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Register a new userDetermination of the Fermi surface and field-induced quasi-particle tunneling around the Dirac nodal-loop in ZrSiS
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Added by
Claudius M\\\"uller
Publication date
2020
fields
Physics
and research's language is
English
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Unambiguous and complete determination of the Fermi surface is a primary step in understanding the electronic properties of topical metals and semi-metals, but only in a relatively few cases has this goal been realized. In this work, we present a systematic high-field quantum oscillation study up to 35 T on ZrSiS, a textbook example of a nodal-line semimetal with only linearly dispersive bands crossing the Fermi energy. The topology of the Fermi surface is determined with unprecedented precision and all pockets are identified by comparing the measured angle dependence of the quantum oscillations to density functional theory calculations. Comparison of the Shubnikov-de Haas and de Haas-van Alphen oscillations at low temperatures and analysis of the respective Dingle plots reveal the presence of significantly enhanced scattering on the electron pocket. Above a threshold field that is aligned along the c-axis of the crystal, the specific cage-like Fermi surface of ZrSiS allows for electron-hole tunneling to occur across finite gaps in momentum space leading to quantum oscillations with a complex frequency spectrum. Additional high-frequency quantum oscillations signify magnetic breakdown orbits that encircle the entire Dirac nodal loop. We suggest that the persistence of quantum oscillations in the resistivity to high temperatures is caused by Stark interference between orbits of nearly equal masses.
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The topological properties of fermions arise from their low-energy Dirac-like band dispersion and associated chiralities. Initially confined to points, extensions of the Dirac dispersion to lines and even loops have now been uncovered and semimetals hosting such features have been identified. However, experimental evidence for the enhanced correlation effects predicted to occur in these topological semimetals has been lacking. Here, we report a quantum oscillation study of the nodal loop semimetal ZrSiS in high magnetic fields that reveals significant enhancement in the effective mass of the quasiparticles residing near the nodal loop. Above a threshold field, magnetic breakdown occurs across gaps in the loop structure with orbits that enclose different windings around its vertices, each winding accompanied by an additional pi-Berry phase. The amplitudes of these breakdown orbits exhibit an anomalous temperature dependence. These findings demonstrate the emergence of novel, correlation-driven physics in ZrSiS associated with the Dirac-like quasiparticles.
We instigate the angle-dependent magnetoresistance (AMR) of the layered nodal-line Dirac semimetal ZrSiS for the in-plane and out-of-plane current directions. This material has recently revealed an intriguing butterfly-shaped in-plane AMR that is not well understood. Our measurements of the polar out-of-plane AMR show a surprisingly different response with a pronounced cusp-like feature. The maximum of the cusp-like anisotropy is reached when the magnetic field is oriented in the $a$-$b$ plane. Moreover, the AMR for the azimuthal out-of-plane current direction exhibits a very strong four-fold $a$-$b$ plane anisotropy. Combining the Fermi surfaces calculated from first principles with the Boltzmanns semiclassical transport theory we reproduce and explain all the prominent features of the unusual behavior of the in-plane and out-of-plane AMR. We are also able to clarify the origin of the strong non-saturating transverse magnetoresistance as an effect of imperfect charge-carrier compensation and open orbits. Finally, by combining our theoretical model and experimental data we estimate the average relaxation time of $2.6times10^{-14}$~s and the mean free path of $15$~nm at 1.8~K in our samples of ZrSiS.
We report a study of quantum oscillations (QO) in the magnetic torque of the nodal-line Dirac semimetal ZrSiS in the magnetic fields up to 35 T and the temperature range from 40 K down to 2 K, enabling high resolution mapping of the Fermi surface (FS) topology in the $k_z=pi$ (Z-R-A) plane of the first Brillouin zone (FBZ). It is found that the oscillatory part of the measured magnetic torque signal consists of low frequency (LF) contributions (frequencies up to 1000 T) and high frequency (HF) contributions (several clusters of frequencies from 7-22 kT). Increased resolution and angle-resolved measurements allow us to show that the high oscillation frequencies originate from magnetic breakdown (MB) orbits involving clusters of individual $alpha$ hole and $beta$ electron pockets from the diamond shaped FS in the Z-R-A plane. Analyzing the HF oscillations we have unequivocally shown that the QO frequency from the dog-bone shaped Fermi pocket ($beta$ pocket) amounts $beta=591(15)$ T. Our findings suggest that most of the frequencies in the LF part of QO can also be explained by MB orbits when intraband tunneling in the dog-bone shaped $beta$ electron pocket is taken into account. Our results give a new understanding of the novel properties of the FS of the nodal-line Dirac semimetal ZrSiS and sister compounds.
The topological nodal-line semimetals (NLSMs) possess a loop of Dirac nodes in the k space with linear dispersion, different from the point nodes in Dirac/Weyl semimetals. While the quantum transport associated with the topologically nontrivial Dirac fermions has been investigated extensively, features uniquely associated with the extended nodal lines remain to be demonstrated. Here, we investigate the quantum oscillations (QOs) in the nodal-line semimetal ZrSiS, with the electron transport along the c axis, and magnetic field rotating in the ab plane. The extremal orbits identified through the field orientation dependence of the QOs interlock with the nodal line, leading to a nonzero Berry phase. Most importantly, the Berry phase shows a significant dependence on the magnetic field orientation, which we argue to be due to the finite spin-orbit coupling gap. Our results demonstrate the importance of the spin-orbit coupling and the nodal-line dispersion in understanding the quantum transport of NLSMs.
We theoretically investigate the barrier tunneling in the three-dimensional model of the hyperhoneycomb lattice, which is a nodal-line semimetal with a Dirac loop at zero energy. In the presence of a rectangular potential, the scattering amplitudes for different injecting states around the nodal loop are calculated, by using analytical treatments of the effective model, as well as numerical simulations of the tight binding model. In the low energy regime, states with remarkable transmissions are only concentrated in a small range around the loop plane. When the momentum of the injecting electron is coplanar with the nodal loop, nearly perfect transmissions can occur for a large range of injecting azimuthal angles if the potential is not high. For higher potential energies, the transmission shows a resonant oscillation with the potential, but still with peaks being perfect transmissions that do not decay with the potential width. These robust transports of the loop-nodal semimetal can be approximately explained by a momentum dependent Dirac Hamiltonian.
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