Correlation, superconductivity, and topology in twisted and untwisted layered systems

Abstract

This thesis is an effort to understand some of the interesting features induced by strong correlation - superconductivity, topology, non-Fermi liquid (NFL) in two dimensional (2D) layered materials. 2D layered materials are exciting due to their extreme tunability and the rich physics that can be invoked without worrying about the complexity of three dimension. In this thesis I explore various interplay of these tuning parameters and their manifestation in real 2D materials.

This thesis has five chapters. In Chapter 1, I introduce some basic concepts like Fermi liquid (FL), NFL, superconductivity, topology etc. to facilitate the understandings in the subsequent chapters. In chapter 2, I present the non-Fermi liquid (NFL) behavior due to momentum-dependent density-density fluctuation method in cuprates. In Fermi-liquid (FL) theory, the imaginary part of the self-energy scales quadratically with energy, which changes to linear behavior in an NFL case. My calculation shows that due to strong momentum dependent distributions of the itinerant, and local densities, the resulting self-energy becomes strongly anisotropic. The computed self-energy exhibits a marginal-FL (MFL)-like frequency dependence only in the antinodal region, and FL-like behavior elsewhere at all dopings. The DC conductivity shows that the resistivity-temperature exponent n =1 near the optimal doping. Surprisingly, in the extreme NFL state (near the optimal doping in cuprates), MFL-like self-energy occupies the largest volume in momentum space but the nodal region still contains FL-like self-energies. Similarly, in the FL state (in overdoped region), not all quasiparticles are necessarily long-lived and the antinodal region remains NFL-like.

Chapter 3 and 4 are about twisted bilayer systems. Condensed matter systems host a plethora of emergent low-energy properties due to the interplay between electronic structure, magnetism, correlation, and topology. Without losing lattice translational invariance, one can tune this interplay with spatially averaged parameters such as doping, pressure, magnetic field, and temperature. Twisted bilayers systems give a new tool to achieve local tunability with discrete translational invariance in the Moire supercell. This allows us to study emergent spatial-dependent phases beyond the typical mean-field order parameters. In chapter 3, I study the formation of superconducting pairs of Wannier orbitals in twisted bilayer graphene. Recently, superconductivity is discovered in twisted bilayer graphene (TBG) which is believed to be unconventional in nature. TBG has flat bands in the Moire supercell, which are describable by Wannier orbitals spreading over many graphene unit cells. Here I have studied the spin-fluctuation mediated superconductivity by employing an effective low energy model for TBG and by solving the linearized superconducting gap equation due to spin-fluctuation mediated pairing potential. I found an extended-s wave as the leading pairing symmetry in TBG, in which the nearest neighbor Wannier sites form Cooper pairs. I have also studied similar systems like single-layer graphene (SLG) without a moiré pattern and graphene on boron-nitride (GBN) possessing a different moiré pattern than TBG. Similar calculation shows that GBN has p + ip-wave pairing between nearest-neighbor Wannier states with odd-parity phase, while SLG has the d + id-wave symmetry for inter-sublattice pairing with even-parity phase.

Recent discovery of 2D Van der Waals (VdW) magnetic layers motivated me to study a similar Moire physics in twisted magnetic bilayers. In Chapter 4, I explore the twisted bi-layers of 2D VdW magnets where spatially modulated inter-layer interactions arise naturally due to Moire geometry. By considering long-ranged Heisenberg exchange (Jp) and dipole-dipole (JD) interlayer interactions and ferromagnetic exchange and z-axis asymmetric intra-layer interactions, I obtain the microscopic spin texture with Monte Carlo simulation. The Jp - JD parameter space unveils a hierarchy of distinct skyrmions phases, ranging from point-, rod-, and ring-shaped topological charge distributions. A novel topological antiferroelectric phase is also found, where oppositely charged antiskyrmion pairs are formed, and the corresponding topological charge distribution shows a dipole formation in the Moire supercell. The dipoles become ordered in a Néel-like state, which form a topological antiferroelectric state.

In chapter 5, I conclude the thesis with a brief summary and impact of the works described here and with a discussion on possible future prospects and outlook.