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Topology and Correlations in Quantum Materials

Verma, Nishchhal
http://orcid.org/0000-0003-2685-9879
http://rave.ohiolink.edu/etdc/view?acc_num=osu1659345682370682

Abstract Details

2022, Doctor of Philosophy, Ohio State University, Physics.
The thesis deals with three fundamental problems lying at the intersection of correlations and topology in quantum materials. They are further divided into two broad classes: superconductivity in strongly correlated systems and Hall effect in chiral magnets. The first questions what material parameters control the superconducting (SC) transition temperature $T_c$. In many novel superconductors, SC phase fluctuations determine $T_c$, rather than the collapse of the pairing amplitude. We derive rigorous upper bounds on the superfluid phase stiffness for multi-band systems, valid in any dimension. This in turn leads to an upper bound on $T_c$ in two dimensions (2D), which holds irrespective of mechanism, pairing interaction strength, or order-parameter symmetry. We first show that $k_BT_c \leq E_F/8$ for a single parabolic band in 2D with Fermi energy $E_F$, a result that has direct implications for systems as diverse as Li-doped ZrNCl and the 2D BCS-BEC crossover in ultra-cold Fermi gases. We further derive bounds on monolayer FeSe on STO and magic-angle twisted bilayer graphene (MA-TBG) using the available band structures. We then discuss the question of deriving rigorous upper bounds on $T_c$ in 3D. In the second project, we present exact results that give insight into how interactions lead to transport and superconductivity in a flat band where the electrons have no kinetic energy. We obtain bounds for the optical spectral weight for flat band superconductors. We focus on on-site attraction $|U|$ on the Lieb lattice with trivial flat bands and on the $\pi$-flux model with topological flat bands. For trivial flat bands, the low-energy optical spectral weight $\widetilde{D}_\text{low} \leq \widetilde{n} |U| \Omega/2$ with $\widetilde{n} = \min\left(n,2-n\right)$, where $n$ is the flat band density and $\Omega$ the Marzari-Vanderbilt spread of the Wannier functions (WFs). We also obtain a lower bound involving the quantum metric. For topological flat bands, with an obstruction to localized WFs respecting all symmetries, we again obtain an upper bound for $D_{\rm low}$ linear in $|U|$. We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte-Carlo results. The third project deals with Hall experiments in chiral magnets. The Hall data is often analyzed as the sum of an anomalous Hall effect, dominated by momentum-space Berry curvature, and a topological Hall effect, arising from the real-space Berry curvature in the presence of skyrmions, in addition to the ordinary Hall resistivity. This raises the questions of how one can incorporate, on an equal footing, the effects of the anomalous velocity and the real space winding of the magnetization, and when such a decomposition of the resistivity is justified. We provide definitive answers to these questions by including the effects of all phase-space Berry curvatures in a semi-classical approach and by solving the Boltzmann equation in a weak spin-orbit coupling regime when the magnetization texture varies slowly on the scale of the mean free path. We use an exact Kubo formalism to numerically investigate the limit of infinite mean path, and discuss the correspondence with semi-classical results.
Mohit Randeria (Advisor)
Christopher Hirata (Committee Member)
Fengyuan Yang (Committee Member)
Yuan-Ming Lu (Committee Member)
157 p.
Physics
Topology, Correlations, Superconductivity, Flat bands, Skyrmions

Recommended Citations

Citations

  • Verma, N. (2022). Topology and Correlations in Quantum Materials [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1659345682370682

    APA Style (7th edition)

  • Verma, Nishchhal. Topology and Correlations in Quantum Materials. 2022. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1659345682370682.

    MLA Style (8th edition)

  • Verma, Nishchhal. "Topology and Correlations in Quantum Materials." Doctoral dissertation, Ohio State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=osu1659345682370682

    Chicago Manual of Style (17th edition)

osu1659345682370682
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© 2022, some rights reserved.Creative Commons License Topology and Correlations in Quantum Materials by Nishchhal Verma is licensed under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. Based on a work at etd.ohiolink.edu.
This open access ETD is published by The Ohio State University and OhioLINK.