arXiv subjects

Geng-Dong Zhou

Publications and source records attributed to Geng-Dong Zhou.

9 recordsLinked to original sources

arXiv2026

Universality of Energy-Space Entanglement in Quantum Impurity Models

Entanglement entropy (EE) is commonly studied using real-space bipartitions. We show that, in quantum impurity models, an energy-space bipartition, equivalent to the momentum-space bipartition of the bath, can display universal behavior. Motivated by poor man's scaling, we logarithmically discretize the bath and partition it into high- and low-energy sectors. For models with Fermi-liquid fixed points, including the Anderson model and fully screened or underscreened Kondo models, the low-energy EE flows to constants independent of model parameters. These constants are integer multiples of $\ln 2$ plus corrections that depend only on the logarithmic discretization parameter $Λ$. We show that scale invariance of the fixed-point wavefunction in energy space maps to effective translation invariance along a one-dimensional chain, allowing the fixed points to be classified by one-dimensional topological band theory. With low-energy chiral symmetry, each $\ln 2$ contribution originates from a topological edge mode. We also study transitions between distinct Fermi-liquid fixed points using the local-singlet--Kondo-singlet transition in a two-orbital Anderson model driven by an inter-orbital antiferromagnetic coupling. The local-singlet phase has an effectively decoupled impurity and nearly vanishing EE, whereas the Kondo-singlet phase has finite EE larger than $\ln 2$ per spin and orbital. When chiral symmetry holds at low energies, this distinction corresponds to a topological transition of the effective bath chain. At the non-Fermi-liquid critical point, the EE develops an unstable plateau. Its $Λ$ dependence resembles that of the overscreened two-channel Kondo model, supporting universality within the same non-Fermi-liquid universality class.

cond-mat.str-el↗

arXiv2026

Strongly Correlated Superconductivity in Twisted Bilayer Graphene: a Gutzwiller Study

We study strongly correlated superconductivity in magic-angle twisted bilayer graphene (MATBG) using a variational Gutzwiller wavefunction $\ket{Ψ_G} = \prod_{\vb{R}} \hat{P}_{\vb{R}} \ket{Φ_0}$, where the Gutzwiller projector $\hat{P}_{\vb{R}}$ is allowed to break charge U(1) symmetry to accommodate superconducting (SC) order. The ground state energy is evaluated via the \textit{Gutzwiller Approximation} applied to an 8-band model consisting of correlated $f$-orbitals and uncorrelated $c$-orbitals, with interactions including onsite Coulomb repulsion $U$, phonon-mediated anti-Hund's coupling $\hat{H}_{J_A}$, and intra-orbital Hund's coupling $\hat{H}_{J_H}$. At filling $ν= 2.5$, we map out the phase diagram as a function of $U$ and $J_A$, and reveal a strongly correlated SC (SC-SC) phase dominates at large $U$, wherethe strong on-site interaction U strongly suppress the $f$-orbital charge fluctuations while maintaining finite pairing order and a sizeable quasiparticle weight Z, distinguishing it from a conventional Mott insulator. For a range of $J_{\rm A}$, SC-SC transitions to FL as $U$ decreases, until the weakly correlated BCS-like SC (BCS-SC) re-enters as $U \to 0$. We further identify a novel small Fermi liquid (sFL) state with effective Fermi surface formed by $c$-orbitals, which is essentially different with the normal Fermi liquid. Interestingly, in the intermediate- ($U \lesssim 40$ meV) and large-$U$ ($U \gtrsim 40$ meV) regimes, the conventional FL and the sFL are the lowest-energy normal phases, respectively, potentially serve as the parent states of the SC-SC phase. These results illuminate the interplay between strong correlations and unconventional pairing in MATBG, and establish a versatile Gutzwiller framework applicable to other strongly correlated superconductors.

cond-mat.str-el↗

arXiv2026

Spin-Valley Anderson Impurity for Moiré Systems: Fermi Liquid, Pairing, and Pseudogap

Recent experiments support that the magic-angle graphene can be modeled by a periodic array of correlated quantum impurities, immersed in a Dirac sea. This work analytically tackles a spin-valley Anderson impurity, featuring a general (anti-)Hund's interaction ($J_D, J_S$) that can originate from electron-phonon couplings. We derive its full phase diagram, which encompasses rich continuous local phase transitions, and presents a unified origin for pairing potential and pseudogap. In particular, $J_D$ favors a valley doublet, and we show it drives a BKT transition out of heavy Fermi liquid, to an anisotropic doublet phase exhibiting a non-analytic zero-energy kink in the impurity spectral function. $J_S$ drives a second-order transition out of heavy Fermi liquid, to a local singlet phase, with a non-Fermi liquid critical point. We analyze the pairing potential across the phase diagram, and unveil their ubiquitous existence triggered by the (anti-)Hund's multiplet splitting. Crucially, we show the pseudogap shoulders in the spectral function represent multiplet excitations induced by an injected electron or hole. All results are obtained analytically, using techniques including bosonization-refermionization, with further verification by numerical renormalization group calculations. Then we derive the correlation self-energy ansatze that account for pseudogap, and apply to the magic-angle graphene lattice.

cond-mat.str-el↗

arXiv2026

Bosonization Solution to Spin-Valley Kondo Problem: Finite-Size Spectrum and Renormalization Group Analysis

Spin-valley Anderson impurities (SVAIM) with (anti-)Hund's splitting provide a natural explanation to the origin of pairing potential and pseudogap in the magic-angle graphene. In this work, we derive and analytically solve the low-energy Kondo theories for SVAIM at half-filling, with especial focus on the two anti-Hund's regimes: the impurity is either dominated by a valley doublet, or a trivial singlet. In the doublet regime, we reveal that a novel pair Kondo scattering $λ_x$ is required to flip the valley doublet, which involves a quartic operator of bath electrons. Our renormalization group (RG) calculation based on the Coulomb gas analog shows $λ_x$ drives a phase transition of the Berezinskii-Kosterlitz-Thouless type. One side of the transition is an anisotropic doublet phase, characterized by non-universal phase shifts of bath electrons and non-analytic impurity susceptibilities, while the other is a Fermi liquid formed by pair-Kondo resonance. The finite-size many-body spectrum, thermodynamic quantities, and correlation functions for both phases are analytically solved. Remarkably, the solution in the pair-Kondo Fermi liquid is achieved via the constructive approach of bosonization-refermionization along a solvable fixed line, where the many-body interaction $λ_x$ is mapped into a pseudo-fermion bilinear in a rigorous manner. Finally, we also apply the RG analysis to the singlet regime, and identify a second-order phase transition between the Kondo Fermi liquid and a local singlet phase.

cond-mat.str-el↗

arXiv2024

Hundness in twisted bilayer graphene: correlated gaps and pairing

We characterize gap-opening mechanisms in the topological heavy fermion (THF) model of magic-angle twisted bilayer graphene (MATBG), with and without electron-phonon coupling, using dynamical mean-field theory (DMFT) with the numerical renormalization group (NRG) impurity solver. In the presence of symmetry breaking associated with valley-orbital ordering (time-reversal-symmetric or Kramers intervalley coherent, or valley polarized), spin anti-Hund and orbital-angular-momentum Hund couplings, induced by the dynamical Jahn-Teller effect, result in a robust pseudogap at filling $2 \lesssim |ν| \lesssim 2.5$. We also find that Hundness enhances the pairing susceptibilities for $1.6 \lesssim |ν| \lesssim 2.8$, which might be a precursor to the superconducting phases neighboring $|ν| = 2$.

cond-mat.str-el↗

arXiv2024

Electron phonon coupling in the topological heavy fermion model of twisted bilayer graphene

On flat bands of the magic-angle twisted bilayer graphene, exotic correlation physics unfolds. Phonons, through mediating an effective electron-electron interaction, can play a crucial role in selecting various electronic phases. In this study, we derive the full electron-phonon coupling (EPC) vertex from the microscopic tight-binding lattice, and identify the significance of each phonon mode. We then project the EPC vertices onto the topological heavy fermion (THF) basis [Song and Bernevig, Phys. Rev. Lett. 129, 047601 (2022)], and show that an anti-Hund's interaction $\hat{H}_{\rm A}$ is induced on each moiré-scale local $f$-orbital, with strengths 1 to 4 meV. We analyze the phonon-induced multiplet splittings, which can significantly affect the local correlation. As an example, we elaborate on the phonon-favored symmetry-breaking orders at even-integer fillings. Through systematic self-consistent Hartree-Fock calculations, we uncover a tight competition between $Γ$-phonon-favored orbital orders, $K$-phonon-favored inter-valley coherent orders, and the kinetic and Coulomb-favored orders. Contrary to EPC, the carbon atom Hubbard repulsion induces an on-$f$-site Hund's interaction $\hat{H}_{\rm H}$ with strengths 1 to 3 meV that partly counteracts the effect of $\hat{H}_{\rm A}$. The combined influence of $\hat{H}_{\rm A,H}$ on the multiplet splitting and symmetry-breaking states is discussed. In the end, we explore the possibility of finding an exotic Dirac semi-metal formed solely by $c$-electrons at the charge-neutrality point, while $f$-impurities exhibit a symmetric Mott gap by forming non-degenerate singlets under $\hat{H}_{\rm A,H}$. Experimental features that distinguish such a state are discussed.

cond-mat.str-el↗

arXiv2024

Molecular Pairing in Twisted Bilayer Graphene Superconductivity

We propose a theory for how the weak phonon-mediated interaction ($J_{\rm A}\!=\!1\!\sim\!4$meV) wins over the prohibitive Coulomb repulsion ($U\!=\!30\!\sim\!60$meV) and leads to a superconductor in magic-angle twisted bilayer graphene (MATBG). We find the pairing mechanism akin to that in the A$_3$C$_{60}$ family of molecular superconductors: Each AA stacking region of MATBG resembles a C$_{60}$ molecule, in that optical phonons can dynamically lift the degeneracy of the moiré orbitals, in analogy to the dynamical Jahn-Teller effect. Such induced $J_{\rm A}$ has the form of an inter-valley anti-Hund's coupling and is less suppressed than $U$ by the Kondo screening near a Mott insulator. Additionally, we also considered an intra-orbital Hund's coupling $J_{\rm H}$ that originates from the on-site repulsion of a carbon atom. Under a reasonable approximation of the realistic model, we prove that the renormalized local interaction between quasi-particles must have a pairing (negative) channel in a doped correlated insulator at $ν=\pm(2+δν)$, albeit the bare interaction is positive definite. The proof is non-perturbative and based on exact asymptotic behaviors of the vertex function imposed by Ward identities. Existence of an optimal $U$ for superconductivity is predicted. We also analyzed the pairing symmetry. In a large area of the parameter space of $J_{\rm A}$, $J_{\rm H}$, the ground state has a nematic $d$-wave singlet pairing, which, however, can lead to a $p$-wave-like nodal structure due to the Berry's phase on Fermi surfaces (or Euler obstruction).

cond-mat.supr-con↗

arXiv2024

Correlated insulators and charge density wave states in chirally twisted triple bilayer graphene

Motivated by recent experimental observations of displacement-field-tuned correlated insulators at integer and half-integer fillings in chirally twisted triple bilayer graphene (CTTBG), we study the single-particle and interacting physics of CTTBG. We find that there are two inequivalent stacking orders, {\it i.e.}, ABABBC and ABABAB, and both exhibit flat bands with nontrivial topology. We then use the Hartree-Fock approximation to calculate the rich phase diagram of CTTBG at all integer and half-integer fillings in both stacking orders and under the vertical displacement field. Under a small displacement field, the groundstates are flavor polarized states for ABABBC stacking order and intervalley coherent states for ABABAB stacking order at all integer and half-integer fillings. A larger displacement field will turn them into layer-polarized states. At half-integer fillings, the groundstates also exhibit charge density wave (CDW) order. For ABABAB stacking, the groundstates are always $2\times1$ stripe state among a range of displacement fields. For ABABBC stacking, the groundstates are also $2\times1$ stripe states under a small displacement field and a larger displacement will possibly favor further translation-symmetry-breaking, depending on filling and the direction of the displacement field. We demonstrate that the CDW states observed in the experiment can originate from the strong Coulomb interaction of the flat band electrons.

cond-mat.mes-hall↗

arXiv2024

Kondo Phase in Twisted Bilayer Graphene -- A Unified Theory for Distinct Experiments

A number of interesting physical phenomena have been discovered in magic-angle twisted bilayer graphene (MATBG), such as superconductivity, correlated gapped and gapless phases, etc. The gapped phases are believed to be symmetry-breaking states described by mean-field theories, whereas gapless phases exhibit features beyond mean field. This work, combining poor man's scaling, numerical renormalization group, and dynamic mean-field theory, demonstrates that the gapless phases are the heavy Fermi liquid state with some symmetries broken and the others preserved. We adopt the recently proposed topological heavy fermion model for MATBG with effective local orbitals around AA-stacking regions and Dirac fermions surrounding them. At zero temperature and most non-integer fillings, the ground states are found to be heavy Fermi liquids and exhibit Kondo resonance peaks. The Kondo temperature $T_K$ is found at the order of 1meV. A higher temperature than $T_K$ will drive the system into a metallic LM phase where disordered LM's and a Fermi liquid coexist. At integer fillings $\pm1,\pm2$, $T_K$ is suppressed to zero or a value weaker than RKKY interaction, leading to Mott insulators or symmetry-breaking states. This theory offers a unified explanation for several experimental observations, such as zero-energy peaks and quantum-dot-like behaviors in STM, the Pomeranchuk effect, and the saw-tooth feature of inverse compressibility, etc. For future experimental verification, we predict that the Fermi surface in the gapless phase will shrink upon heating - as a characteristic of the heavy Fermi liquid. We also conjecture that the heavy Fermi liquid is the parent state of the observed unconventional superconductivity because the Kondo screening reduces the overwhelming Coulomb interaction (~60meV) to a rather small effective interaction (~1meV) comparable to possible weak attractive interactions.

cond-mat.str-el↗