Research

Dissipation and decoherence are usually treated as hinderances that spoil the properties of closed quantum systems. But the general dynamics involving open quantum systems, by default involve dissipation and decoherence as features rather than obstacles. In a series of works with my collaborators, we have predicted novel dynamical topological features in dissipative extensions of closed topological systems [1, 2, 3]. We have studied a Chern insulator coupled to a bath and shown that in the dynamics towards a steady-state (given by Gorini-Kossakowski- Sudarshan-Lindblad equation), there emerges a topologically robust dissipation channel that is localised only along one edge of the system (in contrast to both edges) and for only one of the sub-species of spin[1]. This is rooted in the topology of the spectrum of the dissipation generator itself. This is in strong contrast with the wave function based band-topology that occurs in closed quantum systems. We also reveal non-equilibrium current as a signature of degree of mixedness of the final steady state. These are hitherto unexplored features of manifestation of emergent non-Hermitian topology in the dynamics and steady-states of open quantum systems. We have also considered the question of finite fermion-filling of fermionic many-body(non-interacting) steady states of non-Hermitian Su-Schriefer-Heeger model and charted its phase diagram [2]. We found that there are novel metallic phases that have topologically-protected chiral currents and insulating phases that have particles dynamically entrapped within a unit-cell. In [3], we found that the chiral currents are robust even on introducing disorder and also studied the fate of the non-Hermitian skin-effect for different symmetry classes. These results open up a new avenue in open quantum systems to realise topologically robust quantum channels with possible device engineering applications. Photonic lattice systems have been quite successful in realising dissipative topological phases and our results are highly relevant in such settings.

[1] S. S. Hegde, T. Ehmcke, and T. Meng, “Edge-selective extremal damping from topological heritage of dissipative chern insulators,” Phys. Rev. Lett., vol. 131, p. 256601, Dec 2023.

[2] A. Banerjee, S. S. Hegde, A. Agarwala, and A. Narayan, “Chiral metals and entrapped insulators in a one-dimensional topological non-hermitian system,” Physical Review B, vol. 105, may 2022.

[3] R. Sarkar, S. S. Hegde, and A. Narayan, “Interplay of disorder and point-gap topology: Chiral modes, localization, and non-hermitian anderson skin effect in one dimension,” Physical Review B, vol. 106, jul 2022.

There has been recent interest in mimicking physics around black holes in condensed matter. A series of works with my collaborators [1, 2, 3] go beyond merely mimicking these aspects and provide a unique perspective that such phenomena are not restricted to black holes alone but emerge intrinsically in condensed matter.We have revealed characteristic aspects of black holes manifesting in quantum Hall systems and Weyl semi-metals. This includes Hawking radiation, gravitational lensing, quasi-normal modes, and photon sphere, where the last two have been recently observed in black holes and were one of the breakthrough observations of the century. 

Quantum Hall: The fundamental object of Hawking radiation, called the Rindler Hamiltonian (also related to the entanglement Hamiltonian), can be realised in quantum hall systems through the application of point-contact potential and strains [1, 2]. We identified that the same dynamical symmetry Lie-algebra (sl(2, R) ∼ so(2, 1)) underlies both physical settings though manifesting in very different physical forms. This also implies that full Lorentz kinematics can also be realised in this setting. We also showed that in the same system, wavepacket dynamics can reveal signatures of quasi-normal modes, which are otherwise found in gravitational waves. These phenomena have explicit signatures in the tunnelling conductances of quantum Hall point-contact systems, which are one of the most well-developed experimental set-ups.

Weyl semimetals: We have also studied inhomogeneously strained/tilted Weyl semi-metals in relation to black-hole analogies, using a combination of analytical and numerical techniques [3]. We showed that an analog of ‘black-hole photon sphere’ termed as ‘the separatrix’ forms a boundary beyond which semi-classical methods fail to predict the behaviour of lensed wave- packet trajectories in a lattice system and thus also marks the regime of failure of black hole analogies in such systems. The separatrix also forms a ‘filter’ that sorts trajectories into deflected versus spiralling based on the initial momentum of injection into the system. Thus, it gives a possibility of using it as a ‘high-pass’ or ‘low-pass filter’. Our analytical results could be used to precision-engineer deflection and chirality-selection of electron trajectories in inhomogeneous Weyl semi-metal based quantum devices. We also showed that the precession dynamics of the ‘spin/chirality’ of the Weyl-particle underlies the well-known Berry curvature induced anomalous shifts and it leads to drastic deviations from classical geodesic trajectories of massless particles (something which is not well appreciated in gravitational physics literature as well).

[1] S. S. Hegde, V. Subramanyan, B. Bradlyn, and S. Vishveshwara, “Quasinormal modes and the Hawking-Unruh effect in quantum hall systems: Lessons from black hole phenomena,” Physical Review Letters, vol. 123, Oct 2019.

[2] V. Subramanyan, S. S. Hegde, S. Vishveshwara, and B. Bradlyn, “Physics of the inverted harmonic oscillator: From the lowest landau level to event horizons,” Annals of Physics, vol. 435, p. 168470, dec 2021.

[3] A. Haller, S. Hegde, C. Xu, C. D. Beule, T. L. Schmidt, and T. Meng, “Black hole mirages: Electron lensing and Berry curvature effects in inhomogeneously tilted Weyl semimetals,” SciPost Physics, vol. 14, may 2023.

We've worked on fractional quantum Hall(FQH) states in Graphene [1], which form a platform for an intriguing interplay of symmetry breaking and topology. In the multi-component FQH states with added valley-Zeeman term, we predicted the occurrence of a novel valley-symmetry broken ‘canted-Kekule density phase’ at certain filling fraction. We also predicted a sequence of valley- and spin-symmetry breaking transitions some of which also change the intrinsic topological order distinguished from theircoupling to underlying geometry. The study was motivated by magnon transport experiments on Graphene aligned with a Boron-Nitride substrate and we were able to relate to some of the experimentally observed aspects.

[1] S. S. Hegde and I. S. Villadiego, “Theory of competing charge density wave, kekul ́e , and antiferromagnetically ordered fractional quantum hall states in graphene aligned with boron nitride,”  Physical Review B, vol. 105, may 2022.

Majorana modes have attracted immense attention due to their fundamental importance and relevance for quantum computation. In collaboration with the experimentalists at UIUC we explored the prospect of using superconductor-topological insulator(SC-TI heterostructures) as an alternative platform to the nanowire set ups for realizing and manipulating Majorana modes in topological superconductors [1]. Capitalizing on the mobility of the vortices in these junctions to move the Majorana modes, we have developed two protocols to exchange-braid them in Y-shaped Josephson junctions and also induce a non-Ableian rotation in the ground-state manifold of the system. We obtained the current-phase relations and their signatures in the Josephson diffraction patterns, which supplements the experimental simulations. These diffraction patterns are measured in Josephson interferometry experiments. I have also worked on coupling of Majorana modes to microwave cavities in Transmon systems and related aspects in association with experimental groups at UIUC. We have also studied the relation of Kitaev Majorana chain to Ising spin chain and predicted novel phenomena in their non-equilibrium dynamics [2].

[1]  S. S. Hegde, G. Yue, Y. Wang, E. Huemiller, D. Van Harlingen, and S. Vishveshwara, “A topological josephson junction platform for creating, manipulating, and braiding majorana bound states,” Annals of Physics, vol. 423, p. 168326, Dec 2020.

[2] S. S. Hegde, V. Shivamoggi, S. Vishveshwara, and D. Sen, “Quench dynamics and parity blocking in majorana wires,” New Journal of Physics, vol. 17, no. 5, p. 053036, 2015.

I made an in depth study of disordered Kitaev Majorana chain and its relation to physics of transverse XY-spin chain. Using methods of transfer matrix and random matrix theory, we were able to study the critical properties of Majorana modes and ground-state fermion partiy under disorder, also commenting on a boundary in the phase diagram of Kitaev chain that is closely associated with entanglement transitions in the corresponding spin chain [1]. This has been relevant for many later studies on realistic systems involving disorder. In [2], we have made a detailed study of skin-localisation under disorder in non-Hermitian topological systems of different symmetry classes. Localisation in quasiperiodic systems has been another topic of interest to me and in collaboration with experiments in cold-atoms we studied mobility edges in such systems[3].

[1] S. S. Hegde and S. Vishveshwara, “Majorana wave-function oscillations, fermion parity switches, and disorder in kitaev chains,” Phys. Rev. B, vol. 94, p. 115166, 2016.

[2] R. Sarkar, S. S. Hegde, and A. Narayan, “Interplay of disorder and point-gap topology: Chiral modes, local ization, and non-hermitian anderson skin effect in one dimension,” Physical Review B, vol. 106, jul 2022.

[3] F. A. An, K. Padavi ́c, E. J. Meier, S. Hegde, S. Ganeshan, J. H. Pixley, S. Vishveshwara, and B. Gadway, “Interactions and mobility edges: Observing the generalized aubry-andr ́e model,” Phys. Rev. Lett., vol. 126, p. 040603, Jan 2021.