arXiv subjects

Andrew J. Millis

Publications and source records attributed to Andrew J. Millis.

At least 73 records · Page 4Linked to original sources

arXiv2023

Deep Learning the Functional Renormalization Group

We perform a data-driven dimensionality reduction of the scale-dependent 4-point vertex function characterizing the functional Renormalization Group (fRG) flow for the widely studied two-dimensional $t - t'$ Hubbard model on the square lattice. We demonstrate that a deep learning architecture based on a Neural Ordinary Differential Equation solver in a low-dimensional latent space efficiently learns the fRG dynamics that delineates the various magnetic and $d$-wave superconducting regimes of the Hubbard model. We further present a Dynamic Mode Decomposition analysis that confirms that a small number of modes are indeed sufficient to capture the fRG dynamics. Our work demonstrates the possibility of using artificial intelligence to extract compact representations of the 4-point vertex functions for correlated electrons, a goal of utmost importance for the success of cutting-edge quantum field theoretical methods for tackling the many-electron problem.

cond-mat.str-el↗

arXiv2023

Elastic stripes formation at electronic transitions

We investigate the possibility of a striped inhomoegenous phase occurring as an electronic system with an order parameter linearly coupled to the elastic degrees of freedom is tuned through the electronic phase transition. We find that in finite systems where boundary conditions create an eleastic incompatibility, a stripe pattern may emerge in the vicinity of the electronic transition. Stripes are stabilized when the gained elastic energy overcomes the typical electronic and domain wall energy costs. In thin film geometries, the stripes are found to extend across the entire depth of the system. We also study the behavior of the phase fraction across the spinodal region of a first order phase transition. The orientation of stripes and the possibility of more complicated patterns is also discussed.

cond-mat.str-el↗

arXiv2023

Screening Induced Crossover between Phonon- and Plasmon-Mediated Pairing in Layered Superconductors

Two-dimensional (2D) metals can host gapless plasmonic excitations, which strongly couple to electrons and thus may significantly affect superconductivity in layered materials. To investigate the dynamical interplay of the electron-electron and electron-phonon interactions in the theory of 2D superconductivity, we apply a full momentum- and frequency-dependent one-loop theory treating electron-phonon, electron-plasmon, and phonon-plasmon coupling with the same accuracy. We tune the strength of the Coulomb interaction by varying the external screening $\varepsilon_{ext}$ to the layered superconductor and find three distinct regions. At weak screening, superconductivity is mediated by plasmons. In the opposite limit conventional electron-phonon interactions dominate. In between, we find a suppressed superconducting state. Our results show that even conventional electron-phonon mediated layered superconductors can be significantly affected by the electron-plasmon coupling in a weak screening environment. This unconventional pairing contribution can then be controlled by the external screening.

cond-mat.supr-con↗

arXiv2023

Conductivity of infinite-layer NdNiO$_{2}$ as a probe of spectator bands

Using a density-functional theory plus dynamical mean-field theory methodology, we compute the many-body electronic structure and optical conductivity of NdNiO$_{2}$ under the influence of large scattering rates on the Nd($5d$) bands and including dynamical interactions on the Nd($5d$) orbitals with shifts of the Nd-Ni $d$-level energy difference. We find a robust conducting pathway in the out-of-plane direction arising from strong hybridization between the Ni-$d_{z^2}$ and Nd($5d$) orbitals. This pathway can be ``short-circuited'' if this hybridization is suppressed through large electronic scattering rates but is not reduced to zero even by very large beyond-DFT shifts of the Nd-Ni $d$-level energy splitting. The computed in-plane conductivity for NdNiO$_{2}$ predicts the material to be a ``good metal'' in contrast to experiments indicating the material is a ``bad metal'' or ``weak insulator''. Our results motivate future experiments measuring the $c$-axis resistivity as a proxy for the spectator bands and suggests the essential difference between the infinite-layer nickelates and the cuprates is dimensionality of their electronic structures.

cond-mat.str-el↗

arXiv2022

Phonon-induced disorder in dynamics of optically pumped metals from non-linear electron-phonon coupling

The non-equilibrium dynamics of matter excited by light may produce electronic phases that do not exist in equilibrium, such as laser-induced high-transition-temperature superconductivity. Here we simulate the dynamics of a metal driven at initial time $t=0$ by a spatially uniform pump that excites dipole-active vibrational modes which couple quadratically to electrons. We study in detail the evolution of electronic and vibrational observables and their coherences. We provide evidence for enhancement of local electronic correlations, including double occupancy, accompanied by rapid loss of spatial structure, which we interpret as a signature of emergent effective disorder in the dynamics. This effective disorder, which arises in absence of quenched randomness, dominates the electronic dynamics as the system evolves towards a correlated electron-phonon long-time state, possibly explaining why transient superconductivity is not observed. The pumped electron-phonon systems studied here, which are governed by non-linear coupling, exhibit a much more substantial dynamical response than linearly coupled models relevant in equilibrium, thus presenting a pathway to new modalities for out-of-equilibrium phases. Our results provide a basis within which to understand correlation dynamics in current pump-probe experiments of vibrationally coupled electrons, highlight the importance of the evolution of phase coherence, and demonstrate that pumped electron-phonon systems provide a means of approximately realizing recently proposed scenarios of dynamically induced disorder in translation-invariant systems.

cond-mat.str-el↗

arXiv2022

Real time evolution of Anderson impurity models via tensor network influence functionals

In this work we present and analyze two tensor network-based influence functional approaches for simulating the real-time dynamics of quantum impurity models such as the Anderson model. Via comparison with recent numerically exact simulations, we show that such methods accurately capture the long-time non-equilibrium quench dynamics. The two parameters that must be controlled in these tensor network influence functional approaches are a time discretization (Trotter) error and a bond dimension (tensor network truncation) error. We show that the actual numerical uncertainties are controlled by an intricate interplay of these two approximations which we demonstrate in different regimes. Our work opens the door to using these tensor network influence functional methods as general impurity solvers.

cond-mat.str-el↗

arXiv2022

Real space representation of topological system: twisted bilayer graphene as an example

We construct a Wannier basis for twisted bilayer graphene that is projected only from the Bloch functions of the twisted bilayer flat bands. The $C_3$ and $C_{2} \mathcal{T}$ symmetries act locally on the Wannier functions while the Wannier function charge density is strongly peaked at the triangular sites and becomes fully sublattice-polarized in the chiral limit. The Wannier functions have a power-law tail, due to the topological obstruction, but most of the charge density is concentrated within one unit cell so that the on-site local Coulomb interaction is much larger than the further neighbor interactions and in general the Hamiltonian parameters may be accurately estimated from a modest number of Wannier functions. One exception is the momentum space components of the single-particle Hamiltonian, where because of the topological obstruction convergence is non-uniform across the Brillouin zone. We observe, however, that mixed position and momentum space representations may be used to avoid this difficulty in the context of quantum embedding methods. Our work provides a new route to study systems with topological obstructions and paves the way for the future investigation of correlated states in twisted bilayer graphene, including studies of non-integer fillings and temperature dependence.

cond-mat.mes-hall↗

arXiv2022

The Generalized Green's function Cluster Expansion: A Python package for simulating polarons

We present an efficient implementation of the Generalized Green's function Cluster Expansion (GGCE), which is a new method for computing the ground-state properties and dynamics of polarons (single electrons coupled to lattice vibrations) in model electron-phonon systems. The GGCE works at arbitrary temperature and is well suited for a variety of electron-phonon couplings, including, but not limited to, site and bond Holstein and Peierls (Su-Schrieffer-Heeger) couplings, and couplings to multiple phonon modes with different energy scales and coupling strengths. Quick calculations can be performed efficiently on a laptop using solvers from NumPy and SciPy, or in parallel at scale using the PETSc sparse linear solver engine.

physics.comp-ph↗

arXiv2022

Optical Conductivity of the two dimensional Hubbard model: vertex corrections, emergent Galilean invariance and the accuracy of the single-site dynamical mean field approximation

We compute the frequency dependent conductivity of the two dimensional square lattice Hubbard model at zero temperature as a function of density to second order in the interaction strength, and compare the results to the predictions of single-site dynamical mean field theory computed at the same order. We find that despite the neglect of vertex corrections, the single site dynamical mean field approximation produces semiquantitatively accurate results for most carrier concentrations, but fails qualitatively for the nearly empty or nearly filled band cases where the theory exhibits an emergent Galilean invariance. The theory also becomes qualitatively inaccurate very near half filling if nesting is important.

cond-mat.str-el↗

arXiv2022

Atomically imprinted graphene plasmonic cavities

Plasmon polaritons in van der Waals (vdW) materials hold promise for next-generation photonics. The ability to deterministically imprint spatial patterns of high carrier density in cavities and circuitry with nanoscale features underlies future progress in nonlinear nanophotonics and strong light-matter interactions. Here, we demonstrate a general strategy to atomically imprint low-loss graphene plasmonic structures using oxidation-activated charge transfer (OCT). We cover graphene with a monolayer of WSe$_2$, which is subsequently oxidized into high work-function WOx to activate charge transfer. Nano-infrared imaging reveals low-loss plasmon polaritons at the WOx/graphene interface. We insert WSe$_2$ spacers to precisely control the OCT-induced carrier density and achieve a near-intrinsic quality factor of plasmons. Finally, we imprint canonical plasmonic cavities exhibiting laterally abrupt doping profiles with single-digit nanoscale precision via programmable OCT. Specifically, we demonstrate technologically appealing but elusive plasmonic whispering-gallery resonators based on free-standing graphene encapsulated in WOx. Our results open avenues for novel quantum photonic architectures incorporating two-dimensional materials.

physics.optics↗

arXiv2022

Dynamical Mean Field Theory of Moiré Bilayer Transition Metal Dichalcogenides: Phase Diagram, Resistivity, and Quantum Criticality

We present a comprehensive dynamical mean field study of the triangular lattice moiré Hubbard model, which is believed to represent the physics of moiré bilayer transition metal dichalcogenides. In these materials, important aspects of the band structure including the bandwidth and the order and location of van Hove singularities can be tuned by varying the interlayer potential. We present a magnetic and metal-insulator phase diagram and a detailed study of the dependence of the resistivity on temperature, band filling and interlayer potential. We find that transport displays Fermi liquid, strange metal and quantum critical behaviors in distinct regions of the phase diagram. Specifically, we find that the cube-root van Hove singularity ($ρ(ε) \sim|ε|^{-1 / 3}$) gives a strange metal behavior with a $T$-linear scattering rate and $ω/T$ scaling. We show how magnetic order affects the resistivity. Our results elucidate the physics of the correlated states and the metal-insulator continuous transition recently observed in twisted homobilayer WSe$_2$ and heterobilayer MoTe$_2$/WSe$_2$ experiments.

cond-mat.str-el↗

arXiv2022

Second-order magnetic responses in quantum magnets: Magnetization under ac magnetic fields

We investigate second-order magnetic responses of quantum magnets against ac magnetic fields. We focus on the case where the $z$ component of the spin is conserved in the unperturbed Hamiltonian and the driving field is applied in the $xy$ plane. We find that linearly polarized driving fields induce a second-harmonic response, while circularly polarized fields generate only a zero-frequency response, leading to a magnetization with a direction determined by the helicity. Employing an unbiased numerical method, we demonstrate the nonlinear magnetic effect driven by the circularly polarized field in the XXZ model and show that the magnitude of the magnetization can be predicted by the dynamical spin structure factor in the linear response regime.

cond-mat.str-el↗

arXiv2022

Transient trapping into metastable states in systems with competing orders

The quench dynamics of a system involving two competing orders is investigated using a Ginzburg-Landau theory with relaxational dynamics. We consider the scenario where a pump rapidly heats the system to a high temperature, after which the system cools down to its equilibrium temperature. We study the evolution of the order parameter amplitude and fluctuations in the resulting time dependent free energy landscape. Exponentially growing thermal fluctuations dominate the dynamics. The system typically evolves into the phase associated with the faster-relaxing order parameter, even if it is not the global free energy minimum. This theory offers a natural explanation for the widespread experimental observation that metastable states may be induced by laser induced collapse of a dominant equilibrium order parameter.

cond-mat.str-el↗

arXiv2022

Machine Learning for Optical Scanning Probe Nanoscopy

The ability to perform nanometer-scale optical imaging and spectroscopy is key to deciphering the low-energy effects in quantum materials, as well as vibrational fingerprints in planetary and extraterrestrial particles, catalytic substances, and aqueous biological samples. The scattering-type scanning near-field optical microscopy (s-SNOM) technique has recently spread to many research fields and enabled notable discoveries. In this brief perspective, we show that the s-SNOM, together with scanning probe research in general, can benefit in many ways from artificial intelligence (AI) and machine learning (ML) algorithms. We show that, with the help of AI- and ML-enhanced data acquisition and analysis, scanning probe optical nanoscopy is poised to become more efficient, accurate, and intelligent.

physics.optics↗

arXiv2022

Nonequilibrium phase transition in a driven-dissipative quantum antiferromagnet

A deeper theoretical understanding of driven-dissipative interacting systems and their nonequilibrium phase transitions is essential both to advance our fundamental physics understanding and to harness technological opportunities arising from optically controlled quantum many-body states. This paper provides a numerical study of dynamical phases and the transitions between them in the nonequilibrium steady state of the prototypical two-dimensional Heisenberg antiferromagnet with drive and dissipation. We demonstrate a nonthermal transition that is characterized by a qualitative change in the magnon distribution, from subthermal at low drive to a generalized Bose-Einstein form including a nonvanishing condensate fraction at high drive. A finite-size analysis reveals static and dynamical critical scaling at the transition, with a discontinuous slope of the magnon number versus driving field strength and critical slowing down at the transition point. Implications for experiments on quantum materials and polariton condensates are discussed.

cond-mat.str-el↗

arXiv2022

Common microscopic origin of the phase transitions in Ta$_2$NiS$_5$ and the excitonic insulator candidate Ta$_2$NiSe$_5$

The structural phase transition in Ta$_2$NiSe$_5$ has been envisioned as driven by the formation of an excitonic insulating phase. However, the role of structural and electronic instabilities on crystal symmetry breaking has yet to be disentangled. Meanwhile, the phase transition in its complementary material Ta$_2$NiS$_5$ does not show any experimental hints of an excitonic insulating phase. We present a microscopic investigation of the electronic and phononic effects involved in the structural phase transition in Ta$_2$NiSe$_5$ and Ta$_2$NiS$_5$ using extensive first-principles calculations. In both materials the crystal symmetries are broken by phonon instabilities, which in turn lead to changes in the electronic bandstructure also observed in experiment. A total energy landscape analysis shows no tendency towards a purely electronic instability and we find that a sizeable lattice distortion is needed to open a bandgap. We conclude that an excitonic instability is not needed to explain the phase transition in both Ta$_2$NiSe$_5$ and Ta$_2$NiS$_5$.

cond-mat.mtrl-sci↗

arXiv2022

Superconductivity and Antiferromagnetism in NdNiO$_2$ and CaCuO$_2$: A Cluster DMFT Study

We perform a comparative $2 \times 2$ real space cluster DMFT study on minimal models for NdNiO$_2$ and CaCuO$_2$ obtained from downfolding DFT states, using a Nambu formalism that allows for both superconducting and antiferromagnetic order. We produce a phase diagram in temperature and doping. We find that for the nickelate, like the cuprate, the stoichiometric compound is antiferromagnetic. We find superconductivity in a doping range bounded, with a small coexistence region, by the onset of antiferromagnetism at low doping and with transition temperature becoming immeasurably small at high doping. Superconductivity emerges at around the same hole doping for both compounds, but requires a larger deviation from half filling for the nickelate. Both antiferromagnetic and superconducting order lead to a partial gapping of the $d_{x^2-y^2}$ Fermi surface sheet. Our similar results for the cuprate and nickelate suggest that nickelate superconductivity is cupratelike. We compare our results to the experimental phase diagram.

cond-mat.str-el↗

arXiv2021

Unveiling the underlying interactions in Ta2NiSe5 from photo-induced lifetime change

We present a generic procedure for quantifying the interplay of electronic and lattice degrees of freedom in photo-doped insulators through a comparative analysis of theoretical many-body simulations and time- and angle-resolved photoemission spectroscopy (TR-ARPES) of the transient response of the candidate excitonic insulator Ta2NiSe5. Our analysis demonstrates that the electron-electron interactions dominate the electron-phonon ones. In particular, a detailed analysis of the TRARPES spectrum enables a clear separation of the dominant broadening (electronic lifetime) effects from the much smaller bandgap renormalization. Theoretical calculations show that the observed strong spectral broadening arises from the electronic scattering of the photo-excited particle-hole pairs and cannot be accounted for in a model in which electron-phonon interactions are dominant. We demonstrate that the magnitude of the weaker subdominant bandgap renormalization sensitively depends on the distance from the semiconductor/semimetal transition in the high-temperature state, which could explain apparent contradictions between various TR-ARPES experiments. The analysis presented here indicates that electron-electron interactions play a vital role (although not necessarily the sole one) in stabilizing the insulating state.

cond-mat.str-el↗