arXiv subjects

Nick Bultinck

Publications and source records attributed to Nick Bultinck.

At least 37 records · Page 2Linked to original sources

arXiv2024

Nodal d-wave pairing from spin fluctuations in a thermally disordered anti-ferromagnet

We consider electron pairing in a two-dimensional thermally disordered itinerant anti-ferromagnet. It is shown that transverse spin fluctuations in such a state can give rise to superconductivity with a sizeable critical temperature $T_c$. Below $T_c$ there is quasi-long-range spin-singlet and $d_{x^2-y^2}$ superconducting order, together with fluctuating triplet order at momentum $(π,π)$. The singlet pairs we find are tightly bound together, and the pair wavefunction has a purely inter-sublattice structure due to the U(1) spin rotation symmetry of the anti-ferromagnet.

cond-mat.supr-con↗

arXiv2024

Hawking radiation on the lattice from Floquet and local Hamiltonian quench dynamics

We construct two free fermion lattice models exhibiting Hawking pair creation. Specifically, we consider the simplest case of a d=1+1 massless Dirac fermion, for which the Hawking effect can be understood in terms of a quench of the uniform vacuum state with a non-uniform Hamiltonian that interfaces modes with opposite chirality. For both our models we find that additional modes arising from the lattice discretization play a crucial role, as they provide the bulk reservoir for the Hawking radiation: the Hawking pairs emerge from fermions deep inside the Fermi sea scattering off the effective black hole horizon. Our first model combines local hopping dynamics with a translation over one lattice site, and we find the resulting Floquet dynamics to realize a causal horizon, with fermions scattering from the region outside the horizon. For our second model, which relies on a purely local hopping Hamiltonian, we find the fermions to scatter from the inside. In both cases, for Hawking temperatures up to the inverse lattice spacing we numerically find the resulting Hawking spectrum to be in perfect agreement with the Fermi-Dirac quantum field theory prediction.

quant-ph↗

arXiv2024

Resurgence of superconductivity and the role of $d_{xy}$ hole band in FeSe$_{1-x}$Te$_x$

Iron-chalcogenide superconductors display rich phenomena caused by orbital-dependent band shifts and electronic correlations. Additionally, they are potential candidates for topological superconductivity due to the band inversion between the Fe $d$ bands and the chalcogen $p_z$ band. Here we present a detailed study of the electronic structure of the nematic superconductors FeSe$_{1-x}$Te$_x$ ($0<x<0.4$) using angle-resolved photoemission spectroscopy to understand the role of orbital-dependent band shifts, electronic correlations and the chalcogen band. We assess the changes in the effective masses using a three-band low energy model, and the band renormalization via comparison with DFT band structure calculations. The effective masses decrease for all three-hole bands inside the nematic phase followed by a strong increase for the band with $d_{xy}$ orbital character. Interestingly, this nearly-flat $d_{xy}$ band becomes more correlated as it shifts towards the Fermi level with increasing Te concentrations and as the second superconducting dome emerges. Our findings suggests that the $d_{xy}$ hole band, which is very sensitive to the chalcogen height, could be involved in promoting an additional pairing channel and increasing the density of states to stabilize the second superconducting dome in FeSe$_{1-x}$Te$_x$. This simultaneous shift of the $d_{xy}$ hole band and enhanced superconductivity is in contrast with FeSe$_{1-x}$S$_x$.

cond-mat.supr-con↗

arXiv2024

Finite-Entanglement Scaling of 2D Metals

We extend the study of finite-entanglement scaling from one-dimensional gapless models to two-dimensional systems with a Fermi surface. In particular, we show that the entanglement entropy of a contractible spatial region with linear size $L$ scales as $S\sim L\log[ξf(L/ξ)]$ in the optimal tensor network, and hence area-law entangled, state approximation to a metallic state, where $f(x)$ is a scaling function which depends on the shape of the Fermi surface and $ξ$ is a finite correlation length induced by the restricted entanglement. Crucially, the scaling regime can be realized with numerically tractable bond dimensions. We also discuss the implications of the Lieb-Schultz-Mattis theorem at fractional filling for tensor network state approximations of metallic states.

cond-mat.str-el↗

arXiv2023

Kekulé spirals and charge transfer cascades in twisted symmetric trilayer graphene

We study the phase diagram of magic-angle twisted symmetric trilayer graphene in the presence of uniaxial heterostrain and interlayer displacement field. For experimentally reasonable strain, our mean-field analysis finds robust Kekulé spiral order whose doping-dependent ordering vector is incommensurate with the moiré superlattice, consistent with recent scanning tunneling microscopy experiments, and paralleling the behaviour of closely-related twisted bilayer graphene (TBG) systems. Strikingly, we identify a new possibility absent in TBG: the existence of $\textit{commensurate}$ Kekulé spiral order even at zero strain for experimentally realistic values of the interlayer potential in a trilayer. Our studies also reveal a complex pattern of charge transfer between weakly- and strongly-dispersive bands in strained trilayer samples as the density is tuned by electrostatic gating, that can be understood intuitively in terms of the `cascades' in the compressibility of magic-angle TBG.

cond-mat.str-el↗

arXiv2023

Coulomb-driven band unflattening suppresses $K$-phonon pairing in moiré graphene

It is a matter of current debate whether the gate-tunable superconductivity in twisted bilayer graphene is phonon-mediated or arises from electron-electron interactions. The recent observation of the strong coupling of electrons to so-called $K$-phonon modes in angle-resolved photoemission spectroscopy experiments has resuscitated early proposals that $K$-phonons drive superconductivity. We show that the bandwidth-enhancing effect of interactions drastically weakens both the intrinsic susceptibility towards pairing as well as the screening of Coulomb repulsion that is essential for the phonon attraction to dominate at low temperature. This rules out purely $K$-phonon-mediated superconductivity with the observed transition temperature of $\sim 1$ K. We conclude that the unflattening of bands by Coulomb interactions challenges any purely phonon-driven pairing mechanism, and must be addressed by a successful theory of superconductivity in moiré graphene.

cond-mat.supr-con↗

arXiv2023

Electron-phonon coupling and competing Kekulé orders in twisted bilayer graphene

Recent scanning tunneling microscopy experiments [K.P. Nuckolls et al., arXiv:2303.00024] have revealed the ubiquity of Kekulé charge-density wave order in magic-angle twisted bilayer graphene. Most samples are moderately strained and show `incommensurate Kekulé spiral' (IKS) order involving a graphene-scale charge density distortion uniaxially modulated on the scale of the moiré superlattice, in accord with theoretical predictions. However, ultra-low strain samples instead show graphene-scale Kekulé charge order that is uniform on the moiré scale. This order, especially prominent near filling factor $ν=-2$, is unanticipated by theory which predicts a time-reversal breaking Kekulé current order at low strain. We show that including the coupling of moiré electrons to graphene-scale optical zone-corner (ZC) phonons stabilizes a uniform Kekulé charge ordered state at $|ν|=2$ with a quantized topological (spin or anomalous Hall) response. Our work clarifies how this phonon-driven selection of electronic order emerges in the strong-coupling regime of moiré graphene.

cond-mat.str-el↗

arXiv2023

Superconductivity from repulsive interactions in Bernal-stacked bilayer graphene

A striking series of experiments have observed superconductivity in Bernal-stacked bilayer graphene (BBG) when the energy bands are flattened by applying an electrical displacement field. Intriguingly, superconductivity manifests only at non-zero magnetic fields, or when spin-orbit coupling is induced in BBG by coupling to a substrate. We present detailed functional renormalization group and random-phase approximation calculations that provide a unified explanation for the superconducting mechanism in both cases. Both calculations yield a purely electronic $p$-wave instability of the Kohn-Luttinger (KL) type. The latter can be enhanced either by magnetic fields or Ising spin-orbit coupling, naturally explaining the behaviour seen in experiments.

cond-mat.supr-con↗

arXiv2023

Spin-triplet superconductivity from inter-valley Goldstone modes in magic-angle graphene

We consider magic-angle graphene in the doping regime around charge neutrality and study the connection between a recently proposed inter-valley coherent insulator at zero doping and the neighboring superconducting domes. The magic-angle graphene continuum model has an emergent U(1) valley-charge conservation symmetry, and an emergent SU(2) symmetry corresponding to opposite spin rotations in the two valleys. The inter-valley coherent insulator spontaneously breaks both these emergent symmetries, and as a result has four Goldstone modes which couple to doped charge carriers. We derive the effective interaction mediated by the Goldstone modes, and study its role in electron pair formation. The SU(2) Goldstone modes generate a ferromagnetic interaction, which is attractive in spin-triplet pairing channels and repulsive in spin-singlet channels. From a weak-coupling BCS calculation, we find the leading superconducting instability in the p-wave channel.

cond-mat.str-el↗

arXiv2022

Kekulé spiral order in magic-angle graphene: a density matrix renormalization group study

When the two layers of a twisted moiré system are subject to different degrees of strain, the effect is amplified by the inverse twist angle, e.g., by a factor of 50 in magic angle twisted bilayer graphene (TBG). Samples of TBG typically have heterostrains of 0.1-0.7%, increasing the bandwidth of the "flat'' bands by as much as tenfold, placing TBG in an intermediate coupling regime. Here we study the phase diagram of TBG in the presence of heterostrain with unbiased, large-scale density matrix renormalization group calculations (bond dimension $χ=24576$), including all spin and valley degrees of freedom. Working at filling $ν= -3$, we find a strain of $0.05\%$ drives a transition from a quantized anomalous Hall insulator into an incommensurate-Kekulé spiral (IKS) phase. This peculiar order, proposed and studied at mean-field level by Kwan et al (PRX 11, 041063), breaks both valley conservation and translation symmetry $\hat{T}$, but preserves a modified translation symmetry $\hat{T}'$ with moiré-incommensurate phase modulation. Even higher strains drive the system to a fully symmetric metal.

cond-mat.str-el↗

arXiv2022

Global Phase Diagram of the Normal State of Twisted Bilayer Graphene

We investigate the full doping and strain-dependent phase diagram of the normal state of magic-angle twisted bilayer graphene (TBG). Using comprehensive Hartree-Fock calculations, we show that at temperatures where superconductivity is absent the global phase structure can be understood based on the competition and coexistence between three types of intertwined orders: a fully symmetric phase, spatially uniform flavor-symmetry-breaking states, and an incommensurate Kekulé spiral (IKS) order. For small strain, the IKS phase, recently proposed as a candidate order at all non-zero integer fillings of the moiré unit cell, is found to be ubiquitous for non-integer doping as well. We demonstrate that the corresponding electronic compressibility and Fermi surface structure are consistent with the 'cascade' physics and Landau fans observed experimentally. This suggests a unified picture of the phase diagram of TBG in terms of IKS order.

cond-mat.str-el↗

arXiv2021

Skyrmions in twisted bilayer graphene: stability, pairing, and crystallization

We study the excitations that emerge upon doping the translationally-invariant correlated insulating states in magic angle twisted bilayer graphene at various integer filling factors $ν$. We identify parameter regimes where these are associated with skyrmion textures in the spin or pseudospin degrees of freedom, and explore both short-distance pairing effects and the formation of long-range ordered skyrmion crystals. We perform a comprehensive analysis of the pseudospin skyrmions that emerge upon doping insulators at even $ν$, delineating the regime in parameter space where these are the lowest-energy charged excitations by means of self-consistent Hartree-Fock calculations on the interacting Bistritzer-MacDonald model. We explicitly demonstrate the purely electron-mediated pairing of skyrmions, a key ingredient behind a recent proposal of skyrmion superconductivity. Building upon this, we construct hopping models to extract the effective masses of paired skyrmions, and discuss our findings and their implications for skyrmion superconductivity in relation to experiments, focusing on the dome-shaped dependence of the transition temperature on the twist angle. We also investigate the properties of spin skyrmions about the quantized anomalous Hall insulator at $ν=+3$. In both cases, we demonstrate the formation of robust spin/pseudospin skyrmion crystals upon doping to a finite density away from integer filling.

cond-mat.str-el↗

arXiv2021

Kekulé spiral order at all nonzero integer fillings in twisted bilayer graphene

We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to non-local inter-layer tunneling. We perform a self-consistent Hartree-Fock study that incorporates these effects alongside realistic interaction and substrate potentials, and explore a comprehensive set of competing orders including those that break translational symmetry at arbitrary wavevectors. We find that at all non-zero integer fillings very small strains, comparable to those measured in scanning tunneling experiments, stabilize a fundamentally new type of time-reversal symmetric and spatially non-uniform order. This order, which we dub the 'incommensurate Kekulé spiral' (IKS) order, spontaneously breaks both the emergent valley-charge conservation and moiré translation symmetries, but preserves a modified translation symmetry $\hat{T}'$ -- which simultaneously shifts the spatial coordinates and rotates the $U(1)$ angle which characterizes the spontaneous inter-valley coherence. We discuss the phenomenological and microscopic properties of this order. We argue that our findings are consistent with all experimental observations reported so far, suggesting a unified explanation of the global phase diagram in terms of the IKS order.

cond-mat.str-el↗

arXiv2021

The Chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition

We study the phase diagram of the $(1+1)$-dimensional Gross-Neveu model with both $g_x^2(\barψψ)^2$ and $g_y^2(\barψiγ_5ψ)^2$ interaction terms on a spatial lattice. The continuous chiral symmetry, which is present in the continuum model when $g_x^2=g_y^2$, has a mixed 't~Hooft anomaly with the charge conservation symmetry, which guarantees the existence of a massless mode. However, the same 't~Hooft anomaly also implies that the continuous chiral symmetry is broken explicitly in our lattice model. Nevertheless, from numerical matrix product state simulations we find that, for certain parameters of the lattice model, the continuous chiral symmetry reemerges in the infrared fixed point theory, even at strong coupling. We argue that, to understand this phenomenon, it is crucial to go beyond mean-field theory (or, equivalently, beyond the leading order term in a $1/N$ expansion). Interestingly, on the lattice, the chiral Gross-Neveu model appears at a Landau-forbidden second order phase transition separating two distinct and unrelated symmetry-breaking orders. We point out the crucial role of two different 't Hooft anomalies or Lieb-Schultz-Mattis obstructions for this Landau-forbidden phase transition to occur.

hep-th↗

arXiv2021

Lattice regularisation and entanglement structure of the Gross-Neveu model

We construct a Hamiltonian lattice regularisation of the $N$-flavour Gross-Neveu model that manifestly respects the full $\mathsf{O}(2N)$ symmetry, preventing the appearance of any unwanted marginal perturbations to the quantum field theory. In the context of this lattice model, the dynamical mass generation is intimately related to the Coleman-Mermin-Wagner and Lieb-Schultz-Mattis theorem. In particular, the model can be interpreted as lying at the first order phase transition line between a trivial and symmetry-protected topological (SPT) phase, which explains the degeneracy of the elementary kink excitations. We show that our Hamiltonian model can be solved analytically in the large $N$ limit, producing the correct expression for the mass gap. Furthermore, we perform extensive numerical matrix product state simulations for $N=2$, thereby recovering the emergent Lorentz symmetry and the proper non-perturbative mass gap scaling in the continuum limit. Finally, our simulations also reveal how the continuum limit manifests itself in the entanglement spectrum. As expected from conformal field theory we find two conformal towers, one tower spanned by the linear representations of $\mathsf{O}(4)$, corresponding to the trivial phase, and the other by the projective (i.e. spinor) representations, corresponding to the SPT phase.

hep-lat↗

arXiv2021

Charged Skyrmions and Topological Origin of Superconductivity in Magic Angle Graphene

Spontaneous symmetry breaking plays a pivotal role in many areas of physics, engendering a variety of excitations from sound modes in solids to pions in nuclear physics. Equally important excitations are solitons, nonlinear configurations of the symmetry breaking field, which can enjoy exceptional stability as in the Skyrme model of nuclear forces. Here we argue that similar models may describe magic angle graphene, a remarkable new material . When the angle between two sheets of graphene is near the magic angle of $\sim 1^\circ$, insulating behavior is observed, which gives way to superconductivity on changing the electron density. We propose a unifying description of both the order underlying the insulator as well as the superconductor. While the symmetry breaking condensate leads to the ordered phase, topological solitons in the condensate - skyrmions - are shown to be bosons that carry an electric charge of 2e. Condensation of skyrmions leads to a superconductor whose pairing strength, symmetry and other properties are inferred. More generally, we show how topological textures can mitigate Coulomb repulsion to pair electrons and provide a new route to superconductivity. Our mechanism potentially applies to much wider class of systems but crucially invokes certain key ingredient such as inversion symmetry present in magic angle graphene. We discuss how these insights not only clarify why certain correlated moire materials do not superconduct, they also point to promising new platforms where robust superconductivity is anticipated.

cond-mat.str-el↗

arXiv2020

Strain-induced quantum phase transitions in magic angle graphene

We investigate the effect of uniaxial heterostrain on the interacting phase diagram of magic-angle twisted bilayer graphene. Using both self-consistent Hartree-Fock and density-matrix renormalization group calculations, we find that small strain values ($ε\sim 0.1 - 0.2 \%$) drive a zero-temperature phase transition between the symmetry-broken Kramers intervalley-coherent insulator and a nematic semi-metal. The critical strain lies within the range of experimentally observed strain values, and we therefore predict that strain is at least partly responsible for the sample-dependent experimental observations.

cond-mat.str-el↗

arXiv2020

Efficient simulation of moire materials using the density matrix renormalization group

We present an infinite density-matrix renormalization group (DMRG) study of an interacting continuum model of twisted bilayer graphene (tBLG) near the magic angle. Because of the long-range Coulomb interaction and the large number of orbital degrees of freedom, tBLG is difficult to study with standard DMRG techniques -- even constructing and storing the Hamiltonian already poses a major challenge. To overcome these difficulties, we use a recently developed compression procedure to obtain a matrix product operator representation of the interacting tBLG Hamiltonian which we show is both efficient and accurate even when including the spin, valley and orbital degrees of freedom. To benchmark our approach, we focus mainly on the spinless, single-valley version of the problem where, at half-filling, we find that the ground state is a nematic semimetal. Remarkably, we find that the ground state is essentially a k-space Slater determinant, so that Hartree-Fock and DMRG give virtually identical results for this problem. Our results show that the effects of long-range interactions in magic angle graphene can be efficiently simulated with DMRG, and opens up a new route for numerically studying strong correlation physics in spinful, two-valley tBLG, and other moire materials, in future work.

cond-mat.str-el↗