Publications

Employing unbiased sign-problem-free quantum Monte Carlo, we investigate the effects of long-range Coulomb forces on BEC of bipolarons using a model of bond phonon-modulated electron hopping. In absence of long-range repulsion, this model was recently shown to give rise to small-size, light-mass bipolarons that undergo a superfluid transition at high values of the critical transition temperature T

It is commonly believed that nonuniform Berry curvature destroys the Girvin-MacDonald-Platzman algebra and as a consequence destabilizes fractional Chern insulators. In this work we disprove this common lore by presenting a theory for all topological ideal flatbands with nonzero Chern number C. The smooth single-particle Bloch wavefunction is proved to admit an exact color-entangled form as a superposition of C lowest Landau level type wavefunctions distinguished by boundary conditions. Including repulsive interactions, Abelian and non-Abelian model fractional Chern insulators of Halperin type are stabilized as exact zero-energy ground states no matter how nonuniform Berry curvature is, as long as the quantum geometry is ideal and the repulsion is short-ranged. The key reason behind is the existence of an emergent Hilbert space in which Berry curvature can be exactly flattened by adjusting wavefunction's normalization. In such space, the flatband-projected density operator obeys a closed Girvin-MacDonald-Platzman type algebra, making exact mapping to C-layered Landau levels possible. In the end we discuss applications of the theory to moire flatband systems with a particular focus on the fractionalized phase and spontaneous symmetry breaking phase recently observed in graphene based twisted materials.

We propose a platform for flat Chern band by subjecting two-dimensional Dirac materials -- such as graphene and topological insulator thin films -- to a periodic magnetic field, which can be created by the vortex lattice of a type-II superconductor. As a generalization of the n=0 Landau level, the flat band of Dirac fermion under a nonuniform magnetic field remains at zero energy, exactly dispersionless and topologically protected, while its local density of states is spatially modulated due to the magnetic field variation. In the presence of short-range repulsion, we find fractional Chern insulators emerge at filling factors ν=1/m, whose ground states are generalized Laughlin wavefunctions. We further argue that generalized Wigner crystals may emerge at certain commensurate fillings under a highly nonuniform magnetic field in the form of a flux line lattice.

A pair density wave (PDW) is a superconductor whose order parameter is a periodic function of space, without an accompanying spatially-uniform component. Since PDWs are not the outcome of a weak-coupling instability of a Fermi liquid, a generic pairing mechanism for PDW order has remained elusive. We describe and solve models having robust PDW phases. To access the intermediate coupling limit, we invoke large N limits of Fermi liquids with repulsive BCS interactions that admit saddle point solutions. We show that the requirements for long range PDW order are that the repulsive BCS couplings must be non-monotonic in space and that their strength must exceed a threshold value. We obtain a phase diagram with both finite temperature transitions to PDW order, and a T=0 quantum critical point, where non-Fermi liquid behavior occurs.

We propose the metallic and weakly dispersive surface states of half-Heusler semimetals as a possible domain for the onset of unconventional surface superconductivity ahead of the bulk transition. Using density functional theory (DFT) calculations and the random phase approximation (RPA), we analyse the surface band structure of LuPtBi and its propensity towards Cooper pair formation induced by screened electron-electron interactions in the presence of strong spin-orbit coupling. Over a wide range of model parameters, we find an energetically favoured chiral superconducting condensate featuring Majorana edge modes, while low-dimensional order parameter fluctuations trigger time-reversal symmetry breaking to precede the superconducting transition.

HgTe is a versatile topological material and has enabled the realization of a variety of topological states, including two- and three-dimensional (3D) topological insulators and topological semimetals. Nevertheless, a quantitative understanding of its electronic structure remains challenging, in particular due to coupling of the Te 5p-derived valence electrons to Hg 5d core states at shallow binding energy. We present a joint experimental and theoretical study of the electronic structure in strained HgTe(001) films in the 3D topological-insulator regime, based on angle-resolved photoelectron spectroscopy and density functional theory. The results establish detailed agreement in terms of (i) electronic band dispersions and orbital symmetries, (ii) surface and bulk contributions to the electronic structure, and (iii) the importance of Hg 5d states in the valence-band formation. Supported by theory, our experiments directly image the paradigmatic band inversion in HgTe, underlying its non-trivial band topology.

We explore the effect of Coulomb repulsion on the phonon-mediated BCS-type Cooper instability in the electron gas using a numeric approach that is controllably accurate at small to moderate values of the Coulomb parameter, r

A numerical scheme is presented for the solution of Fredholm second-kind boundary integral equations with right-hand sides that are singular at a finite set of boundary points. The boundaries themselves may be non-smooth. The scheme, which builds on recursively compressed inverse preconditioning (RCIP), is universal as it is independent of the nature of the singularities. Strong right-hand-side singularities, such as $1/|r|^\alpha$ with $\alpha$ close to $1$, can be treated in full machine precision. Adaptive refinement is used only in the recursive construction of the preconditioner, leading to an optimal number of discretization points and superior stability in the solve phase. The performance of the scheme is illustrated via several numerical examples, including an application to an integral equation derived from the linearized BGKW kinetic equation for the steady Couette flow.

Linear systems involving contiguous submatrices of the discrete Fourier transform (DFT)matrix arise in many applications, such as Fourier extension, superresolution, and coherent diffraction imaging. We show that the condition number of any such p\times q submatrix of the N\times NDFT matrix is at least exp\bigl( \pi 2\bigl[ min(p,q) - pqN\bigr] \bigr) , up to algebraic prefactors.That is, fixing the shape parameters (\alpha ,\beta ) := (p/N,q/N)\in (0,1)2, the growth ise\rho NasN\rightarrow \infty , the exponential rate being\rho =\pi 2[min(\alpha ,\beta ) - \alpha \beta ]. Our proof uses theKaiser--Bessel transform pair (of which we give a self-contained proof), plus estimates on sums over distorted sinc functions, to construct a localized trial vector whose DFT is also localized. We warm up with an elementary proof of the above but with half the rate, via a periodized Gaussian trial vector. Using low-rank approximation of the kerneleixt, we also prove another lower bound (4/e\pi \alpha )q, up to algebraic prefactors, which is stronger than the above for small\alpha and\beta . When combined, the bounds are within a factor of two ofthe empirical asymptotic rate, uniformly over (0,1)2, and become sharp in certain regions.However, the results are not asymptotic: they apply to essentially allN,p, andq, and with all constants explicit.

Many high-throughput sequencing data sets in biology are compositional in nature. A prominent example is microbiome profiling data, including targeted amplicon-based and metagenomic sequencing data. These profiling data comprises surveys of microbial communities in their natural habitat and sparse proportional (or compositional) read counts that represent operational taxonomic units or genes. When paired measurements of other covariates, including physicochemical properties of the habitat or phenotypic variables of the host, are available, inference of parsimonious and robust statistical relationships between the microbial abundance data and the covariate measurements is often an important first step in exploratory data analysis. To this end, we propose a sparse robust statistical regression framework that considers compositional and non-compositional measurements as predictors and identifies outliers in continuous response variables. Our model extends the seminal log-contrast model of Aitchison and Bacon-Shone (1984) by a mean shift formulation for capturing outliers, sparsity-promoting convex and non-convex penalties for parsimonious model selection, and data-driven robust initialization procedures adapted to the compositional setting. We show, in theory and simulations, the ability of our approach to jointly select a sparse set of predictive microbial features and identify outliers in the response. We illustrate the viability of our method by robustly predicting human body mass indices from American Gut Project amplicon data and non-compositional covariate data. We believe that the robust estimators introduced here and available in the R package RobRegCC can serve as a practical tool for reliable statistical regression analysis of compositional data, including microbiome survey data.