# Publications

## Approximating observables on eigenstates of large many-body localized systems

PHYSICAL REVIEW B **99** (2019) ARTN 104201

## Onsager symmetries in U(1)-invariant clock models

JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2019) ARTN 043107

## NMR relaxation in Ising spin chains

PHYSICAL REVIEW B **99** (2019) ARTN 035156

## Signatures of the many-body localized regime in two dimensions

NATURE PHYSICS **15** (2019) 164-169

## Topological 'Luttinger' invariants for filling-enforced non-symmorphic semimetals.

Journal of physics. Condensed matter : an Institute of Physics journal **31** (2019) 104001-

Luttinger's theorem is a fundamental result in the theory of interacting Fermi systems: it states that the volume inside the Fermi surface is left invariant by interactions, if the number of particles is held fixed. Although this is traditionally justified in terms of analytic properties of Green's functions, it can be viewed as arising from a momentum balance argument that examines the response of the ground state to the insertion of a single flux quantum (Oshikawa 2000 Phys. Rev. Lett. 84 3370). This reveals that the Fermi volume is a topologically protected quantity, whose change requires a phase transition. However, this sheds no light on the stability or lack thereof of interacting semimetals, that either lack a Fermi surface, or have perfectly compensated electron and hole pockets and hence vanishing net Fermi volume. Here, I show that semimetallic phases in non-symmorphic crystals possess additional topological 'Luttinger invariants' that can be nonzero even though the Fermi volume vanishes. The existence of these invariants is linked to the inability of non-symmorphic crystals to host band insulating ground states except at special fillings. I exemplify the use of these new invariants by showing that they distinguish various classes of two- and three-dimensional semimetals.

## Enhanced bacterial swimming speeds in macromolecular polymer solutions

Nature Physics (2019)

© 2019, The Author(s), under exclusive licence to Springer Nature Limited. The locomotion of swimming bacteria in simple Newtonian fluids can successfully be described within the framework of low-Reynolds-number hydrodynamics 1 . The presence of polymers in biofluids generally increases the viscosity, which is expected to lead to slower swimming for a constant bacterial motor torque. Surprisingly, however, experiments have shown that bacterial speeds can increase in polymeric fluids 2–5 . Whereas, for example, artificial helical microswimmers in shear-thinning fluids 6 or swimming Caenorhabditis elegans worms in wet granular media 7,8 increase their speeds substantially, swimming Escherichia coli bacteria in polymeric fluids show just a small increase in speed at low polymer concentrations, followed by a decrease at higher concentrations 2,4 . The mechanisms behind this behaviour are currently unclear, and therefore we perform extensive coarse-grained simulations of a bacterium swimming in explicitly modelled solutions of macromolecular polymers of different lengths and densities. We observe an increase of up to 60% in swimming speed with polymer density and demonstrate that this is due to a non-uniform distribution of polymers in the vicinity of the bacterium, leading to an apparent slip. However, this in itself cannot predict the large increase in swimming velocity: coupling to the chirality of the bacterial flagellum is also necessary.

## Interaction Effects and Charge Quantization in Single-Particle Quantum Dot Emitters.

Physical review letters **122** (2019) 127701-

We discuss a theoretical model of an on-demand single-particle emitter that employs a quantum dot, attached to an integer or fractional quantum Hall edge state. Via an exact mapping of the model onto the spin-boson problem we show that Coulomb interactions between the dot and the chiral quantum Hall edge state, unavoidable in this setting, lead to a destruction of precise charge quantization in the emitted wave packet. Our findings cast doubt on the viability of this setup as a single-particle source of quantized charge pulses. We further show how to use a spin-boson master equation approach to explicitly calculate the current pulse shape in this setup.

## Active transport in a channel: stabilisation by flow or thermodynamics.

Soft matter (2019)

Recent experiments on active materials, such as dense bacterial suspensions and microtubule-kinesin motor mixtures, show a promising potential for achieving self-sustained flows. However, to develop active microfluidics it is necessary to understand the behaviour of active systems confined to channels. Therefore here we use continuum simulations to investigate the behaviour of active fluids in a two-dimensional channel. Motivated by the fact that most experimental systems show no ordering in the absence of activity, we concentrate on temperatures where there is no nematic order in the passive system, so that any nematic order is induced by the active flow. We systematically analyze the results, identify several different stable flow states, provide a phase diagram and show that the key parameters controlling the flow are the ratio of channel width to the length scale of active flow vortices, and whether the system is flow aligning or flow tumbling.

## Emergence of Active Nematic Behavior in Monolayers of Isotropic Cells.

Physical review letters **122** (2019) 048004-048004

There is now growing evidence of the emergence and biological functionality of liquid crystal features, including nematic order and topological defects, in cellular tissues. However, how such features that intrinsically rely on particle elongation emerge in monolayers of cells with isotropic shapes is an outstanding question. In this Letter, we present a minimal model of cellular monolayers based on cell deformation and force transmission at the cell-cell interface that explains the formation of topological defects and captures the flow-field and stress patterns around them. By including mechanical properties at the individual cell level, we further show that the instability that drives the formation of topological defects, and leads to active turbulence, emerges from a feedback between shape deformation and active driving. The model allows us to suggest new explanations for experimental observations in tissue mechanics, and to propose designs for future experiments.

## Coherent motion of dense active matter

EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS **227** (2019) 2401-2411

## Interacting multi-channel topological boundary modes in a quantum Hall valley system.

Nature **566** (2019) 363-367

Symmetry and topology are central to understanding quantum Hall ferromagnets (QHFMs), two-dimensional electronic phases with spontaneously broken spin or pseudospin symmetry whose wavefunctions also have topological properties1,2. Domain walls between distinct broken-symmetry QHFM phases are predicted to host gapless one-dimensional modes-that is, quantum channels that emerge because of a topological change in the underlying electronic wavefunctions at such interfaces. Although various QHFMs have been identified in different materials3-8, interacting electronic modes at these domain walls have not been probed. Here we use a scanning tunnelling microscope to directly visualize the spontaneous formation of boundary modes at domain walls between QHFM phases with different valley polarization (that is, the occupation of equal-energy but quantum mechanically distinct valleys in the electronic structure) on the surface of bismuth. Spectroscopy shows that these modes occur within a topological energy gap, which closes and reopens as the valley polarization switches across the domain wall. By changing the valley flavour and the number of modes at the domain wall, we can realize different regimes in which the valley-polarized channels are either metallic or develop a spectroscopic gap. This behaviour is a consequence of Coulomb interactions constrained by the valley flavour, which determines whether electrons in the topological modes can backscatter, making these channels a unique class of interacting one-dimensional quantum wires. QHFM domain walls can be realized in different classes of two-dimensional materials, providing the opportunity to explore a rich phase space of interactions in these quantum wires.

## Magnetically-actuated artificial cilium: a simple theoretical model.

Soft matter (2019)

We propose a theoretical model for a magnetically-actuated artificial cilium in a fluid environment and investigate its dynamical behaviour, using both analytical calculations and numerical simulations. The cilium consists of a spherical soft magnet, a spherical hard magnet, and an elastic spring that connects the two magnetic components. Under a rotating magnetic field, the cilium exhibits a transition from phase-locking at low frequencies to phase-slipping at higher frequencies. We study the dynamics of the magnetic cilium in the vicinity of a wall by incorporating its hydrodynamic influence, and examine the efficiency of the actuated cilium in pumping viscous fluids. This cilium model can be helpful in a variety of applications such as transport and mixing of viscous solutions at small scales and fabricating microswimmers.

## Magnetic Excitations of the Classical Spin Liquid MgCr2O4

PHYSICAL REVIEW LETTERS **122** (2019) ARTN 097201

## Fractional oscillations

Nature Physics (2019)

© 2019, Springer Nature Limited. An electrical interferometer device has detected interference patterns that suggest anyons could be conclusively demonstrated in the near future.

## Topological states in chiral active matter: Dynamic blue phases and active half-skyrmions.

The Journal of chemical physics **150** (2019) 064909-064909

We numerically study the dynamics of two-dimensional blue phases in active chiral liquid crystals. We show that introducing contractile activity results in stabilised blue phases, while small extensile activity generates ordered but dynamic blue phases characterised by coherently moving half-skyrmions and disclinations. Increasing extensile activity above a threshold leads to the dissociation of the half-skyrmions and active turbulence. We further analyse isolated active half-skyrmions in an isotropic background and compare the activity-induced velocity fields in simulations to an analytical prediction of the flow. Finally, we show that confining an active blue phase can give rise to a system-wide circulation, in which half-skyrmions and disclinations rotate together.

## Kosterlitz-Thouless scaling at many-body localization phase transitions

Physical Review B **99** (2019)

© 2019 American Physical Society. We propose a scaling theory for the many-body localization (MBL) phase transition in one dimension, building on the idea that it proceeds via a "quantum avalanche." We argue that the critical properties can be captured at a coarse-grained level by a Kosterlitz-Thouless (KT) renormalization group (RG) flow. On phenomenological grounds, we identify the scaling variables as the density of thermal regions and the length scale that controls the decay of typical matrix elements. Within this KT picture, the MBL phase is a line of fixed points that terminates at the delocalization transition. We discuss two possible scenarios distinguished by the distribution of rare, fractal thermal inclusions within the MBL phase. In the first scenario, these regions have a stretched exponential distribution in the MBL phase. In the second scenario, the near-critical MBL phase hosts rare thermal regions that are power-law-distributed in size. This points to the existence of a second transition within the MBL phase, at which these power laws change to the stretched exponential form expected at strong disorder. We numerically simulate two different phenomenological RGs previously proposed to describe the MBL transition. Both RGs display a universal power-law length distribution of thermal regions at the transition with a critical exponent αc=2, and continuously varying exponents in the MBL phase consistent with the KT picture.

## Chemical and hydrodynamic alignment of an enzyme.

The Journal of chemical physics **150** (2019) 115102-

Motivated by the implications of the complex and dynamic modular geometry of an enzyme on its motion, we investigate the effect of combining long-range internal and external hydrodynamic interactions due to thermal fluctuations with short-range surface interactions. An asymmetric dumbbell consisting of two unequal subunits, in a nonuniform suspension of a solute with which it interacts via hydrodynamic interactions as well as non-contact surface interactions, is shown to have two alignment mechanisms due to the two types of interactions. In addition to alignment, the chemical gradient results in a drift velocity that is modified by hydrodynamic interactions between the constituents of the enzyme.

## Quantum Hall valley nematics.

Journal of physics. Condensed matter : an Institute of Physics journal **31** (2019) 273001-

Two-dimensional electron gases in strong magnetic fields provide a canonical platform for realizing a variety of electronic ordering phenomena. Here we review the physics of one intriguing class of interaction-driven quantum Hall states: quantum Hall valley nematics. These phases of matter emerge when the formation of a topologically insulating quantum Hall state is accompanied by the spontaneous breaking of a point-group symmetry that combines a spatial rotation with a permutation of valley indices. The resulting orientational order is particularly sensitive to quenched disorder, while quantum Hall physics links charge conduction to topological defects. We discuss how these combine to yield a rich phase structure, and their implications for transport and spectroscopy measurements. In parallel, we discuss relevant experimental systems. We close with an outlook on future directions.

## Interpretation of thermal conductance of the v=5/2 edge

PHYSICAL REVIEW B **97** (2018) ARTN 121406

## Shape dependent phoretic propulsion of slender active particles

PHYSICAL REVIEW FLUIDS **3** (2018) ARTN 033101