Shubnikov-de Haas Frequencies Research Articles

Shubnikov–de Haas oscillations of biaxial-strain-tuned superconductors in pulsed magnetic field up to 60 T

Two-dimensional (2D) materials have gained increasing prominence not only in fundamental research but also in daily applications. However, to fully harness their potential, it is crucial to optimize their properties with an external parameter and track the electronic structure simultaneously. Magnetotransport over a wide magnetic field range is a powerful method to probe the electronic structure and, for metallic 2D materials, quantum oscillations superimposed on the transport signals encode Fermi surface parameters. In this manuscript, we utilize biaxial strain as an external tuning parameter and investigate the effects of strain on the electronic properties of two quasi-2D superconductors, MoTe2 and RbV3Sb5, by measuring their magnetoresistance in pulsed magnetic fields up to 60 T. With a careful selection of insulating substrates, we demonstrate the possibility of both the compressive and tensile biaxial strains imposed on MoTe2 and RbV3Sb5, respectively. For both systems, the applied strain has led to superconducting critical temperature enhancement compared to their free-standing counterparts, proving the effectiveness of this biaxial strain method at cryogenic temperatures. Clear quantum oscillations in the magnetoresistance—the Shubnikov–de Haas (SdH) effect—are obtained in both samples. In strained MoTe2, the magnetoresistance exhibits a nearly quadratic dependence on the magnetic field and remains non-saturating even at the highest field, whereas in strained RbV3Sb5, two SdH frequencies showed a substantial enhancement in effective mass values, hinting at a possible enhancement of charge fluctuations. Our results demonstrate that combining biaxial strain and pulsed magnetic field paves the way for studying 2D materials under unprecedented conditions.

Microstructuring YbRh2Si2 for resistance and noise measurements down to ultra-low temperatures

The discovery of superconductivity in the quantum critical Kondo-lattice system YbRh2Si2 at an extremely low temperature of 2 mK has inspired efforts to perform high-resolution electrical resistivity measurements down to this temperature range in highly conductive materials. Here we show that control over the sample geometry by microstructuring using focused-ion-beam techniques allows to reach ultra-low temperatures and increase signal-to-noise ratios (SNRs) tenfold, without adverse effects to sample quality. In five experiments we show four-terminal sensing resistance and magnetoresistance measurements which exhibit sharp phase transitions at the Néel temperature, and Shubnikov–de-Haas (SdH) oscillations between 13 T and 18 T where we identified a new SdH frequency of 0.39 kT. The increased SNR allowed resistance fluctuation (noise) spectroscopy that would not be possible for bulk crystals, and confirmed intrinsic -type fluctuations. Under controlled strain, two thin microstructured samples exhibited a large increase of from 67 mK up to 188 mK while still showing clear signatures of the phase transition and SdH oscillations. Superconducting quantum interference device-based thermal noise spectroscopy measurements in a nuclear demagnetization refrigerator down to 0.95 mK, show a sharp superconducting transition at mK. These experiments demonstrate microstructuring as a powerful tool to investigate the resistance and the noise spectrum of highly conductive correlated metals over wide temperature ranges.

Structure and pressure dependence of the Fermi surface of lithium

We report studies of the Fermi surface (FS) of isotopically pure polycrystalline $^{7}\mathrm{Li}$ from ambient pressure to 4.7 GPa. Shubnikov--de Haas (SdH) oscillations at 300 mK in external magnetic fields up to 35 T are measured to map the spherical parts of the FS of lithium. Our ambient pressure data show that the principal SdH frequencies consist of three distinct peaks at $41.25\ifmmode\pm\else\textpm\fi{}0.05, 41.65\ifmmode\pm\else\textpm\fi{}0.05$, and $42.05\ifmmode\pm\else\textpm\fi{}0.05\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{kT}$, which are theoretically consistent with the presence of two crystal structure domains exhibiting nearly spherical FS. The size of the spherical parts of the FS is compatible with bcc and fcc crystal structures. The measured frequencies at 41.25 and 42.65 kT present direct quantitative evidence for the spherical deformation of the FS in fcc Li. Our high-pressure data show that while the FS of Li deforms under compression, it remains mostly spherical up to 4.7 GPa and the pressure dependence of the SdH frequency is consistent with the theoretically calculated pressure dependence in the fcc structure. Finally, we find that the electron effective mass does not deviate under pressure significantly from its ambient pressure value.

Network of Topological Nodal Planes, Multifold Degeneracies, and Weyl Points in CoSi.

We showcase the importance of global band topology in a study of the Weyl semimetal CoSi as a representative of chiral space group (SG) 198. We identify a network of band crossings comprising topological nodal planes, multifold degeneracies, and Weyl points consistent with the fermion doubling theorem. To confirm these findings, we combined the general analysis of the band topology of SG 198 with Shubnikov-de Haas oscillations and material-specific calculations of the electronic structure and Berry curvature. The observation of two nearly dispersionless Shubnikov-de Haas frequency branches provides unambiguous evidence of four Fermi surface sheets at the R point that reflect the symmetry-enforced orthogonality of the underlying wave functions at the intersections with the nodal planes. Hence, irrespective of the spin-orbit coupling strength, SG 198 features always six- and fourfold degenerate crossings at R and Γ that are intimately connected to the topological charges distributed across the network.

Magnetotransport studies of the Sb square-net compound LaAgSb2 under high pressure and rotating magnetic fields

Square-net-layered materials have attracted attention as an extended research platform of Dirac fermions and of exotic magnetotransport phenomena. In this study, we investigated the magnetotransport properties of $\mathrm{La}\mathrm{Ag}{\mathrm{Sb}}_{2}$, which has Sb-square-net layers and shows charge density wave (CDW) transitions at ambient pressure. The application of pressure suppresses the CDWs, and above a pressure of 3.2 GPa a normal metallic phase with no CDWs is realized. By utilizing a mechanical rotator combined with a high-pressure cell, we observed the angular dependence of the Shubnikov--de Haas (SdH) oscillation up to 3.5 GPa, and we confirmed the notable two-dimensional nature of the Fermi surface. In the normal metallic phase, we also observed a remarkable field-angular-dependent magnetoresistance (MR), which exhibited a ``butterflylike'' polar pattern. To understand these results, we theoretically calculated the Fermi surface and conductivity tensor at the normal metallic phase. We showed that the SdH frequency and Hall coefficient calculated based on the present Fermi surface model agree well with the experiment. The transport properties in the normal metallic phase are mostly dominated by the anisotropic Dirac band, which has the highest conductivity due to linear energy dispersions. We also proposed that momentum-dependent relaxation time plays an important role in the large transverse MR and negative longitudinal MR in the normal metallic phase, which is experimentally supported by the considerable violation of Kohler's scaling rule. Although quantitatively complete reproduction was not achieved, the calculation showed that the elemental features of the butterfly MR could be reasonably explained as the geometrical effect of the Fermi surface.

Effect of uniaxial stress on the electronic band structure of NbP

The Weyl semimetal NbP exhibits a very small Fermi surface consisting of two electron and two hole pockets, whose fourfold degeneracy in $k$ space is tied to the rotational symmetry of the underlying tetragonal crystal lattice. By applying uniaxial stress, the crystal symmetry can be reduced, which successively leads to a degeneracy lifting of the Fermi-surface pockets. This is reflected by a splitting of the Shubnikov-de Haas frequencies when the magnetic field is aligned along the $c$ axis of the tetragonal lattice. In this study, we present the measurement of Shubnikov-de Haas oscillations of single-crystalline NbP samples under uniaxial tension, combined with state-of-the-art calculations of the electronic band structure. Our results show qualitative agreement between calculated and experimentally determined Shubnikov-de Haas frequencies, demonstrating the robustness of the band-structure calculations upon introducing strain. Furthermore, we predict a significant shift of the Weyl points with increasing uniaxial tension, allowing for an effective tuning to the Fermi level at only 0.8% of strain along the $a$ axis.

Pressure tuning of the electrical transport properties in the Weyl semimetal TaP

We investigated the pressure evolution of the electrical transport in the almost compensated Weyl semimetal TaP. In addition, we obtained information on the modifications of the Fermi-surface topology with pressure from the analysis of pronounced Shubnikov-de Haas (SdH) quantum oscillations present in the Hall-effect and magnetoresistance data. The simultaneous analysis of the Hall and longitudinal conductivity data in a two-band model revealed an only weak decrease in the electron- and hole charge-carrier densities up to 1.2 GPa, while the mobilities are essentially pressure independent along the a-direction of the tetragonal crystal structure. Only weak changes in the SdH frequencies for B||a and B||c point at a robust Fermi-surface topology. In contrast to the stability of the Fermi-surface topology and of the density of charge carriers, our results evidence a strong pressure variation of the magnitude of transverse magnetoresistance for B||a contrary to the results for B||c. We can relate the former to an increase in the charge-carrier mobilities along the crystallographic c-direction.

Shubnikov–de Haas oscillations in the three-dimensional Dirac fermion system Ca3PbO

Cubic antiperovskite ${\mathrm{Ca}}_{3}\mathrm{PbO}$ is a candidate for three-dimensional (3D) Dirac fermion systems that have recently emerged as a class of topological materials exhibiting linear energy dispersion in the bulk. We report magnetotransport and tunnel diode oscillation (TDO) measurements on Bi-doped ${\mathrm{Ca}}_{3}\mathrm{PbO}$ in magnetic fields up to 55 T and temperatures between 2 and 78 K. By observing the Shubnikov--de Haas (SdH) oscillations, we resolve the bulk 3D Fermi surface (FS) with distinctive features of Dirac fermions including linear magnetoresistance, light effective mass, and a nontrivial phase shift. TDO measurements under high fields reveal the existence of two primary SdH frequencies, one being twice the other. Together with the low effective mass, the oscillations of these two frequencies account for the emergence of the Landau level splitting that persists up to 43 K. The field-angular-dependence of the oscillation frequencies with three branches confirms that the FS is composed of three pairs of hole pockets with uniaxial anisotropy on the \ensuremath{\Gamma}-X path, as predicted for bulk ${\mathrm{Ca}}_{3}\mathrm{PbO}$ crystal by density functional theory calculation.

Shubnikov–de Haas oscillations in topological crystalline insulator SnTe(111) epitaxial films

We report on high-field (up to 30 T) magnetotransport experiments in topological crystalline insulator (111) SnTe epitaxial films. The longitudinal magnetoresistance ${R}_{\mathrm{xx}}$ exhibits pronounced Shubnikov--de Haas (SdH) oscillation at 4.2 K that persists up to 80 K. The second derivative $(\ensuremath{-}{d}^{2}{R}_{\mathrm{xx}}/d{B}^{2})$ versus $1/B$ curve shows a clear beating pattern and the fast Fourier-transform analysis reveals that the SdH oscillations are composed of two close frequencies. As SnTe has elongated bulk Fermi ellipsoids, the $1/cos\ensuremath{\theta}$ dependence obtained in the angular evolution of both SdH frequencies is not sufficient to assure conduction via surface states. The Lifshitz-Kosevich fitting of the ${R}_{\mathrm{xx}}$ oscillatory component confirms the two frequencies and enables us to extract the Berry phase of the charge carriers. The most likely scenario obtained from our analysis is that the beating pattern of these quantum oscillations originates from the Rashba splitting of the bulk longitudinal ellipsoid in SnTe.

Surface termination dependent quasiparticle scattering interference and magneto-transport study on ZrSiS

Dirac nodal line semimetals represent a new state of quantum matters in which the electronic bands touch to form a closed loop with linear dispersion. Here, we report a combined study on ZrSiS by density functional theory calculation, scanning tunnelling microscope (STM) and magneto-transport measurements. Our STM measurements reveal the spectroscopic signatures of a diamond-shaped Dirac bulk band and a surface band on two types of cleaved surfaces as well as a spin-polarized surface band at at E ∼ 0.6 eV on S-surface, consistent with our band calculation. Furthermore, we find the surface termination does not affect the surface spectral weight from the Dirac bulk bands but greatly affect the surface bands due to the change in the surface orbital composition. From our magneto-transport measurements, the primary Shubnikov–de-Haas frequency is identified to stem from the hole-type quasi-two-dimensional Fermi surface between Γ and X. The extracted non-orbital magnetoresistance (MR) contribution D(θ, H) yields a nearly H-linear dependence, which is attributed to the intrinsic MR in ZrSiS. Our results demonstrate the unique Dirac line nodes phase and the dominating role of Zr-d orbital on the electronic structure in ZrSiS and the related compounds.

Electronic Transport and Raman Spectroscopy Characterization in Ion-Implanted Highly Oriented Pyrolytic Graphite

We report on Raman spectroscopy, temperature-dependent in-plane resistivity, and in-plane magnetoresistance experiments in highly oriented pyrolytic graphite (HOPG) implanted with As and Mn. A pristine sample was also studied for comparison. Two different fluences were applied, $$\varphi = 0.5\times 10^{16}\,\, {\hbox {ions}}/{\hbox {cm}}^{2}$$ and $$\varphi = 1.0\times 10^{16}\,\,{\hbox {ions}}/{\hbox {cm}}^{2}$$ . The implantations were carried out with 20 keV ion energy at room temperature. The Raman spectroscopy results reveal the occurrence of drastic changes of the HOPG surface as a consequence of the damage caused by ionic implantation. For the higher dose, the complete amorphization limit is attained. The resistivity and magnetoresistance results were obtained placing electrical contacts on the irradiated sample surface. Owing to the strong anisotropy of HOPG, the electrical current propagates mostly near the implanted surface. Shubnikov–de Haas (SdH) oscillations were observed in the magnetoresistance at low temperatures. These results allow the extraction of the fundamental SdH frequencies and the carriers’ effective masses. In general, the resistivity and magnetoresistance results are consistent with those obtained from Raman measurements. However, one must consider that the electrical conduction in our samples occurs as in a parallel association of a largely resistive thin sheet at the surface strongly modified by disorder with a thicker layer where damage produced by implantation is less severe. The SdH oscillations do not hint to significant changes in the carrier density of HOPG.

Fermi surface of the Weyl type-II metallic candidate WP2

Weyl type-II fermions are massless quasiparticles that obey the Weyl equation and which are predicted to occur at the boundary between electron- and hole-pockets in certain semi-metals, i.e. the (W,Mo)(Te,P)$_2$ compounds. Here, we present a study of the Fermi-surface of WP$_2$ \emph{via} the Shubnikov-de Haas (SdH) effect. Compared to other semi-metals WP$_2$ exhibits a very low residual resistivity, i.e. $\rho_0 \simeq 10$ n$\Omega$cm, which leads to perhaps the largest non-saturating magneto-resistivity $(\rho(H))$ reported for any compound. For the samples displaying the smallest $\rho_0$, $\rho(H)$ is observed to increase by a factor of $2.5 \times 10^{7}$ $\%$ under $\mu_{0}H = 35$ T at $T = 0.35$ K. The angular dependence of the SdH frequencies is found to be in very good agreement with the first-principle calculations when the electron- and hole-bands are slightly shifted with respect to the Fermi level, thus supporting the existence of underlying Weyl type-II points in WP$_2$.

Symmetry breaking of the surface mediated quantum Hall Effect in Bi2Se3 nanoplates using Fe3O4 substrates

Bi2Se3 nanoplate devices are synthesized on SiO2 and ferrimagnetic insulator substrates. We experimentally demonstrate that ferromagnetism is induced into the bottom surface. The symmetry broken bottom states give rise to an additional Shubnikov–de Haas frequency and leads to a decoupling of the top and bottom quantum Hall effects. We present a three-channel model that separates the bulk, top and bottom surface contributions to the Hall resistance, indicating the presence of two symmetry shifted half-integer QHEs.

Shubnikov–de Haas Effect and Angular-Dependent Magnetoresistance in Layered Organic Conductor β′′-(ET)(TCNQ)

This paper reports the experimental results of the Shubnikov–de Haas (SdH) effect and angular-dependent magnetoresistance oscillation (AMRO) for the organic conductor β′′-(ET)(TCNQ). We observed several two dimensional (2D) SdH frequencies, whose cross-sectional areas of the Fermi surfaces (FSs) correspond to only a few percent of the first Brillouin zone. Such small 2D FSs are not predicted by band-structure calculations, suggesting that these FS pockets are created by an imperfect nesting of FSs at low temperatures. It is found that the AMRO consists of a long-period oscillation and a short-period one. The long-period oscillation is associated with the Yamaji oscillation corresponding to the α orbit, whose shape and area are consistent with previous magneto-optical measurement. The short-period oscillation is not caused by peaks instead but dips. The dip structure is discussed in terms of the AMRO of a quasi-2D electron system with a periodic potential caused by the possible density-wave related to the ...

Quantum Oscillation Signatures of Pressure-induced Topological Phase Transition in BiTeI.

We report the pressure-induced topological quantum phase transition of BiTeI single crystals using Shubnikov-de Haas oscillations of bulk Fermi surfaces. The sizes of the inner and the outer FSs of the Rashba-split bands exhibit opposite pressure dependence up to P = 3.35 GPa, indicating pressure-tunable Rashba effect. Above a critical pressure P ~ 2 GPa, the Shubnikov-de Haas frequency for the inner Fermi surface increases unusually with pressure, and the Shubnikov-de Haas oscillations for the outer Fermi surface shows an abrupt phase shift. In comparison with band structure calculations, we find that these unusual behaviors originate from the Fermi surface shape change due to pressure-induced band inversion. These results clearly demonstrate that the topological quantum phase transition is intimately tied to the shape of bulk Fermi surfaces enclosing the time-reversal invariant momenta with band inversion.

Role of spin-orbit coupling and evolution of the electronic structure ofWTe2under an external magnetic field

Here, we present a detailed study on the temperature and angular dependence of the Shubnikov-de-Haas (SdH) effect in the semi-metal WTe$_2$. This compound was recently shown to display a very large non-saturating magnetoresistance which was attributed to nearly perfectly compensated densities of electrons and holes. We observe four fundamental SdH frequencies and attribute them to spin-orbit split, electron- and hole-like, Fermi surface (FS) cross-sectional areas. Their angular dependence seems consistent with ellipsoidal FSs with volumes suggesting a modest excess in the density of electrons with respect to that of the holes. We show that density functional theory (DFT) calculations fail to correctly describe the FSs of WTe$_2$. When their cross-sectional areas are adjusted to reflect the experimental data, the resulting volumes of the electron/hole FSs obtained from the DFT calculations would imply a pronounced imbalance between the densities of electrons and holes. We find evidence for field-dependent Fermi surface cross-sectional areas by fitting the oscillatory component superimposed onto the magnetoresistivity signal to several Lifshitz-Kosevich components. We also observe a pronounced field-induced renormalization of the effective masses. Taken together, our observations suggest that the electronic structure of WTe$_2$ evolves with the magnetic field. This evolution might be a factor contributing to its pronounced magnetoresistivity.

Shubnikov-de Haas oscillation in PuIn3

The Fermi surface of PuIn3 is investigated using flux-grown single crystals. Shubnikov-de Haas (SdH) oscillations were detected by means of the skin-depth measurement using a proximity-detector-oscillator circuit. Angular dependence of the SdH frequency which corresponds to the extremal cross-sectional area of Fermi surface agrees well with the previous magnetic susceptibility measurement using conventional field-modulation method. The SdH oscillation suddenly vanishes when the magnetic field is tilted from the cubic [111] direction.

Fermi Surface Reconstruction inside the Hidden Order Phase of URu2Si2Probed by Thermoelectric Measurements

We report thermoelectric measurements of the low carrier heavy fermion compound URu2Si2 at high fields up to 34T and at low temperatures down to 500mK. The field dependence of the thermoelectric power (TEP) and the Nernst signal shows successive anomalies deep inside the hidden order (HO) phase. The field position of these anomalies correspond to different changes in the Shubnikov-de Haas frequencies and effective masses around 12 T, 17 T, 23 T and 30 T. These results indicate successive reconstructions of the Fermi surface, which imply electronic phase transitions well within the HO phase.

LuRh2Si2: Sensitivity of the Fermi surface to the Si z‐position

AbstractWe present band structure calculations of the non‐magnetic compound LuRh2Si2 which serves as a reference for YbRh2Si2, a prototypical material for the investigation of quantum critical points. The relative z position of the Si atoms is found to have a strong impact on the band structure and the Fermi surface topology. We find the total energy to be minimized for z = 0.381c whereas a comparison of predicted extremal orbits with Shubnikov–de Haas frequencies shows best agreement at the experimental value z = 0.379c. We therefore recommend usage of z = 0.379c for future electronic structure calculations of LuRh2Si2 and YbRh2Si2.

High-Field Fermi Surface Properties in the Low-Carrier Heavy-Fermion Compound URu2Si2

We performed the Shubnikov–de Haas (SdH) experiments of the low-carrier heavy-fermion compound URu 2 Si 2 at high fields up to 34 T and at low temperatures down to 30 mK. All main SdH branches named α, β, and γ were observed for all the measured field-directions ( H ∥[001]→[100], [100]→[110] and [001]→[110]), indicating that they are attributed to the closed Fermi surfaces with nearly spherical shapes. An anomalous split of branch α was detected for the field along the basal plane; the split immediately disappeared by tilting the field to [001] direction, implying a fingerprint of the hidden order state. High-field experiments reveal the complicated field-dependence of the SdH frequencies and the cyclotron masses due to the Zeeman spin-splitting associated with the Fermi surface reconstruction in the hidden order state with small carrier numbers. A new SdH branch named ω with a large cyclotron mass of 25 m 0 was detected at high fields above 23 T close to hidden order instabilities.