Condensed Matter Theory

Abstract:

We study magic angle graphene in the presence of both strain and particle-hole symmetry breaking due to non-local inter-layer tunneling. We perform a self-consistent Hartree-Fock study that incorporates these effects alongside realistic interaction and substrate potentials, and explore a comprehensive set of competing orders including those that break translational symmetry at arbitrary wavevectors. We find that at all non-zero integer fillings very small strains, comparable to those measured in scanning tunneling experiments, stabilize a fundamentally new type of time-reversal symmetric and spatially non-uniform order. This order, which we dub the 'incommensurate Kekul\'e spiral' (IKS) order, spontaneously breaks both the emergent valley-charge conservation and moir\'e translation symmetries, but preserves a modified translation symmetry $\hat{T}'$ -- which simultaneously shifts the spatial coordinates and rotates the $U(1)$ angle which characterizes the spontaneous inter-valley coherence. We discuss the phenomenological and microscopic properties of this order. We argue that our findings are consistent with all experimental observations reported so far, suggesting a unified explanation of the global phase diagram in terms of the IKS order.

Abstract:

We present a framework in which the transition between a many-body localised (MBL) phase and an ergodic one is symmetry breaking. We consider random Floquet spin chains, expressing their averaged spectral form factor (SFF) as a function of time in terms of a transfer matrix that acts in the space direction. The SFF is determined by the leading eigenvalues of this transfer matrix. In the MBL phase the leading eigenvalue is unique, as in a symmetry-unbroken phase, while in the ergodic phase and at late times the leading eigenvalues are asymptotically degenerate, as in a system with degenerate symmetry-breaking phases. We identify the broken symmetry of the transfer matrix, introduce a local order parameter for the transition, and show that the associated correlation functions are long-ranged only in the ergodic phase.

Abstract:

`Active matter' is a term used to describe non-equilibrium systems, such as living organisms and tissues, that do work using an external source of energy. Epithelial cells are a subclass of living systems that derive their energy from ATP hydrolysis and are driven by active processes in the cytoskeleton. Epithelial cells can migrate as individuals, but also organise into two-dimensional monolayers and give rise to rich emergent behaviours such as collective migration and nematic liquid-crystalline order, with implications for morphogenesis, growth, and cancer metastasis. In this Thesis we model epithelia as two-dimensional monolayers to study their collective behaviours.

Using a multi-phase field model for epithelia, we first study the contributions of polar activity and cell-cell adhesion to the rotation of pairs of cells in confinement. Then we dispense with polar activity in favour of dipolar active stresses in order to study bulk epithelia. We investigate the microphase separation of mixtures of extensile and contractile dipolar cells. Cell sorting of this type has been observed in experiment and is relevant to embryogenesis and morphogenesis, and we propose an active origin for the observations.

Then we focus on cell intercalations, which are responsible in part for tissue fluidisation and therefore collective migration. We model fluctuations in the number of cadherin proteins at adherens junctions between cells using an Ornstein-Uhlenbeck process. We vary the timescale and variance of the random process and find a region that promotes translational diffusion and neighbour rearrangements, and show that the orientational order in the system vanishes. We also find that the translational diffusion has a non-monotonic dependence on the timescale of the adhesion fluctuations.

Finally, we study the flow of epithelia confined to a channel. Plug and shear flow have been observed in experiment and have implications for gastrulation in the embryo. First, we recover macroscopic flow for contractile cells by enforcing cell orientations at the edge the channel. Then we reformulate the force balance in the multi-phase field model to include Stokesian dynamics and, therefore, internal friction. The improved model exhibits an oscillatory shear flow that becomes more persistent as the coefficient of internal friction is increased. This development helps to bridge the gap from microscopic models to continuum theories.