arXiv subjects

S. A. Parameswaran

Publications and source records attributed to S. A. Parameswaran.

At least 37 records · Page 2Linked to original sources

arXiv2024

Double-dome Unconventional Superconductivity in Twisted Trilayer Graphene

Graphene moiré systems are ideal environments for investigating complex phase diagrams and gaining fundamental insights into the mechanisms underlying exotic states of matter, as they permit controlled manipulation of electronic properties. Magic-angle twisted trilayer graphene (MATTG) has emerged as a key platform to explore moiré superconductivity, owing to the robustness of its superconducting order and the displacement-field tunability of its energy bands. Recent measurements strongly suggest that superconductivity in MATTG is unconventional. Here, we report the first direct observation of double-dome superconductivity in MATTG. The temperature, magnetic field, and bias current dependence of the superconductivity of doped holes collectively show that it is significantly suppressed near moiré filling $ν^* = -2.6$, leading to a double dome in the phase diagram within a finite window of the displacement field. The temperature dependence of the normal-state resistance and the $I-V$ curves straddling $ν^*$ are suggestive of a phase transition and the potentially distinct nature of superconductivity in the two domes. Hartree-Fock calculations incorporating mild strain yield an incommensurate Kekulé spiral state whose effective spin polarization peaks in the regime where superconductivity is suppressed in experiments. This allows us to draw conclusions about the normal state as well as the unconventional nature of the superconducting order parameter.

cond-mat.mes-hall↗

arXiv2024

Anomalous thermal relaxation and pump-probe spectroscopy of 2D topologically ordered systems

We study the behaviour of linear and nonlinear spectroscopic quantities in two-dimensional topologically ordered systems, which host anyonic excitations exhibiting fractional statistics. We highlight the role that braiding phases between anyons have on the dynamics of such quasiparticles, which as we show dictates the behaviour of both linear response coefficients at finite temperatures, as well as nonlinear pump-probe response coefficients. These quantities, which act as probes of temporal correlations in the system, are shown to obey distinctive universal forms at sufficiently long timescales. As well as providing an experimentally measurable fingerprint of anyonic statistics, the universal behaviour that we find also demonstrates anomalously fast thermal relaxation: correlation functions decay as a `squished exponential' $C(t) \sim \exp(-[t/τ]^{3/2})$ at long times. We attribute this unusual asymptotic form to the nonlocal nature of interactions between anyons, which allows relaxation to occur much faster than in systems with quasiparticles interacting via local, non-statistical interactions. While our results apply to any Abelian or non-Abelian topological phase in two-dimensions, we discuss in particular the implications for candidate quantum spin liquid materials, wherein the relevant quantities can be measured using pre-existing time-resolved terahertz-domain spectroscopic techniques.

cond-mat.str-el↗

arXiv2024

Signatures of fractional statistics in nonlinear pump-probe spectroscopy

We show that the presence of anyons in the excitation spectrum of a two-dimensional system can be inferred from nonlinear spectroscopic quantities. In particular, we consider pump-probe spectroscopy, where a sample is irradiated by two light pulses with an adjustable time delay between them. The relevant response coefficient exhibits a universal form that originates from the statistical phase acquired when anyons created by the first pulse braid around those created by the second. This behaviour is shown to be qualitatively unchanged by non-universal physics including non-statistical interactions and small nonzero temperatures. In magnetic systems, the signal of interest can be measured using currently available terahertz-domain probes, highlighting the potential usefulness of nonlinear spectroscopic techniques in the search for quantum spin liquids.

cond-mat.str-el↗

arXiv2023

Kekulé spirals and charge transfer cascades in twisted symmetric trilayer graphene

We study the phase diagram of magic-angle twisted symmetric trilayer graphene in the presence of uniaxial heterostrain and interlayer displacement field. For experimentally reasonable strain, our mean-field analysis finds robust Kekulé spiral order whose doping-dependent ordering vector is incommensurate with the moiré superlattice, consistent with recent scanning tunneling microscopy experiments, and paralleling the behaviour of closely-related twisted bilayer graphene (TBG) systems. Strikingly, we identify a new possibility absent in TBG: the existence of $\textit{commensurate}$ Kekulé spiral order even at zero strain for experimentally realistic values of the interlayer potential in a trilayer. Our studies also reveal a complex pattern of charge transfer between weakly- and strongly-dispersive bands in strained trilayer samples as the density is tuned by electrostatic gating, that can be understood intuitively in terms of the `cascades' in the compressibility of magic-angle TBG.

cond-mat.str-el↗

arXiv2023

Coulomb-driven band unflattening suppresses $K$-phonon pairing in moiré graphene

It is a matter of current debate whether the gate-tunable superconductivity in twisted bilayer graphene is phonon-mediated or arises from electron-electron interactions. The recent observation of the strong coupling of electrons to so-called $K$-phonon modes in angle-resolved photoemission spectroscopy experiments has resuscitated early proposals that $K$-phonons drive superconductivity. We show that the bandwidth-enhancing effect of interactions drastically weakens both the intrinsic susceptibility towards pairing as well as the screening of Coulomb repulsion that is essential for the phonon attraction to dominate at low temperature. This rules out purely $K$-phonon-mediated superconductivity with the observed transition temperature of $\sim 1$ K. We conclude that the unflattening of bands by Coulomb interactions challenges any purely phonon-driven pairing mechanism, and must be addressed by a successful theory of superconductivity in moiré graphene.

cond-mat.supr-con↗

arXiv2023

Supersymmetry on the honeycomb lattice: resonating charge stripes, superfrustration, and domain walls

We study a model of spinless fermions on the honeycomb lattice with nearest-neighbor exclusion and extended repulsive interactions that exhibits `lattice supersymmetry' [P. Fendley, K. Schoutens, and J. de Boer, Phys. Rev. Lett. 90, 120402 (2003)]. Using a combination of exact diagonalization of large ($N\leq56$ site) systems, mean-field numerics, and symmetry analysis, we establish a rich phase structure as a function of fermion density, that includes non-Fermi liquid behavior, resonating charge stripes, domain-wall and bubble physics, and identify a finite range of fillings with extensive ground state degeneracy and both gapped and gapless spectra. We comment on the stability of our results to relaxing the stringent requirements for supersymmetry, and on their possible broader relevance to systems of strongly-correlated electrons with extended repulsive interactions.

cond-mat.str-el↗

arXiv2023

Multiversality and Unnecessary Criticality in One Dimension

We present microscopic models of spin ladders which exhibit continuous critical surfaces whose properties and existence, unusually, cannot be inferred from those of the flanking phases. These models exhibit either `multiversality' -- the presence of different universality classes over finite regions of a critical surface separating two distinct phases -- or its close cousin, `unnecessary criticality'-- the presence of a stable critical surface within a single, possibly trivial, phase. We elucidate these properties using Abelian bosonization and density-matrix renormalization-group simulations, and attempt to distill the key ingredients required to generalize these considerations.

cond-mat.str-el↗

arXiv2023

Minimal Hubbard models of maximal Hilbert space fragmentation

We show that Hubbard models with nearest-neighbor hopping and a nearest-neighbor hardcore constraint exhibit `maximal' Hilbert space fragmentation in many lattices of arbitrary dimension $d$. Focusing on the $d=1$ rhombus chain and the $d=2$ Lieb lattice, we demonstrate that the fragmentation is strong for all fillings in the thermodynamic limit, and explicitly construct all emergent integrals of motion, which include an extensive set of higher-form symmetries. Blockades consisting of frozen particles partition the system in real space, leading to anomalous dynamics. Our results are potentially relevant to optical lattices of dipolar and Rydberg-dressed atoms.

cond-mat.stat-mech↗

arXiv2023

Electron-phonon coupling and competing Kekulé orders in twisted bilayer graphene

Recent scanning tunneling microscopy experiments [K.P. Nuckolls et al., arXiv:2303.00024] have revealed the ubiquity of Kekulé charge-density wave order in magic-angle twisted bilayer graphene. Most samples are moderately strained and show `incommensurate Kekulé spiral' (IKS) order involving a graphene-scale charge density distortion uniaxially modulated on the scale of the moiré superlattice, in accord with theoretical predictions. However, ultra-low strain samples instead show graphene-scale Kekulé charge order that is uniform on the moiré scale. This order, especially prominent near filling factor $ν=-2$, is unanticipated by theory which predicts a time-reversal breaking Kekulé current order at low strain. We show that including the coupling of moiré electrons to graphene-scale optical zone-corner (ZC) phonons stabilizes a uniform Kekulé charge ordered state at $|ν|=2$ with a quantized topological (spin or anomalous Hall) response. Our work clarifies how this phonon-driven selection of electronic order emerges in the strong-coupling regime of moiré graphene.

cond-mat.str-el↗

arXiv2023

Superconductivity from repulsive interactions in Bernal-stacked bilayer graphene

A striking series of experiments have observed superconductivity in Bernal-stacked bilayer graphene (BBG) when the energy bands are flattened by applying an electrical displacement field. Intriguingly, superconductivity manifests only at non-zero magnetic fields, or when spin-orbit coupling is induced in BBG by coupling to a substrate. We present detailed functional renormalization group and random-phase approximation calculations that provide a unified explanation for the superconducting mechanism in both cases. Both calculations yield a purely electronic $p$-wave instability of the Kohn-Luttinger (KL) type. The latter can be enhanced either by magnetic fields or Ising spin-orbit coupling, naturally explaining the behaviour seen in experiments.

cond-mat.supr-con↗

arXiv2023

Discrete scale invariant fixed point in a quasiperiodic classical dimer model

We study close-packed dimers on the quasiperiodic Ammann-Beenker (AB) graph, that was recently shown to have the unusual feature that hard-core dimer constraints are exactly reproduced at successive discrete length scales. This observation led to a conjecture that it would be possible to construct an exact real-space decimation scheme where each iteration preserves both the quasiperiodic tiling structure and the constraint. Here, we confirm this conjecture by explicitly constructing the corresponding renormalization group transformation and show, using large-scale Monte Carlo simulations, that the dimer distributions flow to a fixed point with non-zero dimer potentials. We use the fixed-point Hamiltonian to demonstrate the existence of slowly decaying dimer correlations. We thus identify a remarkable example of a classical statistical mechanical model whose properties are controlled by the fixed point of an exact renormalization group procedure exhibiting discrete scale invariance but lacking translational and continuous rotational symmetries.

cond-mat.stat-mech↗

arXiv2023

Divergent nonlinear response from quasiparticle interactions

We demonstrate that nonlinear response functions in many-body systems carry a sharp signature of interactions between gapped low-energy quasiparticles. Such interactions are challenging to deduce from linear response measurements. The signature takes the form of a divergent-in-time contribution to the response -- linear in time in the case when quasiparticles propagate ballistically -- that is absent for free bosonic excitations. We give an intuitive semiclassical picture of this singular behaviour, validated against exact results from a form-factor expansion of the Ising chain and tDMRG simulations in a non-integrable model -- the spin-1 AKLT chain. We comment on extensions of these results to more general settings, finite temperature, and higher dimensions.

cond-mat.str-el↗

arXiv2022

Statistical mechanics of dimers on quasiperiodic Ammann-Beenker tilings

We study classical dimers on two-dimensional quasiperiodic Ammann-Beenker (AB) tilings. Despite the lack of periodicity we prove that each infinite tiling admits 'perfect matchings' in which every vertex is touched by one dimer. We introduce an auxiliary 'AB$^*$' tiling obtained from the AB tiling by deleting all 8-fold coordinated vertices. The AB$^*$ tiling is again two-dimensional, infinite, and quasiperiodic. The AB$^*$ tiling has a single connected component, which admits perfect matchings. We find that in all perfect matchings, dimers on the AB$^*$ tiling lie along disjoint one-dimensional loops and ladders, separated by 'membranes', sets of edges where dimers are absent. As a result, the dimer partition function of the AB$^*$ tiling factorizes into the product of dimer partition functions along these structures. We compute the partition function and free energy per edge on the AB$^*$ tiling using an analytic transfer matrix approach. Returning to the AB tiling, we find that membranes in the AB$^*$ tiling become 'pseudomembranes', sets of edges which collectively host at most one dimer. This leads to a remarkable discrete scale-invariance in the matching problem. The structure suggests that the AB tiling should exhibit highly inhomogenous and slowly decaying connected dimer correlations. Using Monte Carlo simulations, we find evidence supporting this supposition in the form of connected dimer correlations consistent with power law behaviour. Within the set of perfect matchings we find quasiperiodic analogues to the staggered and columnar phases observed in periodic systems.

cond-mat.stat-mech↗

arXiv2022

Absolutely Stable Spatiotemporal Order in Noisy Quantum Systems

We introduce a model of non-unitary quantum dynamics that exhibits infinitely long-lived discrete spatiotemporal order robust against any unitary or dissipative perturbation. Ergodicity is evaded by combining a sequence of projective measurements with a local feedback rule that is inspired by Toom's `North-East-Center' classical cellular automaton. The measurements in question only partially collapse the wavefunction of the system, allowing some quantum coherence to persist. We demonstrate our claims using numerical simulations of a Clifford circuit in two spatial dimensions which allows access to large system sizes, and also present results for more generic dynamics on modest system sizes. We also devise explicit experimental protocols realising this dynamics using one- and two-qubit gates that are available on present-day quantum computing platforms.

quant-ph↗

arXiv2022

Global Phase Diagram of the Normal State of Twisted Bilayer Graphene

We investigate the full doping and strain-dependent phase diagram of the normal state of magic-angle twisted bilayer graphene (TBG). Using comprehensive Hartree-Fock calculations, we show that at temperatures where superconductivity is absent the global phase structure can be understood based on the competition and coexistence between three types of intertwined orders: a fully symmetric phase, spatially uniform flavor-symmetry-breaking states, and an incommensurate Kekulé spiral (IKS) order. For small strain, the IKS phase, recently proposed as a candidate order at all non-zero integer fillings of the moiré unit cell, is found to be ubiquitous for non-integer doping as well. We demonstrate that the corresponding electronic compressibility and Fermi surface structure are consistent with the 'cascade' physics and Landau fans observed experimentally. This suggests a unified picture of the phase diagram of TBG in terms of IKS order.

cond-mat.str-el↗

arXiv2022

Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry

We show that the gapless boundary signatures - namely, chiral/helical hinge modes or localized zero modes - of three-dimensional higher-order topological insulators and superconductors with inversion symmetry can be gapped without symmetry breaking upon the introduction of non-Abelian surface topological order. In each case, the fractionalization pattern that appears on surface is `anomalous' in the sense that it can be made consistent with symmetry only on the surface of a three dimensional higher-order insulator/superconductor. Our results show that the interacting manifestation of higher-order topology is the appearance of `anomalous gapped boundaries' between distinct topological orders whose quasiparticles are related by inversion, possibly in conjunction with other protecting symmetries such as TRS and charge conservation.

cond-mat.str-el↗

arXiv2021

Skyrmions in twisted bilayer graphene: stability, pairing, and crystallization

We study the excitations that emerge upon doping the translationally-invariant correlated insulating states in magic angle twisted bilayer graphene at various integer filling factors $ν$. We identify parameter regimes where these are associated with skyrmion textures in the spin or pseudospin degrees of freedom, and explore both short-distance pairing effects and the formation of long-range ordered skyrmion crystals. We perform a comprehensive analysis of the pseudospin skyrmions that emerge upon doping insulators at even $ν$, delineating the regime in parameter space where these are the lowest-energy charged excitations by means of self-consistent Hartree-Fock calculations on the interacting Bistritzer-MacDonald model. We explicitly demonstrate the purely electron-mediated pairing of skyrmions, a key ingredient behind a recent proposal of skyrmion superconductivity. Building upon this, we construct hopping models to extract the effective masses of paired skyrmions, and discuss our findings and their implications for skyrmion superconductivity in relation to experiments, focusing on the dome-shaped dependence of the transition temperature on the twist angle. We also investigate the properties of spin skyrmions about the quantized anomalous Hall insulator at $ν=+3$. In both cases, we demonstrate the formation of robust spin/pseudospin skyrmion crystals upon doping to a finite density away from integer filling.

cond-mat.str-el↗

arXiv2021

High-temperature transport and polaron speciation in the anharmonic Holstein model

We study the finite-temperature transport of electrons coupled to anharmonic local phonons. Our focus is on the high-temperature incoherent regime, where controlled calculations are possible both for weak and strong electron--phonon coupling. At strong coupling, the dynamics is described in terms of a multiple-species gas of small polarons: this emergent `speciation' is driven by energy conservation. We explicitly compute the dc and ac response in this regime. We discuss the breakdown of the polaron picture, and the onset of localization, in the limit where phonons become quasistatic.

cond-mat.str-el↗