Topologically Nontrivial Valley States in Bilayer Graphene Quantum Point Contacts

High-Mobility Compensated Semimetals, Orbital Magnetization, and Umklapp Scattering in Bilayer Graphene Moiré Superlattices

Twist-controlled moiré superlattices (MSs) have emerged as a versatile platform for realizing artificial systems with complex electronic spectra. The combination of Bernal-stacked bilayer graphene (BLG) and hexagonal boron nitride (hBN) can give rise to an interesting MS, which has recently featured a set of unexpected behaviors, such as unconventional ferroelectricity and the electronic ratchet effect. Yet, the understanding of the electronic properties of BLG/hBN MS has, at present, remained fairly limited. Here, we combine magneto-transport and low-energy sub-THz excitation to gain insights into the properties of this MS. We demonstrate that the alignment between BLG and hBN crystal lattices results in the emergence of compensated semimetals at some integer fillings of the moiré bands, separated by van Hove singularities where the Lifshitz transition occurs. A particularly pronounced semimetal develops when eight holes reside in the moiré unit cell, where coexisting high-mobility electron and hole systems feature strong magnetoresistance reaching 2350% already at B = 0.25 T. Next, by measuring the THz-driven Nernst effect in remote bands, we observe valley splitting, indicating an orbital magnetization characterized by a strongly enhanced effective gv-factor of 340. Finally, using THz photoresistance measurements, we show that the high-temperature conductivity of the BLG/hBN MS is limited by electron-electron umklapp processes. Our multifaceted analysis introduces THz-driven magnetotransport as a convenient tool to probe the band structure and interaction effects in van der Waals materials and provides a comprehensive understanding of the BLG/hBN MS.

Tunneling Valley Hall Effect Driven by Tilted Dirac Fermions

Valleytronics is a research field utilizing a valley degree of freedom of electrons for information processing and storage. A strong valley polarization is critical for realistic valleytronic applications. Here, we predict a tunneling valley Hall effect (TVHE) driven by tilted Dirac fermions in all-in-one tunnel junctions based on a two-dimensional (2D) valley material. Different doping of the electrode and spacer regions in these tunnel junctions results in momentum filtering of the tunneling Dirac fermions, generating a strong transverse valley Hall current dependent on the Dirac-cone tilting. Using the parameters of an existing 2D valley material, we demonstrate that such a strong TVHE can host a giant valley Hall angle even in the absence of the Berry curvature. Finally, we predict that resonant tunneling can occur in a tunnel junction with properly engineered device parameters such as the spacer width and transport direction, providing significant enhancement of the valley Hall angle. Our work opens a new approach to generate valley polarization in realistic valleytronic systems.

Electrostatic Tuning of Bilayer Graphene Edge Modes

We study the effect of a local potential shift induced by a side electrode on the edge modes at the boundary between gapped and ungapped bilayer graphene. A potential shift close to the gapped-ungapped boundary causes the emergence of unprotected edge modes, propagating in both directions along the boundary. These counterpropagating edge modes allow edge backscattering, as opposed to the case of valley-momentum-locked edge modes. We then calculate the conductance of a bilayer graphene wire in presence of finger-gate electrodes, finding strong asymmetries with energy inversion and deviations from conductance quantization that can be understood with the gate-induced unprotected edge modes.

Specular Electron Focusing between Gate-Defined Quantum Point Contacts in Bilayer Graphene

We report multiterminal measurements in a ballistic bilayer graphene (BLG) channel, where multiple spin- and valley-degenerate quantum point contacts (QPCs) are defined by electrostatic gating. By patterning QPCs of different shapes along different crystallographic directions, we study the effect of size quantization and trigonal warping on transverse electron focusing (TEF). Our TEF spectra show eight clear peaks with comparable amplitudes and weak signatures of quantum interference at the lowest temperature, indicating that reflections at the gate-defined edges are specular, and transport is phase coherent. The temperature dependence of the focusing signal shows that, despite the small gate-induced bandgaps in our sample (≲45 meV), several peaks are visible up to 100 K. The achievement of specular reflection, which is expected to preserve the pseudospin information of the electron jets, is promising for the realization of ballistic interconnects for new valleytronic devices.

Supercurrent and Phase Slips in a Ballistic Carbon Nanotube Bundle Embedded into a van der Waals Heterostructure

We demonstrate long-range superconducting correlations in a several-micrometers-long carbon nanotube bundle encapsulated in a van der Waals stack between hBN and NbSe₂. We show that a substantial supercurrent flows through the nanotube section beneath the NbSe₂ crystal as well as through the 2 μm long section not in contact with it. The large in-plane critical magnetic field of this supercurrent is an indication that even inside the carbon nanotube Cooper pairs enjoy a degree of paramagnetic protection typical of the parent Ising superconductor. As expected for superconductors of nanoscopic cross section, the current-induced breakdown of superconductivity is characterized by resistance steps due to the nucleation of phase slip centers. All elements of our hybrid device are active building blocks of several recently proposed setups for realization of Majorana fermions in carbon nanotubes.

Effective Landé factors for an electrostatically defined quantum point contact in silicene

The transconductance and effective Landé \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g^*$$\end{document}g∗ factors for a quantum point contact defined in silicene by the electric field of a split gate is investigated. The strong spin–orbit coupling in buckled silicene reduces the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g^*$$\end{document}g∗ factor for in-plane magnetic field from the nominal value 2 to around 1.2 for the first- to 0.45 for the third conduction subband. However, for perpendicular magnetic field we observe an enhancement of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g^*$$\end{document}g∗ factors for the first subband to 5.8 in nanoribbon with zigzag and to 2.5 with armchair edge. The main contribution to the Zeeman splitting comes from the intrinsic spin–orbit coupling defined by the Kane–Mele form of interaction.

Control of Giant Topological Magnetic Moment and Valley Splitting in Trilayer Graphene

Bloch states of electrons in honeycomb two-dimensional crystals with multivalley band structure and broken inversion symmetry have orbital magnetic moments of a topological nature. In crystals with two degenerate valleys, a perpendicular magnetic field lifts the valley degeneracy via a Zeeman effect due to these magnetic moments, leading to magnetoelectric effects which can be leveraged for creating valleytronic devices. In this work, we demonstrate that trilayer graphene with Bernal stacking (ABA TLG), hosts topological magnetic moments with a large and widely tunable valley g factor (g_{ν}), reaching a value g_{ν}∼1050 at the extreme of the studied parametric range. The reported experiment consists in sublattice-resolved scanning tunneling spectroscopy under perpendicular electric and magnetic fields that control the TLG bands. The tunneling spectra agree very well with the results of theoretical modeling that includes the full details of the TLG tight-binding model and accounts for a quantum-dot-like potential profile formed electrostatically under the scanning tunneling microscope tip.

Coherent Jetting from a Gate-Defined Channel in Bilayer Graphene

Graphene has evolved as a platform for quantum transport that can compete with the best and cleanest semiconductor systems. Here, we report on the observation of distinct electronic jets emanating from a narrow split-gate-defined channel in bilayer graphene. We find that these jets, which are visible via their interference patterns, occur predominantly with an angle of 60° between each other. This observation is related to the trigonal warping in the band structure of bilayer graphene, which, in conjunction with electron injection through a constriction, leads to a valley-dependent selection of momenta. This experimental observation of electron jetting has consequences for carrier transport in two-dimensional materials with a trigonally warped band structure in general, as well as for devices relying on ballistic and valley-selective transport.

Emergence of orbital angular moment at van Hove singularity in graphene/h-BN moiré superlattice

Bloch electrons lacking inversion symmetry exhibit orbital magnetic moments owing to the rotation around their center of mass; this moment induces a valley splitting in a magnetic field. For the graphene/h-BN moiré superlattice, inversion symmetry is broken by the h-BN. The superlattice potential generates a series of Dirac points (DPs) and van Hove singularities (vHSs) within an experimentally accessible low energy state, providing a platform to study orbital moments with respect to band structure. In this work, theoretical calculations and magnetothermoelectric measurements are combined to reveal the emergence of an orbital magnetic moment at vHSs in graphene/h-BN moiré superlattices. The thermoelectric signal for the vHS at the low energy side of the hole-side secondary DP exhibited significant magnetic field-induced valley splitting with an effective g-factor of approximately 130; splitting for other vHSs was negligible. This was attributed to the emergence of an orbital magnetic moment at the second vHS at the hole-side.

Observation of the Spin-Orbit Gap in Bilayer Graphene by One-Dimensional Ballistic Transport

We report on measurements of quantized conductance in gate-defined quantum point contacts in bilayer graphene that allow the observation of subband splittings due to spin-orbit coupling. The size of this splitting can be tuned from 40 to 80  μeV by the displacement field. We assign this gate-tunable subband splitting to a gap induced by spin-orbit coupling of Kane-Mele type, enhanced by proximity effects due to the substrate. We show that this spin-orbit coupling gives rise to a complex pattern in low perpendicular magnetic fields, increasing the Zeeman splitting in one valley and suppressing it in the other one. In addition, we observe a spin polarized channel of 6e^{2}/h at high in-plane magnetic field and signatures of interaction effects at the crossings of spin-split subbands of opposite spins at finite magnetic field.

Theory of valley-resolved spectroscopy of a Si triple quantum dot coupled to a microwave resonator

We theoretically study a silicon triple quantum dot (TQD) system coupled to a superconducting microwave resonator. The response signal of an injected probe signal can be used to extract information about the level structure by measuring the transmission and phase shift of the output field. This information can further be used to gain knowledge about the valley splittings and valley phases in the individual dots. Since relevant valley states are typically split by several [Formula: see text], a finite temperature or an applied external bias voltage is required to populate energetically excited states. The theoretical methods in this paper include a capacitor model to fit experimental charging energies, an extended Hubbard model to describe the tunneling dynamics, a rate equation model to find the occupation probabilities, and an input-output model to determine the response signal of the resonator.

Tunable Valley Splitting due to Topological Orbital Magnetic Moment in Bilayer Graphene Quantum Point Contacts

In multivalley semiconductors, the valley degree of freedom can be potentially used to store, manipulate, and read quantum information, but its control remains challenging. The valleys in bilayer graphene can be addressed by a perpendicular magnetic field which couples by the valley g factor g_{v}. However, control over g_{v} has not been demonstrated yet. We experimentally determine the energy spectrum of a quantum point contact realized by a suitable gate geometry in bilayer graphene. Using finite bias spectroscopy, we measure the energy scales arising from the lateral confinement as well as the Zeeman splitting and find a spin g factor g_{s}∼2. g_{v} can be tuned by a factor of 3 using vertical electric fields, g_{v}∼40-120. The results are quantitatively explained by a calculation considering topological magnetic moment and its dependence on confinement and the vertical displacement field.

Low-Magnetic-Field Regime of a Gate-Defined Constriction in High-Mobility Graphene

We report on the evolution of the coherent electronic transport through a gate-defined constriction in a high-mobility graphene device from ballistic transport to quantum Hall regime upon increasing the magnetic field. At a low field, the conductance exhibits Fabry-Pérot resonances resulting from the npn cavities formed beneath the top-gated regions. Above a critical field B* corresponding to the cyclotron radius equal to the npn cavity length, Fabry-Pérot resonances vanish, and snake trajectories are guided through the constriction with a characteristic set of conductance oscillations. Increasing further the magnetic field allows us to probe the Landau level spectrum in the constriction and unveil distortions due to the combination of confinement and deconfinement of Landau levels in a saddle potential. These observations are confirmed by numerical calculations.

Valley Subband Splitting in Bilayer Graphene Quantum Point Contacts

We report a study of one-dimensional subband splitting in a bilayer graphene quantum point contact in which quantized conductance in steps of 4e^{2}/h is clearly defined down to the lowest subband. While our source-drain bias spectroscopy measurements reveal an unconventional confinement, we observe a full lifting of the valley degeneracy at high magnetic fields perpendicular to the bilayer graphene plane for the first two lowest subbands where confinement and Coulomb interactions are the strongest and a peculiar merging or mixing of K and K^{'} valleys from two nonadjacent subbands with indices (N,N+2), which are well described by our semiphenomenological model.