arXiv subjects

Vijay B. Shenoy

Publications and source records attributed to Vijay B. Shenoy.

At least 19 recordsLinked to original sources

arXiv2025

Defect-induced spin textures in magnetic solids

Vacancy defects in isotropic noncollinear antiferromagnets produce long-range spin textures. By developing a "magnetic elasticity theory", we demonstrate that a vacancy-induced readjustment in the spin configuration decays algebraically with distance. The power law exponent depends on the multipole moment of a local spin deformation, which in turn is determined by the lattice symmetry and an equilibrium spin configuration in the absence of defects. The role of these two factors is highlighted for the J1-J2 Heisenberg model on a kagome lattice. A vacancy in this model generates spin deformations that decay as 1/r^2 for the q=0 ground state and as a 1/r for the sqrt{3} x sqrt{3} magnetic structure. The analytic conclusions are confirmed by extensive numerical simulations. We also compute the fractional magnetic moments associated with vacancies and other lattice defects. Our results shed light on relative fragility of different magnetic structures with respect to spin glass formation at higher doping levels.

cond-mat.str-el↗

arXiv2025

Critical States of Fermions with ${\mathbb{Z}}_2$ Flux Disorder

Motivated by many contemporary problems in condensed matter physics where matter particles experience random gauge fields, we investigate the physics of fermions on a square lattice with $π$-flux (that realizes Dirac fermions at low energies), subjected to flux disorder arising from a random ${\mathbb{Z}}_2$ gauge field that results from the presence of flux defects (plaquettes with zero flux). At half-filling, where the system possesses BDI symmetry, we show that a new class of critical phases is realized, with the states at zero energy showing a multifractal character. The multifractal properties depend on the concentration $\mathfrak{c}$ of the $π$-flux defects and spatial correlations between the flux defects. These states are characterized by the singularity spectrum, Lyapunov exponents, and transport properties. For any concentration of flux defects, we find that the multi-fractal spectrum shows termination, but $\textit{not freezing}$. We characterize this class of critical states by uncovering a relation between the conductivity and the Lyapunov exponent, which is satisfied by the states irrespective of the concentration or the local correlations between the flux defects. We demonstrate that renormalization group methods, based on perturbing the Dirac point, fail to capture this new class of critical states. This work not only offers new challenges to theory, but is also likely to be useful in understanding a variety of problems where fermions interact with discrete gauge fields.

cond-mat.dis-nn↗

arXiv2025

Superconductivity in Spin-Orbit coupled SU(8) Dirac Fermions on Honeycomb lattice

We study superconducting (SC) phases that are naturally proximate to a spin-orbit coupled SU(8) Dirac semi-metal on a honeycomb lattice. This system, which offers enhanced low-energy symmetries, presents an interesting platform for realizing unconventional superconductivity in j=3/2 electrons. In particular, we find 72 superconducting charge-$2e$ fermion bilinears which, under classification of microscopic symmetries, lead to 12 different SCs -- four singlets, two doublets, and six triplets -- 7 of them are gapped and 5 are symmetry-protected nodal SCs. The strong spin-orbit coupling leads to locking of the spin of the Cooper pairs with real-space direction -- as is evident from the structure of the Cooper pair wave-functions -- leading to unusual non-unitary superconductors (even singlets), and with finite momentum pairing (for the triplets). This results, in many cases, in the magnitude of multiple pairing gaps being intricately dependent on the direction of the SC order-parameter. The present classification of SCs along with normal phases (Phys. Rev. B 108, 245106 (2023)) provides the complete list of naturally occurring phases in the vicinity of such a SU(8) Dirac semi-metal. This study allows for understanding the global phase diagram of such systems, stimulating further experimental work on candidate materials such as metallic halides (MX$_3$ with M=Zr, Hf, and X=Cl, Br). Further, it provides the starting point for the exploration of unconventional phase transitions in such systems.

cond-mat.str-el↗

arXiv2024

Fractons on the edge

We develop a theory of edge excitations of fractonic systems in two dimensions, and elucidate their connections to bulk transport properties and quantum statistics of bulk excitations. The system we consider has immobile point charges, dipoles constrained to move only along lines perpendicular to their moment, and freely mobile quadrupoles and higher multipoles, realizing a bulk fractonic analog of fractional quantum Hall phases. We demonstrate that a quantized braiding phase between two bulk excitations is obtained only in two cases: when a point quadrupole braids around an immobile point charge, or when two non-orthogonal point dipoles braid with one another. The presence of a boundary edge in the system entails $\textit{two}$ types of gapless edge excitation modes, one that is fractonic with immobile charges and longitudinal dipoles, and a second non-fractonic mode consisting of transverse dipoles. We derive a novel current algebra of the fractonic edge modes. Further, investigating the effect of local edge-to-edge tunneling on these modes, we find that such a process is a relevant perturbation suggesting the possibility of edge deformation.

cond-mat.mes-hall↗

arXiv2024

Arboreal Obstructed Atomic Insulating and Metallic Phases of Fermions

We explore phases of free fermions on arenas that do not tessellate a manifold. Specializing to arboreal arenas described by tree graphs which possess a notion of translation symmetry, we study possible fermionic phases in the BDI symmetry class on the $p$-coordinated Bethe lattice. We find that there are $p$ distinct obstructed atomic insulating phases that are characterized by distinct edge states, pattern of entanglement, and a winding characteristic that we define here. These distinct insulting phases are always separated by a metallic region in the parameter space rather than isolated quantum critical points. The metallic region itself comprises several distinct metallic phases that are distinguished by the winding characteristic and correlation functions. The correlation functions of distinct subsystems display non-analytic behavior at distinct points in the metallic region, signaling a cascade of subsystem transitions. An intriguing feature of these arboreal metals is the presence of truncated subsystems with zero energy boundary modes despite being gapless. This work suggests new opportunities for synthetic quantum systems to realize these novel phases.

cond-mat.mes-hall↗

arXiv2023

Hopf Semimetals

We construct two-band topological semimetals in four dimensions using the unstable homotopy of maps from the three-torus $T^3$ (Brillouin zone of a 3D crystal) to the two-sphere $S^2$. Dubbed ``Hopf semimetals'', these gapless phases generically host nodal lines, with a surface enclosing such a nodal line in the four-dimensional Brillouin zone carrying a Hopf flux. These semimetals show a unique class of surface states: while some three-dimensional surfaces host gapless Fermi-arc states {\em and} drumhead states, other surfaces have gapless Fermi surfaces. Gapless two-dimensional corner states are also present at the intersection of three-dimensional surfaces.

cond-mat.mes-hall↗

arXiv2023

Emergent SU(8) Dirac semimetal and novel proximate phases of spin-orbit coupled fermions on a honeycomb lattice

Emergent Dirac fermions provide the starting point to understanding the plethora of novel condensed matter phases. The nature of the associated phases and phase transitions crucially depends on both the emergent symmetries as well as the implementation of the microscopic ones on the low-energy Dirac fermions. Here, we show that $j=3/2$ electrons in spin-orbit coupled materials on honeycomb lattice can give rise to SU(8) symmetric Dirac semimetals with symmetry implementation very different from that of graphene. This non-trivial embedding of the microscopic symmetries in the low energy is reflected in the nature of phases proximate to the Dirac semimetal. Such phases can arise from finite short-range electron-electron interactions. In particular, we identify 24 such phases - divided into three classes - and their low energy properties obtained by condensing particle-number conserving fermion bilinears that break very different microscopic symmetries and/or are topologically protected by symmetries. The latter includes interesting generalisations of quantum spin-Hall phases. Remarkably some of the resultant phases still support a sub-set of gapless fermions - protected by a sub-group of SU(8) - resulting in interesting density wave semimetals. Near the phase transitions to such density wave semimetals, the surviving gapless fermions strongly interact with the bosonic order parameter field and give rise to novel quantum critical points. Our study is applicable to a wide class of $d^1$ and $d^3$ transition metals with strong spin-orbit coupling and predicts that such materials can harbour a very rich interplay of symmetries and competing interactions in the intermediate correlation regime.

cond-mat.str-el↗

arXiv2022

Obstructed Atomic Insulators and Superfluids of Fermions Coupled to $\mathbb{Z}_2$ Gauge Fields

We study spin-$\frac{1}{2}$ fermions coupled to $\mathbb{Z}_2$ gauge fields on a lattice. We show how a spatial modulation of the fermion hopping allows for the realization of various obstructed atomic insulators that host higher-order band topology. Studying the effect of quantum dynamics of the gauge fields within a simplified model, we find a rich phase diagram of this system with a number of superfluid phases arising from the attractive interactions meditated by the gauge fields. A key finding of this work is that the evolution from the Bardeen-Cooper-Schrieffer (BCS) superfluid state to a Bose-Einstein condensate (BEC) of tightly bound pairs occurs via the realization of these different superfluid phases separated by first-order transitions.

cond-mat.str-el↗

arXiv2021

Arboreal Topological and Fracton Phases

We describe topologically ordered and fracton ordered states on novel geometries which do not have an underlying manifold structure. Using tree graphs such as the $k$-coordinated Bethe lattice ${\cal B}(k)$ and a hypertree called the $(k,n)$-hyper-Bethe lattice ${\cal HB}(k,n)$ consisting of $k$-coordinated hyperlinks (defined by $n$ sites), we construct multidimensional arboreal arenas such as ${\cal B}(k_1) \square {\cal B}(k_2)$ by the notion of a graph Cartesian product $\square$. We study various quantum systems such as the ${\mathbb Z}_2$ gauge theory, generalized quantum Ising models (GQIM), the fractonic X-cube model, and related X-cube gauge theory defined on these arenas. Even the simplest ${\mathbb Z}_2$ gauge theory on a 2d arboreal arena is fractonic -- the monopole excitation is immobile. The X-cube model on a 3d arboreal arena is fully fractonic, all multipoles are rendered immobile. We obtain variational ground state phase diagrams of these gauge theories. Further, we find an intriguing class of dualities in arboreal arenas as illustrated by the ${\mathbb Z}_2$ gauge theory defined on ${\cal B}(k_1) \square {\cal B}(k_2)$ being dual to a GQIM defined on ${\cal HB}(2,k_1) \square {\cal HB}(2,k_2)$. Finally, we discuss different classes of topological and fracton orders on arboreal arenas. We find three distinct classes of arboreal toric code orders on 2d arboreal arenas, those that occur on ${\cal B}(2) \square {\cal B}(2)$, ${\cal B}(k) \square {\cal B}(2), k >2$, and ${\cal B}(k_1) \square {\cal B}(k_2)$, $k_1,k_2>2$. Likewise, four classes of X-cube fracton orders are found in 3d arboreal arenas -- those on ${\cal B}(2)\square{\cal B}(2)\square {\cal B}(2)$, ${\cal B}(k) \square {\cal B}(2)\square {\cal B}(2), k>2$, ${\cal B}(k_1) \square {\cal B}(k_2) \square {\cal B}(2), k_1,k_2 >2$, and ${\cal B}(k_1) \square {\cal B}(k_2) \square {\cal B}(k_3), k_1,k_2,k_3 >2$.

cond-mat.str-el↗

arXiv2020

Tearing Fractons

We offer a fractonic perspective on a familiar observation -- a flat sheet of paper can be folded only along a straight line if one wants to avoid the creation of additional creases or tears. Our core underlying technical result is the establishment of a duality between the theory of elastic plates and a fractonic gauge theory with a second rank symmetric electric field tensor, a scalar magnetic field, a vector charge, and a symmetric tensor current. Bending moment and momentum of the plate are dual to the electric and magnetic fields, respectively. While the flexural waves correspond to the quadratically dispersing photon of the gauge theory, a fold defect is dual to its vector charge. Crucially, the fractonic condition constrains the latter to move only along its direction, i.e., the fold's growth direction. By contrast, fracton motion in the perpendicular direction amounts to tearing the paper.

cond-mat.str-el↗

arXiv2019

$(k,n)$-fractonic Maxwell theory

Fractons emerge as charges with reduced mobility in a new class of gauge theories. Here, we generalise fractonic theories of $U(1)$ type to what we call $(k,n)$-fractonic Maxwell theory, which employs symmetric order-$n$ tensors of $k$-forms (rank-$k$ antisymmetric tensors) as "vector potentials". The generalisation has two key manifestations. First, the objects with mobility restrictions extend beyond simple charges to higher order multipoles (dipoles, quadrupoles, $\ldots$) all the way to $n^\mathrm{th}$-order multipoles. Second, these fractonic charges themselves are characterized by tensorial densities of $(k-1)$-dimensional extended objects. The source-free sector exhibits `photonic' excitations with dispersion $ω\sim q^n$.

cond-mat.str-el↗

arXiv2018

Statistics-tuned phases of pseudofermions in one dimension

We show that a quadratic system of pseudofermions, with tunable fractionalised statistics, can host a rich phase diagram on a one dimensional chain with nearest and next nearest neighbor hopping. Using a combination of numerical and analytical techniques, we show that that by varying the statistical angle and the ratio of the hopping, the system stabilizes two Tomonaga-Luttinger liquids (TLL) with central charges c = 1 and 2 respectively along with the inversion symmetry broken bond ordered (BO) insulating phase. Interestingly, the two quantum phase transitions in the system - (1) between the two TLLs, and, (2) the c = 1 TLL and BO phase can be engendered by solely tuning the statistics of the pseudofermions. Our analysis shows that both these transition are continuous and novel with the former lacking a local order-parameter based description and the latter of Berezinskii-Kosterlitz-Thouless type. These phases and phase transitions can be of direct experimental relevance in context of recent studies of fermionic cold atoms.

cond-mat.str-el↗

arXiv2018

Surprises in the t-J model: Implications for cuprates

The t-J model is a paradigmatic model for the study of strongly correlated electron systems. In particular, it has been argued that it is an appropriate model to describe the cuprate high-Tc superconductors. It turns out that a comprehensive understanding of the gamut of physics encoded by the t-J model is still an open problem. In recent years some remarkable experiments on the cuprates, for example, discovery of nodeless superconductivity in underdoped samples (PNAS 109, 18332 (2012)), discovery of s-wave like gap in the pseudogap phase (Phys. Rev. Lett. 111, 107001 (2013)), and observation of polar Kerr effect (PKE) (Phys. Rev. Lett. 112, 047003 (2014)), have thrown up new challenges for this model. Here, we present results demonstrating that, within the slave-particle formulation of the t-J model, the d-wave superconductor is unstable at low doping to its own anti-symmetric phase mode fluctuations when the effect of fluctuations is treated self-consistently. We then show that this instability gives way to a time reversal symmetry broken d + is-SC in the underdoped region which has superfluid stiffness consistent with Uemura relation, even with a large pair amplitude. We show that our results are consistent with existing experiments on cuprates and suggest that Josephson (SQUID interferometry) experiments can clearly distinguish the d+is-SC from a host of other possibilities alluded to be contributing to the physics of underdoped cuprates. We also comment on other theoretical studies vis-a-vis ours.

cond-mat.supr-con↗

arXiv2018

Fractalized Metals

The classification of gapped phases of non-interacting fermions hinges on the tenfold symmetries and on the spatial dimension. The notion of dimension leads to a well defined demarcation between bulk and edge. Here we explore the nature of topological phases in systems where the distinction between bulk and edge is nebulous, of which fractal lattices are canonical examples. Our key finding is that in homogeneous fractal lattices (where every site is equally coordinated), there are no gapped topological phases. What appears instead is a novel metallic state -- the fractalized metal -- whose low energy states arrange hierarchically on the structure of the fractal that hosts them. We study the properties (such as chiral transport) of this metal and demonstrate its robustness to disorder. Further, by studying a variety of fractal models we establish that the homogeneity of the fractal is a key condition for the realization of such fractalized metallic states.

cond-mat.dis-nn↗

arXiv2017

Higher-dimensional SYK Non-Fermi Liquids at Lifshitz transitions

We address the key open problem of a higher dimensional generalization of the Sachdev-Ye-Kitaev (SYK) model. We construct a model on a lattice of SYK dots with non-random intersite hopping. The crucial feature of the resulting band dispersion is the presence of a Lifshitz point where two bands touch with a tunable powerlaw divergent density of states (DOS). For a certain regime of the powerlaw exponent, we obtain a new class of interaction-dominated non-Fermi liquid (NFL) states, which exhibits exciting features such as a zero-temperature scaling symmetry, an emergent (approximate) time reparameterization invariance, a powerlaw entropy-temperature relationship, and a fermion dimension that depends continuously on the DOS exponent. Notably, we further demonstrate that these NFL states are fast scramblers with a Lyapunov exponent $λ_L\propto T$, although they do not saturate the upper bound of chaos, rendering them truly unique.

cond-mat.str-el↗

arXiv2017

Strange Half Metals and Mott Insulators in SYK Models

We study a dual flavor fermion model where each of the flavors form a Sachdev-Ye-Kitaev (SYK) system with arbitrary and possibly distinct $q$-body interactions. The crucial new element is an arbitrary all-to-all $r$-body interaction between the two flavors. At high temperatures the model shows a strange metal phase where both flavors are gapless, similar to the usual single flavor SYK model. Upon reducing temperature, the coupled system undergoes phase transitions to previously unseen phases - first, a strange half metal (SHM) phase where one flavor remains a strange metal while the other is gapped, and, second, a Mott insulating phase where both flavors are gapped. At a fixed low temperature we obtain transitions between these phases by tuning the relative fraction of sites for each flavor. We discuss the physics of these phases and the nature of transitions between them. This work provides an example of an instability of the strange metal with potential to provide new routes to study strongly correlated systems through the rich physics contained in SYK like models.

cond-mat.str-el↗

arXiv2017

Crucial role of Internal Collective Modes in Underdoped Cuprates

The enigmatic cuprate superconductors have attracted resurgent interest with several recent reports and discussions of competing orders in the underdoped side. Motivated by this, here we address the natural question of fragility of the d-wave superconducting state in underdoped cuprates. Using a combination of theoretical approaches we study t-J like models, and discover an - as yet unexplored - instability that is brought about by an "internal" (anti-symmetric mode) fluctuation of the d-wave state. This new theoretical result is in good agreement with recent STM and ARPES studies of cuprates. We also suggest experimental directions to uncover this physics.

cond-mat.str-el↗

arXiv2017

Topological Insulators in Random Lattices

Our understanding of topological insulators is based on an underlying crystalline lattice where the local electronic degrees of freedom at different sites hybridize with each other in ways that produce nontrivial band topology, and the search for material systems to realize such phases have been strongly influenced by this. Here we theoretically demonstrate topological insulators in systems with a random distribution of sites in space, i. e., a random lattice. This is achieved by constructing hopping models on random lattices whose ground states possess nontrivial topological nature (characterized e. g., by Bott indices) that manifests as quantized conductances in systems with a boundary. By tuning parameters such as the density of sites (for a given range of fermion hopping), we can achieve transitions from trivial to topological phases. We discuss interesting features of these transitions. In two spatial dimensions, we show this for all five symmetry classes (A, AII, D, DIII and C) that are known to host nontrivial topology in crystalline systems. We expect similar physics to be realizable in any dimension and provide an explicit example of a $Z_2$ topological insulator on a random lattice in three spatial dimensions. Our study not only provides a deeper understanding of the topological phases of non-interacting fermions, but also suggests new directions in the pursuit of the laboratory realization of topological quantum matter.

cond-mat.mes-hall↗