Das Group of Quantum Matter Theory

We explore several frontiers of the quantum theory of condensed matters and materials sciences. In a broad sense, our research interests lie in understanding and predicting materials properties driven by quantum phenomena that are amenable to experimental verifications and device implementations. More specifically, we study superconductivity, emergent correlated phases, topological phases of matter, and non-Hermitian quantum properties. The techniques we use in our group include analytical models, density-functional theory (DFT), momentum-resolved density fluctuation (MRDF) theory (homemade code), and numerical simulation, among others.

Research Highlights

Non-Hermitian Quantum Theory
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Many systems, such as open quantum systems, systems out of equilibrium, disordered systems, etc, are describable by non-Hermitian Hamiltonians. However, the quantum theory of non-Hermitian Hamiltonians is not well developed due to the lack of a properly defined Hilbert space and unitary time evolution. We are working on many aspects of this theoretical developments at the fundamental level.

NonHermitian
Non-Hermitian Topology
The IOP editor invited us to write a review article for the Journal of Physics: Condensed Matter on topological phases in non-Hermitian systems. Our review article (31, 263001 (2019)) is well appreciated in the community, earning, so far, 260 citations and the Top Cited Paper Award (2018-2020) from IOP Publishing.
superconductivity
Non-Hermitian superconductivity
Parity and time-reversal (PT in short) symmetric non-Hermitian Hamiltonians, which possess real eigenvalues, have now become a mainstream research program. We introduced a general idea of non-Hermitian, PT invariant superconductivity. This article is published in Physical Review B (97, 014512 (2018)).
Superconductivity
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One of the fascinating facts about superconductivity is that despite more than 100 years of extensive research and 7 Nobel prizes, plenty of surprises is discovered daily. We have been interested in the theoretical studies of conventional and unconventional superconductivity and the interplay of superconductivity with other phases. We often study the the pairing symmetry and pairing mechanism of superconductivity and its competition and coexistence with other exotic phases of matter. We are also interested in studying topological superconductivity.

Recent Highlights
  • Soon after the discovery of superconductivity in infinite-layer nickelates (NdNiO2), with theoretical collaborations with SNBNCBS and IACS, we have theoretically investigated the electronic and superconducting properties of this material [PRB (Letter) 102, 100501; ibid 102 220502 (2020)].
  • We have shown in YBCO cuprates that with selective doping on the CuO chain state, an unconventional f-wave pairing symmetry can be realized. Such an f-wave pairing is long-sought due to its conceptual novelties and topological properties [PRB 101, 214517 (2020)].
  • In Kondo systems, we have shown that as the f-orbitals’ electrons fractionalize to their spin and charge degrees of freedom, the charge fluctuation mediates Cooper pairing between spinon and conduction electrons [SciPost Phys. 7, 078 (2019)]
  • We predicted a novel charge ordering in the electron-doped cuprates, which breaks the rotational symmetry, as also seen experimentally [Nature Physics 15, 335-340 (2019)].
  • With theoretical prediction and experimental confirmation, we have discovered α-BiPd as a noncentrosymmetric topological superconductor [PRL 117, 177001 (2016)].
Topological Phases of Matter
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Roughly speaking, a topological space is a set of points with a sense of continuity between the points, so that it takes a shape which is deformable to another shape without removing any points. Consequently, most of the physical processes, trajectories, patterns are formed in topological spaces. In quantum condensed matter field, it is a new realization that the Hamiltonians’ parameter space can be a topological space - with interesting physical properties such as quantised Hall transport, fractional particles, entanglement, and electromagnetic responses. We study such physics in both electronic structures, spin textures, and Moire lattices.

Recent Highlights
  • We showed that topological phases can be robust to the loss of symmetry in the symmetry-protected topology (SPT) phases [Phys. Rev. B 103, 075139 (2021)].
  • Despite the first prediction of quantum Spin Hall effect in graphene, it took nearly three decades to achieve this, thank to the proximity induced spin-orbit coupling via heterostructure engineering [ACS Nano 15, 916 (2021)].
  • We explored the topology in SU(3) symmetric systems. We uncover salient ingredients required to express a three-component lattice Hamiltonian in a SU(3) format with a nontrivial topological invariant [PRB 95, 165425 (2017)].
2D Materials and Twistronics
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Physics can be drastically different in different dimensions even for the same Hamiltonian. The door to two dimensional materials was opened by graphene, which followed transitional metal dichalcogenides, Kagome materials and now we have 2D magnets. The symmetry classification changes, the correlation effect is enhanced, and electronic, magnetic, optical, superconducting and topological properties are intertwinned. Materials have the blessing and curse of periodicity of atoms, which provide an abundance of symmetries, but at the same time, constraint the possibility of phases. Twisted bilayer systems are a modern technology which allows to dissolve or divert these disadvantages and we can possibly realize anything and everything.

Recent Highlights
  • The twist angle between the layers of two-dimensional materials can change various material properties. We have shown that an extended-s-wave pairing state forms in the flat band of twisted bilayer graphene with gapless Wannier-Bogolyubov quasiparticles [PRB 99, 134515 (2019)]
  • We recently introduced the idea of a Moire´ magnet in twisted bilayers. We have highlighted that this platform gives a unique opportunity to produce spatially varying magnetic textures rather than the usual homogenous magnetic ordered states due to the superlattice formation. Our theoretical study predicts a hierarchy of distinct skyrmion phases - previously unknown in bulk materials and the formation of dipole moments and long-range ordering of topological charges in twisted magnetic systems [PRB 104, 014410 (2021)].
  • We have also worked extensively on various 2D materials in graphene, transition metal dichalcogenides, and related materials. Some of the relevant references are Nano Letter 15, 80-87 (2015), ibid 19, 5703 (2021); ACS Nano 16, 783–791 (2022); ibid 15, 916-922 (2021) ; Adv. Sci 8, 2101516 (2021); PRX 11, 031013 (2021); PRL 119, 226802 (2017).
  • The two-dimensional electron gas at the interface of LaVO3/SrTi03 is characteristically distinct from other interfacial 2D materials. Here both the V-d and Ti-d orbitals are hybridized to produce unconventional superconductivity, while conventional mechanism is proposed in other interfacial superconductors [ACS Appl. Electron. Mater. 4, 5859 (2022)].
Quantum Magnets, Skyrmions
QuantumMagnetic

In going beyond typical mean-field solutions, solitons, emergent gauge/curvature fields, fractionalization/fragmentation, entanglement are presently sought in a variety of setups. Governing such phases require additional materials help, such as geometric frustration, reduced symmetry, chiral interactions, and topology. Cold atoms, photonics systems also can simmulate such lattice.

Recent Highlights
  • We propose that twisted bilayer magnets are new and versatile settings where spatially varying, chiral, and long-range interactions naturally arise. These interactions constitute just the right Hamiltonian to govern skyrmions, Hopfions, and novel spatial textures of spin [Phys. Rev. B 104, 014410 (2021)].
  • In VSe2, we showed that there exists two charge density waves, one that is extended to the 3D bulk while another one is only confined to the 2D surfaces which survives to its monolayer geometry [ACS Nano 16, 783 (2022)].
  • Through DMRG calculation in a Kitaev model with magnetic field, we recently predicted the existence of a quantum glass phase in the cases where number of Z2 fluxes increases beyond half of the plaquettes number in a lattice. The study hints towards a generic glass phase in proximity to the spin-liquid state. [arXiv:2302.14328].
Correlated Electron Systems


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As atoms are arranged in periodic lattices, the orbital wavefunctions of electrons change to Bloch wavefunctions. So they do not remain to be the same electrons, rather become collective excitations which we call quasiparticles. When electron-electron interaction is included, the properties of quasiparticles can drastically change, including the definition of quasiparticles itself. New phenomena such as non-Fermi liquid, strange metal, Mott insulator emerges, which proximitise the unconventional superconductivity, competing orders to more exotic states. In fact, one amay govern even novel excitations, which can be fermionic, bosonic or even more exotic in nature.

The numerical code for the intermediate coupling model is dubbed ‘momentum-resolved density fluctuation (MRDF)’ code.

Recent Highlights
  • Intermediate coupling model: In many transition metal, actinide, and heavy-fermion compounds, it is often seen that the electronic properties at low-energy is quasiparticle like, while those at higher energy become insulating like. This phenomenon has fuelled debate for several decades about the validity of various theories, and quasiparticle properties. We introduce the concept of intermediate coupling model, applicable to the cases where the interaction strength is comparable to the non-interacting kinetic energy term. We showed that in such cases, the states fractionalize into conducting Bloch-like near the Fermi level and atomic like localized states at high-energy. Our work is reviewed in this article [Advances in Physics 63, 151-266 (2014)]
  • The visualization of various bosonic excitations in strongly correlated materials reveal important information about the correlation strength and emergent physics, which is routinely done by resonant inelastic x-ray scattering (RIXS) method. Recently, we introduce a new new methodology for calculating the full RIXS response of a correlated metal in an unbiased fashion in this work [Phys. Rev. X 11, 031013 (2021)].
  • Combining with experimental data and our MRDF simulation to exhibit that the ferromagnetic to antiferromagnetic phase - accompanied by metal-insulator transition - can be efficiently tuned by proximity effect in nickel-oxides. [Advanced Physics 8, 2101516 (2021)].