arXiv subjects

Ya-Hui Zhang

Publications and source records attributed to Ya-Hui Zhang.

82 records · Page 5Linked to original sources

arXiv2019

Tunable Correlated Chern Insulator and Ferromagnetism in Trilayer Graphene/Boron Nitride Moiré Superlattice

Studies on two-dimensional electron systems in a strong magnetic field first revealed the quantum Hall (QH) effect, a topological state of matter featuring a finite Chern number (C) and chiral edge states. Haldane later theorized that Chern insulators with integer QH effects could appear in lattice models with complex hopping parameters even at zero magnetic field. The ABC-trilayer graphene/hexagonal boron nitride (TLG/hBN) moiré superlattice provides an attractive platform to explore Chern insulators because it features nearly flat moiré minibands with a valley-dependent electrically tunable Chern number. Here we report the experimental observation of a correlated Chern insulator in a TLG/hBN moiré superlattice. We show that reversing the direction of the applied vertical electric field switches TLG/hBN's moiré minibands between zero and finite Chern numbers, as revealed by dramatic changes in magneto-transport behavior. For topological hole minibands tuned to have a finite Chern number, we focus on 1/4 filling, corresponding to one hole per moiré unit cell. The Hall resistance is well quantized at h/2e2, i.e. C = 2, for |B| > 0.4 T. The correlated Chern insulator is ferromagnetic, exhibiting significant magnetic hysteresis and a large anomalous Hall signal at zero magnetic field. Our discovery of a C = 2 Chern insulator at zero magnetic field should open up exciting opportunities for discovering novel correlated topological states, possibly with novel topological excitations, in nearly flat and topologically nontrivial moiré minibands.

cond-mat.mes-hall↗

arXiv2019

Landau Level Degeneracy in Twisted Bilayer Graphene: Role of Symmetry Breaking

The degeneracy of Landau levels flanking charge neutrality in twisted bilayer graphene is known to change from eight-fold to four-fold when the twist angle is reduced to values near the magic angle of $\approx 1.05^\circ$. This degeneracy lifting has been reproduced in experiments by multiple groups, and is known to occur even in devices which do not harbor the correlated insulators and superconductors. We propose $C_3$ symmetry breaking as an explanation of such robust degeneracy lifting, and support our proposal by numerical results on the Landau level spectrum in near-magic-angle twisted bilayer graphene. Motivated by recent experiments, we further consider the effect of $C_2$ symmetry breaking on the Landau levels.

cond-mat.str-el↗

arXiv2019

Twisted Bilayer Graphene Aligned with Hexagonal Boron Nitride: Anomalous Hall Effect and a Lattice Model

A recent experiment reported a large anomalous Hall effect in Magic Angle Twisted Bilayer Graphene (TBG) aligned with a hexagonal boron nitride(h-BN) substrate at $\frac{3}{4}$ filling of the conduction band. In this paper we study this system theoretically, and propose explanations of this observation. We emphasize that the physics for this new system is qualitatively different from the pure TBG system. The aligned h-BN breaks in-plane two-fold rotation symmetry and gaps out the Dirac crossings of ordinary TBG. The resulting valence and conduction bands of each valley carry equal and opposite Chern numbers $C=\pm 1$. A useful framework is provided by a lattice extended Hubbard model for this system which we derive. An obvious possible explanation of the anomalous Hall effect is that at $3/4$-filling the system is a spin-valley polarized ferromagnetic insulator where the electrons completely fill a Chern band. We also examine an alternate more radical proposal of a compressible valley polarized but spin unpolarized composite ferm liquid metallic state. We argue that either state is compatible with current experiments, and propose ways to distinguish between them in the future. We also briefly discuss the physics at $1/2$ filling.

cond-mat.str-el↗

arXiv2018

Nearly Flat Chern Bands in Moiré Superlattices

Topology and electron interactions are two central themes in modern condensed matter physics. Here we propose graphene based systems where both the band topology and interaction effects can be simply controlled with electric fields. We study a number of systems of twisted double layers with small twist angle where a moiré super-lattice is formed. Each layer is chosen to be either AB stacked bilayer graphene (BG), ABC stacked trilayer graphene (TG), or hexagonal boron nitride (h-BN). In these systems a vertical applied electric field enables control of the bandwidth, and interestingly also the Chern number. We find that the Chern numbers of the bands associated with each of the two microscopic valleys can be $\pm 0,\pm 1,\pm 2, \pm 3$ depending on the specific system and vertical electrical field. We show that these graphene moiré super-lattices are promising platforms to realize a number of fascinating many-body phenomena, including (Fractional) Quantum Anomalous Hall Effects. We also discuss conceptual similarities and implications for modeling twisted bilayer graphene systems.

cond-mat.str-el↗

arXiv2018

Bridging Hubbard Model Physics and Quantum Hall Physics in Trilayer Graphene/h-BN moiré superlattice

The moiré superlattice formed by ABC stacked trilayer graphene aligned with a hexagonal boron nitride substrate (TG/h-BN) provides an interesting system where both the bandwidth and the topology can be tuned by an applied perpendicular electric field $D$ . Thus the TG/h-BN system can simulate both Hubbard model physics and nearly flat Chern band physics within one sample. We derive lattice models for both signs of $D$ (which controls the band topology) separately through explicit Wannier orbital construction and mapping of Coulomb interaction. When the bands are topologically trivial, we discuss possible candidates for Mott insulators at integer number of holes per site (labeled as $ν_T$). These include both broken symmetry states and quantum spin liquid insulators which may be particularly favorable in the vicinity of the Mott transition. We propose feasible experiments to study carefully the bandwidth tuned and the doping tuned Mott metal-insulator transition at both $ν_T=1$ and $ν_T=2$. We discuss the interesting possibility of probing experimentally a bandwidth (or doping) controlled continuous Mott transition between a Fermi liquid metal and a quantum spin liquid insulator. Finally we also show that the system has a large valley Zeeman coupling to a small out-of-plane magnetic field, which can be used to control the valley degree of freedom.

cond-mat.str-el↗

arXiv2018

Composite Fermion Insulator in Opposite-Fields Quantum Hall Bilayers

Recently several moiré super-lattice systems are proposed to host nearly flat $\pm$ Chern bands: the bands of the two valleys have opposite Chern numbers. In these systems the charge of each valley is separately conserved. For the $C=\pm 1$ case, in the perfect flat band limit, the system can be mapped to two Landau levels from opposite magnetic fields. Motivated by these promising experimental realizations, we consider a quantum Hall bilayers from opposite magnetic fields close to the filling $ν_T=\frac{1}{2}+\frac{1}{2}$. We add inter-layer repulsive interaction starting from two decoupled Composite Fermion Liquids (CFL) with opposite chiralities. In this case physical exciton is frustrated from condensation, unlike the conventional quantum Hall bilayers. We argue that more natural phases are the exciton condensates between composite fermions or between slave bosons. The resulting states are insulators with neutral Fermi surfaces coupled to an emergent $U(1)$ gauge field without Chern-Simons term. This insulating state is a generalization of the well-known CFL state and may potentially emerge in the moiré systems with $C=\pm 1$ narrow bands. Finally we also comment on the possibility of a topological superconductor from charge frustration in opposite-fields quantum Hall bilayers or in $C=\pm 1$ flat bands.

cond-mat.str-el↗

arXiv2018

Paired exciton condensate and topological charge-$4e$ composite fermion pairing in half-filled quantum Hall bilayers

Half-filled Landau levels admit the theoretically powerful fermion-vortex duality but longstanding puzzles remain in their experimental realization as $ν_T=1$ quantum Hall bilayers, further complicated by Zheng et al's recent numerical discovery of an unknown phase at intermediate layer spacing. Here we propose that half-filled quantum Hall bilayers ($ν_T=1$) at intermediate values of the interlayer distance $d/\ell_B$ enter a phase with \textit{paired exciton condensation}. This phase shows signatures analogous to the condensate of interlayer excitons (electrons bound to opposite-layer holes) well-known for small $d$ but importantly condenses only exciton pairs. To study it theoretically we derive an effective Hamiltonian for bosonic excitons $b_k$ and show that the single-boson condensate suddenly vanishes for $d$ above a critical $d_{c1} \approx 0.95 l_B$. The nonzero condensation fraction $n_0=\langle b(0) \rangle ^2$ at $d_{c1}$ suggests that the phase stiffness remains nonzero for a range of $d>d_{c1}$ via an intermediate phase of paired-exciton condensation, exhibiting $\langle bb \rangle \neq 0$ while $\langle b \rangle =0$. Motivated by these results we derive a $K$-matrix description of the paired exciton condensate's topological properties from composite boson theory. The elementary charged excitation is a half meron with $\frac{1}{4}$ charge and fractional self-statistics $θ_s=\fracπ{16}$. Finally we argue for an equivalent description via the $d=\infty$ limit through topological charge-$4e$ pairing of composite fermions. We suggest graphene double layers should access this phase and propose various experimental signatures, including an Ising transition $T_{Ising}$ below the Berezinskii-Kosterlitz-Thouless transition $T_{BKT}$ at $d \sim d_{c1}$.

cond-mat.str-el↗

arXiv2018

Pair density wave, charge density wave and vortex in high Tc cuprates

A recent scanning tunneling microscopy (STM) experiment reports the observation of charge density wave (CDW) with period of approximately 8a in the halo region surrounding the vortex core, in striking contrast to the approximately period 4a CDW that are commonly observed in the cuprates. Inspired by this work, we study a model where a bi-directional pair density wave (PDW) with period 8 is at play. This further divides into two classes, (1) where the PDW is a competing state of the d wave superconductor and can exist only near the vortex core where the d wave order is suppressed, and (2) where the PDW is the primary order, the so called mother state that persists with strong phase fluctuations to high temperature and high magnetic field and lies behind the pseudogap phenomenology. We study the charge density wave structures near the vortex core in these models. We emphasize the importance of the phase winding of the d-wave order parameter. The PDW can be pinned by the vortex core due to this winding and become static. Furthermore, the period 8 CDW inherits the properties of this winding, which gives rise to a special feature of the Fourier transform peak, namely, it is split in certain directions. There are also a line of zeros in the inverse Fourier transform of filtered data. We propose that these are key experimental signatures that can distinguish between the PDW-driven scenario from the more mundane option that the period 8 CDW is primary. We discuss the pros and cons of the options considered above. Finally we attempt to place the STM experiment in the broader context of pseudogap physics of underdoped cuprates and relate this observation to the unusual properties of X ray scattering data on CDW carried out to very high magnetic field.

cond-mat.str-el↗

arXiv2017

Entanglement Entropy of Target Functions for Image Classification and Convolutional Neural Network

The success of deep convolutional neural network (CNN) in computer vision especially image classification problems requests a new information theory for function of image, instead of image itself. In this article, after establishing a deep mathematical connection between image classification problem and quantum spin model, we propose to use entanglement entropy, a generalization of classical Boltzmann-Shannon entropy, as a powerful tool to characterize the information needed for representation of general function of image. We prove that there is a sub-volume-law bound for entanglement entropy of target functions of reasonable image classification problems. Therefore target functions of image classification only occupy a small subspace of the whole Hilbert space. As a result, a neural network with polynomial number of parameters is efficient for representation of such target functions of image. The concept of entanglement entropy can also be useful to characterize the expressive power of different neural networks. For example, we show that to maintain the same expressive power, number of channels $D$ in a convolutional neural network should scale with the number of convolution layers $n_c$ as $D\sim D_0^{\frac{1}{n_c}}$. Therefore, deeper CNN with large $n_c$ is more efficient than shallow ones.

cs.LG↗

arXiv2013

Conserving and Gapless Hartree-Fock-Bogoliubov theory for 3D dilute Bose gas at finite temperature

The energy spectrum for the three dimensional Bose gas in Bose-Einstein Condensation phase is calculated with Modified Hartree-Fock-Bogoliubov theory, which is both conserving and gapless. From Improved $Φ-$% derivable theory, the diagrams needed to preserve Ward-Takahashi Identity are resummed in a systematic and nonperturbative way. The results show significant discrepancies with Popov theory at finite temperature. It is valid up to the critical temperature where the dispersion relation of the low energy excitation spectrum changes from linear to quadratic. Because of the repulsive interaction, the critical temperature has a positive shift from that of idea gas, which is in accordance with the result from the previous calculations in the uncondensed phase.

cond-mat.quant-gas↗