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Various novel physical properties have emerged in Dirac electronic systems, especially the topological characters protected by symmetry. Current studies on these systems have been greatly promoted by the intuitive concepts of Berry phase and Berry curvature, which provide precise definitions of the topological phases. In this topical review, transport properties of topological insulator (
Inspired by the notion of “topological order”, the exploration for novel classifications of matter phases becomes an intriguing theme in condensed-matter physics. Over three decades, the discovery of the quantum Hall effect (QHE) enlightened investigations on topological phases of matters.[1–6] Assisted by the powerful concepts of Berry phase and Berry curvature, precise definitions of topological phases are achieved. Berry phase is the phase generation during an adiabatic evolution process with steady external parameters producing a loop in the parameter space.[1,2] The Berry phase can be written as the integral of the Berry curvature.[2] Moreover, the integrals of the Berry curvature over closed surfaces are always employed to identify topological nontrivial phases, known as quantized Chern numbers.[2] Hence, theoretical predictions for nontrivial matters emerged endlessly for more than a decade, and novel quantum systems were continuously revealed. Such topological nontrivial systems exhibit fascinating properties, especially in transport experiments.
The QHE was discovered by Klaus von Klitzing et al., where the Hall conductivity of a two-dimensional (2D) system was found to be exactly quantized under a strong magnetic field.[7–9] Thouless et al. firstly employed topological considerations to explain the QHE.[5] From their milestone work, researchers began to realize that the electronic topological structure of quantum materials may be directly related to the transport behaviors. Various materials with novel topological phase have already been revealed. Graphene, the first 2D material containing Dirac fermions, has been proved to possess a Berry phase of π, leading to half-integer QHE observed in transport measurements.[10–16] Topological insulators (TIs) like
In this topical review, we generally introduce the experimental investigations about transport behaviors in topological nontrivial systems, mainly based on our own works. We have reported abundant phenomena originating from surface states in topological insulators, topological Dirac semimetal, and monolayer graphene. In Section
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Here we review the photothermoelectric effect in topological insulator
The
![]() | Fig. 1. (color online) (a) Cross-sectional HAADF-STEM image of a ![]() ![]() |
Individual
![]() | Fig. 2. (color online) (a) Optical image of a typical ![]() ![]() ![]() |
At θ = 30°, it is found that the RCP and LCP light have different effects on the photothermoelectric output. When the laser spot is near the electrode connected to the voltmeter positive terminal (the positive electrode), the RCP light induces an obviously enhanced voltage signal, the voltages induced by LCP and LP are similar (Fig.
The phenomena above are dominated by the light polarization selective rule according to the helical character of the carriers (Fig.
When the laser illumination on
Three-dimensional topological insulators have been demonstrated to possess rich physical connotations.[17–24]
The
![]() | Fig. 3. (color online) (a) Schematic of the in-plane magnetic field referring to the sidewall (Se: green spheres; Bi: purple spheres).(b) Optical image of a typical ![]() ![]() ![]() ![]() ![]() |
Considering the Onsager semiclassical quantization relation, a linear relationship can be acquired:
Angle dependent magneto-transport measurements show that the positive magnetoresistance background, which is the contribution from three-dimensional bulk transport, remarkably decreases as the out-of-plane field component gradually disappears (Fig.
![]() | Fig. 4. (color online) (a) Longitudinal resistance ![]() ![]() ![]() |
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The
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Theoretical analysis has shown that the graphene with inversion symmetry breaking can also exhibit the VHE.[92] However, pristine graphene (single layer or bilayer) is under inversion symmetry protection. The experimental investigations on the valley transport in a graphene system have been achieved recently, with the help of improvement on device fabrication.
In 2014, Gorbachev et al. reported a large non-local signal detected in single layer graphene with underlying BN substrate.[93] The inversion symmetry of graphene is believed to be broken as the consequence of A/B sublattice global asymmetry induced by the substrate potential. The inversion symmetry breaking leads to a non-zero Berry curvature distribution in the Brillouin zone. When the Fermi level is tuned to the energy level where non-zero Berry curvature exists, a large non-local signal can be detected from the transport measurements. The anomalously obvious non-local signal is due to the valley Hall effect and the inverse VHE, the latter is the phenomenon where pure valley current gives rise to charge current.
The novel work of Gorbachev et al. not only firstly reported the experimental realization of graphene valley transport, but also provided an efficient method to detect the VHE. In 2015, the valley transport in bilayer graphene was discovered by Sui et al. and Shimazaki et al. The two groups both utilized a perpendicular electric field tuned by a gate voltage to break the inversion symmetry of graphene, a strong non-local signal was detected, which was attributed to the VHE and the inverse VHE.[94,95] Their investigations show that electrically driven inversion symmetry breaking is achievable, shedding light on future valleytronics. Furthermore, the AB/BA stacking domain wall in bilayer graphene has also been reported to support a non-diffusional valley current.[96] The bilayer graphene system with broken inversion symmetry may possess a non-zero “valley” Chern number, leading to a topological valley edge state existing along the domain wall.
Based on the quantum field theory, the fermions of our universe are divided into three kinds: the Dirac fermions, the Weyl fermions, and the Majorana fermions.[97] Interestingly, the condensed-matter systems host quasiparticles possessing the characters of these high-energy physics concepts. The most typical example of Dirac semimetals is graphene, which has a Dirac point protected by time-reversal symmetry and inversion symmetry.[10–16] Extending the 2D linear energy–momentum dispersion relation to 3D momentum space, the 3D Dirac semimetals were recently discovered. Moreover, the Dirac point in 3D Dirac semimetals is composed of two Weyl nodes. The topological Weyl semimetals are the systems where low-energy excitations obey the Weyl equations.[57,98–100] Compared to the Dirac points (four-fold degeneracy), the Weyl nodes are only two-fold degenerate. Thus the Weyl node can only exist in systems with spontaneous symmetry-breaking, because in the systems possessing both the time-reversal and inversion symmetries, the band crossings are always four-fold degenerate.
The topology of the Weyl nodes is also defined by the Berry curvature,[98–100] an analogy of the magnetic flux in momentum space. Generally speaking, the Weyl nodes can be considered as the “magnetic monopoles” in momentum space, which are the origins or ends of the Berry curvature. The chirality (+1 or −1) of a Weyl node is similar to the “magnetic charge”, reflecting the Berry curvature distribution embracing the Weyl node. The Weyl nodes always come in pairs because the Chern number of the Weyl semimetal must be zero, otherwise it becomes a topological insulator.[2]
There are a large number of unusual physical features associated with Weyl semimetal, including open Fermi arcs in the surface and various exotic transport phenomena induced by the chiral anomaly. The open Fermi arcs connect the projections of the bulk Weyl nodes with opposite chiralities onto the surface, and the Fermi arcs can be understood as the surface states of Weyl semimetals.[98] Under the presence of external electric and magnetic fields, the chiral charge of one Weyl node is not conserved, which is the so-called chiral anomaly. The charge pumping effect between Weyl nodes with opposite chiralities gives rise to large negative magnetoresistance.[40,54–57,97,98]
It is worth noting that the Weyl semimetals discussed above have zero density of state at the zero energy, and they obey the Lorentz invariance in quantum field theory. This kind of Weyl semimetals have been predicted to exist in several symmetry-breaking materials, including TaAs, NbP, and other systems.[99,100] By the ARPES technique, the existence of Weyl fermions in TaAs, NbAs has been experimentally confirmed,[101–105] and chiral-anomaly-induced negative magnetoresistance was also detected in TaAs recently.[106]
Recently, a new type of Weyl semimetal has been predicted in the
Topological nontrivial systems provide splendid platforms for uncovering novel physics in mesoscopic scale, and also for practical applications. As a powerful method of physical characterization, transport measurements make significant contributions in exploring these miraculous systems. This topical review summarizes our experimental investigations on transport behaviors in topological insulator (
The past ten years have witnessed great achievements on the graphene system. Moreover, this intriguing 2D material still possesses unpredictable academic and application prospects. Researchers begin to enlarge the functionalization of graphene using graphene-based heterostructures by the proximity effect. Other than the inversion symmetry breaking and enhancement of spin–orbit coupling discussed above, a large exchange field has been introduced into graphene by a magnetic insulator EuS.[108] We believe experimental realizations of QSHE and QAHE in graphene-based heterostructures will come true in the near future. The physical contents and application possibilities are obviously diversified by investigations on the graphene-based heterostructures.
The proximity effect also shows extraordinary talents in other two-dimensional systems. The superconducting proximity effect is believed to induce Majorana fermions in a topological nontrivial system,[109] and transform the hybrid system into a “topological superconductor”. The controllable realization of such fantastic fermions will start the revolution of quantum computing. These features lead the superconducting proximity effect to become a research focus in recent years. Researchers have successfully detected the signature of Majorana fermions in topological superconductor nanowires,[110,111] and we notice that a recent report has provided evidence of the Majorana zero mode in the
Many other novel 2D materials are waiting to be revealed. The black phosphorus, which has both band gap and high mobility, was discovered in recent years.[114–117] Researchers have inquired into its application prospect,[114,115] and the QHE has been realized in black phosphorus.[116,117] Other new systems, like type-2 Weyl semimetal, are explored continuously. The variety of 2D materials affords us incessant inspirations, and the combination of 2D materials and other systems (for example, 2D material with superconductors or ferromagnets) will actually maximize such variety.
On the other hand, the improvement of device fabrication techniques provides substantial foundation for intensive works. The MBE method has been developed to grow high-quality 2D materials and their Van der Waals heterostructures. The interference of impurity potential can be greatly suppressed by the device encapsulation technology (for example, BN encapsulation),[118] leading to an ultraclean device environment. By the help of technological advances, more and more physical phenomena have been discovered experimentally.
We hope the readers of Chinese Physics B may acquire inspirations from our review, and our investigations over these years may shed light on future explorations.