3D Quantum Hall Effect of Fermi Arcs in Topological Semimetals

Observation of 3D acoustic quantum Hall states

Quantum Hall effect, the quantized transport phenomenon of electrons under strong magnetic fields, remains one of the hottest research topics in condensed matter physics since its discovery in 2D electronic systems. Recently, as a great advance in the research of quantum Hall effects, the quantum Hall effect in 3D systems, despite its big challenge, has been achieved in the bulk ZrTe5 and Cd3As2 materials. Interestingly, Cd3As2 is a Weyl semimetal, and quantum Hall effect is hosted by the Fermi arc states on opposite surfaces via the Weyl nodes of the bulk, and induced by the unique edge states on the boundaries of the opposite surfaces. However, such intriguing edge state distribution has not yet been experimentally observed. Here, we aim to reveal experimentally the unusual edge states of Fermi arcs in acoustic Weyl system with the aid of pseudo-magnetic field. Benefiting from the macroscopic nature of acoustic crystals, the pseudo-magnetic field is introduced by elaborately designed the gradient on-site energy, and the edge states of Fermi arcs on the boundaries of the opposite surfaces are unambiguously demonstrated in experiments. Our system serves as an ideal and highly tunable platform to explore the Hall physics in 3D system, and has the potential in the application of new acoustic devices.

Surface spectroscopy and surface-bulk hybridization of Weyl semimetals

Weyl semimetal showing open-arc surface states is a prominent example of topological quantum matter in three dimensions. With the bulk-boundary correspondence present, nontrivial surface-bulk hybridization is inevitable but less understood. Spectroscopies have been often limited to verifying the existence of surface Fermi arcs, whereas its spectral shape related to the hybridization profile in energy-momentum space is not well studied. We present an exactly solvable formalism at the surface for a wide range of prototypical Weyl semimetals. The resonant surface state and the bulk influence coexist as a surface-bulk hybrid and are treated in a unified manner. Directly accessible to angle-resolved photoemission spectroscopy, we analytically reveal universal information about the system obtained from the spectroscopy of resonant topological states. We systematically find inhomogeneous and anisotropic singular responses around the surface-bulk merging borderline crossing Weyl points, highlighting its critical role in the Weyl topology. The response in scanning tunneling spectroscopy is also discussed. The results will provide much-needed insight into the surface-bulk-coupled physical properties and guide in-depth spectroscopic investigation of the nontrivial hybrid in many topological semimetal materials.

High-Mobility Topological Semimetals as Novel Materials for Huge Magnetoresistance Effect and New Type of Quantum Hall Effect

The quantitative description of electrical and magnetotransport properties of solid-state materials has been a remarkable challenge in materials science over recent decades. Recently, the discovery of a novel class of materials-the topological semimetals-has led to a growing interest in the full understanding of their magnetotransport properties. In this review, the strong interplay among topology, band structure, and carrier mobility in recently discovered high carrier mobility topological semimetals is discussed and their effect on their magnetotransport properties is outlined. Their large magnetoresistance effect, especially in the Hall transverse configuration, and a new version of a three-dimensional quantum Hall effect observed in high-mobility Weyl and Dirac semimetals are reviewed. The possibility of designing novel quantum sensors and devices based on solid-state semimetals is also examined.

Antichirality Emergent in Type-II Weyl Phononic Crystals

Chiral anomaly as the hallmark feature lies in the heart of the researches for Weyl semimetal. It is rooted in the zeroth Landau level of the system with an applied magnetic field. Chirality or antichirality characterizes the propagation property of the one-way zeroth Landau level mode, and antichirality means an opposite group velocity compared to the case of chirality. Chirality is commonly observed for Weyl semimetals. Interestingly, the type-II Weyl point, with the overtilted dispersion, may flip the chirality to the antichirality, which, however, is yet to be evidenced despite numerous previous experimental efforts. Here, we implement the type-II Weyl point in sonic crystals, and by creating the pseudomagnetic fields with geometric deformation, the chirality flip of zeroth Landau levels is unambiguously demonstrated. Our Letter unveils the novel antichiral transport in the presence of time-reversal symmetry, and paves the way toward the state-of-the-art manipulation of sound waves.

Anisotropic Three-Dimensional Quantum Hall Effect and Magnetotransport in Mesoscopic Weyl Semimetals

Weyl semimetals are emerging to become a new class of quantum-material platform for various novel phenomena. Especially, the Weyl orbit made from surface Fermi arcs and bulk relativistic states is expected to play a key role in magnetotransport, leading even to a three-dimensional quantum Hall effect (QHE). It is experimentally and theoretically important although yet unclear whether it bears essentially the same phenomenon as the conventional two-dimensional QHE. We discover an unconventional fully three-dimensional anisotropy in the quantum transport under a magnetic field. Strong suppression and even disappearance of the QHE occur when the Hall-bar current is rotated away from being transverse to parallel with respect to the Weyl point alignment, which is attributed to a peculiar absence of conventional bulk-boundary correspondence. Besides, transport along the magnetic field can exhibit a remarkable reversal from negative to positive magnetoresistance. These results establish the uniqueness of this QHE system as a novel three-dimensional quantum matter.

Phase transitions in intrinsic magnetic topological insulator with high-frequency pumping

In this work, we investigate the topological phase transitions in an effective model for a topological thin film with high-frequency pumping. In particular, our results show that the circularly polarized light can break the time-reversal symmetry and induce the quantum anomalous Hall insulator (QAHI) phase. Meanwhile, the bulk magnetic moment can also break the time-reversal symmetry. Therefore, it shows rich phase diagram by tuning the intensity of the light and the thickness of the thin film. Using the parameters fitted by experimental data, we give the topological phase diagram of the Cr-doped Bi₂Se₃thin film, showing that by modulating the strength of the polarized optical field in an experimentally accessible range, there are four different phases: the normal insulator phase, the time-reversal-symmetry-broken quantum spin Hall insulator phase, and two different QAHI phases with opposite Chern numbers. Comparing with the non-doped Bi₂Se₃, it is found that the interplay between the light and bulk magnetic moment separates the two different QAHI phases with opposite Chern numbers. The results show that an intrinsic magnetic topological insulator with high-frequency pumping is an ideal platform for further exploring various topological phenomena with a spontaneously broken time-reversal symmetry.

Experimental Demonstration of Bulk-Hinge Correspondence in a Three-Dimensional Topological Dirac Acoustic Crystal

Three-dimensional topological Dirac semimetal (DSM) is a vital state to explore topological phases and phase transitions. However, its bulk-boundary correspondence is elusive. Here, we experimentally investigate the higher-order hinge states in an acoustic DSM. Not only removable trivial surface states but also robust nontrivial hinge arcs are observed, attributed to the direct correspondence between bulk polarization and hinge charge. We further reveal that a pair of zigzag and bearded hinges possess arcs located in complementary momentum regions. Our work provides solid proof of the bulk-hinge correspondence in DSM and sheds light on the study of topological hierarchy across dimensions.

Electrically controlled spin polarized current in Dirac semimetals

We propose a highly tunable [Formula: see text] spin-polarized current generated in a spintronic device based on a Dirac semimetal (DSM) under a magnetic field, which can be achieved merely by controlling electrical parameters, i.e. the gate voltage, the chemical potential in the lead and the coupling strength between the leads and the DSM. These parameters are all related to the special properties of a semimetal. The spin polarized current generated by gate voltage is guaranteed by its semimetallic feature, because of which the density of state vanishes near Dirac nodes. The barrier controlled current results from the different distance of Weyl nodes generated by the Zeeman field. And the coupling strength controlled spin polarized current originates from the surface Fermi arcs. This DSM-based spintronic device is expected to be realized in [Formula: see text] experimentally.

Coulomb Instabilities of a Three-Dimensional Higher-Order Topological Insulator

Topological insulators (TIs) are an exciting discovery because of their robustness against disorder and interactions. Recently, second-order TIs have been attracting increasing attention, because they host topologically protected 1D hinge states in 3D or 0D corner states in 2D. A significantly critical issue is whether the second-order TIs also survive interactions, but it is still unexplored. We study the effects of weak Coulomb interactions on a 3D second-order TI, with the help of renormalization-group calculations. We find that the 3D second-order TIs are always unstable, suffering from two types of topological phase transitions. One is from second-order TI to TI, the other is to normal insulator. The first type is accompanied by emergent time-reversal and inversion symmetries and has a dynamical critical exponent κ=1. The second type does not have the emergent symmetries but has nonuniversal dynamical critical exponents κ<1. Our results may inspire more inspections on the stability of higher-order topological states of matter and related novel quantum criticalities.

Field-Tunable One-Sided Higher-Order Topological Hinge States in Dirac Semimetals

Recently, higher-order topological matter and 3D quantum Hall effects have attracted a great amount of attention. The Fermi-arc mechanism of the 3D quantum Hall effect proposed to exist in Weyl semimetals is characterized by the one-sided hinge states, which do not exist in all the previous quantum Hall systems, and more importantly, pose a realistic example of the higher-order topological matter. The experimental effort so far is in the Dirac semimetal Cd_{3}As_{2}, where, however, time-reversal symmetry leads to hinge states on both sides of the top and bottom surfaces, instead of the aspired one-sided hinge states. We propose that under a tilted magnetic field, the hinge states in Cd_{3}As_{2}-like Dirac semimetals can be one sided, highly tunable by field direction and Fermi energy, and robust against weak disorder. Furthermore, we propose a scanning tunneling Hall measurement to detect the one-sided hinge states. Our results will be insightful for exploring not only the quantum Hall effects beyond two dimensions, but also other higher-order topological insulators in the future.

Spin-valley locking and bulk quantum Hall effect in a noncentrosymmetric Dirac semimetal BaMnSb2

Spin-valley locking in monolayer transition metal dichalcogenides has attracted enormous interest, since it offers potential for valleytronic and optoelectronic applications. Such an exotic electronic state has sparsely been seen in bulk materials. Here, we report spin-valley locking in a Dirac semimetal BaMnSb2. This is revealed by comprehensive studies using first principles calculations, tight-binding and effective model analyses, angle-resolved photoemission spectroscopy measurements. Moreover, this material also exhibits a stacked quantum Hall effect (QHE). The spin-valley degeneracy extracted from the QHE is close to 2. This result, together with the Landau level spin splitting, further confirms the spin-valley locking picture. In the extreme quantum limit, we also observed a plateau in the z-axis resistance, suggestive of a two-dimensional chiral surface state present in the quantum Hall state. These findings establish BaMnSb2 as a rare platform for exploring coupled spin and valley physics in bulk single crystals and accessing 3D interacting topological states.

Quantum Transport of the 2D Surface State in a Nonsymmorphic Semimetal

In a topological semimetal with Dirac or Weyl points, the bulk-boundary correspondence principle predicts a gapless edge mode if the essential symmetry is still preserved at the surface. The detection of such topological surface state has been considered as the fingerprint prove for crystals with nontrivial topological bulk band. On the contrary, it has been proposed that even with symmetry broken at the surface, a new surface band can emerge in nonsymmorphic topological semimetals. The symmetry reduction at the surface lifts the bulk band degeneracies and produces an unusual "floating" surface band with trivial topology. Here, we first report quantum transport probing to ZrSiSe thin flakes and directly reveal transport signatures of this new surface state. Remarkably, though topologically trivial, such a surface band exhibits substantial two-dimensional Shubnikov-de Haas quantum oscillations with high mobility, which signifies a new protection mechanism and may open applications for quantum computing and spintronic devices.

Intrinsic coupling between spatially-separated surface Fermi-arcs in Weyl orbit quantum Hall states

Topological semimetals hosting bulk Weyl points and surface Fermi-arc states are expected to realize unconventional Weyl orbits, which interconnect two surface Fermi-arc states on opposite sample surfaces under magnetic fields. While the presence of Weyl orbits has been proposed to play a vital role in recent observations of the quantum Hall effect even in three-dimensional topological semimetals, actual spatial distribution of the quantized surface transport has been experimentally elusive. Here, we demonstrate intrinsic coupling between two spatially-separated surface states in the Weyl orbits by measuring a dual-gate device of a Dirac semimetal film. Independent scans of top- and back-gate voltages reveal concomitant modulation of doubly-degenerate quantum Hall states, which is not possible in conventional surface orbits as in topological insulators. Our results evidencing the unique spatial distribution of Weyl orbits provide new opportunities for controlling the novel quantized transport by various means such as external fields and interface engineering.

The spatial distribution of the quantized transport due to the presence of Weyl orbits in topological semimetals remains elusive. Here, the authors report concomitant modulation of doubly-degenerate quantum Hall states, evidencing intrinsic coupling between two spatially separated surface states in the Weyl orbits of a Dirac semimetal film.

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.

Progress in Epitaxial Thin-Film Na3 Bi as a Topological Electronic Material

Trisodium bismuthide (Na₃ Bi) is the first experimentally verified topological Dirac semimetal, and is a 3D analogue of graphene hosting relativistic Dirac fermions. Its unconventional momentum-energy relationship is interesting from a fundamental perspective, yielding exciting physical properties such as chiral charge carriers, the chiral anomaly, and weak anti-localization. It also shows promise for realizing topological electronic devices such as topological transistors. Herein, an overview of the substantial progress achieved in the last few years on Na₃ Bi is presented, with a focus on technologically relevant large-area thin films synthesized via molecular beam epitaxy. Key theoretical aspects underpinning the unique electronic properties of Na₃ Bi are introduced. Next, the growth process on different substrates is reviewed. Spectroscopic and microscopic features are illustrated, and an analysis of semiclassical and quantum transport phenomena in different doping regimes is provided. The emergent properties arising from confinement in two dimensions, including thickness-dependent and electric-field-driven topological phase transitions, are addressed, with an outlook toward current challenges and expected future progress.

Six-membered-ring inorganic materials: definition and prospects

The six-membered ring (SMR) is a common structure unit for numerous material systems. These materials include, but are not limited to, the typical two-dimensional materials such as graphene, h-BN, and transition metal dichalcogenides, as well as three-dimensional materials such as beryllium, magnesium, MgB2 and Bi2Se3. Although many of these materials have already become 'stars' in materials science and condensed-matter physics, little attention has been paid to the roles of the SMR unit across a wide range of compositions and structures. In this article, we systematically analyze these materials with respect to their very basic SMR structural unit, which has been found to play a deterministic role in the occurrence of many intriguing properties and phenomena, such as Dirac electronic and phononic spectra, superconductivity and topology. As a result, we have defined this group of materials as SMR inorganic materials, opening up a new perspective on materials research and development. With their unique properties, SMR materials deserve wide attention and in-depth investigation from materials design, new physical discoveries to target-wizard applications. It is expected that SMR materials will find niche applications in next-generation information technology, renewable energy, space, etc.

Theory for the Charge-Density-Wave Mechanism of 3D Quantum Hall Effect

The charge-density-wave (CDW) mechanism of the 3D quantum Hall effect has been observed recently in ZrTe_{5} [Tang et al., Nature 569, 537 (2019)10.1038/s41586-019-1180-9]. Different from previous cases, the CDW forms on a one-dimensional (1D) band of Landau levels, which strongly depends on the magnetic field. However, its theory is still lacking. We develop a theory for the CDW mechanism of 3D quantum Hall effect. The theory can capture the main features in the experiments. We find a magnetic field induced second-order phase transition to the CDW phase. We find that electron-phonon interactions, rather than electron-electron interactions, dominate the order parameter. We extract the electron-phonon coupling constant from the non-Ohmic I-V relation. We point out a commensurate-incommensurate CDW crossover in the experiment. More importantly, our theory explores a rare case, in which a magnetic field can induce an order-parameter phase transition in one direction but a topological phase transition in other two directions, both depend on one magnetic field.

3D Quantum Hall Effect and a Global Picture of Edge States in Weyl Semimetals

We investigate the 3D quantum Hall effect in Weyl semimetals and elucidate a global picture of the edge states. The edge states hosting 3D quantum Hall effect are combinations of Fermi arcs and chiral Landau bands dispersing along the magnetic field direction. The Hall conductance, σ_{xz}^{H} [see Fig. 4], shows quantized plateaus with the variance of the magnetic field when the Fermi level is at the Weyl node. However, the chiral Landau bands can change the spatial distribution of the edge states, especially under a tilted magnetic field, and the resulting edge states lead to distinctive Hall transport phenomena. A tilted magnetic field contributes an intrinsic value to σ_{xz}^{H} and such an intrinsic value is determined by the tilting angle θ between the magnetic field and the y axis [see Fig. 1(c)]. Particularly, even if the perpendicular magnetic field is fixed, σ_{xz}^{H} will change its sign with an abrupt spatial shift of the edge states when θ exceeds a critical angle θ_{c}. Our work uncovers the novel edge-state nature of the 3D quantum Hall effect in Weyl semimetals.

Vortex End Majorana Zero Modes in Superconducting Dirac and Weyl Semimetals

Time-reversal invariant Dirac and Weyl semimetals in three dimensions (3D) can host open Fermi arcs and spin-momentum locking Fermi loops on the surfaces. We find that when they become superconducting with s-wave pairing and the doping is lower than a critical level, straight π-flux vortex lines terminating at surfaces with Fermi arcs or spin-momentum locking Fermi loops can realize 1D topological superconductivity and harbor Majorana zero modes at their ends. Remarkably, we find that the vortex-generation-associated Zeeman field can open (when the surfaces have only Fermi arcs) or enhance the topological gap protecting Majorana zero modes, which is contrary to the situation in superconducting topological insulators. By studying the tilting effect of bulk Dirac and Weyl cones, we further find that type-I Dirac and Weyl semimetals in general have a much broader topological regime than type-II ones. Our findings build up a connection between time-reversal invariant Dirac and Weyl semimetals and Majorana zero modes in vortices.

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.

Fermi-arc supercurrent oscillations in Dirac semimetal Josephson junctions

One prominent hallmark of topological semimetals is the existence of unusual topological surface states known as Fermi arcs. Nevertheless, the Fermi-arc superconductivity remains elusive. Here, we report the critical current oscillations from surface Fermi arcs in Nb-Dirac semimetal Cd₃As₂-Nb Josephson junctions. The supercurrent from bulk states are suppressed under an in-plane magnetic field ~0.1 T, while the supercurrent from the topological surface states survives up to 0.5 T. Contrary to the minimum normal-state conductance, the Fermi-arc carried supercurrent shows a maximum critical value near the Dirac point, which is consistent with the fact that the Fermi arcs have maximum density of state at the Dirac point. Moreover, the critical current exhibits periodic oscillations with a parallel magnetic field, which is well understood by considering the in-plane orbital effect from the surface states. Our results suggest the Dirac semimetal combined with superconductivity should be promising for topological quantum devices.

Quantized Field-Effect Tunneling between Topological Edge or Interface States

We study the tunneling through a two-dimensional topological insulator with topologically protected edge states. It is shown that the tunneling probability can be quantized in a broad parameter range, 0 or 1, tuned by an applied transverse electric field. Based on this field-effect tunneling, we propose two types of topological transistors based on helical edge or interface states of quantum spin Hall insulators separately. The quantized tunneling conductance is obtained and shown to be robust against nonmagnetic disorders. Usually, the topological transition is necessary in the operation of topological transistors. These findings provide a new strategy for the design of topological transistors without topological transitions.

Topological Lifshitz transitions and Fermi arc manipulation in Weyl semimetal NbAs

Surface Fermi arcs (SFAs), the unique open Fermi-surfaces (FSs) discovered recently in topological Weyl semimetals (TWSs), are unlike closed FSs in conventional materials and can give rise to many exotic phenomena, such as anomalous SFA-mediated quantum oscillations, chiral magnetic effects, three-dimensional quantum Hall effect, non-local voltage generation and anomalous electromagnetic wave transmission. Here, by using in-situ surface decoration, we demonstrate successful manipulation of the shape, size and even the connections of SFAs in a model TWS, NbAs, and observe their evolution that leads to an unusual topological Lifshitz transition not caused by the change of the carrier concentration. The phase transition teleports the SFAs between different parts of the surface Brillouin zone. Despite the dramatic surface evolution, the existence of SFAs is robust and each SFA remains tied to a pair of Weyl points of opposite chirality, as dictated by the bulk topology.

Surface Fermi arcs (SFAs) are characteristic features of a topological Weyl semimetal but there is no easy way to manipulate them so far. Here, the authors report manipulation of the shape, size and connections of SFAs in a Weyl semimetal NbAs, leading to an unusual topological Lifshitz transition.

Quantized surface transport in topological Dirac semimetal films

Unconventional surface states protected by non-trivial bulk orders are sources of various exotic quantum transport in topological materials. One prominent example is the unique magnetic orbit, so-called Weyl orbit, in topological semimetals where two spatially separated surface Fermi-arcs are interconnected across the bulk. The recent observation of quantum Hall states in Dirac semimetal Cd3As2 bulks have drawn attention to the novel quantization phenomena possibly evolving from the Weyl orbit. Here we report surface quantum oscillation and its evolution into quantum Hall states in Cd3As2 thin film samples, where bulk dimensionality, Fermi energy, and band topology are systematically controlled. We reveal essential involvement of bulk states in the quantized surface transport and the resultant quantum Hall degeneracy depending on the bulk occupation. Our demonstration of surface transport controlled in film samples also paves a way for engineering Fermi-arc-mediated transport in topological semimetals.

Weyl Nodal Point-Line Fermion in Ferromagnetic Eu5Bi3

On the basis of ab initio calculations and a low-energy effective k· p model, we propose a Weyl nodal point-line (WNPL) fermion, composed of 0D Weyl points and a 1D Weyl nodal line, in the ferromagnetic material Eu₅Bi₃. In the absence of spin-orbital coupling (SOC), the spin-up bands host a pair of triply degenerate points together with a bird-cage-like node structure. In the presence of SOC with (001) magnetization, each triplet point splits into a double Weyl point and a single Weyl point accompanied by two nodal rings, forming two sets of WNPL fermions near the Fermi level. The novel properties of the WNPL fermion are explored by revealing the unusual Berry curvature field and demonstrating the pinned chiral surface states with exotic Fermi arcs. Our work offers new ideas for exploring novel topological semimetal states with diverse band-crossing dimensions and provides a candidate for future experimental realization.

Observation of an Odd-Integer Quantum Hall Effect from Topological Surface States in Cd_{3}As_{2}

The quantum Hall effect (QHE) in a 3D Dirac semimetal thin film is attributed to either the quantum confinement induced bulk subbands or the Weyl orbits that connect the opposite surfaces via bulk Weyl nodes. However, it is still unknown whether the QHE based on the Weyl orbit can survive as the bulk Weyl nodes are gapped. Moreover, there are closed Fermi loops rather than open Fermi arcs on the Dirac semimetal surface, which can also host the QHE. Here we report the QHE in the 3D Dirac semimetal Cd_{3}As_{2} nanoplate by tuning the gate voltage under a fixed 30 T magnetic field. The quantized Hall plateaus at odd filling factors are observed as a magnetic field along the [001] crystal direction, indicating a Berry's phase π from the topological surface states. Furthermore, even filling factors are observed when the magnetic field is along the [112] direction, indicating the C_{4} rotational symmetry breaking and a topological phase transition. The results shed light on the understanding of QHE in 3D Cd_{3}As_{2}.

Interaction-Driven Surface Chern Insulator in Nodal Line Semimetals

Nodal line semimetals are characterized by nontrivial bulk-band crossings, giving rise to almost flat drumheadlike surface states (DSS), which provide an attractive playground where interaction can induce symmetry-broken states and potential emergent phases. Here, we show that electronic interaction drives a Stoner ferromagnetic instability in the DSS while the bulk remains nonmagnetic, which together with spin-orbit coupling drive the surface states into a 2D Chern insulator. We show that each piece of DSS carries a half-integer topological charge, which for systems containing two pieces of DSS yield a net Chern number C=-1. We show that this phenomenology is robust against chiral-symmetry breaking, which gives a finite dispersion to the DSS. Our results show that nodal line semimetals are a promising platform to implement surface Chern insulators and dissipationless electron transport by exploiting enhanced interaction effects of the DSS.

Quantum Hall effect based on Weyl orbits in Cd3As2

Discovered decades ago, the quantum Hall effect remains one of the most studied phenomena in condensed matter physics and is relevant for research areas such as topological phases, strong electron correlations and quantum computing^1-5. The quantized electron transport that is characteristic of the quantum Hall effect typically originates from chiral edge states-ballistic conducting channels that emerge when two-dimensional electron systems are subjected to large magnetic fields². However, whether the quantum Hall effect can be extended to higher dimensions without simply stacking two-dimensional systems is unknown. Here we report evidence of a new type of quantum Hall effect, based on Weyl orbits in nanostructures of the three-dimensional topological semimetal Cd₃As₂. The Weyl orbits consist of Fermi arcs (open arc-like surface states) on opposite surfaces of the sample connected by one-dimensional chiral Landau levels along the magnetic field through the bulk^6,7. This transport through the bulk results in an additional contribution (compared to stacked two-dimensional systems and which depends on the sample thickness) to the quantum phase of the Weyl orbit. Consequently, chiral states can emerge even in the bulk. To measure these quantum phase shifts and search for the associated chiral modes in the bulk, we conduct transport experiments using wedge-shaped Cd₃As₂ nanostructures with variable thickness. We find that the quantum Hall transport is strongly modulated by the sample thickness. The dependence of the Landau levels on the magnitude and direction of the magnetic field and on the sample thickness agrees with theoretical predictions based on the modified Lifshitz-Onsager relation for the Weyl orbits. Nanostructures of topological semimetals thus provide a way of exploring quantum Hall physics in three-dimensional materials with enhanced tunability.

Fano Interference between Bulk and Surface States of a Dirac Semimetal Cd_{3}As_{2} Nanowire

Dirac semimetals possess Fermi-arc surface states, which will be a set of discrete surface subbands in a nanowire due to the quantum confinement effect. Here, we report a tunable Fano effect induced by the interference between the discrete surface states and continuous bulk states of a Dirac semimetal Cd_{3}As_{2} nanowire. The discrete surface bands lead to a zero bias peak in conductance as the Femi level is tuned to across the surface subbands. The Fano resonance results in an asymmetric line shape in the differential conductance dI/dV spectrum. Furthermore, the Fano interference would introduce an additional phase into the Weyl orbits and lead to a modification of the oscillation frequency. The results are valuable for further understanding the exotic quantum transport properties of topological semimetals.

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.

Gate-tuned quantum Hall states in Dirac semimetal (Cd1-x Zn x )3As2

The recent discovery of topological Dirac semimetals (DSMs) has provoked intense curiosity not only regarding Weyl physics in solids but also about topological phase transitions originating from DSMs. One specific area of interest is controlling the dimensionality to realize two-dimensional quantum phases such as quantum Hall and quantum spin Hall states. For investigating these phases, the Fermi level is a key controlling parameter. From this perspective, we report the carrier density control of quantum Hall states realized in thin films of DSM Cd₃As₂. Chemical doping of Zn combined with electrostatic gating has enabled us to tune the carrier density both over a wide range and continuously, even across the charge neutrality point. Comprehensive analyses of gate-tuned quantum transport have revealed Landau-level formation from linearly dispersed sub-bands and its contribution to the quantum Hall states. Our findings also pave the way for investigating the low-energy physics near the Dirac points of DSMs.

Surface and 3D Quantum Hall Effects from Engineering of Exceptional Points in Nodal-Line Semimetals

We show that, under a strong magnetic field, a 3D nodal-line semimetal is driven into a topological insulating phase in which the electronic transport takes place at the surface of the material. When the magnetic field is perpendicular to the nodal ring, the surface states of the semimetal are transmuted into Landau states which correspond to exceptional points, i.e., branch points in the spectrum of a non-Hermitian Hamiltonian which arise upon the extension to complex values of the momentum. The complex structure of the spectrum then allows us to express the number of zero-energy flat bands in terms of a new topological invariant counting the number of exceptional points. When the magnetic field is parallel to the nodal ring, we find that the bulk states are built from the pairing of surfacelike evanescent waves, giving rise to a 3D quantum Hall effect with a flat level of Landau states residing in parallel 2D slices of the 3D material. The Hall conductance is quantized in either case in units of e^{2}/h, leading in the 3D Hall effect to a number of channels growing linearly with the section of the surface and opening the possibility to observe a macroscopic chiral current at the surface of the material.

Observation of the Quantum Hall Effect in Confined Films of the Three-Dimensional Dirac Semimetal Cd_{3}As_{2}

The magnetotransport properties of epitaxial films of Cd_{3}As_{2}, a paradigm three-dimensional Dirac semimetal, are investigated. We show that an energy gap opens in the bulk electronic states of sufficiently thin films and, at low temperatures, carriers residing in surface states dominate the electrical transport. The carriers in these states are sufficiently mobile to give rise to a quantized Hall effect. The sharp quantization demonstrates surface transport that is virtually free of parasitic bulk conduction and paves the way for novel quantum transport studies in this class of topological materials. Our results also demonstrate that heterostructuring approaches can be used to study and engineer quantum states in topological semimetals.

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.