Lifshitz-Kosevich Theory Research Articles

Shubnikov–de Haas effect in the Falicov–Kimball model: strong correlation meets quantum oscillation

Abstract We present a comprehensive investigation of quantum oscillations (QOs) in the strongly-correlated Falicov-Kimball model (FKM). The FKM is a particularly suitable platform for probing the non-Fermi liquid state devoid of quasiparticles, affording exact Monte Carlo simulation across all parameter spaces.
In the high-correlation regime, we report the presence of prominent QOs in magnetoresistance and electron density at low temperatures within the phase separation state. The frequency behavior of these oscillations uncovers a transition in the Fermi surface as electron density diminishes, switching from hole-like to electron-like. Both types of Fermi surfaces are found to conform to the Onsager relation, establishing a connection between QOs frequency and Fermi surface area.
Upon exploring the temperature dependence of QOs amplitude, we discern a strong alignment with the Lifshitz-Kosevich (LK) theory, provided the effective mass is suitably renormalized. Notwithstanding, the substantial enhancement of the overall effective mass results in a notable suppression of the QOs amplitude within the examined temperature scope, a finding inconsistent with Fermi liquid predictions. For the most part, the effective mass diminishes as the temperature increases, but an unusual increase is observed at the proximity of the second-order phase transition instigated by thermal effects.
As the transition ensues, the regular QOs disappear, replaced by irregular ones in the non-Fermi liquid state under a high magnetic field.
We also uncover significant QOs in the insulating charge density wave state under weak interactions ($0 < U < 1$), a phenomenon we elucidate through analytical calculations.
Our findings shed light on the critical role of quasiparticles in the manifestation of QOs, enabling further understanding of their function in this context.

Unveiling the double-peak structure of quantum oscillations in the specific heat

Quantum oscillation phenomenon is an essential tool to understand the electronic structure of quantum matter. Here we report a systematic study of quantum oscillations in the electronic specific heat Cel in natural graphite. We show that the crossing of a single spin Landau level and the Fermi energy give rise to a double-peak structure, in striking contrast to the single peak expected from Lifshitz-Kosevich theory. Intriguingly, the double-peak structure is predicted by the kernel term for Cel/T in the free electron theory. The Cel/T represents a spectroscopic tuning fork of width 4.8kBT which can be tuned at will to resonance. Using a coincidence method, the double-peak structure can be used to accurately determine the Landé g-factors of quantum materials. More generally, the tuning fork can be used to reveal any peak in fermionic density of states tuned by magnetic field, such as Lifshitz transition in heavy-fermion compounds.

Tunable non-Lifshitz–Kosevich temperature dependence of Shubnikov–de Haas oscillation amplitudes in SmSb

The Lifshitz–Kosevich (LK) theory is the pillar of magnetic quantum oscillations, which have been extensively applied to characterise a wide range of metallic states. In this study, we focus on the Shubnikov–de Haas (SdH) effect observed in SmSb, a rare-earth monopnictide. We observed a significant departure from the expected LK theory near TN = 2.4 K: both a peak-like anomaly and an enhancement in the temperature dependence of quantum oscillation amplitude are seen in SmSb. Moreover, we discovered a remarkable sensitivity of the SdH amplitudes to sample purity. By adjusting the sample purity, we were able to tune the temperature dependence of the α band’s SdH amplitudes from a peak-like anomalous behaviour to an enhancement. Therefore, SdH oscillations from the α band connect the two well-known non-LK behaviours, controllable through varying the sample purity, paving the way for developing further understanding of the mechanism leading to the anomalous quantum oscillations.

Correlation induced instability in topological nodal-line semimetal ZrSiS

Quantum phase transition hosts a quantum criticality around which the collective low-energy excitations are governed by quantum fluctuations. At this quantum critical regime, fluctuations alter the quasiparticle characteristics introducing some instabilities in the system. The experimental signatures of quantum criticality in topological Dirac materials are sparse. Here, we report the transport studies on nodal line semimetal ZrSiS, which is predicted to own excitonic instability at quantum criticality. Our quantum oscillation studies demonstrate a significant change in Berry phase at higher magnetic fields revealing a field-induced gap modification at the nodal line. Notably, the quasiparticle effective mass executes unique field-dependent oscillations, which is unexplainable from present theories. The temperature dependent oscillation amplitude dramatically departs from conventional Lifshitz–Kosevich theory. These unusual phenomena along with a zero field resistivity upturn collectively suggest the possibility of ZrSiS lying at the excitonic instability. Our findings will engender the systematic exploration of correlation induced phenomenon in topological materials.

(Invited) Large Carrier Mobility in Graphene with Enhanced Shubnikov–De Haas Quantum Oscillations

Graphene devices are susceptible to the surrounding environment1-4. For example, the substrate in contact with graphene influences the device performance because the carriers are confined in two-dimensional (2D) atomic thickness. However, 2D van der Waals dielectric materials used as an interface modifier can provide a path to improve the device quality. In this paper, we report an enhanced mobility of 35000 cm2 V-1 s-1 in a CrOCl-coated monolayer graphene on the SiO2/Si substrate through a dielectric shielding effect. When monolayer graphene is sandwiched between two layers of 2D CrOCl insulator, the enhanced mobility can be 70000 cm2 V-1 s-1. Because of the enhanced mobility, the Shubnikov-de Haas (SdH) quantum oscillation is also observed with the amplitude linearly decreasing with increasing temperature, consistent with the standard Lifshitz-Kosevich theory, and the effect persists at temperatures up to 100 K. Our work paves a way to improve graphene mobility and realize nontrivial quantum states at high temperature for the exploration of potential applications in electronics.

Quantum oscillations and stacked quantum Hall effect in HfTe5

We report the magneto-transport measurements on bulk HfTe5 with carrier mobility exceeding 100 000 cm2/(V s). The longitudinal resistance anomaly and the sign change in Hall coefficient with temperature are observed, which may be induced by Lifshitz transition. When the magnetic field is applied along the b-axis and a-axis at low temperature, a series of Shubnikov–de Haas oscillations on the longitudinal transport exhibit, demonstrating a three-dimensional Fermi-surface pocket for HfTe5 rather than two-dimensional (2D). The investigations on Landau level fan diagram confirm the existence of the non-trivial π Berry phase. The cyclotron mass mcyc as around 0.02me and quantum scattering time τ at about 1.76 ps are also estimated with Lifshitz–Kosevich theory. Further detailed analysis suggests that a stacked quantum Hall effect attributed to multi-parallel 2D conduction layers develops in HfTe5.

Nontrivial Fermi surface topology of the kagome superconductor CsV3Sb5 probed by de Haas–van Alphen oscillations

We have investigated the normal state Fermi-surface properties of the kagome superconductor ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ using torque magnetometry with applied fields ($H$) up to 35 T. The torque signal shows clear de Haas--van Alphen (dHvA) oscillations above 15 T. The oscillations are smooth and consist of seven distinct frequencies with values from $\ensuremath{\sim}$ 18 T to 2135 T. The presence of higher frequencies in ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$ is further confirmed by carrying out additional measurements using the tunnel diode oscillator technique. All frequencies measured at different tilt angles ($\ensuremath{\theta}$) of the field direction with respect to the c axis show a $1/\mathrm{cos}\ensuremath{\theta}$ dependence, implying that the Fermi surfaces corresponding to these frequencies are two dimensional (2D). The absence of dHvA oscillations at $\ensuremath{\theta}$ = ${90}^{o}$ further supports the presence of 2D Fermi surfaces. The Berry phase ($\ensuremath{\phi}$) determined from the Landau level fan diagram for all frequencies is $\ensuremath{\sim}$ 0.4. This value is close to the theoretical value of $\ensuremath{\phi}$ = 0.5 for a nontrivial system, which strongly supports the nontrivial topology of the Fermi surfaces of these frequencies. Several quantities characterizing the Fermi surface are calculated employing the Lifshitz-Kosevich theory. These findings are crucial for exploring the interplay between nontrivial band topology, charge-density wave, and unconventional superconductivity of ${\mathrm{CsV}}_{3}{\mathrm{Sb}}_{5}$.

Anomalous Conductance Oscillations in the Hybridization Gap of InAs/GaSb Quantum Wells.

We observe the magnetic oscillation of electric conductance in the two-dimensional InAs/GaSb quantum spin Hall insulator. Its insulating bulk origin is unambiguously demonstrated by the antiphase oscillations of the conductance and the resistance. Characteristically, the in-gap oscillation frequency is higher than the Shubnikov-de Haas oscillation close to the conduction band edge in the metallic regime. The temperature dependence shows both thermal activation and smearing effects, which cannot be described by the Lifshitz-Kosevich theory. A two-band Bernevig-Hughes-Zhang model with a large quasiparticle self-energy in the insulating regime is proposed to capture the main properties of the in-gap oscillations.

Modulation of Crystal and Electronic Structures in Topological Insulators by Rare-Earth Doping

We study magnetotransport in a rare-earth-doped topological insulator, Sm0.1Sb1.9Te3 single crystals, under magnetic fields up to 14 T. It is found that that the crystals exhibit Shubnikov–de Haas (SdH) oscillations in their magnetotransport behavior at low temperatures and high magnetic fields. The SdH oscillations result from the mixed contributions of bulk and surface states. We also investigate the SdH oscillations in different orientations of the magnetic field, which reveal a three-dimensional Fermi surface topology. By fitting the oscillatory resistance with the Lifshitz–Kosevich theory, we draw a Landau-level fan diagram that displays the expected nontrivial phase. In addition, the density functional theory calculations show that Sm doping changes the crystal structure and electronic structure compared with those of pure Sb2Te3. This work demonstrates that rare-earth doping is an effective way to manipulate the Fermi surface of topological insulators. Our results hold potential for the realization of exotic topological effects in magnetic topological insulators.

Bosonization of Fermi liquids in a weak magnetic field

Novel controlled non-perturbative techniques are a must in the study of strongly correlated systems, especially near quantum criticality. One of these techniques, bosonization, has been extensively used to understand one-dimensional, as well as higher dimensional electronic systems at finite density. In this paper, we generalize the theory of two-dimensional bosonization of Fermi liquids, in the presence of a homogeneous weak magnetic field perpendicular to the plane. Here, we extend the formalism of bosonization to treat free spinless fermions at finite density in a uniform magnetic field. We show that particle-hole fluctuations of a Fermi surface satisfy a {\em covariant Schwinger algebra}, allowing to express a fermionic theory with forward scattering interactions as a quadratic bosonic theory representing the quantum fluctuations of the Fermi surface. By means of a coherent-state path integral formalism we compute the fermion propagator as well as particle-hole bosonic correlations functions. We analyze the presence of de Haas-van Alphen oscillations and show how the quantum oscillations of the orbital magnetization, the Lifshitz-Kosevich theory, are obtained by means of the bosonized theory. We also study the effects of forward scattering interactions. In particular, we obtain oscillatory corrections to the Landau zero sound collective mode.

Shubnikov–de Haas oscillations in p and n-type topological insulator (BixSb1−x)2Te3

We show Shubnikov–de Haas (SdH) oscillations in topological insulator (BixSb1−x)2Te3 flakes whose carrier types are p-type (x = 0.29, 0.34) and n-type (x = 0.42). The physical properties such as the Berry phase, carrier mobility, and scattering time significantly changed by tuning the Fermi-level position with the concentration x. The analyses of SdH oscillations by Landau-level fan diagram, Lifshitz–Kosevich theory, and Dingle-plot in the p-type samples with x = 0.29 and 0.34 showed the Berry phase of zero and a relatively low mobility (2000–6000 cm2 V−1 s−1). This is due to the dominant bulk component in transport. On the other hand, the mobility in the n-type sample with x = 0.42 reached a very large value ~17 000 cm2 V−1 s−1 and the Berry phase of near π, whereas the SdH oscillations were neither purely two- nor three-dimensional. These suggest that the transport channel has a surface-bulk coupling state which makes the carrier scattering lesser and enhances the mobility and has a character between two- and three-dimension.

Quantum Oscillation in Narrow-Gap Topological Insulators.

The canonical understanding of quantum oscillation in metals is challenged by the observation of the de Haas-van Alphen effect in an insulator, SmB_{6} [Tan etal, Science 349, 287 (2015)]. Based on a two-band model with inverted band structure, we show that the periodically narrowing hybridization gap in magnetic fields can induce the oscillation of low-energy density of states in the bulk, which is observable provided that the activation energy is small and comparable to the Landau level spacing. Its temperature dependence strongly deviates from the Lifshitz-Kosevich theory. The nontrivial band topology manifests itself as a nonzero Berry phase in the oscillation pattern, which crosses over to a trivial Berry phase by increasing the temperature or the magnetic field. Further predictions to experiments are also proposed.

Quantum oscillations of the topological surface states in low carrier concentration crystals of Bi2−xSbxTe3−ySey

We report a high-field magnetotransport study on selected low-carrier crystals of the topological insulator Bi$_{2-x}$Sb${_x}$Te$_{3-y}$Se$_{y}$. Monochromatic Shubnikov - de Haas (SdH) oscillations are observed at 4.2~K and their two-dimensional nature is confirmed by tilting the magnetic field with respect to the sample surface. With help of Lifshitz-Kosevich theory, important transport parameters of the surface states are obtained, including the carrier density, cyclotron mass and mobility. For $(x,y)=(0.50,1.3)$ the Landau level plot is analyzed in terms of a model based on a topological surface state in the presence of a non-ideal linear dispersion relation and a Zeeman term with $g_s = 70$ or $-54$. Input parameters were taken from the electronic dispersion relation measured directly by angle resolved photoemission spectroscopy on crystals from the same batch. The Hall resistivity of the same crystal (thickness of 40~$\mu$m) is analyzed in a two-band model, from which we conclude that the ratio of the surface conductance to the total conductance amounts to 32~\%.

Observation of π Berry phase in quantum oscillations of three‐dimensional Fermi surface in topological insulator Bi2Se3

We report the quantum transport studies on Bi2Se3 single crystal with bulk carrier concentration of ∼1019 cm–3. The Bi2Se3 crystal exhibits metallic character, and at low temperatures, the field dependence of resistivity shows clear Shubnikov–de Haas (SdH) oscillations above 6 T. The analysis of these oscillations through Lifshitz–Kosevich theory reveals a non‐trivial π Berry phase coming from three‐dimensional (3D) Fermi surface, which is a strong signature of Dirac fermions with three‐dimensional dispersion. The large Dingle temperature and non zero slope of Williamson–Hall plot suggest the presence of enhanced local strain field in our system which possibly transforms the regions of topological insulator to 3D Dirac fermion metal state. (© 2015 WILEY‐VCH Verlag GmbH &Co. KGaA, Weinheim)

Quantum Oscillations without a Fermi Surface and the Anomalous de Haas-van Alphen Effect.

The de Haas-van Alphen effect (dHvAE), describing oscillations of the magnetization as a function of magnetic field, is commonly assumed to be a definite sign for the presence of a Fermi surface (FS). Indeed, the effect forms the basis of a well-established experimental procedure for accurately measuring FS topology and geometry of metallic systems, with parameters commonly extracted by fitting to the Lifshitz-Kosevich (LK) theory based on Fermi liquid theory. Here we show that, in contrast to this canonical situation, there can be quantum oscillations even for band insulators of certain types. We provide simple analytic formulas describing the temperature dependence of the quantum oscillations in this setting, showing strong deviations from LK theory. We draw connections to recent experiments and discuss how our results can be used in future experiments to accurately determine, e.g., hybridization gaps in heavy-fermion systems.

Enhanced Shubnikov-De Haas Oscillation in Nitrogen-Doped Graphene.

N-doped graphene displays many interesting properties compared with pristine graphene, which makes it a potential candidate in many applications. Here, we report that the Shubnikov-de Haas (SdH) oscillation effect in graphene can be enhanced by N-doping. We show that the amplitude of the SdH oscillation increases with N-doping and reaches around 5k Ω under a field of 14 T at 10 K for highly N-doped graphene, which is over 1 order of magnitude larger than the value found for pristine graphene devices with the same geometry. Moreover, in contrast to the well-established standard Lifshitz-Kosevich theory, the amplitude of the SdH oscillation decreases linearly with increasing temperature and persists up to a temperature of 150 K. Our results also show that the magnetoresistance (MR) in N-doped graphene increases with increasing temperature. Our results may be useful for the application of N-doped graphene in magnetic devices.

Shubnikov–de Haas oscillations from topological surface states of metallicBi2Se2.1Te0.9

We have studied the quantum oscillations in the conductivity of metallic, $p$-type ${\mathrm{Bi}}_{2}{\mathrm{Se}}_{2.1}{\mathrm{Te}}_{0.9}$. The dependence of the oscillations on the angle of the magnetic field with the surface as well as the Berry phase determined from the Landau level fan plot indicate that the observed oscillations arise from surface carriers with a characteristic Dirac dispersion. Several quantities characterizing the surface conduction are calculated employing the Lifshitz-Kosevich theory. The low value of the Fermi energy with respect to the Dirac point is consistent with the metallic character of the bulk hole carriers. We conclude that, due to the peculiar shape of the valence band, the Shubnikov--de Haas oscillations of the bulk carriers are shifted to higher magnetic fields, which allows for the detection of the quantum oscillations from the topological surface states at a lower field.

The Lifshitz–Kosevich theory and Coulomb interaction in graphene

The influence of Coulomb interactions on the magnetic susceptibility, chemical potential and heat capacity in graphene is considered.

On the 60th anniversary of the Lifshitz-Kosevich theory

On the 60th anniversary of the Lifshitz-Kosevich theory

The Landau band effects in the quantum magnetic oscillations and the deviations from the quasiclassical Lifshitz–Kosevich theory in quasi-two-dimensional conductors

The quantum magnetic oscillations (QMO) in the layered and quasi-two-dimensional (2D) conductors deviate from the quasiclassical Lifshitz–Kosevich (LK) theory developed for 3D conventional metals. We discuss deviations related to the broadening of the Landau levels into Landau bands by various mechanisms (layer-stacking, magnetic breakdown, incoherence, disorder, localization etc.). Each mechanism yields a specific factor modulating the QMO amplitudes depending on the density of states and electron velocities within the Landau bands. In contrast to the LK theory, these factors differ for the thermodynamic (de Haas–van Alphen (dHvA)) and kinetic (Shubnikov–de Haas (SdH)) oscillations. We calculated the magnetic breakdown damping factors for the SdH and dHvA oscillations in the 2D conductors and analyzed their difference as well as the analogy between the bandwidth and Weiss oscillations. In case of an isotropic 3D metals the kinetic factors become proportional to the thermodynamic ones as is assumed in the LK theory.