ICTS

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

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.

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.

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.    

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).

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.