pseudo-Landau Level Research Articles

Impurity effects on the zeroth pseudo-Landau level in twisted bilayer graphene

We theoretically study the impurity effects on the zeroth pseudo-Landau level (PLL) representation of the flat band in a twisted bilayer graphene (TBG) system. Our research investigates the impact of both short-range and long-range charged impurities on the PLL using the self-consistent Born approximation and random phase approximation. Our findings indicate that short-range impurities have a significant effect on the broadening of the flat band due to impurity scattering. In contrast, the impact of long-range charged impurities on the broadening of the flat band is relatively weak, and the primary impact of the Coulomb interaction is the splitting of the PLL degeneracy when a certain purity condition is satisfied. As a result, spontaneous ferromagnetic flat bands with nonzero Chern numbers emerge. Our work sheds light on the effect of impurities on the quantum Hall plateau transition in TBG systems.

Moiré disorder effect in twisted bilayer graphene

We theoretically study the electronic structure of magic-angle twisted bilayer graphene with disordered moir\'e patterns. By using an extended continuum model incorporating non-uniform lattice distortion, we find that the local density of states of the flat band is hardly broadened, but splits into upper and lower subbands in most places. The spatial dependence of the splitting energy is almost exclusively determined by the local value of the effective vector potential induced by heterostrain, whereas the variation of local twist angle and local moir\'e period give relatively minor effects on the electronic structure. We explain the exclusive dependence on the local vector potential by a pseudo Landau level picture for the magic-angle flat band, and we obtain an analytic expression of the splitting energy as a function of the strain amplitude.

Correlations in the elastic Landau level of spontaneously buckled graphene

Electronic correlations stemming from nearly flat bands in van der Waals materials have demonstrated to be a powerful playground to engineer artificial quantum matter, including superconductors, correlated insulators and topological matter. This phenomenology has been experimentally observed in a variety of twisted van der Waals materials, such as graphene and dichalcogenide multilayers. Here we show that spontaneously buckled graphene can yield a correlated state, emerging from an elastic pseudo Landau level. Our results build on top of recent experimental findings reporting that, when placed on top of hBN or NbSe2 substrates, wrinkled graphene sheets relax forming a periodic, long-range buckling pattern. The low-energy physics can be accurately described by electrons in the presence of a pseudo-axial gauge field, leading to the formation of sublattice-polarized Landau levels. Moreover, we verify that the high density of states at the zeroth Landau level leads to the formation of a periodically modulated ferrimagnetic groundstate, which can be controlled by the application of external electric fields. Our results indicate that periodically strained graphene is a versatile platform to explore emergent electronic states arising from correlated elastic Landau levels.

Observation of supersymmetric pseudo-Landau levels in strained microwave graphene

Using an array of coupled microwave resonators arranged in a deformed honeycomb lattice, we experimentally observe the formation of pseudo-Landau levels in the whole crossover from vanishing to large pseudomagnetic field strengths. This result is achieved by utilising an adaptable setup in a geometry that is compatible with the pseudo-Landau levels at all field strengths. The adopted approach enables us to observe the fully formed flat-band pseudo-Landau levels spectrally as sharp peaks in the photonic density of states and image the associated wavefunctions spatially, where we provide clear evidence for a characteristic nodal structure reflecting the previously elusive supersymmetry in the underlying low-energy theory. In particular, we resolve the full sublattice polarisation of the anomalous 0th pseudo-Landau level, which reveals a deep connection to zigzag edge states in the unstrained case.

Superconductivity in Weyl semimetals in a strong pseudomagnetic field

The superconducting s-wave state in Weyl semimetals in a strong strain-induced pseudomagnetic field is investigated in a model with local four-fermion interaction. It is found that only the inter-node pairing is possible in the lowest pseudo-Landau level approximation. Unlike the case of the lowest Landau level in a conventional magnetic field, the corresponding gap equation has only a trivial solution. Nevertheless, superconductivity can be induced via the proximity effect with a usual s-wave spin-singlet superconductor. Since a pseudomagnetic field is present necessarily at the surface of a Weyl semimetal, the proximity effect is strongly affected by the pseudomagnetic field. The analysis of such an effect showed that while no gap is opened in the spectrum, the degeneracy of energy levels is lifted. The unique character of the proximity effect in Weyl semimetals can be probed via the density of states, the spectral function, and the tunneling current. The density of states does not vanish at small energies and scales linearly with the pseudomagnetic field strength. This scaling is manifested also in the tunneling current.

Graphene Acoustic Phonon-Mediated Pseudo-Landau Levels Tailoring Probed by Scanning Tunneling Spectroscopy.

Graphene has attracted great interests in various areas including optoelectronics, spintronics, and nanomechanics due to its unique electronic structure, a linear dispersion with a zero bandgap around the Dirac point. Shifts of Dirac cones in graphene creates pseudo-magnetic field, which generates an energy gap and brings a zero-magnetic-field analogue of the quantum Hall effect. Recent studies have demonstrated that graphene pseudo-magnetic effects can be generated by vacancy defects, atom adsorption, zigzag or armchair edges, and external strain. Here, a larger than 100 T pseudo-magnetic field is reported that generated on the step area of graphene; and with the ultrahigh vacuum scanning tunneling microscopy, the observed Landau levels can be effectively tailored by graphene phonons. The zero pseudo-Landau level is suppressed due to the phonon-mediated inelastic tunneling, and this is observed by the scanning tunneling spectroscopy spectrum and confirmed by the Vienna ab initio simulation package calculation, where graphene phonons modulate the flow of tunneling electrons and further mediate pseudo-Landau levels. These observations demonstrate a viable approach for the control of pseudo-Landau levels, which tailors the electronic structure of graphene, and further ignites applications in graphene valley electronics.

Pseudo Landau level representation of twisted bilayer graphene: Band topology and implications on the correlated insulating phase

We propose that the electronic structure of twisted bilayer graphene (TBG) can be understood as Dirac fermions coupled with opposite pseudo magnetic fields generated by the moir\'e pattern. The two low-energy flat bands from each monolayer valley originate from the two zeroth pseudo Landau levels of Dirac fermions under such opposite effective magnetic fields, which have opposite sublattice polarizations and carry opposite Chern numbers $\pm1$, giving rise to helical edge states in the gaps below and above the low-energy bulk bands near the first magic angle. We argue that small Coulomb interactions would split the eight-fold degeneracy (including valley and physical spin) of these zeroth pseudo Landau levels, and may lead to insulating phases with non-vanishing Chern numbers at integer fillings. Besides, we show that all the high-energy bands below or above the flat bands are also topologically nontrivial in the sense that for each valley the sum of their Berry phases is quantized as $\pm\pi$. Such quantized Berry phases give rise to nearly flat edge states, which are dependent on truncations on the moir\'e length scale. Our work provides a complete and clear picture for the electronic structure and topological properties of TBG, and has significant implications on the natrue of the correlated insulating phase observed in experiments.

Origin of Room-Temperature Ferromagnetism in Hydrogenated Epitaxial Graphene on Silicon Carbide.

The discovery of room-temperature ferromagnetism of hydrogenated epitaxial graphene on silicon carbide challenges for a fundamental understanding of this long-range phenomenon. Carbon allotropes with their dispersive electron states at the Fermi level and a small spin-orbit coupling are not an obvious candidate for ferromagnetism. Here we show that the origin of ferromagnetism in hydrogenated epitaxial graphene with a relatively high Curie temperature (>300 K) lies in the formation of curved specific carbon site regions in the graphene layer, induced by the underlying Si-dangling bonds and by the hydrogen bonding. Hydrogen adsorption is therefore more favourable at only one sublattice site, resulting in a localized state at the Fermi energy that can be attributed to a pseudo-Landau level splitting. This n = 0 level forms a spin-polarized narrow band at the Fermi energy leading to a high Curie temperature and larger magnetic moment can be achieved due to the presence of Si dangling bonds underneath the hydrogenated graphene layer.

Inhomogeneous Weyl and Dirac Semimetals: Transport in Axial Magnetic Fields and Fermi Arc Surface States from Pseudo-Landau Levels

Topological Dirac and Weyl semimetals have an energy spectrum that hosts Weyl nodes appearing in pairs of opposite chirality. Topological stability is ensured when the nodes are separated in momentum space and unique spectral and transport properties follow. In this work we study the effect of a space dependent Weyl node separation, which we interpret as an emergent background axial vector potential, on the electromagnetic response and the energy spectrum of Weyl and Dirac semimetals. This situation can arise in the solid state either from inhomogeneous strain or non-uniform magnetization and can also be engineered in cold-atomic systems. Using a semiclassical approach we show that the resulting axial magnetic field $\mathbf{B}_{5}$ is observable through an enhancement of the conductivity as $\sigma\sim \mathbf{B}_{5} ^{2}$ due to an underlying chiral pseudo magnetic effect. We then use two lattice models to analyze the effect of $\mathbf{B}_5$ on the spectral properties of topological semimetals. We describe the emergent pseudo-Landau level structure for different spatial profiles of $\mathbf{B}_5$, revealing that (i) the celebrated surface states of Weyl semimetals, the Fermi arcs, can be reinterpreted as $n=0$ pseudo-Landau levels resulting from a $\mathbf{B}_5$ confined to the surface (ii) as a consequence of position-momentum locking a bulk $\mathbf{B}_5$ creates pseudo-Landau levels interpolating in real space between Fermi arcs at opposite surfaces and (iii) there are equilibrium bound currents proportional to $\mathbf{B}_{5}$ that average to zero over the sample, which are the analogs of bound currents in magnetic materials. We conclude by discussing how our findings can be probed experimentally.

Bubbles in graphene - a computational study

Strain-induced deformations in graphene are predicted to give rise to large pseudomagnetic fields. We examine theoretically the case of gas-inflated bubbles to determine whether signatures of such fields are present in the local density of states. Sharp-edged bubbles are found to induce Friedel-type oscillations which can envelope pseudo-Landau level features in certain regions of the bubble. However, bubbles which minimise interference effects are also unsuitable for pseudo-Landau level formation due to more spatially varying field profiles.

Strain-induced modifications of transport in gated graphene nanoribbons

We investigate the effects of homogeneous and inhomogeneous deformations and edge disorder on the conductance of gated graphene nanoribbons. Under increasing homogeneous strain the conductance of such devices initially decreases before it acquires a resonance structure and, finally, becomes completely suppressed at higher strain. Edge disorder induces mode mixing in the contact regions, which can restore the conductance to its ballistic value. The valley-antisymmetric pseudomagnetic field induced by inhomogeneous deformations leads to the formation of additional resonance states, which originate either from the coupling into Fabry-P\'erot states that extend through the system or from the formation of states that are localized near the contacts, where the pseudomagnetic field is largest. In particular, the $n=0$ pseudo-Landau level manifests itself via two groups of conductance resonances close to the charge neutrality point.

Non-AbelianSU(2)gauge fields through density wave order and strain in graphene

Spatially varying strain patterns can qualitatively alter the electronic properties of graphene, acting as effective valley-dependent magnetic fields and giving rise to pseudo-Landau-level (PLL) quantization. Here, we show that the strain-induced magnetic field is one component of a non-Abelian $SU(2)$ gauge field within the low-energy theory of graphene and identify the other two components as period-3 charge-density waves. We show that these density waves, if spatially varied, give rise to PLL quantization. We also argue that strain-induced magnetic fields can induce density-wave order in graphene, thus dynamically gapping out the lowest PLL; moreover, the ordering should generically be accompanied by dislocations. We discuss experimental signatures of these effects.

Superconducting proximity effect in graphene under inhomogeneous strain

The interplay between quantum Hall states and Cooper pairs is usually hindered by the suppression of the superconducting state due to the strong magnetic fields needed to observe the quantum Hall effect. From this point of view, graphene is special since it allows the creation of strong pseudomagnetic fields due to strain. We show that in a Josephson junction made of strained graphene, Cooper pairs will diffuse into the strained region. The pair correlation function will be sublattice polarized due to the polarization of the local density of states in the zero pseudo-Landau level. We uncover two regimes: (1) one in which the cyclotron radius is larger than the junction length, in which case the supercurrent will be enhanced, and (2) the long junction regime where the supercurrent is strongly suppressed because the junction becomes an insulator. In the latter case quantized Hall states form and Andreev scattering at the normal/superconducting interface will induce edge states. Our numerical calculation has become possible due to an extension of the Chebyshev-Bogoliubov--de Gennes method to computations on video cards (GPUs).