The traditional theory of magnetic moments for chiral phonons is based on the picture of the circular motion of the Born effective charge, typically yielding a small fractional value of the nuclear magneton. Here we investigate the adiabatic evolutio
n of electronic states induced by lattice vibration of a chiral phonon and obtain an electronic orbital magnetization in the form of a topological second Chern form. We find that the traditional theory needs to be refined by introducing a $bm{k}$ resolved Born effective charge, and identify another contribution from the phonon-modified electronic energy together with the momentum-space Berry curvature. The second Chern form can diverge when there is a Yangs monopole near the parameter space of interest as illustrated by considering a phonon at the Brillouin zone corner in a gaped graphene model. We also find large magnetic moments for the optical phonon in bulk topological materials where non-topological contribution is also important. The magnetic moment experiences a sign change when the band inversion happens.
Recently, a new type of second-order topological insulator has been theoretically proposed by introducing an in-plane Zeeman field into the Kane-Mele model in the two-dimensional honeycomb lattice. A pair of topological corner states arise at the cor
ners with obtuse angles of an isolated diamond-shaped flake. To probe the corner states, we study their transport properties by attaching two leads to the system. Dressed by incoming electrons, the dynamic corner state is very different from its static counterpart. Resonant tunneling through the dressed corner state can occur by tuning the in-plane Zeeman field. At the resonance, the pair of spatially well separated and highly localized corner states can form a dimer state, whose wavefunction extends almost the entire bulk of the diamond-shaped flake. By varying the Zeeman field strength, multiple resonant tunneling events are mediated by the same dimer state. This re-entrance effect can be understood by a simple model. These findings extend our understanding of dynamic aspects of the second-order topological corner states.
We identify a valley-polarized Chern insulator in the van der Waals heterostructure, Pt$_{2}$HgSe$_{3}$/CrI$_3$, for potential applications with interplay between electric, magnetic, optical, and mechanical effects. The interlayer proximity magnetic
coupling nearly closes the band gap of Pt$_{2}$HgSe$_{3}$ and the strong intra-layer spin-orbit coupling further lifts the valley degeneracy by over 100 meV leading to positive and negative band gaps at opposite valleys. In the valley with negative gap, the interfacial Rashba spin-orbit coupling opens a topological band gap of 17.8 meV, which is enlarged to 30.8 meV by adding an $h$-BN layer. We find large orbital magnetization in Pt$_{2}$HgSe$_{3}$ layer that is much larger than spin, which can induce measurable optical Kerr effect. The valley polarization and Chern number are coupled to the magnetic order of the nearest neighboring CrI$_3$ layer, which is switchable by electric, magnetic, and mechanical means in experiments. The presence of $h$-BN protects the topological phase allowing the construction of superlattices with valley, spin, and layer degrees of freedoms.
A semiclassical theory for the orbital magnetization due to adiabatic evolutions of Bloch electronic states is proposed. It renders a unified theory for the periodic-evolution pumped orbital magnetization and the orbital magnetoelectric response in i
nsulators by revealing that these two phenomena are the only instances where the induced magnetization is gauge invariant. This theory also accounts for the electric-field induced intrinsic orbital magnetization in two-dimensional metals and Chern insulators. We illustrate the orbital magnetization pumped by microscopic local rotations of atoms, which correspond to phonon modes with angular momentum, in toy models based on honeycomb lattice, and the results are comparable to the pumped spin magnetization via strong Rashba spin orbit coupling. We also show the vital role of the orbital magnetoelectricity in validating the Mott relation between the intrinsic nonlinear anomalous Hall and Ettingshausen effects.
Graphene bilayers exhibit zero-energy flat bands at a discrete series of magic twist angles. In the absence of intra-sublattice inter-layer hopping, zero-energy states satisfy a Dirac equation with a non-abelian SU(2) gauge potential that cannot be d
iagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Plancks constant proportional to the twist angle, solving the linearized Dirac equation around AB and BA turning points, and connecting Airy function solutions via bulk WKB wavefunctions. We find zero energy solutions at a discrete set of values of the dimensionless Plancks constant, which we obtain analytically. Our analytic flat band twist angles correspond closely to those determined numerically in previous work.
We study the quantum phase diagram of spinful fermions on kagome lattice with half-filled lowest flat bands. To understand the competition between magnetism, flat band frustration, and repulsive interactions, we adopt an extended $t$-$J$ model, where
the hopping energy $t$, antiferromagnetic Heisenberg interaction $J$, and short-range neighboring Hubbard interaction $V$ are considered. In the weak $J$ regime, we identify a fully spin-polarized phase, which can further support the spontaneous Chern insulating phase driven by the short-range repulsive interaction. This phase still emerges with in-plane ferromagnetism, whereas the non-interacting Chern insulator disappears constrained by symmetry. As $J$ gradually increases, the ferromagnetism is suppressed and the system first becomes partially-polarized with large magnetization and then enters a non-polarized phase with the ground state exhibiting vanishing magnetization. We identify this non-polarized phase as an insulator with a nematic charge density wave. In the end, we discuss the potential experimental observations of our theoretical findings.
We study the electronic transport properties at the intersection of three topological zero-lines as the elementary current partition node that arises in minimally twisted bilayer graphene. Unlike the partition laws of two intersecting zero-lines, we
find that (i) the incoming current can be partitioned into both left-right adjacent topological channels and that (ii) the forward-propagating current is nonzero. By tuning the Fermi energy from the charge-neutrality point to a band edge, the currents partitioned into the three outgoing channels become nearly equal. Moreover, we find that current partition node can be designed as a perfect valley filter and energy splitter controlled by electric gating. By changing the relative electric field magnitude, the intersection of three topological zero-lines can transform smoothly into a single zero line, and the current partition can be controlled precisely. We explore the available methods for modulating this device systematically by changing the Fermi energy, the energy gap size, and the size of central gapless region. The current partition is also influenced by magnetic fields and the system size. Our results provide a microscopic depiction of the electronic transport properties around a unit cell of minimally twisted bilayer graphene and have far-reaching implications in the design of electron-beam splitters and interferometer devices.
The discovery of quantum Hall effect in two-dimensional (2D) electronic systems inspired the topological classifications of electronic systems1,2. By stacking 2D quantum Hall effects with interlayer coupling much weaker than the Landau level spacing,
quasi-2D quantum Hall effects have been experimentally observed3~7, due to the similar physical origin of the 2D counterpart. Recently, in a real 3D electronic gas system where the interlayer coupling is much stronger than the Landau level spacing, 3D quantum Hall effect has been observed in ZrTe58. In this Letter, we report the electronic transport features of its sister bulk material, i.e., HfTe5, under external magnetic field. We observe a series of plateaus in Hall resistance r{ho}xy as magnetic field increases until it reaches the quantum limit at 1~2 Tesla. At the plateau regions, the longitudinal resistance r{ho}xx exhibits local minima. Although r{ho}xx is still nonzero, its value becomes much smaller than r{ho}xy at the last few plateaus. By mapping the Fermi surface via measuring the Shubonikov-de Haas oscillation, we find that the strength of Hall plateau is proportional to the Fermi wavelength, suggesting that its formation may be attributed to the gap opening from the interaction driven Fermi surface instability. By comparing the bulk band structures of ZrTe5 and HfTe5, we find that there exists an extra pocket near the Fermi level of HfTe5, which may lead to the finite but nonzero longitudinal conductance.
We numerically investigate the electronic transport properties between two mesoscopic graphene disks with a twist by employing the density functional theory coupled with non-equilibrium Greens function technique. By attaching two graphene leads to up
per and lower graphene layers separately, we explore systematically the dependence of electronic transport on the twist angle, Fermi energy, system size, layer stacking order and twist axis. When choose different twist axes for either AA- or AB-stacked bilayer graphene, we find that the dependence of conductance on twist angle displays qualitatively distinction, i.e., the systems with top axis exhibit finite conductance oscillating as a function of the twist angle, while the ones with hollow axis exhibit nearly vanishing conductance for different twist angles or Fermi energies near the charge neutrality point. These findings suggest that the choice of twist axis can effectively tune the interlayer conductance, making it a crucial factor in designing of nanodevices with the twisted van der Waals multilayers.
Symmetry, dimensionality, and interaction are crucial ingredients for phase transitions and quantum states of matter. As a prominent example, the integer quantum Hall effect (QHE) represents a topological phase generally regarded as characteristic fo
r two-dimensional (2D) electronic systems, and its many aspects can be understood without invoking electron-electron interaction. The intriguing possibility of generalizing QHE to three-dimensional (3D) systems was proposed decades ago, yet it remains elusive experimentally. Here, we report clear experimental evidence for the 3D QHE observed in bulk ZrTe5 crystals. Owing to the extremely high sample quality, the extreme quantum limit with only the lowest Landau level occupied can be achieved by an applied magnetic field as low as 1.5 T. Remarkably, in this regime, we observe a dissipationless longitudinal resistivity rho_xx=0 accompanied with a well-developed Hall resistivity plateau rho_xy=(1pm0.1) h/e^2 (lambda_(F,z)/2), where lambda_(F,z) is the Fermi wavelength along the field direction (z axis). This striking result strongly suggests a Fermi surface instability driven by the enhanced interaction effects in the extreme quantum limit. In addition, with further increasing magnetic field, both rho_xx and rho_xy increase dramatically and display an interesting metal-insulator transition, representing another magnetic field driven quantum phase transition. Our findings not only unambiguously reveal a novel quantum state of matter resulting from an intricate interplay among dimensionality, interaction, and symmetry breaking, but also provide a promising platform for further exploration of more exotic quantum phases and transitions in 3D systems.
