We study effects of tilted magnetic fields on energy levels in a double-quantum-well (DQW) system, focusing on the coupling of subbands and Landau levels (LLs). The subband-LL coupling induces anticrossings between LLs, manifested directly in the magnetoresistance. The anticrossing gap becomes larger than the spin splitting at the tilting angle $θ\sim 20^\circ $ and larger than the cyclotron energy at $θ\sim 50^\circ $, demonstrating that the subband-LL coupling exerts a strong influence on quantum Hall states even in at a relatively small $θ$ and plays a dominant role for larger $θ$. We also find that when the DQW potential is asymmetric, LL coupling occurs even within a subband. Calculations including higher-order coupling reproduce the experimental results quantitatively well.
We report a study of one-dimensional subband splitting in a bilayer graphene quantum point contact in which quantized conductance in steps of $4\,e^2/h$ 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/mixing of $K$ and $K'$ valleys from two non-adjacent subbands with indi…
The spin filtering effect in the bilayer nanowire with quantum point contact is investigated theoretically. We demonstrate the new mechanism of the spin filtering based on the lateral inter-subband spin-orbit coupling, which for the bilayer nanowires has been reported to be strong. The proposed spin filtering effect is explained as the joint effect of the Landau-Zener inter-subband transitions caused by the hybridization of states with opposite spin (due to the lateral Rashba SO interaction) and the confinement of carriers in the quantum point contact region.
Oscillations of the real component of AC conductivity $σ_1$ in a magnetic field were measured in the n-AlGaAs/GaAs structure with a wide (75 nm) quantum well by contactless acoustic methods at $T$=(20-500)~mK. In a wide quantum well, the electronic band structure is associated with the two-subband electron spectrum, namely the symmetric (S) and antisymmetric (AS) subbands formed due to electrostatic repulsion of electrons. A change of the oscillations amplitude in tilted magnetic field observed in the experiments occurs due to crossings of Landau levels of different subbands (S and AS) at the …
We demonstrate that, at the onset of conduction, an electrostatically defined quantum wire in bilayer graphene (BLG) with an interlayer asymmetry gap may act as a 1D semimetal, due to the multiple minivalley dispersion of its lowest subband. Formation of a non-monotonic subband coincides with a near-degeneracy between the bottom edges of the lowest two subbands in the wire spectrum, suggesting an $8e^2/h$ step at the conduction threshold, and the semimetallic behaviour of the lowest subband in the wire would be manifest as resonance transmission peaks on an $8e^2/h$ conductance plateau.
We report on possibility of charge current generation in nanowire made of two tunnel coupled one-dimensional electron waveguides by means of single magnetic pulse lasting up to 20 ps. Existence of interlayer tunnel coupling plays a crucial role in the effect described here as it allows for hybridization of the wave functions localized in different layers which can be dynamically modified by applying a time changeable in-plane magnetic field. Results of time-dependent DFT calculations performed for a bilayer nanowire confining many electrons show that the effect of such magnetic hybridization r…
Angular magnetoresistance oscillations (AMRO) were originally discovered in organic conductors and then found in many other layered metals. It should be possible to observe AMRO to semiconducting bilayers as well. Here we present an intuitive geometrical interpretation of AMRO as the Aharonov-Bohm interference effect, both in real and momentum spaces, for balanced and imbalanced bilayers. Applications to the experiments with bilayers in tilted magnetic fields in the metallic state are discussed. We speculate that AMRO may be also observed when each layer of the bilayer is in the composite-ferm…
We employ magnetocapacitance and far-infrared spectroscopy techniques to study the spectrum of the double-layer electron system in a parabolic quantum well with a narrow tunnel barrier in the centre. For gate-bias-controlled asymmetric electron density distributions in this soft two-subband system we observe both individual subband gaps and double layer gaps at integer filling factor $ν$. The bilayer gaps are shown to be either trivial common for two subbands or caused by hybridization of electron subbands in magnetic field. We describe the observed hybrid gaps at $ν=1$ and $ν=2$ within a simp…
The magnetotransport of highly mobile 2D electrons in wide GaAs single quantum wells with three populated subbands placed in titled magnetic fields is studied. The bottoms of the lower two subbands have nearly the same energy while the bottom of the third subband has a much higher energy ($E_1\approx E_2<<E_3$). At zero in-plane magnetic fields magneto-intersubband oscillations (MISO) between the $i^{th}$ and $j^{th}$ subbands are observed and obey the relation $Δ_{ij}=E_j-E_i=k\cdot\hbarω_c$, where $ω_c$ is the cyclotron frequency and $k$ is an integer. An application of in-plane magnetic fie…
We observed broken-symmetry quantum Hall effects and level crossings between spin- and valley- resolved Landau levels (LLs) in Bernal stacked trilayer graphene. When the magnetic field was tilted with respect to sample normal from $0^{\circ}$ to $66^\circ$, the LL crossings formed at intersections of zeroth and second LLs from monolayer-graphene-like and bilayer-graphene-like subbands, respectively, exhibited a sequence of transitions. The results indicate the LLs from different subbands are coupled by in-plane magnetic fields ($B_{\parallel}$), which was explained by developing the tight-bind…
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 $μ$eV 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…
We consider a bilayer quantum Hall system at total filling fraction nu=2 in tilted magnetic field allowing for charge imbalance as well as tunneling between the two layers. Using an "unrestricted Hartree Fock," previously discussed by Burkov and MacDonald (Phys Rev B 66 115323 2002), we examine the zero temperature global phase diagrams that would be accessed experimentally by changing the in-plane field and the bias voltage between the layers while keeping the tunneling between the two layers fixed. In accordance with previous work, we find symmetric and ferromagnetic phases as well as a firs…
We use time-dependent Hartree Fock approximation to study the collective mode spectra of nu=2 quantum Hall bilayers in tilted magnetic field allowing for charge imbalance as well as tunneling between the two layers. In a previous companion paper to this work, we studied the zero temperature global phase diagram of this system which was found to include a symmetric and ferromagnetic phases as well as a first order transition between two canted phases with spontaneously broken U(1) symmetry. We further found that this first order transition line ends in a quantum critical point within the canted…
The magnetoelectronic properties of quasi-one-dimensional zigzag graphene nanoribbons are investigated by using the Peierls tight-binding model. Quasi-Landau levels (QLLs), dispersionless Landau subbands within a certain region of k-space, are resulted from the competition between magnetic and quantum confinement effects. In bilayer system, the interlayer interactions lead to two groups of QLLs, one occurring at the Fermi level and the other one occurring at higher energies. Transverse electric fields are able to distort energy spectrum, tilt two groups of QLLs and cause semiconductor-metal tr…
Bilayer two-dimensional electron systems formed by a thin barrier in the GaAs buffer of a standard heterostructure were investigated by magnetotransport measurements. In magnetic fields oriented parallel to the electron layers, the magnetoresistance exhibits an oscillation associated with the depopulation of the higher occupied subband and the field-induced transition into a decoupled bilayer. Shubnikov-de Haas oscillations in slightly tilted magnetic fields allow to reconstruct the evolution of the electron concentration in the individual subbands as a function of the in-plane magnetic field.…
We report on a theoretical study of $ν=2$ bilayer quantum Hall systems with a magnetic field that has a component parallel to the layers. As in the $ν=1$ case, interlayer phase coherence is closely coupled to electron correlations and the Aharonov-Bohm phases introduced by a parallel magnetic field can have a strong influence on the ground state of the system. We find that response of a $ν=2$ system to a parallel field is more subtle than that of a $ν=1$ system because of the interplay between spin and layer degrees of freedom. There is no commensurate-incommensurate transition as the parallel…
In bilayer graphene rotationally faulted to theta=1.1 degrees, interlayer tunneling and rotational misalignment conspire to create a pair of low energy flat band that have been found to host various correlated phenomena at partial filling. Most work to date has focused on the zero magnetic field phase diagram, with magnetic field (B) used as a probe of the B=0 band structure. Here, we show that twisted bilayer graphene (tBLG) in a B as low as 2T hosts a cascade of ferromagnetic Chern insulators with Chern number |C|=1,2 and 3. We argue that the emergence of the Chern insulators is driven by th…
We present a study on the lifting of degeneracy of the size-quantized energy levels in an electrostatically defined quantum point contact in bilayer graphene by the application of in-plane magnetic fields. We observe a Zeeman spin splitting of the first three subbands, characterized by effective Landé $g$-factors that are enhanced by confinement and interactions. In the gate-voltage dependence of the conductance, a shoulder-like feature below the lowest subband appears, which we identify as a $0.7$ anomaly stemming from the interaction-induced lifting of the band degeneracy. We employ a phenom…
We employ magnetocapacitance measurements to study the spectrum of a double layer system with gate-voltage-tuned electron density distributions in tilted magnetic fields. For the dissipative state in normal magnetic fields at filling factor $ν=3$ and 4, a parallel magnetic field component is found to give rise to opening a gap at the Fermi level. We account for the effect in terms of parallel-field-caused orthogonality breaking of the Landau wave functions with different quantum numbers for two subbands.
We study non-linear transport phenomena in a high-mobility bilayer system with two closely spaced populated electronic subbands in a perpendicular magnetic field. For a moderate direct current excitation, we observe zero-differential-resistance states with a characteristic 1/B periodicity. We investigate, both experimentally and theoretically, the Hall field-induced resistance oscillations which modulate the high-frequency magneto-intersubband oscillations in our system if we increase the current. We also observe and describe the influence of direct current on the magnetoresistance in the pres…
We have measured the spin splitting in single-layer and bilayer graphene by means of tilted magnetic field experiments. Applying the Lifshitz-Kosevich formula for the spin-induced decrease of the Shubnikov de Haas amplitudes with increasing tilt angle we directly determine the product between the carrier cyclotron mass m* and the effective g-factor g* as a function of the charge carrier concentration. Using the cyclotron mass for a single-layer and a bilayer graphene we find an enhanced g-factor g* = 2.7 \pm 0.2 for both systems.
Proposed even-denominator fractional quantum Hall effect (FQHE) states suggest the possibility of excitations with non-Abelian braid statistics. Recent experiments on wide square quantum wells observe even-denominator FQHE even under electrostatic tilt. We theoretically analyze these structures and develop a procedure to accurately test proposed quantum Hall wavefunctions. We find that tilted wells favor partial subband polarization to yield Abelian even-denominator states. Our results show that tilting quantum wells effectively engineers different interaction potentials allowing exploration o…
We report phonon renormalisation in bilayer graphene as a function of doping. The Raman G peak stiffens and sharpens for both electron and hole doping, as a result of the non-adiabatic Kohn anomaly at the $Γ$ point. The bilayer has two conduction and valence subbands, with splitting dependent on the interlayer coupling. This results in a change of slope in the variation of G peak position with doping, which allows a direct measurement of the interlayer coupling strength.
We present a theoretical study on the orbital magnetism in multilayer graphenes within the effective mass approximation. The Hamiltonian and thus susceptibility can be decomposed into contributions from sub-systems equivalent to monolayer or bilayer graphene. The monolayer-type subband exists only in odd layers and exhibits a delta-function susceptibility at $E_F=0$. The bilayer-type subband appearing in every layer number gives a singular structure in the vicinity of $E_F=0$ due to the trigonal warping as well as a logarithmic tail away from $E_F=0$. The integral of the susceptibility over en…
We have studied the edge spin accumulation in a high mobility two-dimensional electron gas formed in a symmetric well with two subbands. This study is strongly motivated by the recent experiment of Hernandez et al. [Phys. Rev. B {\bf 88}, 161305(R) (2013)] who demonstrated the spin accumulation near the edges of a bilayer symmetric GaAs structure in contrast to no effect in a single-layer configuration. The intrinsic mechanism of the spin-orbit interaction we consider arises from the coupling between two subband states of opposite parities. We obtain a parametrically large magnitude of the edg…
The single electron magnetotransport in a vertical bi-layer semiconductor nanowire made of InAlAs/InGaAs and AlGaAs/GaAs heterostructure is theoretically studied. The magnetic field is directed perpendicularily to the main (transport) axis of the quantum wire and both non-zero components of magnetic field, that is the transverse and the vertical ones, allow to change the magnitude of intra-layer and inter-layer subbands mixing, respectively. We analyze in detail the changes introduced to energy dispersion relation E(k) by strong titled magnetic field up to several teslas for a symmetric and an…
Transport properties of highly mobile 2D electrons are studied in symmetric GaAs quantum wells placed in titled magnetic fields. Quantum positive magnetoresistance (QPMR) is observed in magnetic fields perpendicular to the 2D layer. Application of in-plane magnetic field produces a dramatic decrease of the QPMR. This decrease correlates strongly with the reduction of the amplitude of Shubnikov de Haas resistance oscillations due to modification of the electron spectrum via enhanced Zeeman splitting. Surprisingly no quantization of the spectrum is detected when the Zeeman energy exceeds the hal…
We report a multiband transport study of bilayer graphene at high carrier densities. Employing a poly(ethylene)oxide-CsClO$_4$ solid polymer electrolyte gate we demonstrate the filling of the high energy subbands in bilayer graphene samples at carrier densities $|n|\geq2.4\times 10^{13}$ cm$^{-2}$. We observe a sudden increase of resistance and the onset of a second family of Shubnikov de Haas (SdH) oscillations as these high energy subbands are populated. From simultaneous Hall and magnetoresistance measurements together with SdH oscillations in the multiband conduction regime, we deduce the …
By using the effective bosonic spin theory, which is recently proposed by Demler and Das Sarma [ Phys. Rev. Lett. 82, 3895 (1999) ], we analyze the effect of an external in-plane magnetic field on the magnetic phase transitions of the bilayer quantum Hall system at filling factor nu=2. It is found that the quantum phase diagram is modified by the in-plane magnetic field. Therefore, quantum phase transitions can be induced simply by tilting the magnetic field. The general behavior of the critical tilted angle for different layer separations and interlayer tunneling amplitudes is shown. We find …
We discuss the orbital effect of a tilted magnetic field on the quantum Hall effect in parabolic quantum wells. Many-body states realized at the fractional 1/3 and 1/2 filling of the second electronic subband are studied using finite-size exact diagonalization. In both cases, we obtain the phase diagram consisting of a fractional quantum Hall fluid phase that persists for moderate tilts, and eventually undergoes a direct transition to the stripe phase. It is shown that tilting of the field probes the geometrical degree of freedom of fractional quantum Hall fluids, and can be partly related to …
Nonlinear intensity dependence of photogalvanics and photoconductance induced by terahertz laser radiation in twisted bilayer graphene close to magic angle
University of Regensburg（雷根斯堡大学）；ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（巴塞罗那科学和技术研究所光子科学研究所）；National Institute for Materials Science（国立材料研究所）；Institute of High Pressure Physics, Polish Academy of Sciences（波兰科学院高压物理研究所）
The far-infrared absorption in two-dimensional electron layers subject to magnetic field of general orientation was studied theoretically. The Kubo formula was employed to derive diagonal components of the magneto-conductivity tensor of two-dimensional electron single-layers and double-layers. A parabolic quantum well was used to model single-layer systems. Bilayer systems were represented by a pair of tunnel-coupled, strictly two-dimensional quantum wells. Obtained results were compared to experimental data.
Magneto-luminescence studies in electron bilayers reveal the hallmarks of the even-denominator and other quantum Hall states in the intensities and energies of the inter-band optical recombination lines. In the presence of a small tunneling gap between the layers the magneto-optical emission from the lowest anti-symmetric subband, not populated in a single-electron picture, displays maxima at filling factors 1 and 2/3. These findings uncover a loss of pseudospin polarization, where the pseudospin describes the layer index degree of freedom, that is linked to an anomalous population of the anti…
We have observed in a low density two-dimensional hole system (2DHS) of extremely high quality (with hole density p=1.6x10^{10} cm^{-2} and mobility μ=0.8x10^6 cm^2/Vs) that, as the 2DHS is continuously tilted with respect to the direction of the magnetic field, the ν=1/3 fractional quantum Hall effect (FQHE) state is weakened and its magnetoresistivity rises from ~ 0.4 kohm/square in the normal orientation to ~ 180 kohm/square at tilt angle θ\~ 80 degrees. We attribute this phenomenon to the transition of the 2DHS from the FQHE liquid state to the pinned Wigner solid state, and argue that its…
We show that the spectrum of subbands in an electrostatically defined quantum wire in gapped bilayer graphene directly manifests the minivalley structure and reflects Berry curvature via the associated magnetic moment of the states in the low-energy bands of this two-dimensional material. We demonstrate how these appear in degeneracies of the low-energy minibands and their valley splitting, which develops linearly in a weak magnetic field. Consequently, magneto-conductance of a ballistic point contact connecting two non-gapped areas of a bilayer through a gapped (top and bottom gated) barrier …
We study the commensurately-tilted bilayer graphene in the tight-binding model with changing the interlayer distance, which can be tuned by pressure. We find that at the commensurately-tilted bilayer graphene with moderate rotating angles, when the energy gap at K point is not negligible, the other Dirac points within the upper two bands move along the $Γ$-K-M line in the bilayer Brillouzone, when the interlayer distance is changed. The velocity at K point becomes zero due to the merging of the four Dirac points within upper two bands. This mechanism of zero velocity at K point is expected to …
Here we report on a transparent method to characterize individual layers in a double-layer electron system which forms in a wide quantum well and to determine their electron densities. The technique relies on the simultaneous measurement of the capacitances between the electron system and gates located on either side of the well. Modifications to the electron wave function due to the population of the second subband and appearance of an additional electron layer can be detected. The magnetic field dependence of these capacitances is dominated by quantum corrections caused by the occupation of …
We experimentally demonstrate, for the first time, formation of point-like topological defects in the edge state structure in the quantum Hall effect regime. By using of a selective population technique, we investigate equilibration processes between the edge states in bilayer electron structures with a high tunnelling rate between layers. Unexpected flattening of the I-V curves in perpendicular magnetic field at a specific filling factor combination and the recovery of the conventional nonlinear I-V characteristics in tilted fields give a strong evidence for the existence of topological defec…
We present measurements of quantized conductance in electrostatically induced quantum point contacts in bilayer graphene. The application of a perpendicular magnetic field leads to an intricate pattern of lifted and restored degeneracies with increasing field: at zero magnetic field the degeneracy of quantized one-dimensional subbands is four, because of a twofold spin and a twofold valley degeneracy. By switching on the magnetic field, the valley degeneracy is lifted. Due to the Berry curvature states from different valleys split linearly in magnetic field. In the quantum Hall regime fourfold…
A review work is done for electronic and optical properties of graphene nanoribbons in magnetic, electric, composite, and modulated fields. Effects due to the lateral confinement, curvature, stacking, non-uniform subsystems and hybrid structures are taken into account. The special electronic properties, induced by complex competitions between external fields and geometric structures, include many one-dimensional parabolic subbands, standing waves, peculiar edge-localized states, width- and field-dependent energy gaps, magnetic-quantized quasi-Landau levels, curvature-induced oscillating Landau…
In the quantum Hall regime, the longitudinal resistivity $ρ_{xx}$ plotted as a density--magnetic-field ($n_{2D}-B$) diagram displays ringlike structures due to the crossings of two sets of spin split Landau levels from different subbands [e.g., Zhang \textit{et al.}, Phys. Rev. Lett. \textbf{95}, 216801 (2005)]. For tilted magnetic fields, some of these ringlike structures "shrink" as the tilt angle is increased and fully collapse at $θ_c \approx 6^\circ$. Here we theoretically investigate the topology of these structures via a non-interacting model for the 2DEG. We account for the inter Landa…
Under a magnetic field perpendicular to an monolayer graphene, the existence of a two-dimensional periodic scatter array can not only mix Landau levels of the same valley for displaying split electron-hole Hofstadter-type energy spectra, but also couple two sets of Landau subbands from different valleys in a bilayer graphene. Such a valley mixing effect with a strong scattering strength has been found observable and studied thoroughly in this paper by using a Bloch-wave expansion approach and a projected $2\times 2$ effective Hamiltonian including interlayer effective mass, interlayer coupling…
The relativistic-like behavior of electrons in graphene significantly influences the interaction properties of these electrons in a quantizing magnetic field, resulting in more stable fractional quantum Hall effect states as compared to those in conventional (non-relativistic) semiconductor systems. In bilayer graphene the interaction strength can be controlled by a bias voltage and by the orientation of the magnetic field. The finite bias voltage between the graphene monolayers can in fact, enhance the interaction strength in a given Landau level. As a function of the bias voltage, a graphene…
We measured the critical current of the bilayer Nb/Co in the applied magnetic field. When the magnetic field was tilted to the axis which was perpendicular to the plane of the bilayer we observed a large difference in critical currents flowing in opposite directions. We found that the largest critical current of the bilayer exceeded the critical current of the superconductor without Co layer in a wide range of the tilted magnetic fields. The theory which takes into account the surface barrier effect for vortex entry and magnetic field of the magnetic layer gave a quantitative explanation of ou…
The direct-current (dc) $σ_{xx}^{dc}$ and alternating-current (ac) $σ_{xx}^{ac}=σ_1-iσ_2$ conductivities of a wide (46 nm) GaAs quantum well with the bilayer electron density distribution are measured. It is found that the magnetic field dependence of $σ_{xx}$ exhibits three sets of oscillations related to the transitions between Landau levels in symmetric and antisymmetric subbands and with the transitions occurring owing to the Zeeman splitting of these subbands. The analysis of the frequency dependence of the ac conductivity and the $σ_1 / σ_2$ ratio demonstrates that the conductivity at th…
We investigate a domain structure of pseudospins, a soliton lattice in the bilayer quantum Hall state at total Landau level filling factor $ν=1$, in a tilted magnetic field, where the pseudospin represents the layer degree of freedom. An anomalous peak in the magnetoresistance $R_{xx}$ appears at the transition point between the commensurate and incommensurate phases. The $R_{xx}$ at the peak is highly anisotropic for the angle between the in-plain magnetic field $B_\parallel $ and the current, and indicates a formation of the soliton lattice aligned parallel to $B_\parallel $. Temperature dep…
We study the magnetotransport properties of high mobility holes in monolayer and bilayer WSe$_2$, which display well defined Shubnikov-de Haas (SdH) oscillations, and quantum Hall states (QHSs) in high magnetic fields. In both mono and bilayer WSe$_2$, the SdH oscillations and the QHSs occur predominantly at even filling factors, evincing a two-fold Landau level degeneracy. The Fourier transform analysis of the SdH oscillations in bilayer WSe$_2$ reveal the presence of two subbands localized in the top or the bottom layer, as well as negative compressibility. From the temperature dependence of…
We design, fabricate, and study a hole bilayer in a strained germanium double quantum well. Magnetotransport characterisation of double quantum well field-effect transistors as a function of gate voltage reveals the population of two hole channels with a high combined mobility of 3.34$\times$10$^5$ cm$^2$/Vs and a low percolation density of 2.38$\times$10$^{10}$ cm$^{-2}$. We resolve the individual population of the channels from the interference patterns of the Landau fan diagram. At a density of 2.0$\times$10$^{11}$ cm$^{-2}$ the system is in resonance and we observe an anti-crossing of the …
We consider graphene bilayer in a constant magnetic field of arbitrary orientation (i.e. tilted with respect to the graphene plane). In the low energy approximation to tight binding model with Peierls substitution, we find the exact spectrum of Landau levels. This spectrum is two-fold degenerate in the limit of large in-plane field, which gives rise to a new SU(2) symmetry in this limit.
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…
The most celebrated property of the quantum spin Hall effect is the presence of spin-polarized counter-propagating edge states. This novel edge state configuration has also been predicted to occur in graphene when spin-split electron- and hole-like Landau levels are forced to cross at the edge of the sample. In particular, a quantum spin Hall analogue has been predicted at ν=0 in bilayer graphene if the ground state is a spin ferromagnet. Previous studies have demonstrated that the bilayer ν=0 state is an insulator in a perpendicular magnetic field, though the exact nature of this state has no…
The electronic properties and optical excitations are investigated in the geometry- and field-modulated bilayer graphene systems, respectively, by using the tight-binding model and Kubo formula. The stacking symmetry of bilayer graphene can be manipulated by varying the width and position of domain wall (DW) within two normally stacked graphene. All the layer-dependent atomic interactions are taken into consideration under external fields. The modulation of stacking configuration gives rise to significant effects of zone folding on energy subbands, subenvelope wave functions, density of states…
Unconventional responses upon breaking discrete or crystal symmetries open avenues for exploring emergent physical systems and materials. By breaking inversion symmetry, a nonlinear Hall signal can be observed, even in the presence of time-reversal symmetry, quite different from the conventional Hall effects. Low-symmetry two-dimensional materials are promising candidates for the nonlinear Hall effect, but it is less known when a strong nonlinear Hall signal can be measured, in particular, its connections with the band-structure properties. By using model analysis, we find prominent nonlinear …
Magnetotransport measurements on two-dimensional electrons confined to wide GaAs quantum wells reveal a remarkable evolution of the ground state at filling factor $ν=1/2$ as we tilt the sample in the magnetic field. Starting with a compressible state at zero tilt angle, a strong $ν=1/2$ fractional quantum Hall state appears at intermediate angles. At higher angles an insulating phase surrounds this state and eventually engulfs it at the highest angles. This evolution occurs because the parallel component of the field renders the charge distribution increasingly bilayer-like.
We report a change of three orders of magnitudes in the resistance of a suspended bilayer graphene flake which varies from a few k$Ω$s in the high carrier density regime to several M$Ω$s around the charge neutrality point (CNP). The corresponding transport gap is 8 meV at 0.3 K. The sequence of appearing quantum Hall plateaus at filling factor $ν=2$ followed by $ν=1$ suggests that the observed gap is caused by the symmetry breaking of the lowest Landau level. Investigation of the gap in a tilted magnetic field indicates that the resistance at the CNP shows a weak linear decrease for increasing…
