Research
The central theme of my research is to explore the interplay of topology, interactions and periodic driving in quantum many-body systems. Topological phases are special in the sense that they cannot be described by local observables/order parameters in the conventional Ginzburg-Landau theory. Instead, they are characterized by global geometric properties of the gapped many-body ground state, which are robust against symmetry-preserving perturbations that do not close the energy gap. Thus, a topologically non-trivial state cannot be adiabatically connected to a trivial state (a tensor product of single-particle states) without crossing a quantum phase transition.
Higher-order topological insulators
"First-order" topological insulators are characterized by the presence of robust, gapless states on their boundaries with codimension one. In contrast, "higher-order" topological insulators (HOTIs) host robust, gapless states on their boundaries with codimension two or higher. For example, a 2D second-order topological insulator hosts gapless, bound states at its 0D corners, while a 3D second-order topological insulator hosts gapless, bound states at its 1D hinges. HOTIs usually require the presence of certain crystalline symmetries for their protection, and thus extend the notion of topological crystalline insulators.
In particular, the topological classification of HOTIs with anti-commuting crystalline mirror symmetries is still an active area of research. This is due to the complex relationship between edge topology, Wilson loop operators and crystalline symmetries. In our work, we have developed momentum-space topological invariants from Wilson loops and "periodicized" Wilson lines to characterize the topology of the Wilson loop spectra of HOTIs with anti-commuting mirror symmetries. We also study effects of mirror-symmetry-breaking perturbations on edge gap closings and find novel "edge-selective" topological phase transitions, resulting in bound states appearing at a subset of boundaries.
Publications:
- Wilson loop invariants and bulk-boundary correspondence in higher-order topological insulators with anticommuting mirror symmetries, Suman Aich and Babak Seradjeh, Phys. Rev. B 114, 065133 (2026).
- Selective bulk-boundary correspondence in higher-order topological insulators with anticommuting mirror and chiral symmetries, Suman Aich and Babak Seradjeh, arXiv:2509.22304.
Periodically-driven (Floquet) systems
Periodically driving a quantum system out of equilibrium, also known as Floquet engineering, can lead to the emergence of novel phases of matter that are not possible in static systems. Specifically in graphene, Floquet engineering using circularly-polarized lasers can open a topologically non-trivial gap at the Dirac points, due to broken time-reversal symmetry, resulting in a Floquet Chern insulator. Recent experiments have even measured the quantized Hall conductance (light-induced anomalous quantum Hall effect) and observed Floquet-Bloch states in graphene.
An interesting scenario arises when the vector potential amplitude of the driving field has a radial vortex profile with a phase twist, due to a non-zero orbital angular momentum (OAM) of light, about the vortex core. This is known as twisted light or optical vortex beam. As a result of non-zero OAM, a twisted light beam with linear polarization can also break time-reversal symmetry and open a topologically non-trivial gap at the Dirac points in graphene. In our work, we have studied the topological properties of graphene driven by circularly-polarized twisted light. We find multiple quasienergy band crossings spatially distributed along the radial direction within the graphene sample, at fixed light frequency and amplitude. These band crossings are associated with topological phase transitions, and are characterized by a change in the Floquet topological invariants. Additionally, by bulk-boundary correspondence, there are bound Floquet-Bloch states that are exponentially localized at the radial positions of the band crossings. Thus, twisted circularly-polarized light can be used to create multiple Floquet topological phases within a single graphene sample, that are tunable via the light frequency and amplitude
Publications:
- Multiple tunable real-space degeneracies in graphene irradiated by twisted light, Suman Aich and Babak Seradjeh, Phys. Rev. B 110, 054314 (2024).
Simulation of quantum spin Hamiltonians using polar molecules
Ultracold polar molecules are promising candidates for quantum simulation of strongly-correlated many-body systems, due to their long-range, anisotropic dipole-dipole interactions. In particular, the rotational hyperfine states of polar molecules can be used to encode spin degrees of freedom, and the dipolar interactions can be used to engineer effective spin-spin interactions.
In our work, we have proposed a scheme to simulate a generalized spin-1 Hamiltonian with tunable long-range interactions using ultracold polar molecules trapped in a 1D optical lattice. The many-body phase diagram of Heisenberg-type spin-1 Hamiltonians in 1D has been well established, and includes the symmetry-protected topological Haldane phase. Going beyond Heisenberg interactions, in our proposed molecular platform, we simulate generic spin-1 SU(3) interactions. Interestingly, we find that the Haldane phase is robust against such SU(3) interactions, and accessible in an experimentally feasible parameter regime.
Publications:
- Quantum simulation of the Haldane phase using open shell molecules, Suman Aich, Ceren B. Dag, H.A. Fertig, Debayan Mitra and Babak Seradjeh, arXiv:2603.14874.