Materials are generally classified as metal, insulator, semiconductor, semimetal, etc. based on their electronic band structure. With the perspective of topological invariance in band structure, a new set of materials such as Topological Insulators (TI) and Topological Semimetals (TSM) have been predicated, which have distinctive metallic surface and insulating/semimetallic bulk states. Unlike the normal metals, the quasi-particles in TSM obey relativistic Dirac or Weyl type equation of motion, which is reflected in the linear energy-momentum dispersion relation near the band crossing point. Thus, these systems provide a great opportunity to study the novel physics of relativistic particles in low-energy condensed matter physics.
Due to the unique band topology, these materials are the subject of considerable research interest for understanding the relativistic phenomenon in tabletop experiment. Apart from fundamental interest, the exotic transport properties of these materials such as giant magnetoresistance (i.e., change in resistivity with magnetic field) and ultra-high carrier mobility are equally compelling for technological application. Indeed, a new terminology “Topotronics” has been coined for possible applications of these materials as electronic devices such as sensors, magnetic switch, memory devices, high efficient low-power electronics, spintronic systems, quantum computation, high thermoelectric figure of merit, etc. For applications, however, the material should show linear energy-momentum dispersion over a wide range of energy so that its unique transport properties can be exploited efficiently. Only ZrSiS is found to exhibit linear dispersion up to as high as 2 eV [L. M. Schoop, et al. Nat Commun (2016)] and host multiple Dirac cones.
A team of researcher at SINP [Ratnadwip Singha, Arnab Kumar Pariari, Biswarup Satpati and Prabhat Mandal], has grown very high quality single crystals of ZrSiS and measured magnetotransport properties to understand both the technological importance and electronic band structure of this material. The work has been recently published in Proceedings of the National Academy of Sciences [PNAS 114(10), 2468 (2017) | DOI: 10.1073/pnas.1618004114].


Fig. 1 (A) ZrSiS single crystal with different crystallographic directions. (B) Selected area electron diffraction pattern obtained in HRTEM.

The single crystals used in this work has been grown via chemical vapor transport technique and characterized using high-resolution transmission electron microscopy (HRTEM) [Fig.1]. The transport properties have been measured over a wide temperature range (300–2 K) in presence of magnetic field. With magnetic field (B) applied parallel to crystallographic c-axis and perpendicular to current (I) direction, an extremely large and non-saturating magnetoresistance [MR = R (B)-R (0)/R (0)] ~ 1.4 × 10⁵ % at 2 K and 9 Tesla [Fig. 2(A)] has been observed. This is one of the largest values of MR reported so far. Surprisingly, with field along b-axis, a drastic reduction in the value of MR (~10³ %) is observed [Fig. 2(B)]. The giant value of magnetoresistance and it’s highly anisotropic nature, has revealed immense technological impact for the fabrication of magnetic field sensor.
On the other hand, an increase in conductivity with the increase in field strength has been seen for B//I configuration [Fig. 2(C)]. This enhanced magneto-conductance is a unique signature of Adler–Bell–Jackiw chiral anomaly which is a relativistic phenomenon in condensed matter system, and originates due to the charge transfer between two Weyl nodes of opposite chirality, under broken time-reversal symmetry.


Fig. 2 Transverse magnetoresistance with current along the a-axis and magnetic field parallel to the (A) c-axis and (B) b-axis, measured at different temperatures, up to 9 T.  (C) Enhanced magnetoconductivity data at 2 K and it’s theoretical fitting. The low field minimum is due to weak anti localization effect.

Due to the formation of Landau levels, the field dependence of resistivity is accompanied by quantum oscillations [Fig. 3(A) and Fig. 3(B)], which have been analyzed to obtain information on Fermi surface. The non-trivial p Berry’s phase acquired by the charge carriers due to cyclotron orbit around the Dirac nodes has been calculated from the Landau level index plot [Fig. 3(C)]. Through this detection of non-trivial Berry’s phase and observation of enhanced magneto-conductance in B // I configuration, we have established that the bulk state of ZrSiS hosts Dirac-like linear band dispersion. Combining the results of quantum oscillation and Hall measurements, the presence of multiple Dirac nodes at different energies of electronic band structure have been demonstrated.


Fig. 3 (A) and (B) Two independent Quantum oscillations, obtained by subtracting the smooth background from the field dependence of resistivity. Insets show the corresponding Fourier transformed spectrum results. (C) Landau-level index plot showing the intercept ~ 0.15, which is very close to the value zero corresponds to non-trivial pi Berry’s phase.