A remarkable recent experiment has observed Mott insulator and proximate superconductor phases in twisted bilayer graphene when electrons partly fill a nearly flat mini-band that arises a `magic' twist angle. However, the nature of the Mott insulator, origin of superconductivity and an effective low energy model remain to be determined. We propose a Mott insulator with intervalley coherence that spontaneously breaks U(1) valley symmetry, and describe a mechanism that selects this order over the competing magnetically ordered states favored by the Hunds coupling. We also identify symmetry related features of the nearly flat band that are key to understanding the strong correlation physics and constrain any tight binding description. First, although the charge density is concentrated on the triangular lattice sites of the moir$\\text{e }$ pattern, the Wannier states of the tight-binding model must be centered on different sites which form a honeycomb lattice. Next, spatially localizing electrons derived from the nearly flat band necessarily breaks valley and other symmetries within any mean-field treatment, which is suggestive of a valley-ordered Mott state, and also dictates that additional symmetry breaking is present to remove symmetry-enforced band contacts. Tight-binding models describing the nearly flat mini-band are derived, which highlight the importance of further neighbor hopping and interactions. We discuss consequences of this picture for superconducting states obtained on doping the valley ordered Mott insulator. We show how important features of the experimental phenomenology may be explained and suggest a number of further experiments for the future. We also describe a model for correlated states in trilayer graphene heterostructures and contrast it with the bilayer case.

Origin of Mott Insulating Behavior and Superconductivity in Twisted Bilayer Graphene

The recently discovered family of vanadium-based kagome metals with topological band structures offer a new opportunity to study frustrated, correlated and topological quantum states. These layered compounds are nonmagnetic and undergo charge density wave (CDW) transitions before developing superconductivity at low temperatures. Here we report the observation of unconventional superconductivity and pair density wave (PDW) in the vanadium-based kagome lattice CsV3Sb5 using scanning tunneling microscope/spectroscopy (STM/STS) and Josephson STS. The differential conductance exhibits a V-shaped pairing gap about 0.5 meV below a transition temperature Tc about 2.3 K. Superconducting phase coherence is observed by Josephson effect and Cooper-pair tunneling to a superconducting tip. We find that CsV3Sb5 is a strong-coupling superconductor (2delta/kBTc about 5) and coexists with 4a0 unidirectional and 2x2 charge order. Remarkably, we discover a 4a0/3 bidirectional PDW accompanied by spatial modulations of the coherence peak and gap-depth in the tunneling conductance. We term the latter as a roton-PDW that can produce a commensurate vortex-antivortex lattice to account for the observed conductance modulations. Above Tc, we observe long-range ordered 4a0 unidirectional and 2a0 bidirectional CDW and a large V-shaped pseudogap in the density of state. Electron-phonon calculations attribute the 2x2 CDW to phonon softening induced structural reconstruction, but the phonon mediated pairing cannot describe the observed strong-coupling superconductor. Our findings show that electron correlations in the charge sector can drive the 4a0 unidirectional CDW, unconventional superconductivity, and roton-PDW with striking analogies to the phenomenology of cuprate high-Tc superconductors, and provide the groundwork for understanding their microscopic origins in the vanadium-based kagome superconductors.

Roton pair density wave and unconventional strong-coupling superconductivity in a topological kagome metal

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

The light of carbon dots: From mechanism to applications

Charge-density-wave-driven electronic nematicity in a kagome superconductor

Kagome metals $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A=\mathrm{K}$, Rb, and Cs) exhibit intriguing superconductivity below $0.9\ensuremath{\sim}2.5\text{ }\text{ }\mathrm{K}$, a charge density wave (CDW) transition around $80\ensuremath{\sim}100\text{ }\text{ }\mathrm{K}$, and ${\mathbb{Z}}_{2}$ topological surface states. The nature of the CDW phase and its relation to superconductivity remains elusive. In this work, we investigate the electronic and structural properties of CDW by first-principles calculations. We reveal an inverse Star of David deformation as the $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2$ CDW ground state of the kagome lattice. The kagome lattice shows softening breathing-phonon modes, indicating the structural instability. However, electrons play an essential role in the CDW transition via Fermi surface nesting and van Hove singularity. The inverse Star of David structure agrees with recent experiments by scanning tunneling microscopy (STM). The CDW phase inherits the nontrivial ${\mathbb{Z}}_{2}$-type topological band structure. Further, we find that the electron-phonon coupling is too weak to account for the superconductivity ${T}_{c}$ in all three materials. It implies the existence of unconventional pairing of these kagome metals. Our results provide essential knowledge toward understanding the superconductivity and topology in kagome metals.

Charge Density Waves and Electronic Properties of Superconducting Kagome Metals.

Topological aspects of the geometry of DNA and similar chiral molecules have received a lot of attention, but the topology of their electronic structure is less explored. Previous experiments revealed that DNA can efficiently filter spin-polarized electrons between metal contacts, a process called chiral-induced spin selectivity. However, the underlying correlation between chiral structure and electronic spin remains elusive. In this work, we reveal an orbital texture in the band structure, a topological characteristic induced by the chirality. We found that this orbital texture enables the chiral molecule to polarize the quantum orbital. This orbital polarization effect (OPE) induces spin polarization assisted by the spin–orbit interaction of a metal contact and leads to magnetoresistance and chiral separation. The orbital angular momentum of photoelectrons also plays an essential role in related photoemission experiments. Beyond chiral-induced spin selectivity, we predict that the orbital polarization effect could induce spin-selective phenomena even in achiral but inversion-breaking materials. An orbital polarization effect is proposed to understand chiral-induced spin selectivity.

Chirality-driven topological electronic structure of DNA-like materials.

Summary Twisted bilayer graphene (TBG) exhibits fascinating correlation-driven phenomena like the superconductivity and Mott insulating state, with flat bands and a chiral lattice structure. We find by quantum-transport calculations that the chirality leads to a giant unidirectional magnetoresistance (UMR) in TBG, where the unidirectionality refers to the resistance change under the reversal of the direction of current or magnetic field. We point out that flat bands significantly enhance this effect. The UMR increases quickly upon reducing the twist angle, and reaches about 20% for an angle of 1.5° in a 10 T in-plane magnetic field. We propose the band structure topology (asymmetry), which leads to a direction-sensitive mean free path, as a useful way to anticipate the UMR effect. The UMR provides a probe for chirality and band flatness in the twisted bilayers.

Chirality-Induced Giant Unidirectional Magnetoresistance in Twisted Bilayer Graphene

The intrinsic orbital Hall effect (OHE), the orbital counterpart of the spin Hall effect, was predicted and studied theoretically for more than one decade, yet to be observed in experiments. Here we propose a strategy to convert the orbital current in OHE to the spin current via the spin-orbit coupling from the contact. Furthermore, we find that OHE can induce large nonreciprocal magnetoresistance when employing magnetic contact. Both the generated spin current and the orbital Hall magnetoresistance can be applied to probe the OHE in experiments and design orbitronic devices.

Detection of the Orbital Hall Effect by the Orbital-Spin Conversion

In the anomalous Hall effect (AHE), the magnetization, electric field, and Hall current are presumed to be mutually vertical to each other. In this paper, we propose an unconventional AHE where the magnetization, electric field, and Hall current stay inside the same plane. Such an AHE is odd under time reversal and exists even when the magnetization is parallel to the electric field or Hall current, different from the planar Hall effect which is even under time reversal. Here, we term it parallel anomalous Hall effect (PAHE). We reveal that the PAHE exists when all the point group rotational and reflection symmetries are broken where the Berry curvature field is not necessarily parallel to the magnetization axis. We further demonstrate the PAHE in a ferrimagnetic Weyl semimetal ${\mathrm{FeCr}}_{2}{\mathrm{Te}}_{4}$.

Yizhou Liu

Papers

Charge Density Waves and Electronic Properties of Superconducting Kagome Metals.

Chirality-driven topological electronic structure of DNA-like materials.

Chirality-Induced Giant Unidirectional Magnetoresistance in Twisted Bilayer Graphene

Detection of the Orbital Hall Effect by the Orbital-Spin Conversion

Unconventional anomalous Hall effect from magnetization parallel to the electric field