Browsing Open Access Publications by Author "Bajpai, Utkarsh"
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ItemQuantum many-body states and Green's functions of nonequilibrium electron-magnon systems: Localized spin operators versus their mapping to Holstein-Primakoff bosons(Physical Review B, 2021-11-22) Bajpai, Utkarsh; Suresh, Abhin; Nikolić, Branislav K.It is well-known that operators of localized spins within a magnetic material satisfy neither fermionic nor bosonic commutation relations. Thus, to construct diagrammatic many-body perturbation theory requiring the Wick theorem, the spin operators are usually mapped to the bosonic ones with Holstein-Primakoff (HP) transformation being the most widely used in magnonics and spintronics literature. However, to make calculations tractable, the square root of operators in the HP transformation is expanded into a Taylor series truncated to some low order. This poses a question on the range of validity of the truncated HP transformation when describing nonequilibrium dynamics of localized spins interacting with each other or with conduction electron spins—a problem frequently encountered in numerous transport phenomena in magnonics and spintronics. Here we apply exact diagonalization techniques to a Hamiltonian of fermions (i.e., electrons) interacting with HP bosons versus a Hamiltonian of fermions interacting with the original localized spin operators to compare their many-body states and one-particle equilibrium and nonequilibrium Green's functions (GFs). We employ as a test bed a one-dimensional quantum Heisenberg ferromagnetic spin-S XXX chain of N≤7 sites, where S=1 or S=5/2, and the ferromagnet can be made metallic by allowing electrons to hop between the sites while interacting with the localized spins via sd exchange interaction. For these two different versions of the Hamiltonian of this model, we compare the structure of their ground states, time evolution of excited states, spectral functions computed from the retarded GF in equilibrium, and matrix elements of the lesser GF out of equilibrium. Interestingly, magnonic spectral function can be substantially modified by acquiring additional peaks due to quasibound states of electrons and magnons once the interaction between these subsystems is turned on. The Hamiltonian of fermions interacting with HP bosons gives an incorrect ground state and electronic spectral function unless a large number of terms are retained in the truncated HP transformation. Furthermore, tracking the nonequilibrium dynamics of localized spins over longer time intervals requires a progressively larger number of terms in truncated HP transformation, even if a small magnon density is excited initially, but the required number of terms is reduced when interaction with conduction electrons is turned on. Finally, we show that recently proposed [M. Vogl et al., Phys. Rev. Res. 2, 043243 (2020); J. König et al., SciPost Phys. 10, 007 (2021)] resummed HP transformation, where spin operators are expressed as polynomials in bosonic operators, resolves the trouble with truncated HP transformation while allowing us to derive an exact quantum many-body (manifestly Hermitian) Hamiltonian consisting of a finite and fixed number of boson-boson and electron-boson interacting terms. ItemRobustness of quantized transport through edge states of finite length: Imaging current density in Floquet topological versus quantum spin and anomalous Hall insulators(Physical Review Research, 2020-09-17) Bajpai, Utkarsh; Ku, Mark J. H.; Nikolić, Branislav K.The theoretical analysis of topological insulators (TIs) has been traditionally focused on infinite homogeneous crystals with band gap in the bulk and nontrivial topology of their wave functions, or infinite wires whose boundaries host surface or edge metallic states. Such infinite-length edge states exhibit quantized conductance which is insensitive to edge disorder, as long as it does not break the underlying symmetry or introduce energy scale larger than the bulk gap. However, experimental devices contain finite-size topological region attached to normal metal (NM) leads, which poses a question about how precise is quantization of longitudinal conductance and how electrons transition from topologically trivial NM leads into the edge states. This particularly pressing issue for recently conjectured two-dimensional (2D) Floquet TI where electrons flow from time-independent NM leads into time-dependent edge states, the very recent experimental realization [J. W. McIver et al., Nat. Phys. 16, 38 (2020)] of Floquet TI using graphene irradiated by circularly polarized light did not exhibit either quantized longitudinal or Hall conductance. Here, we employ a charge-conserving solution for Floquet-nonequilibrium Green functions of irradiated graphene nanoribbon to compute longitudinal two-terminal conductance, as well as spatial profiles of local current density as electrons propagate from NM leads into the Floquet TI. For comparison, we also compute conductance of graphene-based realization of 2D quantum Hall, quantum anomalous Hall, and quantum spin Hall insulators. Although zero-temperature conductance within the gap of these three conventional time-independent 2D TIs of finite length exhibits small oscillations due to reflections at the NM-lead/2D-TI interface, it remains very close to perfectly quantized plateau at 2e2/h and completely insensitive to edge disorder. This is due to the fact that inside conventional TIs there is only edge local current density which circumvents any disorder. In contrast, in the case of Floquet TI both bulk and edge local current densities contribute equally to total current, which leads to longitudinal conductance below the expected quantized plateau that is further reduced by edge vacancies. We propose two experimental schemes to detect coexistence of bulk and edge current densities within Floquet TI: (i) drilling a nanopore in the interior of irradiated region of graphene will induce backscattering of bulk current density, thereby reducing longitudinal conductance by ∼28%; (ii) imaging of magnetic field produced by local current density using diamond nitrogen-vacancy centers.