR has exploded MR identified by the temperature (T ) dependence of dia- following the discovery of topological semimetals. These magnetic susceptibility, χ(T ) and the H dependence of ρxy σxy the Hall angle, tan θH = = , where ρxx and ρxy materials are regularly reported to exhibit record high ρxx σxx 2 low temperatures when H > HS ' 8 T, while ρxx(T ) has a peculiar H dependent non-monotonic form. The α measured MR defined as ∆ρ/ρ0 / H at low T exhibits a crossover from quasi-linear [α ∼ 1:5 ± 0:1] to linear [ α ∼ 1:0 ± 0:1], where the crossover field, HS is set by the scale at which tan θH (H) saturates. In H > HS, MR remains linear in H up to µ0H = 31 T, the high- est applied field in this study. Finally, χ(T )'s for the phosphides exhibit a pronounced minimum at Tmin. All of these features can be explained if we assume that the phosphides are semimetals with linear dispersion, even without invoking compensation, and that the magnetore- sistance arises due to guiding center motion [see e.g. [25] FIG. 1: Schematically depicted non-saturating MR phe- for a recent discussion]. Moreover, χ(T ) allows to ex- nomena and representative energy dispersions for phosphides tract doping levels relative to the charge neutrality point [TaP] (left) and antimonates [TaSb2] (right). Phosphides' MR is characterized by quasi-linear to linear transition as H in- as fit parameters. (2) Meanwhile, in the antimonates, the −2 creases, while antimonates' by persistent quadratic H depen- Hall angle remains close to zero (< 10 ) at all accessi- dence, arising from semiclassical charge compensation. Each ble fields in this study. The magnetoresistance is nearly 5 bar indicates ∆ρ/ρ0 = 5 × 10 % up to µ0H = ±31 T at quadratic in H from room temperature down to T = 0:3 T = 0:3 K. K, obeying Kohler's rule. The field dependence of the Hall resistivity strongly deviates from linearity in the an- timonates. The diamagnetic susceptibility for the anti- monates is mostly T -independent. These features of the are longitudinal and Hall resistivity respectively and σ xx antimonates are archetypical for compensated semimet- and σ are corresponding conductivities. xy als with usual quadratic bands. One type of MR originates from the presence of smooth Our finding is well-consistent with existing electronic disorder that governs guiding center motion of charge car- structure calculations : NbP and TaP have been studied H riers. The linear -dependence of this type arises from thoroughly via first principle calculations and photoemis- the squeezed trajectories of carriers in semi-classically sion studies [17, 27, 28], where multiple Weyl nodes were νB ≥ large magnetic fields 1 (easily achieved in linearly identified in vicinity of Fermi energy. The calculations for dispersing topological semimetals, see e.g., Table I), and NbSb2 and TaSb2 are also consistent with our picture does not require the involvement of multiple bands for of nearly compensated semimetals [29], yet the photoe- the charge compensation. The other type of MR comes mission studies are not yet avaialble for the antimonates. from charge compensation in the two band model and it accompanies other transport and magnetic characteris- Methods Single crystals of NbP, TaP, NbSb , and tics within the conventional frame work. 2 TaSb2 were grown using the chemical vapor transport Using a combination of magnetic susceptibility and method following known synthesis procedure [17, 30{32]. magnetotransport measurements to interrogate the dif- Standard electrical contacts were made directly on sin- ferent facets of magneto-response, we are able to catego- gle crystals using Ag paint (Dupont 4966) with contact rize the phosphides into the former and the antimonates resistance ranges in ≤ 1 − 2 Ω. The magnetotransport the latter. Our results can be summarized as follows and measurements were performed with applied field perpen- depicted in Fig. 1. (1) In the phosphides, the magni- dicular to the direction of current on the plane up to tude of tan θH saturates to a H-independent constant at 31T down to 0:3 K. Magnetic susceptibilities of the sam- ples were measured by the Magnetic Properties Measure- ments System by Quantum Design. 2 −1 tan θH ν (T ) ρ0 (µΩ cm) ∆ρ/ρ0 Results NbP 7.6 99 0.5 561 Magneto-transport Fig.
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