The gap in bilayer graphene (BLG) can directly be controlled by a perpendicular electric field. By tuning the field through zero at a finite rate in neutral BLG, excited states are produced. Due to screening, the resulting dynamics is determined by coupled non-linear Landau-Zener models. The generated defect density agrees with Kibble-Zurek theory in the presence of subleading logarithmic corrections. After the quench, population inversion occurs for wavevectors close to the Dirac point. This could, at least in principle provide a coherent source of infra-red radiation with tunable spectral properties (frequency and broadening). Cold atoms with quadratic band crossing exhibit the same dynamics.
We introduce different types of quenches to probe the non-equilibrium dynamics and multiple collective modes of bilayer fractional quantum Hall states. We show that applying an electric field in one layer induces oscillations of a spin-1 degree of freedom, whose frequency matches the long-wavelength limit of the dipole mode. On the other hand, oscillations of the long-wavelength limit of the quadrupole mode, i.e., the spin-2 graviton, as well as the combination of two spin-1 states, can be activated by a sudden change of band mass anisotropy. We construct an effective field theory to describe …
This paper presents a mathematical and numerical analysis of the flatband wavefunctions occurring in the chiral model of twisted bilayer graphene at the "magic" twist angles. We show that the chiral model possesses an exact intra-valley inversion symmetry. Writing the flatband wavefunction as a product of a lowest Landau level quantum Hall state and a spinor, we show that the components of the spinor are anti-quantum Hall wavefunctions related by the inversion symmetry operation introduced here. We then show numerically that as one moves from the lowest to higher magic angles, the spinor compo…
In this paper a systematic examination of graphene/hexagonal boron nitride (g/hBN) bilayers is presented, through a recently developed two-dimensional phase field crystal model that incorporates out-of-plane deformations. The system parameters are determined by closely matching the stacking energies and heights of graphene/hBN bilayers to those obtained from existing quantum-mechanical density functional theory calculations. Out-of-plane deformations are shown to reduce the energies of inversion domain boundaries in hBN, and the coupling between graphene and hBN layers leads to a bilayer defec…
The gapless energy band spectra make the structures based on graphene and graphene bilayers with the population inversion created by optical or injection pumping to be promising media for the interband terahertz (THz) lasing. However, a strong intraband absorption at THz frequencies still poses a challenge for efficient THz lasing. In this paper, we show that in the pumped graphene bilayer structures, the indirect interband radiative transitions accompanied by scattering of carriers caused by disorder can provide a substantial negative contribution to the THz conductivity (together with the di…
The recent demonstration of saturable absorption and negative optical conductivity in the Terahertz range in graphene has opened up new opportunities for optoelectronic applications based on this and other low dimensional materials. Recently, population inversion across the Dirac point has been observed directly by time- and angle-resolved photoemission spectroscopy (tr-ARPES), revealing a relaxation time of only ~ 130 femtoseconds. This severely limits the applicability of single layer graphene to, for example, Terahertz light amplification. Here we use tr-ARPES to demonstrate long-lived popu…
Moiré materials have become one of the most active fields in material science in recent years due to their high tunability, and their unique properties emerge from the Moiré-scale structure modulation. Here, we propose twisted bilayer Bi$_2$(Te$_{1-x}$Se$_x$)$_3$ as a new Moiré material where the Moiré-scale modulation induces a topological phase transition. We show, in twisted bilayer Bi$_2$(Te$_{1-x}$Se$_x$)$_3$, a topological insulator domain and a normal insulator domain coexist in the Moiré lattice structure, and edge states on the domain boundary make nearly flat bands that dominate the …
Van Hove singularities (VHS's) in the density of states play an outstanding and diverse role for the electronic and thermodynamic properties of crystalline solids. At the critical point the Fermi surface connectivity changes and topological properties undergo a transition. Opportunities to systematically pass a VHS at the turn of a voltage knob and study its diverse impact are however rare. With the advent of van der Waals heterostructures, control over the atomic registry of neigbouring graphene layers offers an unprecedented tool to generate a low energy VHS easily accessible with convention…
We demonstrate pronounced electric-field-induced second-harmonic generation in naturally inversion symmetric 2H stacked bilayer MoS$_{2}$ embedded into microcapacitor devices. By applying strong external electric field perturbations ($|F| = \pm 2.6 MVcm^{-1}$) perpendicular to the basal plane of the crystal we control the inversion symmetry breaking and, hereby, tune the nonlinear conversion efficiency. Strong tunability of the nonlinear response is observed throughout the energy range ($E_ω \sim 1.25 eV - 1.47 eV$) probed by measuring the second-harmonic response at $E_{2ω}$, spectrally detun…
We show that the Wannier obstruction and the fragile topology of the nearly flat bands in twisted bilayer graphene at magic angle are manifestations of the nontrivial topology of two-dimensional real wave functions characterized by the Euler class. To prove this, we examine the generic band topology of two dimensional real fermions in systems with space-time inversion $I_{ST}$ symmetry. The Euler class is an integer topological invariant classifying real two band systems. We show that a two-band system with a nonzero Euler class cannot have an $I_{ST}$-symmetric Wannier representation. Moreove…
Valley pseudospin, the quantum degree of freedom characterizing the degenerate valleys in energy bands, is a distinct feature of two-dimensional Dirac materials. Similar to spin, the valley pseudospin is spanned by a time reversal pair of states, though the two valley pseudospin states transform to each other under spatial inversion. The breaking of inversion symmetry induces various valley-contrasted physical properties; for instance, valley-dependent topological transport is of both scientific and technological interests. Bilayer graphene (BLG) is a unique system whose intrinsic inversion sy…
Using the Büttiker-Landauer formulation of transport theory in the linear response regime, the valley currents and non-local resistances of bilayer graphene nanostructures with broken inversion symmetry are calculated. It is shown that broken inversion symmetry in bilayer graphene nanostructures leads to striking enhancement of the non-local 4-terminal resistance and to valley currents several times stronger than the conventional electric current when the Fermi energy is in the spectral gap close to the energy of Dirac point. The scaling relation between local and non-local resistances is inve…
We model the magnetic ratchet effect in bilayer graphene in which a dc electric current is produced by an ac electric field of frequency $ω$ in the presence of a steady in-plane magnetic field and inversion-symmetry breaking. In bilayer graphene, the ratchet effect is tunable by an external metallic gate which breaks inversion symmetry. For zero in-plane magnetic field, we show that trigonal warping and inversion-symmetry breaking are able to produce a large dc valley current, but not a non-zero total dc charge current. For the magnetic ratchet in a tilted magnetic field, the perpendicular fie…
We consider the orbital effect of an in-plane magnetic field on electrons in bilayer graphene, deriving linear-in-field contributions to the low-energy Hamiltonian arising from the presence of either skew interlayer coupling or interlayer potential asymmetry, the latter being tunable by an external metallic gate. To illustrate the relevance of such terms, we consider the ratchet effect in which a dc current results from the application of an alternating electric field in the presence of an in-plane magnetic field and inversion-symmetry breaking. By comparison with recent experimental observati…
Inversion symmetry in bilayer graphene allows for layered opposite Rashba spin-orbit coupling (LO-RSOC) -- the situation when the RSOC has the same magnitude but the opposite sign in two coupled spatially separated layers. We show that the LO-RSOC results in the loss of spin chirality in the momentum space, in contrast to the common uniform RSOC. This chirality loss makes it difficult to experimentally establish whether the LO-RSOC (on the scale of 10 meV) exists, because the band structure is insensitive to it. To solve this problem, we propose to identify the LO-RSOC either by gating to brea…
Atomically thin transition metal dichalcogenides (TMDs) possess coupling of spin and valley degrees of freedom, making them promising for spin-valleytronics. ln monolayer TMDs, the emission helicity is locked to the valleys as a consequence of spin-orbit coupling and inversion symmetry breaking, leading to a valley analog of Zeeman effect in presence of out-of-plane magnetic field. As inversion symmetry is recovered in bilayers, the emission helicity should no longer be locked to the valleys. Here we show that Zeeman splitting, however, still persists in bilayers, as a result of an additional …
Spin orbit coupling (SOC) is the key to realizing time-reversal invariant topological phases of matter. Famously, SOC was predicted by Kane and Mele to stabilize a quantum spin Hall insulator; however, the weak intrinsic SOC in monolayer graphene has precluded experimental observation. Here, we exploit a layer-selective proximity effect---achieved via van der Waals contact to a semiconducting transition metal dichalcogenide--to engineer Kane-Mele SOC in ultra-clean \textit{bilayer} graphene. Using high-resolution capacitance measurements to probe the bulk electronic compressibility, we find th…
We present a study of the nonlinear optical response of twisted bilayer graphene. We discuss the contribution of the Berry phase to the non-linearity when inversion symmetry is broken, thus underlining the interplay between band and real space geometry, and nonlinear response. We also highlight an effect which is characteristic of extreme nonlinear optics: the generation of harmonics in disguise. This effect emerges in twisted bilayer graphene at relatively moderate fields strengths because of the much reduced band width. Our findings contribute to the understanding of the link between geometr…
Unlike the conventional (linear) anomalous Nernst effect, the non-linear anomalous Nernst effect (NLANE) can survive in an inversion symmetry broken system even in the presence of time-reversal symmetry. Using semiclassical Boltzmann transport theory, we derive the general expression of the non-linear anomalous Nernst coefficient as the second-order response function to the applied temperature gradient. We find that the non-linear Nernst current, which flows perpendicular to the temperature gradient even in the absence of a magnetic field, arises due to the Berry curvature of the states near t…
Proximity effects resulting from depositing a graphene layer on a TMD substrate layer change the dynamics of the electronic states in graphene, inducing spin orbit coupling (SOC) and staggered potential effects. An effective Hamiltonian that describes different symmetry breaking terms in graphene, while preserving time reversal invariance, shows that an inverted mass band gap regime is possible. The competition of different perturbation terms causes a transition from an inverted mass phase to a staggered gap in the bilayer heterostructure, as seen in its phase diagram. A tight-binding calculat…
Graphene superlattices have recently been attracting growing interest as an emergent class of quantum metamaterials. In this paper, we report the observation of nonlocal transport in bilayer graphene (BLG) superlattices encapsulated between two hexagonal boron nitride (hBN) layers, which formed hBN/BLG/hBN moiré superlattices. We then employed these superlattices to detect a long-range charge-neutral valley current using an all-electrical method. The moiré superlattice with broken inversion symmetry leads to a hot spot with Berry curvature accumulating at the charge neutral point (CNP), and it…
In 1H monolayer transition metal dichalcogenide, the inversion symmetry is broken, while the reflection symmetry is maintained. On the contrary, in the bilayer, the inversion symmetry is restored, but the reflection symmetry is broken. As a consequence of these contrasting symmetries, here we show that bilayer WS$_2$ exhibits a quantum confined Stark effect (QCSE) that is linear with the applied out-of-plane electric field, in contrary to a quadratic one for a monolayer. The interplay between the unique layer degree of freedom in the bilayer and the field driven partial inter-conversion betwee…
We show that bilayer graphene exhibits magneto-electric effects that are formally similar to those commonly seen in band insulators with broken inversion and time-reversal symmetries. Three unusual features characterize the magneto-electric responses exhibited by bilayer graphene: (i) unlike most other magneto-electric media, bilayer graphene is a conductor, (ii) bilayer graphene has a non-quantized magneto-electric coupling even though its electronic structure does not break parity and time-reversal symmetry, and (iii) the magnitude of the magneto-electric coupling in bilayer graphene is dete…
Twisted bilayer graphene (tBLG) devices with ion gel gate dielectrics are studied using Raman spectroscopy in the twist angle regime where a resonantly enhanced G band can be observed. We observe prominent splitting and intensity quenching on the G Raman band when the carrier density is tuned away from charge neutrality. This G peak splitting is attributed to asymmetric charge doping in the two graphene layers, which reveals individual phonon self-energy renormalization of the two weakly-coupled layers of graphene. We estimate the effective interlayer capacitance at low doping density of tBLG …
Injection or optical generation of electrons and holes in graphene bilayers (GBLs) can result in the interband population inversion enabling the terahertz (THz) radiation lasing. The intraband radiative processes compete with the interband transitions. We demonstrate that remote doping enhances the indirect interband generation of photons in the proposed GBL heterostructures. Therefore such remote doping helps surpassing the intraband (Drude) absorption and results in large absolute values of the negative dynamic THz conductivity in a wide range of frequencies at elevated (including room) temp…
Theory predicts that the application of an electric field breaks the inversion symmetry of AB and BA stacked domains in twisted bilayer graphene, resulting in the formation of a triangular network of one-dimensional valley-protected helical states. This two-dimensional network of one-dimensional states has been observed in several studies, but direct experimental evidence that the electronic transport in these one-dimensional states is valley-protected is still lacking. In this study, we report the existence of the network in small-angle twisted bilayer graphene at room temperature. Moreover, …
Crystal symmetry of two-dimensional (2D) materials plays an important role in their electronic and optical properties. Engineering symmetry in 2D materials has recently emerged as a promising way to achieve novel properties and functions. The noncentrosymmetric structure of monolayer transition metal dichalcogenides (TMDCs), such as molybdenum disulfide (MoS2), has allowed for valley control via circularly polarized optical excitation. In bilayer TMDCs, inversion symmetry can be controlled by varying the stacking sequence, thus providing a pathway to engineer valley selectivity. Here, we repor…
We investigate the electronic confinement in bilayer graphene by topological loops of different shapes. These loops are created by lateral gates acting via gap inversion on the two graphene sheets. For large-area loops the spectrum is well described by a quantization rule depending only on the loop perimeter. For small sizes, the spectrum depends on the loop shape. We find that zero-energy states exhibit a characteristic pattern that strongly depends on the spatial symmetry. We show this by considering loops of higher to lower symmetry (circle, square, rectangle and irregular polygon). Interes…
Graphene bilayers with layer antisymmetric strains are studied using the Dirac-Harper model for a pair of single layer Dirac Hamiltonians coupled by a one-dimensional moiré-periodic interlayer tunneling amplitude. This model hosts low energy, nearly dispersionless bands near charge neutrality that support anomalous polarizations of its charge multipole distributions. These are analyzed introducing a generalized Berry curvature that encodes the field-induced dynamics of multipole fields allowed in a chiral medium with time reversal symmetry. The formulation identifies a reciprocity relation bet…
We theoretically investigate the electronic structures of moiré superlattices arising in monolayer / bilayer graphene stacked on hexagonal boron nitride (hBN) in presence and absence of magnetic field. We develop an effective continuum model from a microscopic tight-binding lattice Hamiltonian, and calculate the electronic structures of graphene-hBN systems with different rotation angles. Using the effective model, we explain the characteristic band properties such as the gap opening at the corners of the superlattice Brillouin zone (mini-Dirac point). We also investigate the energy spectrum a…
Although several multiferroic materials/heterostructures have been extensively studied, finding strong magnetoelectric couplings for the electric field control of the magnetization remains challenging. Here, a novel interfacial magnetoelectric coupling based on three components (ferroelectric dipole, magnetic moment, and antiferromagnetic order) is analytically formulated. As an extension of carrier-mediated magnetoelectricity, the new coupling is shown to induce an electric-magnetic hysteresis loop. Realizations employing BiFeO$_3$ bilayers grown along the [$111$] axis are proposed. Without i…
We analyze the effects of the long-range Coulomb interaction on the distribution of Berry curvature among the bands near charge neutrality of twisted bilayer graphene (TBG) closely aligned with hexagonal boron nitride (hBN). Due to the suppressed dispersion of the narrow bands, the band structure is strongly renormalized by electron-electron interactions, and thus, the associated topological properties of the bands are sensitive to filling. Using a Hartree formalism, we calculate the linear and nonlinear Hall conductivities, and find that for certain fillings, the remote bands contribute subst…
Generally, stacking two quantum spin Hall insulators gives rise to a trivial insulator. Here, based on first-principles electronic structure calculations, we confirm that monolayer TaIrTe$_{4}$ is a quantum spin Hall insulator and remarkably find that bilayer TaIrTe$_{4}$ is still a quantum spin Hall insulator. Theoretical analysis indicates that the covalent-like interlayer interaction in combination with the small bandgap at time-reversal invariant $Γ$ point results in new band inversion in bilayer TaIrTe$_{4}$, namely, the emergence of quantum spin Hall phase. Meanwhile, a topological phase…
Flat electronic bands can accommodate a plethora of interaction driven quantum phases, since kinetic energy is quenched therein and electronic interactions therefore prevail. Twisted bilayer graphene, near so-called the "magic angles", features \emph{slow} Dirac fermions close to the charge-neutrality point that persist up to high-energies. Starting from a continuum model of slow, but strongly interacting Dirac fermions, we show that with increasing chemical doping away from the charge-neutrality point, a time-reversal symmetry breaking, valley pseudo-spin-triplet, topological $p+ip$ supercond…
Twisted graphene bilayers provide a versatile platform to engineer metamaterials with novel emergent properties by exploiting the resulting geometric moiré superlattice. Such superlattices are known to host bulk valley currents at tiny angles ($α\approx 0.3 ^\circ$) and flat bands at magic angles ($α\approx 1^\circ$). We show that tuning the twist angle to $α^*\approx 0.8^\circ$ generates flat bands away from charge neutrality with a triangular superlattice periodicity. When doped with $\pm 6$ electrons per moiré cell, these bands are half-filled and electronic interactions produce a symmetry-…
Chirality is one of the key features governing the electronic properties of single- and bilayer graphene: the basics of this concept and its consequences on transport are presented in this review. By breaking the inversion symmetry, a band gap can be opened in the band structures of both systems at the K-point. This leads to interesting consequences for the pseudospin and, therefore, for the chirality. These consequences can be accessed by investigating the evolution of the Berry phase in such systems. Experimental observations of Fabry-Perot interference in a dual-gated bilayer graphene devic…
We study the magneto-optical conductivity of a number of Van der Waals heterostructures, namely, twisted bilayer graphene, AB-AB and AB-BA stacked twisted double bilayer graphene and monolayer graphene and AB-stacked bilayer graphene on hexagonal boron nitride. As magnetic field increases, the absorption spectrum exhibits a self-similar recursive pattern reflecting the fractal nature of the energy spectrum. Whilst twisted bilayer graphene displays only weak circular dichroism, monolayer graphene and AB-stacked bilayer graphene on hexagonal boron nitride show specifically strong circular dichro…
We propose to uncover the topology of a pseudo-Hermitian Chern insulator by quantum quench dynamics. The Bloch Hamiltonian of the pseudo-Hermitian Chern insulator is defined in the basis of the q-deformed Pauli matrices, which are related to the representation of the deformed algebras. We show the bulk-surface duality of the pseudo-Hermitian phases, then further build a concrete relation between the static band topology and quench dynamics, in terms of the time-averaged spin textures. The results are also generalized into a fully nonequilibrium case where the postquench evolution is governed b…
Topological phase diagram of twisted bilayer graphene as a function of the twist angle
Universidad Nacional Autónoma de México (UNAM)（墨西哥国立自治大学）；IMDEA Nanoscience（IMDEA纳米科学研究所）；Colorado State University（科罗拉多州立大学）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）
Valley is a useful degree of freedom for non-dissipative electronics since valley current that can flow even in an insulating material does not accompany electronic current. We use dual-gated bilayer graphene in the Hall bar geometry to electrically control broken inversion symmetry or Berry curvature as well as the carrier density to generate and detect the pure valley current. We find a large nonlocal resistance and a cubic scaling between the nonlocal resistance and the local resistivity in the insulating regime at zero-magnetic field and 70 K as evidence of the pure valley current. The ele…
We investigate the magnetic minibands of a heterostructure consisting of bilayer graphene (BLG) and hexagonal boron nitride (hBN) by numerically diagonalizing a two-band Hamiltonian that describes electrons in BLG in the presence of a moire potential. Due to inversion-symmetry breaking characteristic for the moire potential, the valley symmetry of the spectrum is broken, but despite this, the zero-energy Landau level in BLG survives, albeit with reduced degeneracy. In addition, we derive effective models for the low-energy features in the magnetic minibands and demonstrate the appearance of se…
