Critical Majorana fermion at a topological quantum Hall bilayer transition
School of Physics and Astronomy, University of Leeds（利兹大学物理与天文学学院）；Institute of Natural Sciences, Westlake Institute for Advanced Study（西湖高等研究院自然科学研究院）；Department of Physics, School of Science, Westlake University（西湖大学理学院物理系）；Center for Computational Quantum Physics, Flatiron Institute（西蒙斯平坦研究所计算量子物理中心）；Department of Physics, Princeton University（普林斯顿大学物理系）；Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité（巴黎高等师范学校物理实验室，ENS，PSL大学，法国国家科学研究中心，索邦大学，巴黎第七大学，索邦巴黎城）
Cristian Voinea, Wei Zhu, Nicolas Regnault, Zlatko Papić
Quantum Hall bilayers are a uniquely tunable platform that can realize continuous transitions between distinct topological phases of matter. One prominent example is the transition between the Halperin state and the Moore--Read Pfaffian, long predicted to host a critical theory of Majorana fermions but so far not verified in unbiased microscopic simulations. Using the fuzzy sphere regularization, we identify the low-energy spectrum at this transition with the 3D gauged Majorana conformal field theory. We show that the transition is driven by the closing of the neutral fermion gap, and we directly extract the operator content in both integer and half-integer spin sectors. Our results resolve the long-standing question of the nature of a topological phase transition in a setting relevant to quantum Hall experiments, while also providing the first realization of a fermionic theory on the fuzzy sphere, previously limited to bosonic theories.
We consider the time-reversal odd dynamics of the bilayer graphene at low energies in the quantum Hall regime. A generating functional for the effective action that captures the electromagnetic response to all orders in momentum and frequency is presented and evaluated to the third order in the space-time gradient $\mathcal O(\partial^3)$. In addition, we calculate the Hall viscosity and derive an explicit relationship with the $q^2$ coefficient of the Hall conductivity. It is reminiscent of the Hoyos--Son relation in the Galilean invariant systems, which can be recovered in the limit of large…
We present a microscopic study of the interlayer spacing d versus in-plane magnetic field $B_\parallel$ phase diagram for bilayer quantum Hall (QH) pseudo-ferromagnets. In addition to the interlayer charge balanced commensurate and incommensurate states analyzed previously, we address the corresponding interlayer charge unbalanced "canted" QH states. We predict a large anomaly in the bilayer capacitance at the canting transition and the formation of dipole stripe domains with periods exceeding 1 micron in the canted state.
Twisted bilayer graphene (TBG) realizes a highly tunable, strongly interacting system featuring superconductivity and various correlated insulating states. We establish gate-defined wires in TBG with proximity-induced spin-orbit coupling as $(i)$ a tool for revealing the nature of correlated insulators and $(ii)$ a platform for Majorana-based topological qubits. In particular, we show that the band structure of a gate-defined wire immersed in an `inter-valley coherent' correlated insulator inherits electrically detectable fingerprints of symmetry breaking native to the latter. Surrounding the …
We present a microscopic theory of the Hall current in the bilayer quantum Hall system on the basis of noncommutative geometry. By analyzing the Heisenberg equation of motion and the continuity equation of charge, we demonstrate the emergence of the phase current in a system where the interlayer phase coherence develops spontaneously. The phase current arranges itself to minimize the total energy of the system, as induces certain anomalous behaviors in the Hall current in the counterflow geometry and also in the drag experiment. They explain the recent experimental data for anomalous Hall resi…
We derive the low-energy theory of semi-quantized quantum Hall states, a recently observed class of gapless bilayer fractional quantum Hall states. Our theory shows these states to feature gapless quasiparticles of fractional charge coupled to an emergent Chern-Simons gauge field. These gapless quasiparticles can be understood as composites of electrons and Laughlin-like quasiparticles. We show that semi-quantized quantum Hall states exhibit perfect interlayer drag, host non-Fermi liquid physics, and serve as versatile parent states for fully gapped topological phases hosting anyonic excitatio…
We study the fractional quantum Hall effect in a bilayer with charge-distribution imbalance induced, for instance, by a bias gate voltage. The bilayer can either be intrinsic or it can be formed spontaneously in wide quantum wells, due to the Coulomb repulsion between electrons. We focus on fractional quantum Hall effect in asymmetric bilayer systems at filling factor nu=4/11 and show that an asymmetric Halperin-like trial wavefunction gives a valid description of the ground state of the system.
We discuss the quantum Hall effect of bilayer graphene with finite gate voltage where the Fermi energy exceeds the interlayer hopping energy. We calculated magnetic susceptibility, diagonal and off-diagonal conductivities in finite-magnetic-field formalism, and observed crossover of integer quantum Hall effect from two independent monolayer type system to strongly coupled bilayer systems by changing the ratio of interlayer hopping energy and the gate voltage. We also discuss the case of multilayer systems with Bernal stacking
We argue on the basis of phenomenological and microscopic considerations that there is no d.c. Josephson effect in ordered bilayer quantum Hall systems, even at T=0. Instead the tunnel conductance is strongly enhanced, approaching a finite value proportional to the square of the order parameter as the interlayer tunneling amplitude vanishes.
Spin transport properties of a coupled bilayer electron gas with Rashba spin-orbit coupling are studied. The definition of the spin currents in each layer as well as the corresponding continuity-like equations in the bilayer system are given. The curves of the spin Hall conductivities obtained in each layer exhibit sharp cusps around a particular value of the tunnelling strength and the conductivities undergo sign changes across this point. Our investigation on the impurity effect manifests that an arbitrarily small concentration of nonmagnetic impurities does not suppress the spin Hall conduc…
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.
We present a phase diagram for a double quantum well bilayer electron gas in the quantum Hall regime at total filling factor $ν=1$, based on exact numerical calculations of the topological Chern number matrix and the (inter-layer) superfluid density. We find three phases: a quantized Hall state with pseudo-spin superfluidity, a quantized Hall state with pseudo-spin ``gauge-glass'' order, and a decoupled composite Fermi liquid. Comparison with experiments provides a consistent explanation of the observed quantum Hall plateau, Hall drag plateau and vanishing Hall drag resistance, as well as the …
We use high-mobility bilayer hole systems with negligible tunneling to examine how the bilayer nu = 1 quantum Hall state evolves as charge is transferred from one layer to the other at constant total density. We map bilayer nu = 1 state stability versus imbalance for five total densities spanning the range from strongly interlayer coherent to incoherent. We observe competition between single-layer correlations and interlayer coherence. Most significantly, we find that bilayer systems that are incoherent at balance can develop spontaneous interlayer coherence with imbalance, in agreement with r…
We discuss the composite fermion pairing state in bilayer quantum Hall systems. After the evaluation of the range of the inter-layer separation in which the quantum Hall state is stabilized, we discuss the effect of inter-layer tunneling on the composite fermion pairing state at ν=1/2. We show that there is a cusp at the transition point between the Halperin (3,3,1) state and the Pfaffian state.
Bilayer quantum Hall states support a flow of nearly dissipationless staggered current which can only decay through collective channels. We study the dominant finite-temperature dissipation mechanism which in narrow bars is driven by thermal nucleation of pseudospin solitons. We find the finite-temperature resistivity, predict the resulting staggered current-voltage characteristics, and calculate the associated zero-temperature critical staggered current and gate voltage.
The frictional drag between parallel two-dimensional electron systems has been measured in a regime of strong interlayer correlations. When the bilayer system enters the excitonic quantized Hall state at total Landau level filling factor ν_T=1 the longitudinal component of the drag vanishes but a strong Hall component develops. The Hall drag resistance is observed to be accurately quantized at h/e^2.
We study the magnetotransport properties of dual-gated graphene bilayers, in which the total density and layer density imbalance are independently controlled. As the bilayer is imbalanced we observe the emergence of a quantum Hall state (QHS) at filling factor $ν=0$ evinced by a plateau in the Hall conductivity, consistent with the opening of a gap between the electron and hole bands. By varying the layer density imbalance at fixed total density, we observe a suppression of the QHS at filling factors $ν=8$ and $ν=12$ when the layer densities are balanced, an observation at variance with theore…
The tilting angular dependence of the energy gap was measured in the bilayer quantum Hall state at the Landau level filling $ν=1$ by changing the density imbalance between the two layers. The observed gap behavior shows a continuous transformation from the bilayer balanced density state to the monolayer state. Even a sample with 33 K tunneling gap shows the same activation energy anomaly reported by Murphy {\it et al.}. We discuss a possible relation between our experimental results and the quantum Hall ferromagnet of spins and pseudospins.
Tunneling spectroscopy reveals evidence for interlayer electron-hole correlations in quantum Hall bilayer two-dimensional electron systems at layer separations near, but above, the transition to the incompressible exciton condensate at total Landau level filling $ν_T=1$. These correlations are manifested by a non-linear suppression of the Coulomb pseudogap which inhibits low energy interlayer tunneling in weakly-coupled bilayers. The pseudogap suppression is strongest at $ν_T=1$ and grows rapidly as the critical layer separation for exciton condensation is approached from above.
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.
The quantum Hall phase diagram of the half-filled bilayer system in the second Landau level is studied as a function of tunneling and layer separation using exact diagonalization. We make the striking prediction that bilayer structures would manifest two distinct branches of incompressible fractional quantum Hall effect (FQHE) corresponding to the Abelian 331 state (at moderate to low tunneling and large layer separation) and the non-Abelian Pfaffian state (at large tunneling and small layer separation). The observation of these two FQHE branches and the quantum phase transition between them w…
We systematically discuss properties of quantum disordered states of the quantum Hall bilayer at ν_T = 1. For one of them, so-called vortex metal state, we find ODLRO (off-diagonal long-range order) of algebraic kind, and derive its transport properties. It is shown that this state is relevant for the explanation of the "imperfect" superfluid behavior, and persistent intercorrelations, for large distances between layers, that were found in experiments.
By tilting the samples in the magnetic field, we measured and compared the Skyrmion excitations in the bilayer quantum Hall (QH) state at the Landau-level filling factor $ν=2$ and in the monolayer QH state at $ν=1$. The observed number of flipped spins is $N_s=14$ in the bilayer system with a large tunneling gap, and $N_s=7$ in the bilayer system with a small tunneling gap, while it is $N_s=7$ in the monolayer system. The difference is interpreted due to the interlayer exchange interaction. Moreover, we have observed seemingly preferred numbers $N_s=14,7,1$ for the flipped spins by tilting bil…
We demonstrate that counterflowing electrical currents can move through the bulk of the excitonic quantized Hall phase found in bilayer two-dimensional electron systems (2DES) even as charged excitations cannot. These counterflowing currents are transported by neutral excitons which are emitted and absorbed at the inner and outer boundaries of an annular 2DES sample via an Andreev reflection process.
The Halperin $(m,m',n)$ bilayer quantum Hall states are studied on thin cylinders. In this limit, charge density wave patterns emerge that are characteristic of the underlying quantum Hall state. The general patterns are worked out from a variant of the plasma analogy. Torus degeneracies are recovered, and for some important special cases a connection to well-known spin chain physics is made. By including interlayer tunneling, we also work out the critical behavior of a possible phase transition between the $(331)$ state and the non-abelian Moore-Read state in the thin cylinder limit.
We examine the quantum phase diagram of the fractional quantum Hall effect in the lowest Landau level in half-filled bilayer structures as a function of tunneling strength and layer separation. Using numerical exact diagonalization we investigate the important question of whether this system supports a fractional quantum Hall effect described by the non-Abelian Moore-Read Pfaffian state in the strong tunneling regime. We find that, although it is in principle possible, it is unlikely that the non-Abelian FQHE exists in the lowest Landau level. We establish that all so far observed FQHE states …
The Hartree-Fock paradigm of bilayer quantum Hall states with finite tunneling at filling factor $ν$=1 has full pseudospin ferromagnetic order with all the electrons in the lowest symmetric Landau level. Inelastic light scattering measurements of low energy spin excitations reveal major departures from the paradigm at relatively large tunneling gaps. The results indicate the emergence of a novel correlated quantum Hall state at $ν$=1 characterized by reduced pseudospin order. Marked anomalies occur in spin excitations when pseudospin polarization collapses by application of in-plane magnetic f…
Double-layer electron systems in the quantum Hall regime have excitonic condensate ground states when the layers are close together and the total Landau level filling factor is close to an odd integer. In this paper we discuss the microscopic physics of these states and recent progress toward building a theory of the anomalous collective transport effects that occur in separately contacted bilayers when the condensate is present.
We analyze bilayer quantum Hall ferromagnets, whose underlying symmetry group is SU(4). Spin-pseudospin coherence develops spontaneously when the total electron density is low enough. Quasiparticles are CP^3 skyrmions. One skyrmion induces charge modulations on both of the two layers. At the filling factor$ν=2/m$ one elementary excitation consists of a pair of skyrmions and its charge is $2e/m$. Recent experimental data due to Sawada et al. [Phys. Rev. Lett. {\bf 80}, 4534 (1998)] support this conclusion.
Utilizing the Baym-Kadanoff formalism with the polarization function calculated in the random phase approximation, the dynamics of the $ν=0$ quantum Hall state in bilayer graphene is analyzed. Two phases with nonzero energy gap, the ferromagnetic and layer asymmetric ones, are found. The phase diagram in the plane $(\tildeΔ_0,B)$, where $\tildeΔ_0$ is a top-bottom gates voltage imbalance, is described. It is shown that the energy gaps in these phases scale linearly, $ΔE\sim 10 B[T]K, with magnetic field. The comparison of these results with recent experiments in bilayer graphene is presented.
Bilayer quantum Hall system at total filling factor $ν=1$ shows a rich variety of broken symmetry ground states because of the competition between the interlayer and intralayer Coulomb interactions. When the layers are sufficiently close, a bilayer system develops spontaneous interlayer phase-coherence that manifests itself through a spectacular enhancement of the zero-bias interlayer tunneling conductance. We present a theory of this tunneling conductance anomaly, and show that the zero-bias conductance is proportional to the square of the {\it quasiparticle} tunneling amplitude.
Composite fermion metal states emerge in quantum Hall bilayers at total Landau level filling factor $ν_T$=1 when the tunneling gap collapses by application of in-plane components of the external magnetic field. Evidence of this transformation is found in the continua of spin excitations observed by inelastic light scattering below the spin-wave mode at the Zeeman energy. The low-lying spin modes are interpreted as quasiparticle excitations with simultaneous changes in spin orientation and composite fermion Landau level index.
We discuss the interplay between transport and intrinsic dissipation in quantum Hall bilayers, within the framework of a simple thought experiment. We compute, for the first time, quantum corrections to the semiclassical dynamics of this system. This allows us to re-interpret tunnelling measurements on these systems. We find a strong peak in the zero-temperature tunnelling current that arises from the decay of Josephson-like oscillations into incoherent charge fluctuations. In the presence of an in-plane field, resonances in the tunnelling current develop an asymmetric lineshape.
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.
We propose a phenomenological model that describes counterflow and drag experiments with quantum Hall bilayers in a ν_T=1 state. We consider the system consisting of statistically distributed areas with local total filling factors ν_{T1}>1 and ν_{T2}<1. The excess or deficit of electrons in a given area results in an appearance of vortex excitations. The vortices in quantum Hall bilayers are charged. They are responsible for a decay of the exciton supercurrent, and, at the same time, contribute to the conductivity directly. The experimental temperature dependence of the counterflow and drive r…
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.
The natures of the ground state in a $ν_{\rm T}=1$ bilayer quantum Hall system at a variety of layer spacing are investigated. At small layer separations the system exhibits spontaneous interlayer phase coherence. It is claimed that the Halperin's (1,1,1) state is not relevant in the incompressible regime near the incompressible to compressible transition point in which the Josephson-like effect was observed. The two-particle correlation function shows the deflated correlation hole at this regime. An effective model that can give a good approximation to the ground state is proposed. A connecti…
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 nature of fractional quantum Hall (FQH) states is determined by the interplay between the Coulomb interaction and the symmetries of the system. The unique combination of spin, valley, and orbital degeneracies in bilayer graphene is predicted to produce novel and tunable FQH ground states. Here we present local electronic compressibility measurements of the FQH effect in the lowest Landau level of bilayer graphene. We observe incompressible FQH states at filling factors v = 2p + 2/3 with hints of additional states appearing at v = 2p + 3/5, where p = -2,-1, 0, and 1. This sequence of states…
Bilayer graphene has been predicted to give unprecedented tunability of the electron-electron interaction with the help of external parameters, allowing one to stabilize different fractional quantum Hall states. Recent experimental works make theoretical analysis of such systems extremely relevant. In this paper we describe a methodology for investigating the possibility of realizing specific fractional quantum Hall states in bilayer graphene taking into account polarization effects and virtual interband transitions. We apply this methodology to explore the possibility of realizing the Moore-R…
We study continuous quantum phase transitions that can occur in bilayer fractional quantum Hall (FQH) systems as the interlayer tunneling and interlayer repulsion are tuned. We introduce a slave-particle gauge theory description of a series of continuous transitions from the (ppq) Abelian bilayer states to a set of non-Abelian FQH states, which we dub the orbifold FQH states, of which the Z4 parafermion (Read-Rezayi) state is a special case. This provides an example in which Z2 electron fractionalization leads to non-Abelian topological phases. The naive "ideal" wave functions and ideal Hamilt…
We show that the $ν=8$ integer quantum Hall state can support Majorana zero modes at domain walls between its two different stable chiral edge phases without superconductivity. This is due to the existence of an edge phase that does not support gapless fermionic excitations; all gapless excitations are bosonic in this edge phase. Majorana fermion zero modes occur at a domain wall between this edge phase and the more conventional one that does support gapless fermions. Remarkably, due to the chirality of the system, the topological degeneracy of these zero modes has exponential protection, as a…
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 investigate the electron spin states in the bilayer quantum Hall system at total Landau level filling factor nu =2 exploiting current-pumped and resistively detected NMR. The measured Knight shift, KS, of 75As nuclei reveals continuous variation of the out-of-plane electronic spin polarization between nearly full and zero as a function of density imbalance. Nuclear spin relaxation measurements indicate a concurrent development of an in-plane spin component. These results provide direct information on the spin configuration in this system and comprise strong evidence for the spin canting sug…
Measurements in GaAs hole bilayers with unequal layer densities reveal a pronounced magneto-resistance hysteresis at the magnetic field positions where either the majority or minority layer is at Landau level filling factor one. At a fixed field in the hysteretic regions, the resistance exhibits an unusual time dependence, consisting of random, bidirectional jumps followed by slow relaxations. These anomalies are apparently caused by instabilities in the charge distribution of the two layers.
In this work, we investigate the conductance and current correlations properties of a quantum topological inteferometer consisting of a QD coupled to two Majorana Bound States (MBSs) confined at both ends of a 1D topological superconductor ring nanowire. We analyze the ring in its topological non trivial and trivial phases to show that the tunneling conductance, shot noise and fano factor present unique characteristics to distinguish the hallmark of MBSs. We reinforce our findings by taking advantage of the correspondence between the quantum topological interferometer and a dot effectively cou…
We propose a method for studying the strong interaction regimes in twisted bilayer graphene using hybrid Wannier functions, that are Wannier-like in one direction and Bloch-like in the other. We focus on the active bands as given by the continuum model proposed by Bistritzer and MacDonald, and discuss the properties of corresponding hybrid Wannier functions. We then employ the method for a study of the fillings of $\pm 3$ electrons per moiré cell using the Hartree-Fock method. We discuss at length different regimes under which a quantized anomalous Hall effect is seen in these two fillings.
We calculate the topological entanglement entropy in bilayer quantum Hall systems, dividing the set of quantum numbers into four parts. This topological entanglement entropy allows us to draw a phase diagram in the parameter space of layer separation and tunneling amplitude. We perform the finite size scaling analysis of the topological entanglement entropy in order to see the quantum phase transition clearly.
We have investigated the topological Hall effect (THE) in MnGa/Pt and MnGa/Ta bilayers induced by interfacial Dzyaloshinskii-Moriya interaction (DMI). The most evident THE signals have been found based on the MnGa films with small critical DMI energy constant Dc. The large topological portion of the Hall signal from the total Hall signal has been extracted in the whole temperature range from 5 to 300 K. These results open up the exploration of the DMI induced magnetic behavior based on the bulk perpendicular magnetic anisotropy materials for fundamental physics and magnetic storage technologie…
In this work, we calculate the optical response and the nonlinear Hall response of twisted bilayer graphene (TBG) in the insulating states. Different insulating states, including spin-valley polarized (SPVP) state, spin-polarized quantum Hall(SPQH) state, spin-polarized valley Hall (SPVH) state, and spin polarized Kramers-intervalley coherence (SPKIVC) state, are considered. We calculate the optical conductivity ($σ_{xx}$) of these four states and we find that the spin-valley polarized state shows a two-peak feature which is different from the other three states. In order to distinguish the ot…
Recent experiments on quantum Hall bilayers near total filling factor 1 have demonstrated that they support an ``imperfect'' two-dimensional superfluidity, in which there is nearly dissipationless transport at non-vanishing temperature observed both in counterflow resistance and interlayer tunneling. We argue that this behavior may be understood in terms of a {\it coherence network} induced in the bilayer by disorder, in which an incompressible, coherent state exists in narrow regions separating puddles of dense vortex-antivortex pairs. A renormalization group analysis shows that it is appropr…
Twisted bilayer graphene (TBG) with interlayer twist angles near the magic angle $\approx 1.08^{\circ}$ hosts flat bands and exhibits correlated states including Mott-like insulators, superconductivity and magnetism. Here we report combined temperature-dependent transport measurements of the longitudinal and Hall resistivities in close to magic-angle TBG. While the observed longitudinal resistivity follows linear temperature $T$ dependence consistent with previous reports, the Hall resistance shows an anomalous $T$ dependence with the cotangent of the Hall angle cot $Θ{_H} \propto T^2$. Boltzm…
Recently, iron-chalcogenide superconductors have emerged as a new and promising platform for studying and manipulating Majorana zero mode (MZM). By combining topological band structure and superconductivity in a multiband material, they provide significant advantages such as higher superconducting transition temperature (Tc) and isolated Majorana mode. However, iron-chalcogenide superconductors, especially Fe(Te,Se), suffer from strong inhomogeneity which may hamper their practical application. On the other hand, some iron-pnictide (Fe-As) superconductors, such as LiFeAs, have been demonstrate…
Synthetic quantum Hall bilayer (SQHB), realized by optically driven monolayer graphene in the quantum Hall regime, provides a flexible platform for engineering quantum Hall phases as discussed in [Phys. Rev. Lett. 119, 247403]. The coherent driving which couples two Landau levels mimicks an effective tunneling between synthetic layers. The tunneling strength, the effective Zeeman coupling, and two-body interaction matrix elements are tunable by varying the driving frequency and the driving strength. Using infinite density matrix renormalization group (iDMRG) techniques combined with exact diag…
Motivated by the fact that many bilayer quantum magnets occur in nature, we generalize the study of thermal Hall transports of spin excitations to bilayer magnetic systems. It is shown that bilayer magnetic systems can be coupled either ferromagnetically or antiferromagnetically. We study both scenarios on the honeycomb lattice and show that the system realizes topologically nontrivial magnon bands induced by alternating next-nearest-neighbour Dzyaloshinsky-Moriya interaction (DMI). As a result, the bilayer system realizes both magnon Hall effect and magnon spin Nernst effect. We show that ant…
After the recognition of the possibility to implement Majorana fermions using the building blocks of solid-state matters, the detection of this peculiar particle has been an intense focus of research. Here we experimentally demonstrate a collection of Majorana fermions living in a one-dimensional transport channel at the boundary of a superconducting quantum anomalous Hall insulator thin film. A series of topological phase changes are controlled by the reversal of the magnetization, where a half-integer quantized conductance plateau (0.5e2/h) is observed as a clear signature of the Majorana ph…
Several recent works have proposed that electron-electron interactions in bilayer graphene can be tuned with the help of external parameters, making it possible to stabilize different fractional quantum Hall states. In these prior works, phase diagrams were calculated based on a single Landau level approximation. We go beyond this approximation and investigate the influence of polarization effects and virtual interband transitions on the stability of fractional quantum Hall states in bilayer graphene. We find that for realistic values of the dielectric constant, the phase diagram is strongly m…
Semiconductor double-layers in the quantum Hall regime tend to have superfluid exciton condensate ground states when the total filling factor is an odd integer, provided that the Landau orbitals at the Fermi level in the two layers have the same orbital character. Since the $N=0$ Landau level of bilayer graphene contains states with both $n=0$ and $n=1$ orbital character, the physics of double bilayers falls outside previously studied cases. We show that the superfluid phase stiffness vanishes in double bilayer graphene when $n=0$ and $n=1$ orbitals states are degenerate in one of the layers, …
Single-layer and Bilayer of graphene are new classes of two-dimensional electron systems with unconventional band structures and valley degrees of freedom. The ground states and excitations in the integer and fractional quantum Hall regimes are investigated on torus and spherical geometries with the use of the density matrix renormalization group (DMRG) method. At nonzero Landau level indices, the ground states at effective filling factors 1, 1/3, 2/3 and 2/5 are valley polarized both in single-layer and bilayer graphenes. We examine the elementary charge excitations which could couple with th…
