Interlayer exchange coupling (IEC) between two magnetic layers sandwiched by a nonmagnetic spacer layer plays a critical role in shaping the magnetic properties of such heterostructures. The quantum anomalous Hall (QAH) effect has been realized in a structure composed of two magnetically doped topological insulator (TI) layers separated by an undoped TI layer. In this work, we employ molecular beam epitaxy to synthesize a series of magnetic TI sandwiches with varying thicknesses of the middle TI spacer layer. The well-quantized QAH effect is observed in all these samples, and the IEC modulates its critical behavior between the top and bottom magnetic TI layers. Near the plateau phase transition (PPT), thinner QAH samples exhibit a two-dimensional critical metal behavior with nearly temperature-independent longitudinal resistance. In contrast, thicker QAH samples behave as a three-dimensional insulator with reduced longitudinal resistance at higher temperatures. We employ a magnetic TI Hamiltonian with random magnetic domains to understand the IEC-induced critical-metal-to-insulator transition observed near QAH PPT.
Magnetic proximity effect between topological insulator (TI) and ferromagnetic insulator (FMI) is considered to have great potential in spintronics. However, a complete determination of interfacial magnetic structure has been highly challenging. We theoretically investigate the interlayer exchange coupling of two FMIs separated by a TI thin film, and show that the particular electronic states of the TI contributing to the proximity effect can be directly identified through the coupling behavior between two FMIs, together with a tunability of coupling constant. Such FMI/TI/FMI structure not onl…
We report on the quantum Hall effect in two stacked graphene layers rotated by 2 degree. The tunneling strength among the layers can be varied from very weak to strong via the mechanism of magnetic breakdown when tuning the density. Odd-integer quantum Hall physics is not anticipated in the regime of suppressed tunneling for balanced layer densities, yet it is observed. We interpret this as a signature of Coulomb interaction induced interlayer coherence and Bose Einstein condensation of excitons that form at half filling of each layer. A density imbalance gives rise to reentrant behavior due t…
Moiré superlattices in van der Waals heterostructures have emerged as a powerful tool for engineering novel quantum phenomena. Here we report the observation of a correlated interlayer exciton insulator in a double-layer heterostructure composed of a WSe2 monolayer and a WS2/WSe2 moiré bilayer that are separated by an ultrathin hexagonal boron nitride (hBN). The moiré WS2/WSe2 bilayer features a Mott insulator state at hole density p/p0 = 1, where p0 corresponds to one hole per moiré lattice site. When electrons are added to the Mott insulator in the WS2/WSe2 moiré bilayer and an equal number …
We introduce a novel two-dimensional electronic system with ultrastrong interlayer interactions, namely twisted bilayer graphene with a large twist angle, as an ideal ground for realizing interlayer-coherent excitonic condensates. In these systems, subnanometer atomic separation between the layers allows significant interlayer interactions, while interlayer electron tunneling is geometrically suppressed due to the large twist angle. By fully exploiting these two features we demonstrate that a sequence of odd-integer quantum Hall states with interlayer coherence appears at the second Landau lev…
The problem of screening the Coulomb interaction between charge carriers in type II heterostructures based on transition metal dichalcogenides is Analytically solved. At a sufficiently high density of charge carriers, the density dependence of the interlayer exciton energy is obtained. The energy of the interlayer exciton tends to zero in the metal--insulator transition point. The presented scheme of calculations makes it possible to find the temperature dependence of the density of this transition.
Excitonic insulators conduct neither electrons nor holes but bound electron-hole pairs, excitons. Unfortunately, it is not possible to inject and detect the electron and hole currents independently within a single semiconducting layer. However, interlayer excitonic insulators provide a spatial separation of electrons and holes enabling exciton current measurements. The problem is that the spatial separation weakens electron-hole pairing and may lead to interlayer exciton disassociation. Here we develop an explicitly solvable model to determine an interlayer separation that is strong enough to …
Magnetization switching by spin-orbit torque (SOT) via spin Hall effect represents as a competitive alternative to that by spin-transfer torque (STT) used for magnetoresistive random access memory (MRAM), as it does not require high-density current to go through the tunnel junction. For perpendicular MRAM, however, SOT driven switching of the free layer requires an external in-plane field, which poses limitation for viability in practical applications. Here we demonstrate field-free magnetization switching of a perpendicular magnet by utilizing an Iridium (Ir) layer. The Ir layer not only prov…
Bilayer quantum Hall systems have a broken symmetry ground state at filling factor $ν=1$ which can be viewed either as an excitonic superfluid or as a pseudospin ferromagnet. We present a theory of inter-layer transport in quantum Hall bilayers that highlights remarkable similarities and critical differences between transport in Josephson junction and ferromagnetic metal spin-transfer devices. Our theory is able to explain the size of the large but finite low bias interlayer conductance and the voltage width of this collective transport anomaly.
We report a La2CuO4-like interlayer antiferromagnetic order in Sr2IrO4 films with large orthorhombic distortion (> 1.5%). The biaxial lattice strain in epitaxial heterostructures of Sr2IrO4/Ca3Ru2O7 lowers the crystal symmetry of Sr2IrO4 from tetragonal (C4) to orthorhombic (C2), guiding the Ir 5d Jeff = 1/2 pseudospin moment parallel to the elongated b-axis via magnetic anisotropy. From resonant X-ray scattering experiments, we observed an antiferromagnetic order in the orthorhombic Sr2IrO4 film whose interlayer stacking pattern is inverted from that of the tetragonal Sr2IrO4 crystal. This in…
This tutorial paper reviews some of the physics of quantum Hall bilayers with a focus on the case where there is low or zero tunnelling between the two layers. We describe the interlayer coherent states at filling factors nu=1 and nu=2 as exciton condensates and discuss some of the theory associated with these states.
Correlated interlayer quantum Hall state in large-angle twisted trilayer graphene
Daegu Gyeongbuk Institute of Science and Technology (DGIST)（大邱庆北科学技术院）；Ulsan National Institute of Science and Technology（蔚山科学技术院）；University of Seoul（首尔大学）；Pohang University of Science and Technology（浦项科技大学）；National Institute for Materials Science（物质材料研究机构）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；Institute for Basic Science（基础科学研究所）
The electromagnetic characteristics of bilayer quantum Hall systems in the presence of interlayer coherence and tunneling are studied by means of a pseudospin-texture effective theory and an algebraic framework of the single-mode approximation, with emphasis on clarifying the nature of the low-lying neutral collective mode responsible for interlayer tunneling phenomena. A long-wavelength effective theory, consisting of the collective mode as well as the cyclotron modes, is constructed. It is seen explicitly from the electromagnetic response that gauge invariance is kept exact, this implying, i…
We study the effect that the electron-electron interaction has on the properties of a multilayer electron system. We consider the case corresponding to filling factor unity in each layer. We find that as a function of the sample parameters the system has ferromagnetic, canted antiferromagnetic or paramagnetic interlayer spin correlations. These three ground states are QHE phases, because of the existence of a finite activation energy. In the ferromagnetic phase the gap is due to the intrawell exchange energy, whereas in the paramagnetic phase the gap appears due to the spatial modulation of th…
At the spin transition point of $ν=2/3$ quantum Hall states, nuclear spins in a two-dimensional electron gas are polarized by an electric current. Using GaAs/AlGaAs double-quantum-well samples, we first observed the spatial diffusion of nuclear spin polarization between the two layers when the nuclear spin polarization is current-induced in one layer. By numerical simulation, we estimated the diffusion constant of the nuclear spin polarization to be $15 \pm 7$\,nm$^2$/s.
We have measured the Hall-plateau width and the activation energy of the bilayer quantum Hall (BLQH) states at the Landau-level filling factor $ν=1$ and 2 by tilting the sample and simultaneously changing the electron density in each quantum well. The phase transition between the commensurate and incommensurate states are confirmed at $ν=1$ and discovered at $ν=2$. In particular, three different $ν=2$ BLQH states are identified; the compound state, the coherent commensurate state, and the coherent incommensurate state.
For monolayer transition metal chalcogenides (TMDs), electrons and excitons in different valleys can be driven to opposite directions by the Berry curvature, serving as a valley-dependent effective magnetic field. In addition to monolayer TMDs, Van der Waals heterostructures provide an attractive platform for emerging valley physics and devices with superior physics properties. Interlayer excitons in TMD heterostructures have a long valley lifetime as compared to monolayer intralayer excitons. Here we report an interlayer exciton valley polarization and valley Hall effect in MoS2/WSe2 in room …
We study the pairing symmetry of the interlayer paired state of composite fermions in quantum Hall bilayers. Based on the Halperin-Lee-Read (HLR) theory, the effect of the long-range Coulomb interaction and the internal Chern-Simons gauge fluctuation is analyzed with the random-phase approximation beyond the leading order contribution in small momentum expansion, and we observe that the interlayer paired states with a relative angular momentum $l=+1$ are energetically favored for filling $ν=\frac{1}{2}+\frac{1}{2}$ and $\frac{1}{4}+\frac{1}{4}$. The degeneracy between states with $\pm l$ is li…
The possibility of the existence of states with a spontaneous interlayer phase coherence in multilayer electron systems in a high perpendicular to the layers magnetic field is investigated. It is shown that phase coherence can be established in such systems only within individual pairs of adjacent layers, while such coherence does not exist between layers of different pairs. The conditions for stability of the state with interlayer phase coherence against transition to a charge-ordered state are determined. It is shown that in the system with the number of layers N\leq 10 these conditions are …
We develop a theory of interlayer tunneling in the exciton condensate of bilayer quantum Hall systems, which predicts strongly enhanced, but finite, tunneling conductance peaks near zero bias even at zero temperature. It is emphasized that, though this strongly enhanced tunneling originates from spontaneous interlayer phase coherence, it is fundamentally not the Josephson effect. Because of strong interlayer correlation, the bilayer system behaves as a single system so that conventional tunneling theories treating two layers as independent systems are not applicable. Based on our theory, we co…
We show that the interlayer tunneling I--V in double-layer quantum Hall states displays a rich behavior which depends on the relative magnitude of sample size, voltage length scale, current screening, disorder and thermal lengths. For weak tunneling, we predict a negative differential conductance of a power-law shape crossing over to a sharp zero-bias peak. An in-plane magnetic field splits this zero-bias peak, leading instead to a ``derivative'' feature at $V_B(B_{||})=2π\hbar v B_{||}d/eϕ_0$, which gives a direct measure of the dispersion of the Goldstone mode corresponding to the spontaneou…
We consider a fully spin-polarized quantum Hall system with no interlayer tunneling at total filling factor $ν=1/k$ (where $k$ is an odd integer) using the Chern-Simons-Ginzburg-Landau theory. Exploiting particle-vortex duality and the concept of quantum disordering, we find a large number of possible compressible and incompressible ground states, some of which may have relevance to recent experiments of Spielman {\it et.al.}. We find interlayer coherent compressible states without Hall quantization and interlayer-incoherent incompressible with Hall quantization in addition to the usual $(k,k,…
The effect of tunneling on the transport properties of} quantum Hall double layers in the regime of the excitonic condensate at total filling factor one is studied in counterflow experiments. If the tunnel current $I$ is smaller than a critical $I_C$, tunneling is large and is effectively shorting the two layers. For $I > I_C$ tunneling becomes negligible. Surprisingly, the transition between the two tunneling regimes has only a minor impact on the features of the filling-factor one state as observed in magneto-transport, but at currents exceeding $I_C$ the resistance along the layers increase…
Moiré interlayer exciton in transition metal dichalcogenide heterobilayer features a permanent electric dipole that enables the electrostatic control of its flow, and optical dipole that is spatially varying in the moiré landscape. We show the hybridization of moiré interlayer exciton with photons in a planar 2D cavity leads to two types of moiré polaritons that exhibit distinct forms of topological transport phenomena including the spin/valley Hall and polarization Hall effects, which feature remarkable electrical tunability through the control of exciton-cavity detuning by the interlayer bia…
We study bilayer quantum Hall systems at total Landau level filling factor $ν=1$ in the presence of interlayer tunneling and coupling to a dissipative normal fluid. Describing the dynamics of the interlayer phase by an effective quantum dissipative XY model, we show that there exists a critical dissipation $σ_c$ set by the conductance of the normal fluid. For $σ> σ_c$, interlayer tunnel splitting drives the system to a $ν=1$ quantum Hall state. For $σ<σ_c$, interlayer tunneling is irrelevant at low temperatures, the system exhibits a superfluid transition to a collective quantum Hall state sup…
We report a proximity-driven large anomalous Hall effect in all-telluride heterostructures consisting of ferromagnetic insulator Cr2Ge2Te6 and topological insulator (Bi,Sb)2Te3. Despite small magnetization in the (Bi,Sb)2Te3 layer, the anomalous Hall conductivity reaches a large value of 0.2e2/h in accord with a ferromagnetic response of the Cr2Ge2Te6. The results show that the exchange coupling between the surface state of the topological insulator and the proximitized Cr2Ge2Te6 layer is effective and strong enough to open the sizable exchange gap in the surface state.
The chirality associated with broken time reversal symmetry in magnetically doped topological insulators has important implications to the quantum transport phenomena. Here we report the anomalous Hall effect studies in Mn- and Cr-doped Bi$_2$Te$_3$ topological insulators with varied thickness and doping content. By tracing the chirality of the Hall loops, we find that the Mn-type anomalous Hall effect with clockwise chirality is strengthened by the reduction of film thickness, which is opposite to that of the Cr-type anomalous Hall effect with counterclockwise chirality. We provide a phenomen…
We experimentally study the interlayer interaction in a magnetic multilayer system ferromagnet/insulator/ferromagnet with different spacer thickness. We demonstrate that the sign and the magnitude of the interaction can be deduced from the FMR peak shape rather than from the FMR peak shift. The proposed technique allows studying the interlayer interaction using a single sample (without a reference sample for comparison).
Bilayer quantum Hall systems develop strong interlayer phase-coherence when the distance between layers is comparable to the typical distance between electrons within a layer. The phase-coherent state has until now been investigated primarily via transport measurements. We argue here that interlayer current and charge-imbalance noise studies in these systems will be able to address some of the key experimental questions. We show that the characteristic frequency of current-noise is that of the zero wavevector collective mode, which is sensitive to the degree of order in the system. Local elect…
At small layer separations, the ground state of a nu=1 bilayer quantum Hall system exhibits spontaneous interlayer phase coherence and has a charged-excitation gap E_g. The evolution of this state with increasing layer separation d has been a matter of controversy. In this letter we report on small system exact diagonalization calculations which suggest that a single phase transition, likely of first order, separates coherent incompressible (E_g >0) states with strong interlayer correlations from incoherent compressible states with weak interlayer correlations. We find a dependence of the phas…
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…
We study the Josephson-like interlayer tunneling signature of the strongly correlated $ν_T = 1$ quantum Hall phase in bilayer two-dimensional electron systems as a function of the layer separation, temperature and interlayer charge imbalance. Our results offer strong evidence that a finite temperature phase transition separates the interlayer coherent phase from incoherent phases which lack strong interlayer correlations. The transition temperature is dependent on both the layer spacing and charge imbalance between the layers.
By breaking the time-reversal-symmetry in three-dimensional topological insulators with introduction of spontaneous magnetization or application of magnetic field, the surface states become gapped, leading to quantum anomalous Hall effect or quantum Hall effect, when the chemical potential locates inside the gap. Further breaking of inversion symmetry is possible by employing magnetic topological insulator heterostructures that host nondegenerate top and bottom surface states. Here, we demonstrate the tailored-material approach for the realization of robust quantum Hall states in the bilayer s…
An electric charge near the surface of a topological insulator induces an image magnetic monopole. Here, we show that if the topological insulator surface has a negative curvature, namely in the case of a semispherical cavity, the induced Hall current reverses its rotation as the electric charge crosses the semisphere geometric focus. Such a reversion is shown to be equivalent of inverting the charge of the image magnetic monopole. We also discuss upon the case of a semicylindrical cavity, where Hall current reversion appears to be feasible of probing in realistic experiments.
We consider a number of strongly-correlated quantum Hall states which are likely to be realized in bilayer quantum Hall systems at total Landau level filling fraction ${ν_T}=1$. One state, the $(3,3,-1)$ state, can occur as an instability of a compressible state in the large $d/l_B$ limit, where $d$ and $l_B$ are the interlayer distance and magnetic length, respectively. This state has a hierarchical descendent which is interlayer coherent. Another interlayer coherent state, which is expected in the small $d/l_B$ limit is the well-known Halperin $(1,1,1)$ state. Using the concept of composite …
Recent theories predict dissipationless spin current induced by an electric field in doped semiconductors. Nevertheless, the charge current is still dissipative in these systems. In this work, we theoretically predict the dissipationless spin Hall effect, without any accompanying charge current, in some classes of band insulators, including zero-gap semiconductors such as HgTe and narrow-gap semiconductors such as PbTe. This effect is similar to the quantum Hall effect in that all the states below the gap contribute and there occurs no dissipation. However the spin Hall conductance is not quan…
We study ring shaped (Corbino) devices made of bilayer two-dimensional electron gases in the total filling factor one quantized Hall phase which is considered to be a coherent BCS-like state of interlayer excitons. Identical Josephson currents are observed at the two edges while only a negligible conductance between them is found. The maximum Josephson current observed at either edge can be controlled by passing a second interlayer Josephson current at the other edge. Due to the large electric resistance between the two edges, the interaction between them can only be mediated by the neutral in…
In two-dimensional (2D) electron systems under strong magnetic fields, interactions can cause fractional quantum Hall (FQH) effects. Bringing two 2D conductors to proximity, a new set of correlated states can emerge due to interactions between electrons in the same and opposite layers. Here we report interlayer correlated FQH states in a system of two parallel graphene layers separated by a thin insulator. Current flow in one layer generates different quantized Hall signals in the two layers. This result is interpreted by composite fermion (CF) theory with different intralayer and interlayer C…
The pseudo-spin model for double layer quantum Hall system with total landau level filling factor $ν=1$ is discussed. Unlike the "traditional" one where interlayer voltage enters as static magnetic field along pseudo- spin hard axis, in our model we consider applied interlayer voltage as a frequency of precessing pseudo-magnetic field lying into the easy plane. It is shown that a Landau-Lifshitz equation for the considered pseudo magnetic system well describes existing experimental data. Besides that, the mentioned model predicts novel directed intra-layer transport phenomenon in the system: u…
Using exact diagonalization of bilayer quantum Hall systems at total filling factor $ν_T=1$ in the torus geometry, we show that there is a new long-range interlayer phase coherence due to spontaneous pseudospin spiral order at interlayer distances larger than the critical value at which the pseudospin ferromagnetic order is destroyed. We emphasize the distinction between the interlayer phase coherence and the pseudospin ferromagnetic order.
We study coherence and entanglement properties of the state space of a composite bi-fermion (two electrons pierced by $λ$ magnetic flux lines) at one Landau site of a bilayer quantum Hall system. In particular, interlayer imbalance and entanglement (and its fluctuations) are analyzed for a set of $U(4)$ coherent (\emph{quasiclassical}) states generalizing the standard pseudospin $U(2)$ coherent states for the spin-frozen case. The interplay between spin and pseudospin degrees of freedom opens new possibilities with regard to the spin-frozen case. Actually, spin degrees of freedom make interlay…
Due to strong interlayer correlations, the bilayer quantum Hall system is a single coherent system as a whole rather than a weakly-coupled set of two independent systems, which makes conventional tunnelling theories inapplicable. In this paper, we develop a theory of interlayer tunnelling in coherent exciton condensates of bilayer quantum Hall systems at total filling factor $ν_T=1$. One of the most important consequences of our theory is that the zero-bias interlayer tunnelling conductance peak is strongly enhanced, but fundamentally finite even at zero temperature. We explicitly compute the …
Hall and diagonal resistances of bilayer fractional quantum Hall systems are discussed theoretically. The bilayers have electrodes attached separately to each layer. They are assumed to be coupled weakly by interlayer tunneling, while the interlayer Coulomb interaction is negligibly small. It is shown that source-drain voltage dependence of the resistances reflects the Luttinger liquid parameter of the edge state.
We argue that broken-symmetry states with either spatially diagonal or spatially off-diagonal order are likely in the quantum Hall regime, for clean multiple quantum well (MQW) systems with small layer separations. We find that for MQW systems, unlike bilayers, charge order tends to be favored over spontaneous interlayer coherence. We estimate the size of the interlayer tunneling amplitude needed to stabilize superlattice Bloch minibands by comparing the variational energies of interlayer-coherent superlattice miniband states with those of states with charge order and states with no broken sym…
We argue that all anomalous transport properties of coherent quantum quantum Hall bilayers can be understood in terms of a mean-field transport theory in which the condensate phase is nearly uniform across the sample, and the strength of condensate coupling to interlayer tunneling processes is substantially reduced compared to the predictions of disorder-free microscopic mean-field theory. These ingredients provide a natural explanation for recently established I-V characteristics which feature a critical current above which the tunneling resistance abruptly increases and a non-local interacti…
Fractional quantum Hall states in bilayer system at total filling fraction $ν=1/2$ are examined numerically under some ranges of the layer separation and interlayer tunneling. It is shown that the ground state changes continuously from two-component state to one-component state as the interlayer tunneling rate is increased, while the lowest excited state changes discontinuously. This fact explains observed unusual behavior of the activation energy which reveals upward cusp as a function of interlayer tunneling. Some trial wave functions for the ground state and quasihole states are inspected.
Double-layer quantum Hall systems possess interlayer phase coherence at sufficiently small layer separations, even without interlayer tunneling. When interlayer tunneling is present, application of a sufficiently strong in-plane magnetic field $B_\parallel > B_c$ drives a commensurate-incommensurate (CI) transition to an incommensurate soliton-lattice (SL) state. We calculate the Hartree-Fock ground-state energy of the SL state for all values of $B_\parallel$ within a gradient approximation, and use it to obtain the anisotropic SL stiffness, the Kosterlitz-Thouless melting temperature for the …
