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Electronic Transport In Mesoscopic Systems

This article reviews the theoretical and experimental work related to the electronic properties of bilayer graphene systems. Three types of bilayer stackings are discussed: the AA, AB, and twisted bilayer graphene. This review covers single-electron properties, effects of static electric and magnetic fields, bilayer-based mesoscopic systems, spin-orbit coupling, dc transport and optical response, as well as spontaneous symmetry violation and other interaction effects. The selection of the material aims to introduce the reader to the most commonly studied topics of theoretical and experimental research in bilayer graphene.

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Electronic properties of graphene-based bilayer systems

Quantum anomalous Hall goes intrinsic Quantum anomalous Hall effect—the appearance of quantized Hall conductance at zero magnetic field—has been observed in thin films of the topological insulator Bi2Se3 doped with magnetic atoms. The doping, however, introduces inhomogeneity, reducing the temperature at which the effect occurs. Two groups have now observed quantum anomalous Hall effect in intrinsically magnetic materials (see the Perspective by Wakefield and Checkelsky). Serlin et al. did so in twisted bilayer graphene aligned to hexagonal boron nitride, where the effect enabled the switching of magnetization with tiny currents. In a complementary work, Deng et al. observed quantum anomalous Hall effect in the antiferromagnetic layered topological insulator MnBi2Te4. Science, this issue p. 900, p. 895; see also p. 848 Transport measurements indicate quantized Hall conductance without a magnetic field. The quantum anomalous Hall (QAH) effect combines topology and magnetism to produce precisely quantized Hall resistance at zero magnetic field. We report the observation of a QAH effect in twisted bilayer graphene aligned to hexagonal boron nitride. The effect is driven by intrinsic strong interactions, which polarize the electrons into a single spin- and valley-resolved moiré miniband with Chern number C = 1. In contrast to magnetically doped systems, the measured transport energy gap is larger than the Curie temperature for magnetic ordering, and quantization to within 0.1% of the von Klitzing constant persists to temperatures of several kelvin at zero magnetic field. Electrical currents as small as 1 nanoampere controllably switch the magnetic order between states of opposite polarization, forming an electrically rewritable magnetic memory.

Intrinsic Quantized Anomalous Hall Effect in a Moiré Heterostructure, Part III: Scanning Probe Magnetometry

Three-dimensional (3D) topological Dirac semimetals (TDSs) are a recently proposed state of quantum matter that have attracted increasing attention in physics and materials science. A 3D TDS is not only a bulk analogue of graphene; it also exhibits non-trivial topology in its electronic structure that shares similarities with topological insulators. Moreover, a TDS can potentially be driven into other exotic phases (such as Weyl semimetals, axion insulators and topological superconductors), making it a unique parent compound for the study of these states and the phase transitions between them. Here, by performing angle-resolved photoemission spectroscopy, we directly observe a pair of 3D Dirac fermions in Cd3As2, proving that it is a model 3D TDS. Compared with other 3D TDSs, for example, β-cristobalite BiO2 (ref. 3) and Na3Bi (refs 4, 5), Cd3As2 is stable and has much higher Fermi velocities. Furthermore, by in situ doping we have been able to tune its Fermi energy, making it a flexible platform for exploring exotic physical phenomena.

https://absimage.aps.org/image/MAR15/MWS_MAR15-2014-003558.pdf

ARPES study on a stable three-dimensional topological Dirac semimetal Cd3As2

We utilize the variational method to study the Kondo screening of a $\text{spin}\ensuremath{-}1/2$ magnetic impurity in a three-dimensional (3D) Weyl semimetal with two Weyl nodes along the ${k}_{z}$ axis. The model reduces to a 3D Dirac semimetal when the separation of the two Weyl nodes vanishes. When the chemical potential lies at the nodal point, $\ensuremath{\mu}=0$, the impurity spin is screened only if the coupling between the impurity and the conduction electron exceeds a critical value. For finite but small $\ensuremath{\mu}$, the impurity spin is weakly bound due to the low density of states, which is proportional to ${\ensuremath{\mu}}^{2}$, contrary to that in a 2D Dirac metal such as graphene and 2D helical metal, where the density of states is proportional to $|\ensuremath{\mu}|$. The spin-spin correlation function ${J}_{uv}(\mathbf{r})$ between the spin $v$ component of the magnetic impurity at the origin and the spin $u$ component of a conduction electron at spatial point $\mathbf{r}$ is found to be strongly anisotropic due to the spin-orbit coupling, and it decays in the power law. The main difference of the Kondo screening in 3D Weyl semimetals and in Dirac semimetals is in the spin $x\phantom{\rule{0.28em}{0ex}}(y)$ component of the correlation function in the spatial direction of the $z$ axis.

Magnetic impurity in a Weyl semimetal

A Weyl semimetal (WSM) is a topological material that hosts Weyl fermions as quasiparticles in the bulk. We study the combined effect of intra- and interorbital disorders on WSMs by adopting a tight-binding model that supports the WSM, three-dimensional quantum anomalous Hall insulator (3D QAHI), and normal insulator (NI) phases in the clean limit. Based on the calculation of the localization length and the Hall conductivity, we present rich phase diagrams due to the interplay of intra- and interorbital disorders. We find that the WSM with well-separated Weyl nodes is stable to both weak intra- and interorbital disorders. However, weak intraorbital disorder can gap out a WSM close to the 3D QAHI phase in the clean phase diagram, forming a 3D QAHI, and it can also drive a NI near the WSM phase to a WSM. By contrast, weak interorbital disorder can cause a 3D QAHI-WSM transition for a 3D QAHI in proximity to the WSM phase in the clean limit, and it can annihilate a WSM near the NI phase, bringing about a WSM-NI transition. We observe a diffusive anomalous Hall metal (DAHM) phase at moderate disorder strength. The DAHM appears in a wide range of the phase diagram when the intraorbital disorder dominates over the interorbital disorder, while the DAHM is found to exist in a narrow region or be missing in the phase diagram when the interorbital disorder dominates.

Phase diagrams of Weyl semimetals with competing intraorbital and interorbital disorders

We theoretically study the localized magnetic states and the Kondo screening of a magnetic impurity in the bulk of Weyl semimetals (SMs). The linear dispersion near the Weyl nodes and the anomalous broadening of the impurity level lead to a nonvanishing magnetic moment in a wide region of parameters. The magnetic susceptibility is significantly enhanced by increasing the chirality imbalance for the chemical potential fixed at the Weyl nodes. The Kondo effect takes place whenever the chemical potential is tuned away from the nodes. The low-temperature susceptibility is determined by both the Kondo screening and the broadening of the magnetic impurity level. In the presence of chiral anomaly, the Kondo screening displays opposite behaviors for the chemical potential situated below and above the Weyl nodes. The magnetic susceptibility can be tuned by the charge imbalance of the nodes, which provides a scheme to study the chiral anomaly in Weyl SMs.

Magnetic states and Kondo screening in Weyl semimetals with chiral anomaly

In this paper, we study quantum phase transitions and magnetic properties of a one-dimensional spin-1/2 Gamma model, which describes the off-diagonal exchange interactions between edge-shared octahedra with strong spin-orbit couplings along the sawtooth chain. The competing exchange interactions between the nearest neighbors and the second neighbors stabilize the semimetallic ground state in terms of spinless fermions, and give rise to a rich phase diagram, which consists of three gapless phases. We find distinct phases are characterized by the number of Weyl nodes in the momentum space, and such changes in the topology of the Fermi surface without symmetry breaking produce a variety of Lifshitz transitions, in which the Weyl nodes situating at $k=\ensuremath{\pi}$ change from type I to type II. A coexistence of type-I and type-II Weyl nodes is found in phase II. The information measures including concurrence, entanglement entropy, and relative entropy can effectively signal the second-order transitions. The results indicate that the Gamma model can act as an exactly solvable model to describe Lifshitz phase transitions in correlated electron systems.

Lifshitz phase transitions in a one-dimensional Gamma model

We utilize variational method to investigate the Kondo screening of a spin-1/2 magnetic impurity in tilted Dirac surface states with the Dirac cone tilted along the ${k}_{y}$ axis. We mainly study about the effect of the tilting term on the binding energy and the spin-spin correlation between magnetic impurity and conduction electrons. The binding energy has a critical value while the Dirac cone is slightly tilted. However, as the tilting term increases, the density of states near the Dirac node becomes significant, such that the impurity and the host material always favor a bound state. The diagonal and the off-diagonal terms of the spin-spin correlation between the magnetic impurity and conduction electrons are also studied. Due to the spin-orbit coupling and the tilting of the spectra, various components of spin-spin correlation show very strong anisotropy in coordinate space and are of power-law decay with respect to the spatial displacements.

Jin-Hua Sun

Papers

Magnetic impurity in a Weyl semimetal

Phase diagrams of Weyl semimetals with competing intraorbital and interorbital disorders

Magnetic states and Kondo screening in Weyl semimetals with chiral anomaly

Lifshitz phase transitions in a one-dimensional Gamma model

Single magnetic impurity in tilted Dirac surface states