arXiv subjects

Ya-Hui Zhang

Publications and source records attributed to Ya-Hui Zhang.

At least 37 records · Page 2Linked to original sources

arXiv2025

Anyon superfluid in trilayer quantum Hall systems

Intertwining intrinsic topological order with gapless collective modes remains a central challenge in many-body physics. We show that a quantum-Hall trilayer at $ν_{1}=ν_{2}=ν_{3}= \frac13$, tuned solely by the inter-layer spacing $d$, realizes this goal. Large-scale density-matrix renormalization group (DMRG) calculations and a Chern-Simons field theory analysis reveal an intermediate ``anyon-exciton condensate'' separating the familiar $ν_{\mathrm{tot}}=1$ exciton condensate ($d \to 0$) from three decoupled Laughlin liquids ($d \to \infty$). In this phase, neutral bi-excitons condense while a $ν=\frac23$ Laughlin topological order survives, yielding a Goldstone mode coexisting with fractionalized anyons. A Ginzburg-Landau analysis maps out the finite-temperature phase diagram. The anyon-exciton condensate can be experimentally verified through a vanishing double-counter-flow resistance and a fractional layer-resolved Hall resistivity $R_{xy}=\frac{5}{2} h/e^{2}$, both within reach of existing high-mobility trilayer devices.

cond-mat.str-el↗

arXiv2025

Continuous transition from Fermi liquid to A fractional Chern insulator

Recent experiments in moiré materials have observed fractional Chern insulators (FCI) at zero magnetic field, providing an opportunity to study the transition from FCI to the more conventional phases such as Fermi liquid (FL) and superconductor (SC) by tuning the interaction strength or bandwidth. In this work, we formulate a critical theory for a continuous transition at the filling $ν=\frac{2}{3}$ between the FL and a FCI* phase that hosts an additional neutral sector, but has the same transport signatures as the usual FCI. In our framework, this corresponds to a transition from a composite Fermi liquid (CFL) to a superfluid* phase of the composite bosons. The Fermi liquid close to the transition has an additional factor $|z_i-z_j|^6$ in its wavefunction. Also, the transport behavior at high temperature on the FL side is actually like an `anyon gas' phase on top of the FCI, with $ρ_{xy}$ close to $\frac{3}{2}\frac{h}{e^2}$. FL behavior with $ρ_{xy} \approx 0$ is recovered only at very low temperature. We also briefly discuss the possibility of a chiral superconductor as the descendant of this strongly correlated FL and the potential relevance to the twisted MoTe$_2$ system.

cond-mat.str-el↗

arXiv2025

Mixed valence Mott insulator and composite excitation in twisted bilayer graphene

Interplay of strong correlation and flat topological band has been a central problem in moiré systems such as the magic angle twisted bilayer graphene (TBG). Recent studies show that Mott-like states may still be possible in TBG despite the Wannier obstruction. However, the nature of such unconventional states is still not well understood. In this work we construct the ground state wavefunction and exotic excitations of a symmetric correlated semimetal or insulator at even integer filling using a parton mean field theory of the topological heavy fermion model. We label the valence of the $f$ orbital based on its occupation $n_f$. At $ν=-2$, we show that the $f$ orbital is not in the simple $f^{2+}$ valence expected from a trivial Mott localization. Instead, around $1/3$ of AA sites are self doped, with holes entering the $c$ orbitals away from AA sites. As a result, the $f$ orbital is in a superposition of $f^{2+}$ and $f^{3+}$ valences and should not be viewed as local moment. We dub the phase as \textit{mixed valence Mott insulator}. This unconventional insulator has a large hybridization $\langle c^\dagger f \rangle\neq 0$ and is sharply distinct from the usual `kondo breakdown' picture. In most of the momentum space away from the $Γ$ point, there is a Mott gap equal to the Hubbard $U$. At the $Γ$ point, we have a `charge transfer gap' much smaller than $U$. In particular, the top of the lower band is dominated by a composite excitation, which is a linear combination of $|f^{1+}\rangle\langle f^{2+}|$ and $|f^{2+}\rangle\langle f^{3+}|$ with a sign structure such that it is orthogonal to the microscopic $f$ operator. At $ν=0$, similar approach leads to a Mott semimetal. We hope this work will inspire more explorations of the Anderson models with a large hybridization, a regime which may host new physics beyond the familiar Kondo or heavy fermion systems.

cond-mat.str-el↗

arXiv2025

New classes of quantum anomalous Hall crystals in multilayer graphene

The recent experimental observation of quantum anomalous Hall (QAH) effects in the rhombohedrally stacked pentalayer graphene has motivated theoretical discussions on the possibility of quantum anomalous Hall crystal (QAHC), a topological version of Wigner crystal. Conventional topological Wigner crystals typically have one electron per unit cell. In this work we propose new types of topological Wigner crystals labeled as QAHC-$z$, with $z$ electrons per unit cell. In the pentalayer graphene system, we find parameter regimes where QAHC-2 and QAHC-3 have lower energy than the conventional QAHC-1 at total filling $ν=1$ per moiré unit cell. These states all have total Chern number $C_\mathrm{tot}=1$ and are consistent with the QAH effect observed in the experiments. The larger period QAHC states have lower kinetic energy due to the unique Mexican-hat dispersion of the pentalayer graphene, which can compensate for the loss in the interaction energy. Unlike QAHC-1, QAHC-2 and QAHC-3 break the moiré translation symmetry and are sharply distinct from a moiré band insulator. We also briefly discuss the competition between integer QAH and fractional QAH states at filling $ν=2/3$. Moreover, we find that a stronger moiré potential can significantly change the phase diagram and even favors a QAHC-1 ansatz with $C=2$ Chern band.

cond-mat.str-el↗

arXiv2025

The Future of the Correlated Electron Problem

A central problem in modern condensed matter physics is the understanding of materials with strong electron correlations. Despite extensive work, the essential physics of many of these systems is not understood and there is very little ability to make predictions in this class of materials. In this manuscript we share our personal views on the major open problems in the field of correlated electron systems. We discuss some possible routes to make progress in this rich and fascinating field. This manuscript is the result of the vigorous discussions and deliberations that took place at Johns Hopkins University during a three-day workshop January 27, 28, and 29, 2020 that brought together six senior scientists and 46 more junior scientists. Our hope, is that the topics we have presented will provide inspiration for others working in this field and motivation for the idea that significant progress can be made on very hard problems if we focus our collective energies.

cond-mat.str-el↗

arXiv2025

Ancilla theory of twisted bilayer graphene I: topological Mott localization and pseudogap metal in twisted bilayer graphene

The recent experimental studies of twisted bilayer graphene (TBG) raise a fundamental question: how do we understand Mott localization in a topological band? In this work, we offer a new perspective of Mott physics, which can be generalized to TBG directly in momentum space. In our theory, the Mott gap is understood as from an exciton-like hybridization $Φ(\mathbf k) c^\dagger(\mathbf k)ψ(\mathbf k)$ between the physical electron $c$ and an ancilla fermion $ψ$. In the conventional Mott insulator of trivial band, the hybridization is $s$-wave with $Φ(\mathbf k)=\frac{U}{2}$, where $U$ is the on-site Hubbard interaction. On the other hand, the band topology in TBG enforces a topological Mott hybridization with $Φ(\mathbf k)\sim k_x \pm i k_y$ in a small region around $\mathbf{k}=0$. We dub this new Mott state as topological Mott localization because of the $p\pm ip$ order parameter analogous to the topological superconductor. At $ν=0$, we find a topological Mott semimetal with a low energy effective theory resembling that of the untwisted bilayer graphene. For $ν=\pm 1, \pm 2, \pm 3$, we show transitions from correlated insulators to Mott semimetals at smaller $U$. In the most intriguing density region $ν=-2-x$, we propose a symmetric pseudogap metal at small $x$, which hosts a small Fermi surface and violates the perturbative Luttinger theorem. Interestingly, the quasiparticle is primarily formed by ancilla fermion, which we interpret as a composite fermion formed by a hole bound to a particle-hole pair. Our theory offers a unified language to describe the Mott localization in both trivial and topological bands in momentum space, and we anticipate applications in other moiré systems with topological Wannier obstruction, such as the twisted transition-metal dichalcogenide (TMD) homobilayer.

cond-mat.str-el↗

arXiv2025

High-temperature superconductivity from kinetic energy

Superconductivity is usually assumed to arise from attractive interaction. In this work we show that strong pairing is possible soley from kinetic energy even without a net attraction. We demonstrate a high-temperature kinetic superconductor in a simple lattice model with nearest-neighbor hopping ($t$) projected onto a constrained Hilbert space, analogous to the $t$-$J$ model with $J=0$, where kinetic magnetism has been previously studied. Using density matrix renormalization group (DMRG) on cylinders up to width $L_y=8$, we find a superconducting ground state exhibiting a key difference from high-$T_c$ cuprates: both the pairing gap and phase stiffness \textit{increase} with doping ($x$). We find pairing gaps, determined from spin and single-electron charge gaps, exceeding $1.5t$. This model can be realized within the double Kondo lattice model, relevant to bilayer nickelates, in the limit of strong inter-layer spin coupling ($J_\perp/t \rightarrow +\infty$) and a balancing inter-layer repulsion ($V$). Importantly, the double Kondo model does not fundamentally restrict $J_\perp/t$, suggesting the potential for high critical temperatures ($T_c$) approaching $0.5t$. While this idealized limit predicts large pairing gaps, we show a smooth connection to the more realistic regime with $J_\perp \sim t$, albeit with a reduced pairing gap of approximately $0.1t$. Assuming $t \sim 10^3$ K in typical solid state systems, our model suggests the exciting possibility of achieving $T_c$ of hundreds of Kelvin. We propose searching for bilayer materials with reduced out-of-plane lattice constants to better approximate the conditions of our ideal model.

cond-mat.str-el↗

arXiv2025

A model of $d$-wave superconductivity, antiferromagnetism, and charge order on the square lattice

Early studies proposed a connection between cuprate superconductivity and fractionalized spin liquid states. But the low temperature phase diagram is dominated by states without fractionalization, with a competition between superconductivity and charge-ordered states which break translational symmetry. Our theory uncovers novel features associated with a particular spin-liquid presumed to underlie the pseudogap metal, and shows that it has multiple nearly-degenerate instabilities to confinement of fractionalized excitations, leading to antiferromagnetism, $d$-wave superconductivity, and/or charge order. Our theory provides routes to resolving a number of open puzzles on the cuprate phase diagram. The spin liquid is described by a SU(2) gauge theory of $N_f=2$ massless fundamental Dirac fermions, has an emergent SO(5)$_f$ global symmetry, and is presumed to confine at low energies to the Néel state. At non-zero doping (or smaller Hubbard repulsion at half-filling) we argue that confinement occurs via the Higgs condensation of bosonic chargons carrying fundamental SU(2) gauge charges moving in $π$ flux. At half-filling, the low energy Higgs sector has $N_b=2$ relativistic bosons with a possible emergent SO(5)$_b$ global symmetry describing rotations between a $d$-wave superconductor, period-2 charge stripes, and the time-reversal breaking `$d$-density wave' state. We propose a deconfined quantum critical point between a confining state which breaks SO(5)$_f$ and a confining state which breaks SO(5)$_b$. The pattern of symmetry breaking within both SO(5)s is determined by terms likely irrelevant at the critical point, which can be chosen to obtain a transition between Néel order and $d$-wave superconductivity. A similar theory applies at non-zero doping and large $U$, with longer-range couplings of the chargons leading to charge order with longer periods.

cond-mat.str-el↗

arXiv2025

Electronic spectra with paramagnon fractionalization in the single band Hubbard model

We examine the spectral properties of a recently proposed theory of the intermediate temperature pseudogap metal phase of the cuprates. We show that this theory can be obtained from the familiar paramagnon theory of nearly antiferromagnetic metals by fractionalizing the paramagnon into two `hidden' layers of S=1/2 spins. The first hidden layer of spins hybridizes with the electrons as in a Kondo lattice heavy Fermi liquid, while the second hidden layer of spins forms a spin liquid with fractionalized spinon excitations. We compute the imaginary part of the electronic self energy induced by the spinon excitations. The energy and momentum dependence of the photoemission spectrum across the Brillouin zone provides a good match to observations by He et al. in Bi2201 (Science 331, 1579 (2011)) and by Chen et al. in Bi2212 (Science 366, 1099 (2019)).

cond-mat.str-el↗

arXiv2025

Dirac and chiral spin liquids on spin-1/2 square-lattice Heisenberg antiferromagnet

We revisit the challenging problem of identifying the quantum spin liquid candidate in the spin-1/2 $J_1$-$J_2$ Heisenberg antiferromagnet on the square lattice. By integrating the Gutzwiller-guided density matrix renormalization group method with analytical analyses, we present clear evidence that the ground state is a Z$_2$ Dirac spin liquid. This state can be efficiently described by a Gutzwiller-projected parton theory characterized by its projective symmetry group. To distinguish the difference between the projected Z$_2$ and U(1) parton state, we investigate the chiral spin liquid ground states as topological orders by incorporating a $J_χ$ term into the $J_1$-$J_2$ model and observe a transition from a Z$_2$ chiral spin liquid to a U(1)$_2$ chiral spin liquid as $J_χ$ increases.

cond-mat.str-el↗

arXiv2024

Topological incommensurate Fulde-Ferrell-Larkin-Ovchinnikov superconductor and Bogoliubov Fermi surface in rhombohedral tetra-layer graphene

We performed a random phase approximation (RPA) calculation for a spin-valley polarized model of the rhombohedral tetra-layer graphene to study the possibility of chiral superconductor from the Kohn-Luttinger mechanism. We included the realistic band structure and form factor in our calculation and solved the self-consistent equation numerically by sampling 20,000 points in the momentum space at a given temperature. Around the Van-Hove singularity (VHS), we find p-ip pairing with Chern number switching from $C=-1$ to $C=0$ through a gap closing at $\mathbf k=(0,0)$ (defined relative to $\mathbf K$). Although the superconductor is generically fully gapped at low temperature, we find Bogoliubov Fermi surface at temperature just below mean field $T_c$. Besides, through calculation of the free energy, we conclude that the optimal Cooper pair momentum $\mathbf Q$ is generically finite and can be as large as $0.1 k_F$. We dub the $\mathbf Q\neq 0$ phase as an incommensurate Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) superconductor to distinguish it from the $\mathbf Q=0$ phase. Compared to the $\mathbf Q=0$ phase, our incommensurate $\mathbf Q$ phase is a nematic superconductor if it is in the Fulde-Ferrell(FF) phase or exhibts charge density wave (CDW) if it is in the Larkin-Ovchinnikov (LO) phase. Our work demonstrates the rhombohedral tetra-layer graphene as a wonderful platform to explore Majorana zero-mode, FFLO physics and Bogoliubov fermi surface within one single platform.

cond-mat.supr-con↗

arXiv2024

Topological electronic crystals in twisted bilayer-trilayer graphene

In a dilute two-dimensional electron gas, Coulomb interactions can stabilize the formation of a Wigner crystal. Although Wigner crystals are topologically trivial, it has been predicted that electrons in a partially-filled band can break continuous translational symmetry and time-reversal symmetry spontaneously to form a form of topological electron crystal known as an anomalous Hall crystal. Here, we report the observation of a generalized version of the anomalous Hall crystal in twisted bilayer-trilayer graphene, whose formation is driven by the moire potential. The crystal forms at a band filling factor of one electron per four moiré unit cells ($ν=1/4$) and quadruples the unit-cell area, coinciding with an integer quantum anomalous Hall effect. The Chern number of the state is exceptionally tunable, and can be switched reversibly between $+1$ and $-1$ by electric and magnetic fields. Several other topological electronic crystals arise in a modest magnetic field, originating from $ν=1/3$, $1/2$, $2/3$, and $3/2$. The quantum geometry of the folded bands is likely very different from that of the original parent band, enabling possible future discoveries of correlation-driven topological phenomena

cond-mat.mes-hall↗

arXiv2024

Variational wavefunction for Mott insulator at finite $U$ using ancilla qubits

The Mott regime with finite $U$ offers a promising platform for exploring novel phases of matter, such as quantum spin liquids (QSL) that exhibit fractionalization and emergent gauge field. Here, we provide a new class wavefunction, dubbed ancilla wavefunction, to capture both charge and spin (gauge) fluctuations in QSLs at finite $U$. The ancilla wavefunction can unify the Fermi liquid and Mott insulator phases with a single variation parameter $Φ$ tuning the charge gap. As $Φ\rightarrow\infty$, the wavefunction reduces to the Gutzwiller projected state, while at $Φ=U/2$, it is effectively equivalent to applying an inverse Schrieffer-Wolff transformation to the Gutzwiller projected state. This wavefunction can be numerically simulated in the matrix product state representation, and its performance is supported by numerical results for both one- and two-dimensional Hubbard models. Besides, we propose the possibility of a narrow regime of fractional Fermi liquid phase between the usual Fermi liquid and the Mott insulator phases close to the metal insulator transition -- a scenario typically overlooked by the conventional slave rotor theory. Our ancilla wavefunction offers a novel conceptual framework and a powerful numerical tool for understanding Mott physics.

cond-mat.str-el↗

arXiv2024

Interplay of electronic crystals with integer and fractional Chern insulators in moiré pentalayer graphene

The rapid development of moiré quantum matter has recently led to the remarkable discovery of the fractional quantum anomalous Hall effect, and sparked predictions of other novel correlation-driven topological states. Here, we investigate the interplay of electronic crystals with integer and fractional Chern insulators in a moiré lattice of rhomobohedral pentalayer graphene (RPG) aligned with hexagonal boron nitride. At a doping of one electron per moiré unit cell, we see a correlated insulator with a Chern number that can be tuned between $C=0$ and $+1$ by an electric displacement field, accompanied by an array of other such insulators formed at fractional band fillings, $ν$. Collectively, these states likely correspond to trivial and topological electronic crystals, some of which spontaneously break the discrete translational symmetry of the moiré lattice. Upon applying a modest magnetic field, a narrow region forms around $ν=2/3$ in which transport measurements imply the emergence of a fractional Chern insulator, along with hints of weaker states at other fractional $ν$. In the same sample, we also see a unique sequence of incipient Chern insulators arising over a broad range of incommensurate band filling near two holes per moiré unit cell. Our results establish moiré RPG as a fertile platform for studying the competition and potential intertwining of electronic crystallization and topological charge fractionalization.

cond-mat.mes-hall↗

arXiv2024

Fractional quantum anomalous Hall effects in rhombohedral multilayer graphene in the moiréless limit and in Coulomb imprinted superlattice

The standard theoretical framework for fractional quantum anomalous Hall effect (FQAH) assumes an isolated flat Chern band in the single particle level. In this paper we challenges this paradigm for the FQAH recently observed in the pentalayer rhombohedral stacked graphene aligned with hexagon boron nitride (hBN). We show that the external moiré superlattice potential is simply a perturbation in a model with continuous translation symmetry. Through Hartree Fock calculation, we find that interaction opens a sizable remote band gap, resulting an isolated narrow $C=1$ Chern band at filling $ν=1$. From exact diagonalization (ED) we identify FQAH phases at various fillings. But they exist also in the calculations without any external moiré potential. We suggest that the QAH insulator at $ν=1$ should be viewed as an interaction driven topological Wigner crystal with QAH effect, which is then pinned by a small moiré potential. The $C=1$ QAH crystal is robust with a crystal period around $10\mathrm{nm}$ in 4-layer, 5-layer, 6-layer and 7-layer graphene systems. Our work suggests a new direction to exploring the interplay of topology and FQAH with spontaneous crystal formation in the vanishing moiré potential limit. We also propose a new system to generate and control both honeycomb and triangular moiré superlattice potential through Coulomb interaction from another control layer, which can stabilize or suppress the QAH crystal depending on the density of the control layer.

cond-mat.str-el↗

arXiv2024

Strong pairing and symmetric pseudogap metal in double Kondo lattice model: from nickelate superconductor to tetralayer optical lattice

In this work, we propose and study a double Kondo lattice model which hosts robust superconductivity. The system consists of two identical Kondo lattice model, each with Kondo coupling $J_K$ within each layer, while the localized spin moments are coupled together via an inter-layer on-site antiferromagnetic spin coupling $J_\perp$. We consider the strong $J_\perp$ limit, wherein the local moments tend to form rung singlets and are thus gapped. However, the Kondo coupling $J_K$ transmits the inter-layer entanglement between the local moments to the itinerant electrons. Consequently, the itinerant electrons experience a strong inter-layer antiferromangetic spin coupling and form strong inter-layer pairing, which is confirmed through numerical simulation in one dimensional system. Experimentally, the $J_K \rightarrow -\infty$ limits of the model describes the recently found bilayer nickelate La$_3$Ni$_2$O$_7$, while the $J_K>0$ side can be realized in tetralayer optical lattice of cold atoms. Two extreme limits, $J_K \rightarrow -\infty$ and $J_K \rightarrow +\infty$ limit are shown to be simplified to a bilayer type II t-J model and a bilayer one-orbital t-J model, respectively. Thus, our double Kondo lattice model offers a unified framework for nickelate superconductor and tetralayer optical lattice quantum simulator upon changing the sign of $J_K$. We highlight both the qualitative similarity and the quantitative difference in the two sides of $J_K$. Finally, we discuss the possibility of a symmetric Kondo breakdown transition in the model with a symmetric pseudogap metal corresponding to the usual heavy Fermi liquid.

cond-mat.str-el↗

arXiv2024

Deconfined Fermi liquid to Fermi liquid transition and superconducting instability

Deconfined quantum critical points (DQCP) have attracted lots of attentions in the past decades, but were mainly restricted to incompressible phases. On the other hand, various experimental puzzles call for new theory of unconventional quantum criticality between metals at a generic density. Here we explore the possibility of a deconfined transition between two symmetric Fermi liquids in a bilayer model tuned by inter-layer antiferromagnetic spin-spin coupling $J_\perp$. Across the transition the Fermi surface volume per flavor jumps by $1/2$ of the Brillouin zone (BZ), similar to the small to large Fermi surface transitions in heavy Fermion systems and maybe also in the high Tc cuprates. But in the bilayer case the small Fermi surface phase (dubbed as sFL) has neither symmetry breaking nor fractionalization, akin to the symmetric mass generation (SMG) discussed in high energy physics. We formulate a deconfined critical theory where the two Fermi liquids correspond to higgs and/or confined phases of a $U(1)\times U(1)$ gauge theory. We show that this deconfined FL to FL transition (DFFT) fixed point is unstable to pairing and thus a superconductor dome is expected at low temperature. At finite temperature above the pairing scale, microscopic electron is a three particle bound state of the deconfined fractional fermions in the critical theory. We also introduce another parameter which can suppress the pairing instability, leading to a deconfined tri-critical point stable to zero temperature. We also provide numerical results of the bilayer model in one dimension, with a Luther-Emery liquid between two different Luttinger liquids, similar to the phase diagram from the field theory in two dimension. Our work opens a new direction to exploring deconfined metallic criticality and new pairing mechanism from critical gauge field.

cond-mat.str-el↗

arXiv2024

Topological flat bands in a family of multilayer graphene moiré lattices

Moiré materials host a wealth of intertwined correlated and topological states of matter, all arising from flat electronic bands with nontrivial quantum geometry. A prominent example is the family of alternating-twist magic-angle graphene stacks, which exhibit symmetry-broken states at rational fillings of the moiré band and superconductivity close to half filling. Here, we introduce a second family of twisted graphene multilayers made up of twisted sheets of $M$- and $N$-layer Bernal-stacked graphene flakes. Calculations indicate that applying an electric displacement field isolates a flat and topological moiré conduction band that is primarily localized to a single graphene sheet below the moiré interface. Phenomenologically, the result is a striking similarity in the hierarchies of symmetry-broken phases across this family of twisted graphene multilayers. Our results show that this family of structures offers promising new opportunities for the discovery of exotic new correlated and topological phenomena, enabled by using the layer number to fine tune the flat moiré band and its screening environment.

cond-mat.mes-hall↗