# Publications by Siddharth Parameswaran

## Erratum: Charge Transport in Weyl Semimetals (Physical Review Letters (2012) 108 (046602) DOI: 10.1103/PhysRevLett.108.046602)

Physical Review Letters **123** (2019)

© 2019 American Physical Society. This erratum corrects errors in numerical factors in Eqs. (1), (7), and (8), and the overall scale of the dc resistivity plotted in Fig. 2. We recently discovered an algebraic error in Eq. (7), which led to incorrect numerical factors in Eqs. (1) and (8). The correct Eqs. (1), (7) and (8), respectively, are (Formula Presented). An error was also found in the overall scale of pdc = 1/σdc calculated from (1) and plotted in Fig. 2 of the Letter. With these corrections our theory underestimates ?dc of the samples in Ref. [12] of the Letter, which is understandable since the samples are polycrystalline while our theory specializes to single crystals. However, correcting both errors gives excellent agreement with recent experiments on Eu 0.96 Bi 0.04 Ir 2 O 7 [1] for reasonable values of parameters, as shown in Fig. 1. Moreover, Ref. [1] finds pdc ( T ) ∼ 1 / T , as predicted by our theory, only at low temperatures, which is where our theory is best applicable since it contains only Coulomb scattering but ignores phonon scattering. Thus, it is likely that the low-temperature transport in Eu 0.96 Bi 0.04 Ir 2 O 7 is dominated by Coulomb scattering. We thank Surjeet Singh and Prachi Telang for bringing the error in the computation of pdc to our attention (Figure Presented).

## Topology- and symmetry-protected domain wall conduction in quantum Hall nematics

PHYSICAL REVIEW B **100** (2019) ARTN 165103

## 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.

## Quantum Brownian motion in a quasiperiodic potential

PHYSICAL REVIEW B **100** (2019) ARTN 060301

## 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.

## 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.

## Signatures of information scrambling in the dynamics of the entanglement spectrum

PHYSICAL REVIEW B **100** (2019) ARTN 125115

## 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.

## Topological entanglement entropy of fracton stabilizer codes

Physical Review B American Physical Society **97** (2018) 1-16

Entanglement entropy provides a powerful characterization of two-dimensional gapped topolog- ical phases of quantum matter, intimately tied to their description by topological quantum field theories (TQFTs). Fracton topological orders are three-dimensional gapped topologically ordered states of matter that lack a TQFT description. We show that three-dimensional fracton phases are nevertheless characterized, at least partially, by universal structure in the entanglement entropy of their ground state wave functions. We explicitly compute the entanglement entropy for two archety- pal fracton models - the `X-cube model' and `Haah's code' - and demonstrate the existence of a non-local contribution that scales linearly in subsystem size. We show via Schrieffer-Wolff transfor- mations that this piece of the entanglement entropy of fracton models is robust against arbitrary local perturbations of the Hamiltonian. Finally, we argue that these results may be extended to characterize localization-protected fracton topological order in excited states of disordered fracton models.

## Correlation function diagnostics for type-I fracton phases

PHYSICAL REVIEW B **97** (2018) ARTN 041110

## Many-body localization, symmetry and topology.

Reports on progress in physics. Physical Society (Great Britain) **81** (2018) 082501-

We review recent developments in the study of out-of-equilibrium topological states of matter in isolated systems. The phenomenon of many-body localization, exhibited by some isolated systems usually in the presence of quenched disorder, prevents systems from equilibrating to a thermal state where the delicate quantum correlations necessary for topological order are often washed out. Instead, many-body localized systems can exhibit a type of eigenstate phase structure wherein their entire many-body spectrum is characterized by various types of quantum order, usually restricted to quantum ground states. After introducing many-body localization and explaining how it can protect quantum order, we then explore how the interplay of symmetry and dimensionality with many-body localization constrains its role in stabilizing topological phases out of equilibrium.

## Strong-disorder renormalization group for periodically driven systems

PHYSICAL REVIEW B **98** (2018) ARTN 174203

## Localization-protected order in spin chains with non-Abelian discrete symmetries

PHYSICAL REVIEW B **98** (2018) ARTN 064203

## Floquet quantum criticality.

Proceedings of the National Academy of Sciences of the United States of America **115** (2018) 9491-9496

We study transitions between distinct phases of one-dimensional periodically driven (Floquet) systems. We argue that these are generically controlled by infinite-randomness fixed points of a strong-disorder renormalization group procedure. Working in the fermionic representation of the prototypical Floquet Ising chain, we leverage infinite randomness physics to provide a simple description of Floquet (multi)criticality in terms of a distinct type of domain wall associated with time translational symmetry-breaking and the formation of "Floquet time crystals." We validate our analysis via numerical simulations of free-fermion models sufficient to capture the critical physics.

## Recoverable information and emergent conservation laws in fracton stabilizer codes

PHYSICAL REVIEW B **97** (2018) ARTN 134426

## Non-Fermi Glasses: Localized Descendants of Fractionalized Metals.

Physical review letters **119** (2017) 146601-

Non-Fermi liquids are metals that cannot be adiabatically deformed into free fermion states. We argue for the existence of "non-Fermi glasses," phases of interacting disordered fermions that are fully many-body localized (MBL), yet cannot be deformed into an Anderson insulator without an eigenstate phase transition. We explore the properties of such non-Fermi glasses, focusing on a specific solvable example. At high temperature, non-Fermi glasses have qualitatively similar spectral features to Anderson insulators. We identify a diagnostic based on ratios of correlators that sharply distinguishes between the two phases even at infinite temperature. Our results and diagnostic should generically apply to the high-temperature behavior of MBL descendants of fractionalized phases.

## Filling-enforced nonsymmorphic Kondo semimetals in two dimensions

Physical Review B **96** (2017)

© 2017 American Physical Society. We study the competition between Kondo screening and frustrated magnetism on the nonsymmorphic Shastry-Sutherland Kondo lattice at a filling of two conduction electrons per unit cell. This model is known to host a set of gapless partially Kondo screened phases intermediate between the Kondo-destroyed paramagnet and the heavy Fermi liquid. Based on crystal symmetries, we argue that (i) both the paramagnet and the heavy Fermi liquid are semimetals protected by a glide symmetry; and (ii) partial Kondo screening breaks the symmetry, removing this protection and allowing the partially Kondo screened phase to be deformed into a Kondo insulator via a Lifshitz transition. We confirm these results using large-N mean-field theory and then use nonperturbative arguments to derive a generalized Luttinger sum rule constraining the phase structure of two-dimensional nonsymmorphic Kondo lattices beyond the mean-field limit.

## Valley-selective Landau-Zener oscillations in semi-Dirac p-n junctions

PHYSICAL REVIEW B **96** (2017) ARTN 045424

## Disorder-driven destruction of a non-Fermi liquid semimetal studied by renormalization group analysis

PHYSICAL REVIEW B **95** (2017) ARTN 205106