Anomalous Phase Shift of Quantum Oscillations in 3D Topological Semimetals

Gate-Tunable Quantum Acoustoelectric Transport in Graphene

Transport probes the motion of quasi-particles in response to external excitations. Apart from the well-known electric and thermoelectric transport, acoustoelectric transport induced by traveling acoustic waves has rarely been explored. Here, by adopting hybrid nanodevices integrated with piezoelectric substrates, we establish a simple design of acoustoelectric transport with gate tunability. We fabricate dual-gated acoustoelectric devices based on hBN-encapsulated graphene on LiNbO3. Longitudinal and transverse acoustoelectric voltages are generated by launching a pulsed surface acoustic wave. The gate dependence of zero-field longitudinal acoustoelectric signal presents strikingly similar profiles to that of Hall resistivity, providing a valid approach for extracting carrier density without magnetic field. In magnetic fields, acoustoelectric quantum oscillations appear due to Landau quantization, which are more robust and pronounced than Shubnikov-de Haas oscillations. Our work demonstrates a feasible acoustoelectric setup with gate tunability, which can be extended to the broad scope of various van der Waals materials.

Quantum-classical correspondence and dissipative to dissipationless crossover in magnetotransport phenomena

The three-dimensional magneto-conductivity tensor was derived in a gauge invariant form based on the Kubo formula considering quantum effects under a magnetic field, such as the Landau quantization and quantum oscillations. We analytically demonstrated that the quantum formula of the magneto-conductivity can be obtained by adding a quantum oscillation factor to the classical formula. This result establishes the quantum-classical correspondence, which has long been missing in magnetotransport phenomena. Moreover, we found dissipative-to-dissipationless crossover in the Hall conductivity by paying special attention to the analytic properties of the thermal Green's function. Finally, by calculating the magnetoresistance of semimetals, we identified a phase shift in quantum oscillation originating from the dissipationless transport predominant at high fields.

Gate-Tunable Berry Curvature Dipole Polarizability in Dirac Semimetal Cd_{3}As_{2}

We reveal the gate-tunable Berry curvature dipole polarizability in Dirac semimetal Cd_{3}As_{2} nanoplates through measurements of the third-order nonlinear Hall effect. Under an applied electric field, the Berry curvature exhibits an asymmetric distribution, forming a field-induced Berry curvature dipole, resulting in a measurable third-order Hall voltage with a cubic relationship to the longitudinal electric field. Notably, the magnitude and polarity of this third-order nonlinear Hall effect can be effectively modulated by gate voltages. Furthermore, our scaling relation analysis demonstrates that the sign of the Berry curvature dipole polarizability changes when tuning the Fermi level across the Dirac point, in agreement with theoretical calculations. The results highlight the gate control of nonlinear quantum transport in Dirac semimetals, paving the way for promising advancements in topological electronics.

Topological charge-entropy scaling in kagome Chern magnet TbMn6Sn6

In ordinary materials, electrons conduct both electricity and heat, where their charge-entropy relations observe the Mott formula and the Wiedemann-Franz law. In topological quantum materials, the transverse motion of relativistic electrons can be strongly affected by the quantum field arising around the topological fermions, where a simple model description of their charge-entropy relations remains elusive. Here we report the topological charge-entropy scaling in the kagome Chern magnet TbMn6Sn6, featuring pristine Mn kagome lattices with strong out-of-plane magnetization. Through both electric and thermoelectric transports, we observe quantum oscillations with a nontrivial Berry phase, a large Fermi velocity and two-dimensionality, supporting the existence of Dirac fermions in the magnetic kagome lattice. This quantum magnet further exhibits large anomalous Hall, anomalous Nernst, and anomalous thermal Hall effects, all of which persist to above room temperature. Remarkably, we show that the charge-entropy scaling relations of these anomalous transverse transports can be ubiquitously described by the Berry curvature field effects in a Chern-gapped Dirac model. Our work points to a model kagome Chern magnet for the proof-of-principle elaboration of the topological charge-entropy scaling.

Magneto-transport evidence for strong topological insulator phase in ZrTe5

The identification of a non-trivial band topology usually relies on directly probing the protected surface/edge states. But, it is difficult to achieve electronically in narrow-gap topological materials due to the small (meV) energy scales. Here, we demonstrate that band inversion, a crucial ingredient of the non-trivial band topology, can serve as an alternative, experimentally accessible indicator. We show that an inverted band can lead to a four-fold splitting of the non-zero Landau levels, contrasting the two-fold splitting (spin splitting only) in the normal band. We confirm our predictions in magneto-transport experiments on a narrow-gap strong topological insulator, zirconium pentatelluride (ZrTe5), with the observation of additional splittings in the quantum oscillations and also an anomalous peak in the extreme quantum limit. Our work establishes an effective strategy for identifying the band inversion as well as the associated topological phases for future topological materials research.

Orbit topology analyzed from π phase shift of magnetic quantum oscillations in three-dimensional Dirac semimetal

With the emergence of Dirac fermion physics in the field of condensed matter, magnetic quantum oscillations (MQOs) have been used to discern the topology of orbits in Dirac materials. However, many previous researchers have relied on the single-orbit Lifshitz-Kosevich (LK) formula, which overlooks the significant effect of degenerate orbits on MQOs. Since the single-orbit LK formula is valid for massless Dirac semimetals with small cyclotron masses, it is imperative to generalize the method applicable to a wide range of Dirac semimetals, whether massless or massive. This report demonstrates how spin-degenerate orbits affect the phases in MQOs of three-dimensional massive Dirac semimetal, NbSb2 With varying the direction of the magnetic field, an abrupt π phase shift is observed due to the interference between the spin-degenerate orbits. We investigate the effect of cyclotron mass on the π phase shift and verify its close relation to the phase from the Zeeman coupling. We find that the π phase shift occurs when the cyclotron mass is half of the electron mass, indicating the effective spin gyromagnetic ratio as g s = 2. Our approach is not only useful for analyzing MQOs of massless Dirac semimetals with a small cyclotron mass but also can be used for MQOs in massive Dirac materials with degenerate orbits, especially in topological materials with a sufficiently large cyclotron mass. Furthermore, this method provides a useful way to estimate the precise g s value of the material.

Rare Earth Engineering in RMn_{6}Sn_{6} (R=Gd-Tm, Lu) Topological Kagome Magnets

Exploration of the topological quantum materials with electron correlation is at the frontier of physics, as the strong interaction may give rise to new topological phases and transitions. Here we report that a family of kagome magnets RMn_{6}Sn_{6} manifest the quantum transport properties analogical to those in the quantum-limit Chern magnet TbMn_{6}Sn_{6}. The topological transport in the family, including quantum oscillations with nontrivial Berry phase and large anomalous Hall effect arising from Berry curvature field, points to the existence of Chern gapped Dirac fermions. Our observation demonstrates a close relationship between rare-earth magnetism and topological electron structure, indicating the rare-earth elements can effectively engineer the Chern quantum phase in kagome magnets.

Anisotropic magnetotransport in tilted magnetic topological semimetals

We systematically investigate the anisotropic magneto-conductivity and planar Hall effect in tilted magnetic topological semimetals in the frame of Kubo formula by considering the vertex correction of velocity. The nonzero anisotropic magneto-conductivity is due to the intrinsic magnetization by magnetic doping rather than the external magnetic field previously studied in literatures. In the scenario, tilt, which is common in band structure, plays a key role in this anisotropic magneto-conductivity. This anisotropic magneto-conductivity completely originates from the band anisotropy. The vertex correction only amends the magnitude, but does not change the qualitative behavior of the longitudinal conductivity. However, the planar Hall conductivity is always zero for tilt along bothxandydirections in vivid contrast to the case arising from an external magnetic field. Our work offers a route to understand the anisotropic magneto-conductivity effect in tilted Weyl semimetals with Zeeman field. It will be helpful to get a deeper understanding of the transport characteristic in tilted topological semimetals.

Topological Quantum Materials from the Viewpoint of Chemistry

Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space, namely atoms, valence electrons, bonds, and orbitals, and reciprocal space, namely bands and Fermi surfaces, via symmetry and topology, classifying topological materials within a single-particle picture is possible. Currently, most materials are classified as trivial insulators, semimetals, and metals or as topological insulators, Dirac and Weyl nodal-line semimetals, and topological metals. The key ingredients for topology are certain symmetries, the inert pair effect of the outer electrons leading to inversion of the conduction and valence bands, and spin-orbit coupling. This review presents the topological concepts related to solids from the viewpoint of a solid-state chemist, summarizes techniques for growing single crystals, and describes basic physical property measurement techniques to characterize topological materials beyond their structure and provide examples of such materials. Finally, a brief outlook on the impact of topology in other areas of chemistry is provided at the end of the article.

Topological Semimetal Nanostructures: From Properties to Topotronics

Characterized by bulk Dirac or Weyl cones and surface Fermi-arc states, topological semimetals have sparked enormous research interest in recent years. The nanostructures, with large surface-to-volume ratio and easy field-effect gating, provide ideal platforms to detect and manipulate the topological quantum states. Exotic physical properties originating from these topological states endow topological semimetals attractive for future topological electronics (topotronics). For example, the linear energy dispersion relation is promising for broadband infrared photodetectors, the spin-momentum locking nature of topological surface states is valuable for spintronics, and the topological superconductivity is highly desirable for fault-tolerant qubits. For real-life applications, topological semimetals in the form of nanostructures are necessary in terms of convenient fabrication and integration. Here, we review the recent progresses in topological semimetal nanostructures and start with the quantum transport properties. Then topological semimetal-based electronic devices are introduced. Finally, we discuss several important aspects that should receive great effort in the future, including controllable synthesis, manipulation of quantum states, topological field effect transistors, spintronic applications, and topological quantum computation.

Rich topological nodal line bulk states together with drum-head-like surface states in NaAlGe with anti-PbFCl type structure

The band topology in condensed matter has attracted widespread attention in recent years. Due to the band inversion, topological nodal line semimetals (TNLSs) have band crossing points (BCPs) around the Fermi level, forming a nodal line. In this work, by means of first-principles, we observe that the synthesized NaAlGe intermetallic compound with anti-PbFCl type structure is a TNLS with four NLs in the k_z = 0 and k_z = π planes. All these NLs in NaAlGe exist around the Fermi level, and what is more, these NLs do not overlap with other bands. The exotic drum-head-like surface states can be clearly observed, and therefore, the surface characteristics of NaAlGe may more easily be detected by experiments. Biaxial strain has been explored for this system, and our results show that rich TNL states can be induced. Furthermore, the spin-orbit coupling effect has little effect on the band structure of NaAlGe. It is hoped that this unique band structure can soon be examined by experimental work and that its novel topological elements can be fully explored for electronic devices.

Superconductivity and Shubnikov - de Haas effect in polycrystalline Cd3As2 thin films

In this study we observed the reproducible superconducting state in Cd₃As₂ thin films without any external stimuli. Comparison with our previous results reveals similar qualitative behavior for films synthesized by different methods, while the difference in the values of the critical parameters clearly shows the possibility to control this state. The X-ray diffraction measurements demonstrate the presence of the tetragonal Cd₃As₂ crystal phase in studied films. Measurements of high-field magnetoresistance reveal pronounced Shubnikov - de Haas oscillations. The analysis of these oscillations suggests that, due to high carrier concentration in studied Cd₃As₂ films, the initial Dirac semimetal phase may be partially suppressed, which, however, does not contradict with possible topological nature of the observed superconductivity.

Novel topological nodal lines and exotic drum-head-like surface states in synthesized CsCl-type binary alloy TiOs

Very recently, searching for new topological nodal line semimetals (TNLSs) and drum-head-like (DHL) surface states has become a hot topic in the field of physical chemistry of materials. Via first principles, in this study, a synthesized CsCl type binary alloy, TiOs, was predicted to be a TNLS with three topological nodal lines (TNLs) centered at the X point in the kx/y/z = π plane, and these TNLs, which are protected by mirror, time reversal (T) and spatial inversion (P) symmetries, are perpendicular to one another. The exotic drum-head-like (DHL) surface states can be clearly observed inside and outside the crossing points (CPs) in the bulk system. The CPs, TNLs, and DHL surface states of TiOs are very robust under the influences of uniform strain, electron doping, and hole doping. Spin-orbit coupling (SOC)-induced gaps can be found in this TiOs system when the SOC is taken into consideration. When the SOC is involved, surface Dirac cones can be found in this system, indicating that the topological properties are still maintained. Similar to TiOs, ZrOs and HfOs alloys are TNLSs under the Perdew-Burke-Ernzerhof method. The CPs and the TNLs in both alloys disappear, however, under the Heyd-Scuseria-Ernzerhof method. It is hoped that the DHL surface property in TiOs can be detected by surface sensitive probes in the near future.

Nontrivial quantum oscillation geometric phase shift in a trivial band

Quantum oscillations provide a notable visualization of the Fermi surface of metals, including associated geometrical phases such as Berry's phase, that play a central role in topological quantum materials. Here we report the existence of a new quantum oscillation phase shift in a multiband system. In particular, we study the ABA-trilayer graphene, the band structure of which is composed of a weakly gapped linear Dirac band, nested within a quadratic band. We observe that Shubnikov-de Haas (SdH) oscillations of the quadratic band are shifted by a phase that sharply departs from the expected 2π Berry's phase and is inherited from the nontrivial Berry's phase of the linear band. We find this arises due to an unusual filling enforced constraint between the quadratic band and linear band Fermi surfaces. Our work indicates how additional bands can be exploited to tease out the effect of often subtle quantum mechanical geometric phases.

Nontrivial topology of bulk HgSe from the study of cyclotron effective mass, electron mobility and phase shift of Shubnikov-de Haas oscillations

In this paper, the authors report the results of an experimental study of effective mass, electron mobility and phase shift of Shubnikov-de Haas oscillations of transverse magnetoresistance in an extended electron concentration region from 8.8  ×  10¹⁵ cm^-3 to 4.3  ×  10¹⁸ cm^-3 in single crystals of mercury selenide. The revealed features indicate that Weyl semimetal phase may exist in HgSe at low electron density. The most significant result is the discovery of an abrupt change of Berry phase [Formula: see text] at electron concentration [Formula: see text] 2  ×  10¹⁸ cm^-3, which we explain in terms of a manifestation of topological Lifshitz transition in HgSe that occurs by tuning Fermi energy via doping.

Non-saturating quantum magnetization in Weyl semimetal TaAs

Detecting the spectroscopic signatures of relativistic quasiparticles in emergent topological materials is crucial for searching their potential applications. Magnetometry is a powerful tool for fathoming electrons in solids, by which a clear method for discerning relativistic quasiparticles has not yet been established. Adopting the probes of magnetic torque and parallel magnetization for the archetype Weyl semimetal TaAs in strong magnetic field, we observed a quasi-linear field dependent effective transverse magnetization and a non-saturating parallel magnetization when the system enters the quantum limit. Distinct from the saturating magnetic responses for non-relativistic quasiparticles, the non-saturating signals of TaAs in strong field is consistent with our newly developed magnetization calculation for a Weyl fermion system in an arbitrary angle. Our results establish a high-field thermodynamic method for detecting the magnetic response of relativistic quasiparticles in topological materials.

Vanishing quantum oscillations in Dirac semimetal ZrTe5

One of the characteristics of topological materials is their nontrivial Berry phase. Experimental determination of this phase largely relies on a phase analysis of quantum oscillations. We study the angular dependence of the oscillations in a Dirac material [Formula: see text] and observe a striking spin-zero effect (i.e., vanishing oscillations accompanied with a phase inversion). This indicates that the Berry phase in [Formula: see text] remains nontrivial for arbitrary field direction, in contrast with previous reports. The Zeeman splitting is found to be proportional to the magnetic field based on the condition for the spin-zero effect in a Dirac band. Moreover, it is suggested that the Dirac band in [Formula: see text] is likely transformed into a line node other than Weyl points for the field directions at which the spin zero occurs. The results underline a largely overlooked spin factor when determining the Berry phase from quantum oscillations.

Galvanomagnetic properties of the putative type-II Dirac semimetal PtTe2

Platinum ditelluride has recently been characterized, based on angle-resolved photoemission spectroscopy data and electronic band structure calculations, as a possible representative of type-II Dirac semimetals. Here, we report on the magnetotransport behavior (electrical resistivity, Hall effect) in this compound, investigated on high-quality single-crystalline specimens. The magnetoresistance (MR) of PtTe₂ is large (over 3000% at T = 1.8 K in B = 9 T) and unsaturated in strong fields in the entire temperature range studied. The MR isotherms obey a Kohler’s type scaling with the exponent m = 1.69, different from the case of ideal electron-hole compensation. In applied magnetic fields, the resistivity shows a low-temperature plateau, characteristic of topological semimetals. In strong fields, well-resolved Shubnikov – de Haas (SdH) oscillations with two principle frequencies were found, and their analysis yielded charge mobilities of the order of 10³ cm² V⁻¹ s⁻¹ and rather small effective masses of charge carriers, 0.11 m_e and 0.21 m_e. However, the extracted Berry phases point to trivial character of the electronic bands involved in the SdH oscillations. The Hall effect data corroborated a multi-band character of the electrical conductivity in PtTe₂, with moderate charge compensation.

Bulk Fermi Surfaces of the Dirac Type-II Semimetallic Candidates MAl_{3} (Where M=V, Nb, and Ta)

We report a de Haas-van Alphen (dHvA) effect study on the Dirac type-II semimetallic candidates MAl_{3} (where, M=V, Nb and Ta). The angular dependence of their Fermi surface (FS) cross-sectional areas reveals a remarkably good agreement with our first-principles calculations. Therefore, dHvA supports the existence of tilted Dirac cones with Dirac type-II nodes located at 100, 230 and 250 meV above the Fermi level ϵ_{F} for VAl_{3}, NbAl_{3} and TaAl_{3} respectively, in agreement with the prediction of broken Lorentz invariance in these compounds. However, for all three compounds we find that the cyclotron orbits on their FSs, including an orbit nearly enclosing the Dirac type-II node, yield trivial Berry phases. We explain this via an analysis of the Berry phase where the position of this orbit, relative to the Dirac node, is adjusted within the error implied by the small disagreement between our calculations and the experiments. We suggest that a very small amount of doping could displace ϵ_{F} to produce topologically nontrivial orbits encircling their Dirac node(s).

Towards the manipulation of topological states of matter: a perspective from electron transport

The introduction of topological invariants, ranging from insulators to metals, has provided new insights into the traditional classification of electronic states in condensed matter physics. A sudden change in the topological invariant at the boundary of a topological nontrivial system leads to the formation of exotic surface states that are dramatically different from its bulk. In recent years, significant advancements in the exploration of the physical properties of these topological systems and regarding device research related to spintronics and quantum computation have been made. Here, we review the progress of the characterization and manipulation of topological phases from the electron transport perspective and also the intriguing chiral/Majorana states that stem from them. We then discuss the future directions of research into these topological states and their potential applications.

Rules for Phase Shifts of Quantum Oscillations in Topological Nodal-Line Semimetals

Nodal-line semimetals are topological semimetals in which band touchings form nodal lines or rings. Around a loop that encloses a nodal line, an electron can accumulate a nontrivial π Berry phase, so the phase shift in the Shubnikov-de Haas (SdH) oscillation may give a transport signature for the nodal-line semimetals. However, different experiments have reported contradictory phase shifts, in particular, in the WHM nodal-line semimetals (W=Zr/Hf, H=Si/Ge, M=S/Se/Te). For a generic model of nodal-line semimetals, we present a systematic calculation for the SdH oscillation of resistivity under a magnetic field normal to the nodal-line plane. From the analytical result of the resistivity, we extract general rules to determine the phase shifts for arbitrary cases and apply them to ZrSiS and Cu_{3}PdN systems. Depending on the magnetic field directions, carrier types, and cross sections of the Fermi surface, the phase shift shows rich results, quite different from those for normal electrons and Weyl fermions. Our results may help explore transport signatures of topological nodal-line semimetals and can be generalized to other topological phases of matter.

Quantum Hall states observed in thin films of Dirac semimetal Cd3As2

A well known semiconductor Cd₃As₂ has reentered the spotlight due to its unique electronic structure and quantum transport phenomena as a topological Dirac semimetal. For elucidating and controlling its topological quantum state, high-quality Cd₃As₂ thin films have been highly desired. Here we report the development of an elaborate growth technique of high-crystallinity and high-mobility Cd₃As₂ films with controlled thicknesses and the observation of quantum Hall effect dependent on the film thickness. With decreasing the film thickness to 10 nm, the quantum Hall states exhibit variations such as a change in the spin degeneracy reflecting the Dirac dispersion with a large Fermi velocity. Details of the electronic structure including subband splitting and gap opening are identified from the quantum transport depending on the confinement thickness, suggesting the presence of a two-dimensional topological insulating phase. The demonstration of quantum Hall states in our high-quality Cd₃As₂ films paves a road to study quantum transport and device application in topological Dirac semimetal and its derivative phases.

Evolution of Weyl orbit and quantum Hall effect in Dirac semimetal Cd3As2

Owing to the coupling between open Fermi arcs on opposite surfaces, topological Dirac semimetals exhibit a new type of cyclotron orbit in the surface states known as Weyl orbit. Here, by lowering the carrier density in Cd3As2 nanoplates, we observe a crossover from multiple-frequency to single-frequency Shubnikov-de Haas (SdH) oscillations when subjected to out-of-plane magnetic field, indicating the dominant role of surface transport. With the increase of magnetic field, the SdH oscillations further develop into quantum Hall state with non-vanishing longitudinal resistance. By tracking the oscillation frequency and Hall plateau, we observe a Zeeman-related splitting and extract the Landau level index as well as sub-band number. Different from conventional two-dimensional systems, this unique quantum Hall effect may be related to the quantized version of Weyl orbits. Our results call for further investigations into the exotic quantum Hall states in the low-dimensional structure of topological semimetals.

Extremely Large Magnetoresistance in a Topological Semimetal Candidate Pyrite PtBi_{2}

While pyrite-type PtBi_{2} with a face-centered cubic structure has been predicted to be a three-dimensional (3D) Dirac semimetal, experimental study of its physical properties remains absent. Here we report the angular-dependent magnetoresistance measurements of a PtBi_{2} single crystal under high magnetic fields. We observed extremely large unsaturated magnetoresistance (XMR) up to (11.2×10^{6})% at T=1.8  K in a magnetic field of 33 T, which is comparable to the previously reported Dirac materials, such as WTe_{2}, LaSb, and NbP. The crystals exhibit an ultrahigh mobility and significant Shubnikov-de Hass quantum oscillations with a nontrivial Berry phase. The analysis of Hall resistivity indicates that the XMR can be ascribed to the nearly compensated electron and hole. Our experimental results associated with the ab initio calculations suggest that pyrite PtBi_{2} is a topological semimetal candidate that might provide a platform for exploring topological materials with XMR in noble metal alloys.

Thermoelectric quantum oscillations in ZrSiS

Topological semimetals are systems in which conduction and valence bands cross each other and the crossings are protected by topological constraints. These materials provide intriguing tests for fundamental theories, while their unique physical properties promise a wide range of possible applications in low-power spintronics, optoelectronics, quantum computing and green energy harvesting. Here we report our study of the thermoelectric power of single-crystalline ZrSiS that is believed to be a topological nodal-line semimetal. We show that the thermoelectric power is an extremely sensitive probe of multiple quantum oscillations that are visible in ZrSiS at temperatures as high as 100 K. Two of these oscillations are shown to arise from three- and two-dimensional electronic bands, each with linear dispersion and the additional Berry phase predicted theoretically for materials with non-trivial topology. Our work not only provides further information on ZrSiS but also suggests a different route for studying other topological semimetals.