arXiv subjects

Tamaghna Hazra

Publications and source records attributed to Tamaghna Hazra.

12 recordsLinked to original sources

arXiv2026

New class of exactly flat topological bands - compact localised states protected by local graph topology

Strongly correlated quantum matter is fundamentally defined by the tension between non-commuting quantum operators. Hamiltonians exhibiting macroscopic degeneracies are of general interest in this field because they imply an infinite susceptibility to any non-commuting perturbation. In moiré heterostructures, engineering such extensive degeneracies in the kinetic Hamiltonian creates a fertile garden for exotic strongly correlated phases of matter to emerge from the resulting flat bands. Here, we introduce a prescription to construct an infinite family of exact flat band Hamiltonians supported on the faces of arbitrary graphs. We demonstrate this algorithm on the faces of four Bravais lattices. Using a discrete graph generalization of the Atiyah-Singer index theorem, we prove that the extensive degeneracies of such face-graph Hamiltonians are protected by the local topology of the face-graph connectivity. The resulting macroscopic null spaces yield compact localised states that remain localised over time due to frustration in hopping pathways. We discuss the broad implications of such non-dispersing quantum modes in diverse settings, from arrested dynamics in quantum networks and quantum machine learning algorithms to Majorana-free topological quantum computation.

cond-mat.str-el↗

arXiv2026

Obstructed Cooper pairs in flat band systems -- weakly-coherent superfluids and exact spin liquids

Superconductivity in a partially filled flat band presents a vexing conceptual hurdle because the absence of a Fermi surface precludes a weak-coupling regime where one can extend insights from the Bardeen-Cooper-Schrieffer picture of a Fermi surface instability. We approach the strongly correlated problem of flat band superconductivity from the strong coupling limit of local attractive interactions on line-graph lattices, whose non-interacting bandstructures host exactly flat bands due to frustrated hopping. In this limit, the pair kinetic energy which sets the superfluid stiffness is expected to scale inversely with the pair binding interaction. Here we demonstrate a striking counterexample. We show that when doped charges propagate on the line-graph of a lattice with strong pairing interaction and broken time-reversal symmetry, they bind into obstructed Cooper pairs whose motion is frustrated by destructive interference. As a result, the leading-order pair kinetic energy vanishes identically in the strong-coupling expansion, producing a flat bosonic band of compact localised pair states, zero superfluid stiffness at leading order, and an extensively degenerate many-body ground state manifold. At quarter filling, the frustrated pair dynamics maps onto a quantum dimer model which has a $d$-wave resonating-valence-bond ground state when time-reversal is broken. The pairing Hamiltonian in this limit thus has a topologically ordered spin liquid ground state which becomes exact at the analytically solvable Rokhsar-Kivelson point with long-range entanglement and deconfined holon excitations. Interestingly, we find exact compact localised eigenstates and extensive degeneracies in the many-body eigenstates of this emergent dimer model. Our results establish a disorder-free mechanism for interaction-driven localisation, in which strong pairing collapses the kinetic energy of Cooper pairs.

cond-mat.supr-con↗

arXiv2025

Buckyballs directly probe inter-valley coherence in moire heterostructures

Moire materials like twisted bilayer graphene have emerged as a rich playground of strongly correlated physics, where the effect of interactions can be drastically enhanced by tuning the non-interacting density of states via twist angle. A key feature of bilayer graphene at small twist angles is that the two valleys of graphene are effectively decoupled at the non-interacting level, leading to an emergent U(1) symmetry corresponding to the conservation of valley-charge. Theoretical studies invariably find that short-ranged interactions tend to break this symmetry, leading to inter-valley coherence (IVC). Here, I propose an experimental signature of IVC order by coupling with a closely related system where valley-mixing is guaranteed - the pentagonal disclinations of graphene. Such disclinations are naturally found in fullerenes. The tunneling current between twisted bilayer graphene and an appropriately oriented large buckyball has a sharp signature of the onset of IVC order. Successfully integrating these fullerenes in a scanning tunneling microscope would allow spatial resolution of the IVC order parameter on a sub-moire scale. Experimentally constraining the broken symmetries and order parameters in the multitude of emerging correlated insulators is a crucial first step to understanding the superconductivity that develops on doping these exotic `normal' states.

cond-mat.str-el↗

arXiv2024

Pair-Kondo effect: a mechanism for time-reversal broken superconductivity in UTe$_2$

An important open puzzle in the superconductivity of UTe$_2$ is the emergence of time-reversal broken superconductivity from a non-magnetic normal state. Breaking time-reversal symmetry in a single second-order superconducting transition requires the existence of two degenerate superconducting order parameters, which is not natural for orthorhombic UTe$_2$. Moreover, experiments under pressure (Braithwaite et. al., Comm. Phys. \bf{2}, 147 (2019), arXiv:1909.06074 [cond-mat.str-el]) suggest that superconductivity sets in at a single transition temperature in a finite parameter window, in contrast to the splitting between the symmetry breaking temperatures expected for accidental degenerate orders. Motivated by these observations, we propose a mechanism for the emergence of time-reversal breaking superconductivity without accidental or symmetry-enforced order parameter degeneracies in systems close to a magnetic phase transition. We demonstrate using Landau theory that a cubic coupling between incipient magnetic order and magnetic moments of Cooper pairs (pair-Kondo coupling) can drive time-reversal symmetry breaking superconductivity that onsets in a single, weakly first order transition over an extended region of the phase diagram. We discuss the experimental signatures of such transition in thermodynamic and resonant ultrasound measurements. A microscopic origin of pair-Kondo coupling is identified as screening of magnetic moments by chiral Cooper pairs, built out of two non-degenerate order parameters - an extension of Kondo screening to unconventional pairs.

cond-mat.supr-con↗

arXiv2022

Triplet pairing mechanisms from Hund's-Kondo models: applications to UTe$_{2}$ and CeRh$_{2}$As$_{2}$

Observing that several U and Ce based candidate triplet superconductors share a common structural motif, with pairs of magnetic atoms separated by an inversion center, we hypothesize a triplet pairing mechanism based on an interplay of Hund's and Kondo interactions that is unique to this structure. In the presence of Hund's interactions, valence fluctuations generate a triplet superexchange between electrons and local moments. The offset from the center of symmetry allows spin-triplet pairs formed by the resulting Kondo effect to delocalize onto the Fermi surface, precipitating superconductivity. We demonstrate this mechanism within a minimal two-channel Kondo lattice model and present support for this pairing mechanism from existing experiments.

cond-mat.supr-con↗

arXiv2021

Optical Spectral Weight, Phase Stiffness and Tc Bounds for Trivial and Topological Flat Band Superconductors

We present exact results that give insight into how interactions lead to transport and superconductivity in a flat band where the electrons have no kinetic energy. We obtain bounds for the optical spectral weight for flat band superconductors, that lead to upper bounds for the superfluid stiffness and the 2D $T_c$. We focus on on-site attraction $|U|$ on the Lieb lattice with trivial flat bands and on the $π$-flux model with topological flat bands. For trivial flat bands, the low-energy optical spectral weight $\widetilde{D}_\text{low} \leq \widetilde{n} |U| Ω/2$ with $\widetilde{n} = \min\left(n,2-n\right)$, where $n$ is the flat band density and $Ω$ the Marzari-Vanderbilt spread of the Wannier functions (WFs). We also obtain a lower bound involving the quantum metric. For topological flat bands, with an obstruction to localized WFs respecting all symmetries, we again obtain an upper bound for $D_{\rm low}$ linear in $|U|$. We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte-Carlo results.

cond-mat.supr-con↗

arXiv2021

Luttinger sum rules and spin fractionalization in the SU(N) Kondo Lattice

We show how Oshikawa's theorem for the Fermi surface volume of the Kondo lattice can be extended to the SU$(N)$ symmetric case. By extending the theorem, we are able to show that the mechanism of Fermi surface expansion seen in the large $N$ mean-field theory is directly linked to the expansion of the Fermi surface in a spin-$1/2$ Kondo lattice. This linkage enables us to interpret the expansion of the Fermi surface in a Kondo lattice as a fractionalization of the local moments into heavy electrons. Our method allows extension to a pure U(1) spin liquid, where we find the volume of the spinon Fermi surface by applying a spin-twist, analogous to Oshikawa's flux insertion. Lastly, we discuss the possibility of interpreting the FL$^*$ phase characterised by a small Fermi surface in the absence of symmetry breaking, as a non-topological coexistence of such a U(1) spin liquid and an electronic Fermi liquid.

cond-mat.str-el↗

arXiv2020

Spectral functions across an Insulator to Superconductor Transition

In a minimal 2-band model with attractive interactions between fermions, we calculate the gap to single and two-particle excitations, the band-dependent spectral functions, the superfluid density and compressibility using quantum Monte Carlo (QMC) methods. We find Fermi and Bose insulating phases with signatures of incipient pairing evident in the single-particle spectral functions, and a superconducting state with three different spectral functions: (i) both bands show "BCS" behavior in which the minimum gap locus occurs on a closed contour on the underlying Fermi surface; (ii) both bands show "BEC" behavior in which the minimum gap occurs at a point; and (iii) band selective spectral characteristics, in which one band shows "BCS" while the other shows "BEC" behavior. At large interactions, we find a Mott phase of rung bosons in which the filling is one boson for every two sites, half the typical density constraint for Mott insulators.

cond-mat.supr-con↗

arXiv2019

Band inversion and topology of the bulk electronic structure in FeSe${}_{0.45}$Te${}_{0.55}$

FeSe${}_{0.45}$Te${}_{0.55}$ (FeSeTe) has recently emerged as a promising candidate to host topological superconductivity, with a Dirac surface state and signatures of Majorana bound states in vortex cores. However, correlations strongly renormalize the bands compared to electronic structure calculations, and there is no evidence for the expected bulk band inversion. We present here a comprehensive angle resolved photoemission (ARPES) study of FeSeTe as function of photon energies ranging from 15 - 100 eV. We find that although the top of bulk valence band shows essentially no $k_z$ dispersion, its normalized intensity exhibits a periodic variation with $k_z$. We show, using ARPES selection rules, that the intensity oscillation is a signature of band inversion indicating a change in the parity going from $Γ$ to Z. Thus we provide the first direct evidence for a topologically non-trivial bulk band structure that supports protected surface states.

cond-mat.str-el↗

arXiv2019

Upper bounds on the superfluid stiffness and superconducting $T_c$: Applications to twisted-bilayer graphene and ultra-cold Fermi gases

Understanding the material parameters that control the superconducting transition temperature $T_c$ is a problem of fundamental importance. In many novel superconductors, phase fluctuations determine $T_c$, rather than the collapse of the pairing amplitude. We derive rigorous upper bounds on the superfluid phase stiffness for multi-band systems, valid in any dimension. This in turn leads to an upper bound on $T_c$ in two dimensions (2D), which holds irrespective of pairing mechanism, interaction strength, or order-parameter symmetry. Our bound is particularly useful for the strongly correlated regime of low-density and narrow-band systems, where mean field theory fails. For a simple parabolic band in 2D with Fermi energy $E_F$, we find that $k_BT_c \leq E_F/8$, an exact result that has direct implications for the 2D BCS-BEC crossover in ultra-cold Fermi gases. Applying our multi-band bound to magic-angle twisted bilayer graphene (MA-TBG), we find that band structure results constrain the maximum $T_c$ to be close to the experimentally observed value. Finally, we discuss the question of deriving rigorous upper bounds on $T_c$ in 3D.

cond-mat.supr-con↗

arXiv2019

Topological superconductivity in Dirac honeycomb systems

We predict two topological superconducting phases in microscopic models arising from the Berry phase associated with the valley degree of freedom in gapped Dirac honeycomb systems. The first one is a topological helical spin-triplet superconductor with a nonzero center-of-mass momentum that does not break time-reversal symmetry. We also find a topological chiral-triplet superconductor with Chern number $\pm 1$ with equal-spin-pairing in one valley and opposite-spin-triplet pairing in the other valley. Our results are obtained for the Kane-Mele model in which we have explored the effect of three different interactions, onsite attraction $U$, nearest-neighbor density-density attraction $V$, and nearest-neighbor antiferromagnetic exchange $J$, within self-consistent Bogoliubov--de Gennes theory. Transition metal dichalcogenides and cold atom experiments are promising platforms to explore these phases.

cond-mat.supr-con↗

arXiv2012

Exact solutions of coupled Liénard-type nonlinear systems using factorization technique

General solutions of nonlinear ordinary differential equations (ODEs) are in general difficult to find although powerful integrability techniques exist in the literature for this purpose. It has been shown that in some scalar cases particular solutions may be found with little effort if it is possible to factorize the equation in terms of first order differential operators. In our present study we use this factorization technique to address the problem of finding solutions of a system of general two-coupled Liénard type nonlinear differential equations. We describe a generic algorithm to identify specific classes of Liénard type systems for which solutions may be found. We demonstrate this method by identifying a class of two-coupled equations for which the particular solution can be found by solving a Bernoulli equation. This class of equations include coupled generalization of the modified Emden equation. We further deduce the general solution of a class of coupled ordinary differential equations using the factorization procedure discussed in this manuscript.

nlin.SI↗