Monday, 28 July 2025
TBA
I will present a very efficient way to implement the string of braidings needed to realise a generic SU(2) quantum gate using Fibonacci anyons and icosahedral group
The experimental detection of anyons in quantum Hall systems based on interferometer and beam-splitter principles has created of resurgence of interest in the topic in recent years. Here, I will present a theoretical description of coherent state bulk anyons and their signatures in two particle correlators. I will demonstrate how a saddle potential, for instance created in a pinched point contact geometry, can model a beam-splitter. Anyon dynamics in such a potential reflects Hanbury-Brown Twiss correlations that can directly probe fractional statistics. I will also illustrate how the same setting can probe dynamics akin to that found in the astrophysical realm of black holes. Specifically, point-contact geometries can exhibit phenomena parallel to Hawking-Unruh radiation and black hole quasinormal modes associated with ringdowns in gravitational wave detection.
Considering a range of candidate quantum phases of matter, half-integer thermal conductance (κth) is believed to be an unambiguous evidence of non-Abelian states. It has been long known that such half-integer values arise due to the presence of Majorana edge modes, representing a significant step towards topological quantum computing platforms. Here, we challenge this prevailing notion by presenting a comprehensive theoretical and experimental study where half-integer two-terminal thermal conductance plateau is realized employing Abelian phases. Our proposed setup features a confined geometry of bilayer graphene, interfacing distinct particle-like and hole-like integer quantum Hall states. Each segment of the device exhibits full charge and thermal equilibration. Our approach is amenable to generalization to other quantum Hall platforms, and may give rise to other values of fractional (electrical and thermal) quantized transport. Our study demonstrates that the observation of robust non-integer values of thermal conductance can arise as a manifestation of mundane equilibration dynamics as opposed to underlying non-trivial topology.
In this talk, I provide an effective description of Hall crystal phases, which are phases with topological order and broken translational symmetry. Recently there is experimental evidence for their existence in rhombohedral graphene.
Fractional quantum Hall (FQH) effect realized in graphene platforms allows for new measurements and insights about FQH states. Here I discuss two experiments and associated models using composite fermion theory (1) The exposed surface of graphene allows tunneling from an STM tip to the FQH state. We interpret the resulting sharp resonances found in the STM spectroscopy in terms of the bound states of clusters of anyons. (2) Absence of long range disorder correlations in Graphene, unlike delta-doped GaAs, allows cleaner access to QH and FQH transition regions, allowing for newer insights into the criticality therein. We show compelling evidence for a universality of quantum Hall transitions across IQH and FQH regimes; and present numerical evidence for analogy between quasiparticle hopping in FQH states and electron hopping in IQH states.
The 2016 Nobel Prize was awarded in part for discovery of “topological quantum states of matter”. The most interesting discoveries are surprises that were completely unexpected by everyone (including the discoverers), otherwise, someone would have already discovered them! Topological states of matter, including the quantum Hall effect, “Haldane gap” spin chains, and topological insulators, are in this category. I will describe the history behind some of these discoveries, and why they were surprises when made.
Tuesday, 29 July 2025
The pseudogap metal phase of the cuprate high-temperature superconductors presents a long-standing puzzle, marked by seemingly contradictory features in its electronic spectrum. While photoemission and scanning tunneling microscopy (STM) experiments reveal a truncated “Fermi arc,” recent high-field magnetotransport studies provide compelling evidence for small hole pockets. I propose a unified framework for these observations by describing the pseudogap phase as a fractionalized Fermi liquid (FL*), consisting of hole-pocket Fermi surfaces coexisting with a quantum spin liquid background. In the FL* state with doping p, each pocket was predicted to have fractional area of p/8, in excellent agreement with the Yamaji angle observed in a recent magnetotransport experiment.
To capture the interplay between spin-liquid correlations and charge carriers, I present a SU(2) lattice gauge theory that couples the hole pockets to the spin liquid. Monte Carlo simulations of the thermal fluctuations of this gauge theory reveal that Fermi arc spectra can naturally emerge from the thermally fluctuating FL* state, while preserving signatures of p/8 quantum oscillations. Upon cooling from the pseudogap metal, the simulations display a Kosterlitz-Thouless transition into a nodal d-wave superconducting phase characterized by h/2e vortices, each surrounded by a charge-order halo.
Engineering artificial systems by twisting and stacking van der Waals (vdW) materials has proven to be an excellent platform for exploring emergent quantum phenomena that can be significantly different from the constituents. Recent advances in the fabrication of high-quality twisted interfaces provide a unique opportunity to study the little-explored interfacial superconducting order in
twisted cuprate superconductors, which was not possible till now. In our work, we fabricate superconducting quantum interference devices (SQUIDs) that utilize the twisted interface of Bi2Sr2CaCu2O8+δ (BSCCO), a high-Tc cuprate superconductor. These SQUIDs are suitable for investigating the charge transport mechanisms and symmetry of the superconducting order at the interface.
Quantum Spin liquids are topological phases with fractionalized excitations. I will present experimental results pointing to fractionalization in two QSL families of materials: the Kitaev iridates and the Kagome bilayer material Ca-Cr-O.
Thermal Hall transport is a valuable tool for probing fractionalised excitations in topological quantum matter. For gapped phases, while the quantized value of the thermal Hall conductivity at low temperatures (below the spectral gap) provides a direct measure of the chiral central charge of the edge excitations, the experimental validation of quantized thermal Hall response is quite challenging and very often has been controversial. This motivated us to analyse the thermal Hall response at finite temperatures -- a more accessible parameter regime for probing fractionalised excitations. We report here two of our recent studies, namely a Kagome system [1] with abelian semionic topological order and a perturbed honeycomb Kitaev model [2] whose parent state has non-abelian Ising topological order.
References:
[1] Avijit Maity, Haoyu Guo, Subir Sachdev, and Vikram Tripathi, Thermal Hall response of an abelian chiral spin liquid at finite temperatures, Phys. Rev. B 111, 205119 (2025).
[2] Aman Kumar and Vikram Tripathi, Thermal Hall conductivity near field-suppressed magnetic order in a Kitaev-Heisenberg model, Phys. Rev. B 107, L220406 (2023).
In spite of quenched impurities, macroscopic properties of disordered samples are usually self-averaging in the large-size limit, i.e. their sample-to-sample fluctuations are small in relative terms. Even when self-averaging is violated, two disordered samples prepared using the same protocol are at a minimum expected to be in the same phase of matter. This more basic expectation is valid in essentially all physical systems with short-range interactions. Our focus here is an unusual percolation phenomenon that violates not just self-averaging, but also this more basic expectation. This is seen in the large-scale geometry and dynamics of maximum-density dimer packings of the site-diluted triangular lattice. Our results imply that weak vacancy disorder will lead to similar unconventional behavior in short-range resonating valence bond spin liquid states of triangular lattice antiferromagnets and in the randomly-pinned triangular vortex lattice state of p + ip superconductors.
We present evidence that the spin-1/2 Heisenberg J1-J2 antiferromagnets on the Shastry-Sutherland, square, and checkerboard lattices share the same Z2 Dirac quantum spin liquid phase. Our results are based on a multi-method investigation employing mapping of projective symmetry groups between these lattices followed by variational Monte Carlo calculations of Gutzwiller projected wave functions, exact diagonalization calculations accessing the level spectroscopy and fidelity, Keldysh functional renormalization group and density-matrix renormalization group calculations.