Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “twisted bilayer graphene”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

In-Plane Critical Magnetic Fields in Magic-Angle Twisted Trilayer Graphene

It has recently been shown that superconductivity in magic-angle twisted trilayer graphene survives to in-plane magnetic fields that are well in excess of the Pauli limit, and much stronger than the in-plane critical magnetic fields of magic-angle twisted bilayer graphene. The difference is surprising because twisted bilayers and trilayers both support the magic-angle flat bands thought to be the fountainhead of twisted graphene superconductivity. In this study, we show that the difference in critical magnetic fields can be traced to a C 2 M h symmetry in trilayers that survives in-plane magnetic fields, and also relative displacements between top and bottom layers that are not under experimental control at present. An gate electric field breaks the C 2 M h symmetry and therefore limits the in-plane critical magnetic field.

2-dimensional systems↗
DOE OSTI2022

Effect of superconductivity on the shape of flat bands

Abstract For the first time, basing both on experimental facts and our theoretical consideration, we show that Fermi systems with flat bands should be tuned with the superconducting state. Experimental measurements on magic-angle twisted bilayer graphene of the Fermi velocity V F as a function of the temperature T c of superconduction phase transition have revealed , where N s (0) is the density of states at the Fermi level. We show that the high- T c compounds exhibit the same behavior. Such observation is a challenge to theories of high- T c superconductivity, since V F is negatively correlated with T c , for . We show that the theoretical idea of forming flat bands in strongly correlated Fermi systems can explain this behavior and other experimental data collected on both and twisted bilayer graphene. Our findings place stringent constraints on theories describing the nature of high- T c superconductivity and the deformation of flat band by the superconducting phase transition.

Physics↗
DOE OSTI2021

Imaging orbital ferromagnetism in a moiré Chern insulator

Capturing exotic magnetism Ferromagnetism is associated with the breaking of time-reversal symmetry, most frequently by the spin degree of freedom. Although the orbital motion of electrons can also contribute to ferromagnetism, in most materials, it is small relative to the spin contribution. Tschirhart et al. showed that the reverse is true in an unusual magnetic state hosted by twisted bilayer graphene. Their scanning magnetometry measurements were consistent with ferromagnetism of predominantly orbital origin. Science , abd3190, this issue p. 1323

Science & Technology - Other Topics↗
DOE OSTI2024

Continuously tunable uniaxial strain control of van der Waals heterostructure devices

Uniaxial strain has been widely used as a powerful tool for investigating and controlling the properties of quantum materials. However, existing strain techniques have so far mostly been limited to use with bulk crystals. Although recent progress has been made in extending the application of strain to two-dimensional van der Waals (vdW) heterostructures, these techniques have been limited to optical characterization and extremely simple electrical device geometries. Here, we report a piezoelectric-based in situ uniaxial strain technique enabling simultaneous electrical transport and optical spectroscopy characterization of dual-gated vdW heterostructure devices. Critically, our technique remains compatible with vdW heterostructure devices of arbitrary complexity fabricated on conventional silicon/silicon dioxide wafer substrates. We demonstrate a large and continuously tunable strain of up to –0.15% at millikelvin temperatures, with larger strain values also likely achievable. We quantify the strain transmission from the silicon wafer to the vdW heterostructure, and further demonstrate the ability of strain to modify the electronic properties of twisted bilayer graphene. Our technique provides a highly versatile new method for exploring the effect of uniaxial strain on both the electrical and optical properties of vdW heterostructures and can be easily extended to include additional characterization techniques.

Electrical properties and parameters↗
DOE OSTI2022

$O(N)$ ab initio calculation scheme for large-scale moiré structures

Here we present a two-step method specifically tailored for band structure calculation of the small-angle moiré-pattern materials which contain tens of thousands of atoms in a unit cell. In the first step, the self-consistent field calculation for the ground state is performed with the O(N) Krylov subspace method implemented in openmx. Second, the crystal momentum-dependent Bloch Hamiltonian and overlap matrix are constructed from the results obtained in the first step and only a small number of eigenvalues near the Fermi energy are solved with shift-invert and Lanczos techniques. By systematically tuning two key parameters, the cutoff radius for electron hopping interaction and the dimension of the Krylov subspace, we obtained the band structures for both rigid and corrugated twisted bilayer graphene structures down to the first magic angle (θ = 1.08°) with high enough accuracy at affordable costs. The band structures are in good agreement with those from tight-binding models, continuum models, plane-wave pseudopotential based ab initio calculations, and experimental observations. This method is also shown to be efficient in twisted double-bilayer graphene and bilayer WSe 2 . We think this two-step method can play a crucial role in other twisted two-dimensional materials, especially those with much more complex band structure and where the effective model is hard to construct.

36 MATERIALS SCIENCE↗
DOE OSTI2021

WKB Estimate of Bilayer Graphene’s Magic Twist Angles

We report that graphene bilayers exhibit zero-energy flatbands at a discrete series of magic twist angles. In the absence of intrasublattice interlayer hopping, zero-energy states satisfy a Dirac equation with a non-Abelian SU(2) gauge potential that cannot be diagonalized globally. We develop a semiclassical WKB approximation scheme for this Dirac equation by introducing a dimensionless Planck’s 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 wave functions. We find zero-energy solutions at a discrete set of values of the dimensionless Planck’s constant, which we obtain analytically. Our analytic flatband twist angles correspond closely to those determined numerically in previous work.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Electrodynamics of Thin Sheets of Twisted Material

We construct a minimal theory describing the optical activity of a thin sheet of a twisted material, the simplest example of which is twisted bilayer graphene. We introduce the notion of "twisted electrical conductivity", which parametrizes the parity-odd response of a thin film to a perpendicularly falling electromagnetic waves with wavelength larger than the thickness of the sheet. Here, we show that the low-frequency Faraday rotation angle has different behaviors in different phases. For an insulator, the Faraday angle behaves as ω 2 at low frequencies, with the coefficient being determined by the linear relationship between a component of the electric quadrupole moment and the external electric field. For superconductors, the Faraday rotation angle is constant when the frequency of the incoming EM waves is below the superconducting gap and is determined by the coefficient of the Lifshitz invariant in the Ginzburg-Landau functional describing the superconducting state. In the metallic state, we show that the twisted conductivity is proportional to the "magnetic helicity" (scalar product of the velocity and the magnetic moment) of the quasiparticle, averaged around the Fermi surface. The theory is general and is applicable to strongly correlated phases.

Son, Dam Thanh↗
DOE OSTI2020

Ground State and Hidden Symmetry of Magic-Angle Graphene at Even Integer Filling

In magic angle twisted bilayer graphene (TBG), electron-electron interactions play a central role, resulting in correlated insulating states at certain integer fillings. Identifying the nature of these insulators is a central question, and it is potentially linked to the relatively high-temperature superconductivity observed in the same devices. Here, we address this question using a combination of analytical strong-coupling arguments and a comprehensive Hartree-Fock numerical calculation, which includes the effect of remote bands. The ground state we obtain at charge neutrality is an unusual ordered state, which we call the Kramers intervalley-coherent (K-IVC) insulator. In its simplest form, the K-IVC order exhibits a pattern of alternating circulating currents that triples the graphene unit cell, leading to an “orbital magnetization density wave.” Although translation and time-reversal symmetry are broken, a combined “Kramers” time-reversal symmetry is preserved. Our analytic arguments are built on first identifying an approximate U⁡(4) × U⁡(4) symmetry, resulting from the remarkable properties of the TBG band structure, which helps select a low-energy manifold of states that are further split to favor the K-IVC state. This low-energy manifold is also found in the Hartree-Fock numerical calculation. We show that symmetry-lowering perturbations can stabilize other insulators and the semimetallic state, and we discuss the ground state at half-filling and give a comparison with experiments.

Bultinck, Nick↗
DOE OSTI2024

Superconductivity in a topological lattice model with strong repulsion

The highly tunable nature of synthetic quantum materials-both in the solid-state and cold atom contexts-invites examining which microscopic ingredients aid in the realization of correlated phases of matter such as superconductors. Recent experimental advances in moiré materials suggest that unifying the features of the Fermi-Hubbard model and quantum Hall systems creates a fertile ground for the emergence of such phases. Here, we introduce the "double Hofstadter"model, a minimal 2D lattice model that incorporates exactly these features: Time-reversal symmetry, band topology, and strong repulsive interactions. By using infinite cylinder density matrix renormalization group methods (cylinder iDMRG), we investigate the ground state phase diagram of this model. We find that it hosts an interaction-induced quantum spin Hall insulator and demonstrate that weakly hole-doping this state gives rise to a superconductor at a finite circumference, with indications that this behavior persists on larger cylinders. Further, at the aforementioned circumference, the superconducting phase is surprisingly robust to perturbations including additional repulsive interactions in the pairing channel. By developing a technique to probe the superconducting gap function in iDMRG, we phenomenologically characterize the superconductor. Namely, we demonstrate that it is formed from the weak pairing of holes atop the quantum spin Hall insulator. Furthermore, we determine the pairing symmetry of the superconductor, finding it to be p-wave-reminiscent of the unconventional superconductivity reported in experiments on twisted bilayer graphene (TBG). Motivated by this, we elucidate structural similarities and differences between our model and those of TBG in its chiral limit. Finally, to provide a more direct experimental realization, we detail an implementation of our Hamiltonian in a system of cold fermionic alkaline-earth atoms in an optical lattice.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Quantum-Well Bound States in Graphene Heterostructure Interfaces

We present experimental evidence of electronic and optical interlayer resonances in graphene van der Waals heterostructure interfaces. Using the spectroscopic mode of a low-energy electron microscope (LEEM), we characterized these interlayer resonant states up to 10 eV above the vacuum level. Compared with nontwisted, AB-stacked bilayer graphene (AB BLG), an ≈ 0.2 Å increase was found in the interlayer spacing of 30° twisted bilayer graphene (30°-tBLG). In addition, we used Raman spectroscopy to probe the inelastic light-matter interactions. A unique type of Fano resonance was found around the D and G modes of the graphene lattice vibrations. This anomalous, robust Fano resonance is a direct result of quantum confinement and the interplay between discrete phonon states and the excitonic continuum.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Exact Ground State of Interacting Electrons in Magic Angle Graphene

One of the most remarkable theoretical findings in magic angle twisted bilayer graphene (TBG) is the emergence of ferromagnetic Slater determinants as exact ground states for the interacting Hamiltonian at the chiral limit. This discovery provides an explanation for the correlated insulating phase which has been experimentally observed at half filling. This work is the first mathematical study of interacting models in magic angle graphene systems. These include not only TBG but also TBG-like systems featuring four flat bands per valley, and twisted trilayer graphene systems with equal twist angles. We identify symmetries of the chiral limit of the Bistritzer-MacDonald Hamiltonian that are responsible for characterizing the Hartree-Fock ground states as zero energy many-body ground states. Furthermore, for a general class of Hamiltonian, we establish criteria that the ferromagnetic Slater determinants are the unique ground states within the class of uniformly half-filled, translation invariant Slater determinants. We then demonstrate that these criteria can be explicitly verified for TBG and TBG-like systems at the chiral limit, using properties of Jacobi-θ$${\theta }$$ and Weierstrass-℘$${\wp }$$ functions.

Becker, Simon↗
DOE OSTI2021

Twisted symmetric trilayer graphene. II. Projected Hartree-Fock study

The Hamiltonian of the magic-angle twisted symmetric trilayer graphene (TSTG) can be decomposed into a twisted-bilayer-graphene- (TBG-) like flat band Hamiltonian and a high-velocity Dirac fermion Hamiltonian. We use Hartree-Fock mean field approach to study the projected Coulomb interacting Hamiltonian of TSTG developed in Calugaru et al. [Phys. Rev. B 103, 195411 (2021)] at integer fillings ν = -3, -2, -1, and 0 measured from charge neutrality. We study the phase diagram with w 0 /w 1 , the ratio of AA and AB interlayer hoppings, and the displacement field, which introduces an interlayer potential U and hybridizes the TBG-like bands with the Dirac bands. At small U, we find the ground states at all fillings ν are in the same phases as the tensor products of a Dirac semimetal with the filling ν TBG insulator ground states, which are spin-valley polarized at ν = -3, and fully (partially) intervalley coherent at ν = -2, 0(ν = -1) in the flat bands. An exception is ν = -3 with w 0 /w 1 ≳ 0.7 , which possibly becomes a metal with competing orders at small U due to charge transfers between the Dirac and flat bands. At strong U where the bandwidths exceed interactions, all the fillings ν enter a metal phase with small or zero valley polarization and intervalley coherence. Lastly, at intermediate U, semimetal or insulator phases with zero intervalley coherence may arise for ν = -2, -1, 0. Finally, our results provide a simple picture for the electron interactions in TSTG systems, and reveal the connection between the TSTG and TBG ground states.

2-dimensional systems↗
DOE OSTI2024

Uncovering the spin ordering in magic-angle graphene via edge state equilibration

Abstract The flat bands in magic-angle twisted bilayer graphene (MATBG) provide an especially rich arena to investigate interaction-driven ground states. While progress has been made in identifying the correlated insulators and their excitations at commensurate moiré filling factors, the spin-valley polarizations of the topological states that emerge at high magnetic field remain unknown. Here we introduce a technique based on twist-decoupled van der Waals layers that enables measurement of their electronic band structure and–by studying the backscattering between counter-propagating edge states–the determination of the relative spin polarization of their edge modes. We find that the symmetry-broken quantum Hall states that extend from the charge neutrality point in MATBG are spin unpolarized at even integer filling factors. The measurements also indicate that the correlated Chern insulator emerging from half filling of the flat valence band is spin unpolarized and suggest that its conduction band counterpart may be spin polarized.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Flat-band topology of magic angle graphene on a transition metal dichalcogenide

In this work, we consider twisted bilayer graphene on a transition metal dichalcogenide substrate, where proximity-induced spin-orbit coupling significantly alters the eight flat bands which occur near the magic angle. The resulting band structure features a pair of extremely flat bands across most of the mini-Brillouin zone. Further details depend sensitively on the symmetries of the heterostructure; we find semiconducting band structures when all twofold rotations around the in-plane axis are broken, and semimetallic band structures otherwise. We calculate the Chern numbers of the different isolated bands, and identify the parameter regimes and filling factors where valley Chern insulators and topological insulators are realized. Interestingly, we find that for realistic values of the proximity-induced terms, it is possible to realize a topological insulator protected by time-reversal symmetry by doping two holes or two electrons per superlattice unit cell into the system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗