arXiv subjects

Bitan Roy

Publications and source records attributed to Bitan Roy.

At least 19 recordsLinked to original sources

arXiv2026

Hidden-ordered Dirac fermions

I propose a Hermitian extension of the Lorentz-symmetric Dirac theory by complementing the associated Hamiltonian with another \emph{masslike} anticommuting Dirac operator. The resulting theory manifests the iconic linear energy-momentum relationship in any dimension ($d$) and hence the emergent nodal quasiparticle excitations are named \emph{hidden-ordered Dirac fermions}, which are symmetry protected and their responses are analogous to those in original Dirac systems, however, in terms of a renormalized (due to the hidden ordering) Fermi velocity. Typically, such a hidden ordering pushes any quantum phase transition into an insulation toward even stronger coupling in any $d>1$. However, depending on the internal algebra between the candidate insulating order parameter and masslike Dirac operator, the hidden-ordering may survive or disappear near the corresponding itinerant quantum critical point. I construct lattice models for such hidden-ordered massless Dirac fermions and outline promising platforms (numerical and experimental) to test these predictions.

cond-mat.str-el↗

arXiv2026

Dirac fermions in non-Hermitian magnetic fields: Zero modes and index theorem

In a Lorentz symmetric non-Hermitian (NH) Dirac theory, containing the canonical relativistic Hamiltonian accompanied by a masslike anti-Hermitian Dirac operator, when the associated NH parameter becomes spatially modulated it couples massless Dirac fermions as NH gauge fields. With specific choices of such resulting NH gauge potential, the system experiences NH magnetic fields. When a planar Dirac system encloses a finite flux of such NH magnetic fields, a manifold of spatially localized \emph{right or left} zero-energy eigenmodes appear in the spectrum, which we numerically anchor from microscopic realizations of NH magnetic fields on graphene's honeycomb lattice. Potential experimental platforms to test these predictions are discussed. Altogether, zero-energy NH flat bands of right or left modes promise fascinating future realizations of NH magnetic catalysis, strongly-coupled NH fractional topological phases, and NH chiral anomaly, to name a few.

cond-mat.mes-hall↗

arXiv2026

Anisotropic marginal Fermi liquid for Coulomb interacting generalized Weyl fermions

Owing to the power-law anisotropy in the quasiparticle dispersion, yielding an enhanced density of states, the effects of long range Coulomb interaction get amplified in three-dimensional generalized Weyl semimetals, characterized by integer monopole charge $n>1$ of the underlying Weyl nodes. Using a Wilsonian renormalization group approach controlled by a large-$N$ expansion with $N$ as the number of Weyl fermion flavors and a gauge-consistent regularization fixed by the Ward-Takahashi identity, we uncover for $n\ge 2$ an extended interaction-dominated scaling regime with intrinsically anisotropic dynamic Coulomb screening, a finite fermionic anomalous dimension, and a power-law suppression of the quasiparticle residue, yielding an \emph{anisotropic} marginal non-Fermi liquid at intermediate energies. Ultimately, the effective fine structure constant flows to zero, albeit only logarithmically slowly, so the marginal Fermi liquid phenomenology emerges as a broad crossover, controlled by a slowly running coupling. By contrast, for $n=1$ the system retains an isotropic marginal Weyl-liquid character. These predictions can be tested via scaling in thermodynamics (specific heat and compressibility), direction-dependent optical conductivity, and by anisotropic broadening of the single-particle spectral function in angle-resolved photoemission spectroscopy.

cond-mat.str-el↗

arXiv2025

Pair density wave in quarter metals from a repulsive fermionic interaction in graphene heterostructures: A renormalization group study

Electronic bands in chirally stacked $n$ layer carbon-based honeycomb heterostructures, encompassing rhombohedral or ABC ($n \geq 3$), Bernal or AB bilayer ($n=2$), and monolayer ($n=1$) graphene, possess four-fold valley and spin degeneracy. Such systems with $n \geq 2$, when subject to external perpendicular electric displacement fields, feature a fully degenerate metal at high doping, a spin polarized but valley degenerate half-metal at moderate doping, and a non-degenerate quarter metal at low doping. Due to the fully polarized nature of the quasiparticles in the quarter metal, realized around one particular valley otherwise chosen spontaneously, it can sustain a single local superconducting ground state, representing a pair density wave that is chiral and odd parity in nature. From a leading order renormalization group analysis, here we show that repulsive density-density interaction among such polarized fermionic excitations can foster the pair density wave phase at low temperatures. Connections with experimentally observed superconducting states in the close vicinity of the quarter metal in some members of such graphene heterostructures family are discussed and possible routes to realize such a paired state in optical honeycomb lattices are highlighted.

cond-mat.mes-hall↗

arXiv2025

Global phase diagram of two-dimensional dirty hyperbolic Dirac liquids

Within the framework of the canonical nearest-neighbor tight-binding model for spinless fermions, a family of two-dimensional bipartite hyperbolic lattices hosts massless Diraclike excitations near half-filling with the iconic vanishing density of states (DOS) near zero energy. We show that a collection of such ballistic quasiparticles remains stable against sufficiently weak pointlike charge impurities, a feature captured by the vanishing average [$\rho_{a}(0)$] and typical [$\rho_{t}(0)$] DOS at zero energy, computed by employing the kernel polynomial method in sufficiently large $\{ 10, 3\}$ hyperbolic lattices (Schl\"afli symbol) with open boundary condition containing more than $10^8$ and $10^6$ sites, respectively. However, at moderate disorder the system enters a metallic state via a continuous quantum phase transition where both $\rho_{a}(0)$ and $\rho_{t}(0)$ become finite. With increasing strength of disorder, ultimately an Anderson insulator sets in, where only $\rho_{t}(0) \to 0$. The resulting phase diagram for dirty Dirac fermions living on a hyperbolic space solely stems from the background negative spatial curvature, as confirmed from the vanishing $\rho_{t}(0)$ for arbitrarily weak disorder on honeycomb lattices, fostering relativistic fermions on a flatland, as the thermodynamic limit is approached.

cond-mat.mes-hall↗

arXiv2025

Strained hyperbolic Dirac fermions: Zero modes, flat bands, and competing orders

Starting from the nearest-neighbor tight-binding model on {10,3} and {14,3} hyperbolic lattices that, for a uniform hopping amplitude, gives rise to emergent Dirac fermions on a curved space with a constant negative curvature, displaying a vanishing density of states, we propose spatially modulated hopping pattern therein that preserve the underlying 5- and 7-fold rotational symmetries, respectively, and effectively couples fermions to time-reversal symmetric axial magnetic fields. Such strain-induced axial fields produce a flat band near zero-energy, triggering nucleation of a charge density-wave, featuring a staggered pattern of fermionic density between two sublattices, and the Haldane phase fostering intra-sublattice circulating currents with a net zero magnetic flux for weak nearest- and next-nearest-neighbor Coulomb repulsions, respectively. Sufficiently weak on-site Hubbard repulsion destabilizes such flat bands toward the formation of a magnetic phase that simultaneously supports antiferromagnetic and ferromagnetic orders in the whole system. While the magnetization in the bulk and boundary cancel each other, the Ne\'el order is of the same sign everywhere, thereby yielding a global antiferromagnet. Throughout, we draw parallels between these findings and the well-studied qualitatively similar results on a 3-fold rotational symmetric strained honeycomb lattice, thereby unifying the phenomenon of axial magnetic catalysis for Dirac fermions, encompassing the ones living on the Euclidean plane. Finally, we show that with a specific class of non-Hermiticity, manifesting via an imbalance in the hopping amplitudes between two sublattices in the opposite directions, magnitudes of all these orders can be boosted substantially when all the eigenvalues in the noninteracting systems are real, staging a non-Hermitian amplification of axial magnetic catalysis.

cond-mat.str-el↗

arXiv2025

Ordinary lattice defects as probes of topology

In addition to topological lattice defects such as dislocations and disclinations, crystals are also accompanied by unavoidable ordinary defects, devoid of any non-trivial geometry or topology, among which vacancies, Schottky defects, substitutions, interstitials, and Frenkel pairs are the most common. In this work, we demonstrate that these ubiquitous ordinary lattice defects, although geometrically trivial, can nonetheless serve as universal probes of the non-trivial topology of electronic Bloch bands, and any change in the local topological environment in an otherwise normal insulator in terms of mid-gap bound states in their vicinity. We theoretically establish these generic findings by implementing a minimal model Hamiltonian describing time-reversal symmetry breaking topological and normal insulators on a square lattice, fostering such point defects. The defect-bound mid-gap modes are also shown to be robust against sufficiently weak random point-like charge impurities. Furthermore, we showcase experimental observation of such bound states by embedding ordinary crystal defects in two-dimensional acoustic Chern lattices, where precision-controlled hopping amplitudes are implemented via active meta-atoms and Green's-function-based spectroscopy is used to reconstruct spectra and eigenstates. Our combined theory-experiment study establishes ordinary lattice defects as probes of topology that should be germane in crystals of any symmetry and dimension, raising the possibility of arresting localized Majorana modes near such defects in the bulk of topological superconductors and to emulate ordinary-defect-engineered topological devices.

cond-mat.mes-hall↗

arXiv2025

Charge density waves and stripes in quarter metals of graphene heterostructures

Motivated by recent experiments, here we identify valley-coherent charge density wave (VC-CDW) in the nondegenerate quarter metal for the entire family of chirally-stacked $n$ layer graphene, encompassing rhombohedral multilayer, Bernal bilayer, and monolayer cousins. Besides the hallmark broken translational symmetry, yielding a modulated charge density over an enlarged unit-cell with a characteristic $2{\bf K}$ periodicity, where $\pm {\bf K}$ are the valley momenta, this phase lacks the three-fold ($C_3$) rotational symmetry but only for $n=1$ and even integer $n$. The VC-CDW then represents a stripe order, as observed in hexalayer graphene [\href{https://arxiv.org/abs/2504.05129}{arXiv:2504.05129}], but preserves the $C_3$ symmetry for other odd integer $n$ as observed in trilayer graphene [\href{https://www.nature.com/articles/s41567-024-02560-7}{Nat.\ Phys.\ {\bf 20}, 1413 (2024)} and \href{https://arxiv.org/abs/2411.11163}{arXiv:2411.11163}]. From a \emph{universal} Clifford algebraic argument, we show that the VC-CDW and an anomalous Hall order can lift the residual valley degeneracy of an antiferromagnetically ordered spin-polarized half metal, when these systems are subject to perpendicular displacement fields. Only the anomalous Hall order displays a hysteresis in off-diagonal resistivity, as observed in all the systems with $2 \leq n \leq 6$. We showcase a confluence of VC-CDW and anomalous Hall orders within the quarter metal, \emph{generically} displaying a regime of coexistence, otherwise separating the pure phases.

cond-mat.mes-hall↗

arXiv2025

Amplified magnetic catalysis in non-Hermitian Euclidean and hyperbolic Dirac liquids

Due to their iconic linearly vanishing density of states near the zero-energy, half-filled two-dimensional Dirac materials in flat Euclidean and negatively-curved hyperbolic spaces exhibit dynamic mass generation only once a critical interaction strength is surpassed. Application of external magnetic fields onto these systems can, however, trigger the formation of such ordered phases yielding isotropic insulation near the band-center at arbitrarily weak coupling, a phenomenon known as magnetic catalysis. Recently, it has been proposed that a specific type of non-Hermiticity, allowing the system to feature an all-real eigenvalue spectrum otherwise squeezed toward the zero-energy, can bring down the requisite critical coupling of a specific family of ordered phases, commuting class masses, to a desired lower finite value in Dirac systems, a phenomenon known as non-Hermitian catalysis (arXiv:2501.18591). Here, we predict that a confluence of external magnetic fields and such a non-Hermiticity can amplify the magnitude of commuting class masses for subcritical strengths of interactions in Dirac liquids, an emergent phenomenon named non-Hermitian amplification of magnetic catalysis. We anchor this prediction from numerical self-consistent mean-field solutions of the commuting class mass charge-density-wave (antiferromagnetic) order displaying a staggered pattern of average electronic density (magnetization) between the nearest neighboring sites of the half-filled Euclidean honeycomb and hyperbolic {10, 3} and {14, 3} lattices, all featuring emergent non-Hermitian Dirac quasiparticles, after decomposing the nearest-neighbor Coulomb (on-site Hubbard) repulsion in the Hartree channel. We discuss the scaling behavior of these two orders with magnetic field and non-Hermiticity over a wide range of subcritical interactions.. Possible experimental setups to test our predictions are discussed.

cond-mat.str-el↗

arXiv2025

Zero modes and index theorems for non-Hermitian Dirac fermions

Dirac fermions, subject to external magnetic fields and in the presence of mass orders that assume topologically nontrivial spatial textures such as domain wall and vortices, for example, bind robust midgap states at zero energy, the number of which is governed by the Aharonov-Casher and Jackiw-Rebbi or Jackiw-Rossi index theorems, respectively. Here I extend the jurisdiction of these prominent index theorems to Lorentz invariant non-Hermitian (NH) Dirac operators, constructed by augmenting the celebrated Dirac Hamiltonian by a masslike anti-Hermitian operator that also scales linearly with momentum. The resulting NH Dirac operator manifests all-real eigenvalues over an extended NH parameter regime, characterized by a real effective Fermi velocity for NH Dirac fermions ($v_{_{\rm F}}$). From the explicit solutions of the zero-energy bound states, I show that in the presence of external magnetic fields of arbitrary shape such modes always exist when the system encloses a finite number of magnetic flux quanta, while in the presence of spatially nontrivial textures of the mass orders localized zero-energy modes can only be found in the spectrum when $v_{_{\rm F}}$ is real. These findings pave a concrete route to realize nucleation of competing orders from the topologically robust zero-energy manifold in NH or open Dirac systems. Possible extensions of these outcomes to other index theorems and tabletop experimental setups to test these predictions are discussed.

cond-mat.mes-hall↗

arXiv2025

Two-dimensional Disordered Projected Branes: Stability and Quantum Criticality via Dimensional Reduction

The interplay of disorder and dimensionality governs the emergence and stability of electronic phases in quantum materials and quantum phase transitions among them. While three-dimensional (3D) dirty Fermi liquids and Weyl semimetals support robust metallic states, undergoing disorder-driven Anderson localization transitions at strong disorder and the later ones exhibiting additional semimetal-to-metal transition at moderate disorder, conventional two-dimensional (2D) non-interacting systems localize for arbitrarily weak disorder. Here, we show that 2D disordered projected branes, constructed by systematically integrating out degrees of freedom from a 3D cubic lattice via the Schur decomposition, faithfully reproduce the full quantum phase diagram of their 3D parent systems. Using large-scale exact diagonalization and kernel polynomial method, we numerically demonstrate that 2D projected branes host stable metallic and semimetallic phases. Remarkably, the critical exponents governing the semimetal-to-metal and metal-insulator transitions on such 2D projected branes are sufficiently close to those of their 3D counterparts. Our findings thus establish 2D projected branes as genuine quantum holographic images of their higher-dimensional disordered parent crystals, supporting stable semimetallic and metallic phases that are otherwise inaccessible in conventional 2D lattices. Finally, we point to experimentally accessible metamaterial platforms, most notably the photonic lattices with tunable refractive-index disorder, as promising systems to realize and probe these phenomena.

cond-mat.dis-nn↗

arXiv2025

Projected branes as platforms for crystalline, superconducting, and higher-order topological phases

Projected branes are constituted by only a small subset of sites of a higher-dimensional crystal, otherwise placed on a hyperplane oriented at an irrational or a rational slope therein, for which the effective Hamiltonian is constructed by systematically integrating out the sites of the parent lattice that fall outside such branes [Commun. Phys. 5, 230 (2022)]. Specifically, when such a brane is constructed from a square lattice, it gives rise to an aperiodic Fibonacci quasi-crystal or its rational approximant in one dimension. In this work, starting from square lattice-based models for topological crystalline insulators, protected by the discrete four-fold rotational ($C_4$) symmetry, we show that the resulting one-dimensional projected topological branes encode all the salient signatures of such phases in terms of robust endpoint zero-energy modes, quantized local topological markers, and mid-gap modes bound to dislocation lattice defects, despite such linear branes being devoid of the $C_4$ symmetry of the original lattice. Furthermore, we show that such branes can also feature all the hallmarks of two-dimensional strong and weak topological superconductors through Majorana zero-energy bound states residing near their endpoints and at the core of dislocation lattice defects, besides possessing suitable quantized local topological markers. Finally, we showcase a successful incarnation of a square lattice-based second-order topological insulator with the characteristic corner-localized zero modes in its geometric descendant one-dimensional quasi-crystalline or crystalline branes that feature a quantized localizer index and endpoint zero-energy modes only when one of its end points passes through a corner of the parent crystal. Possible designer quantum and meta material-based platforms to experimentally harness our theoretically proposed topological branes are discussed.

cond-mat.mes-hall↗

arXiv2025

Emergent fractals in dirty topological crystals

Non-trivial geometry of electronic Bloch states gives rise to topological insulators which are robust against sufficiently weak randomness inevitably present in any quantum material. However, increasing disorder triggers a quantum phase transition into a featureless normal insulator. As the underlying quantum critical point is approached from the topological side, small scattered droplets of normal insulators start to develop in the system and their coherent nucleation causes ultimate condensation into a trivial insulator. Unless disorder is too strong, the normal insulator accommodates disjoint tiny topological puddles. Furthermore, in the close vicinity of such a transition the emergent islands of topological and trivial insulators display spatial fractal structures, a feature that is revealed only by local topological markers. Here we showcase this (possibly) generic phenomenon that should be apposite to dirty topological crystals of any symmetry class in any dimension from the Bott index and local Chern marker for a square-lattice-based disordered Chern insulator model.

cond-mat.dis-nn↗

arXiv2025

Observation of dislocation bound states and skin effects in non-Hermitian Chern insulators

The confluence of non-Hermitian (NH) topology and crystal defects has culminated significant interest, yet its experimental exploration has been limited due to the challenges involved in design and measurements. Here, we showcase experimental observation of NH dislocation bound states (NHDS) and the dislocation-induced NH skin effect in two-dimensional acoustic NH Chern lattices. By embedding an edge dislocations-antidislocation pair in such acoustic lattices and implementing precision-controlled hopping and onsite gain/loss via active meta-atoms, we reveal robust defect-bound states localized at dislocation cores within the line gap of the complex energy spectrum. We experimentally identify the emergence of bulk exceptional points (EPs) via spectral coalescence and phase rigidity analysis. We demonstrate that the NHDS survive against moderate NH perturbations but gradually delocalize and merge with the bulk (skin) states driven by these EPs under periodic (open) boundary conditions. Furthermore, our experiments demonstrate that the dislocation core can feature weak NH skin effects when its direction is perpendicular to the Burgers vector in periodic systems. Our findings, therefore, pave an experimental pathway for probing NH topology via lattice defects and open new avenues for defect-engineered topological devices.

cond-mat.mes-hall↗

arXiv2025

Superconductivity in doped planar Dirac insulators: A renormalization group study

From a leading-order unbiased renormalization group analysis we here showcase the emergence of superconductivity (including the topological ones) from purely repulsive electron-electron interactions in two-dimensional doped Dirac insulators, featuring a Fermi surface. In the absence of chemical doping, such systems describe quantum anomalous or spin Hall and normal insulators. Otherwise a simply connected Fermi surface becomes annular deep inside the topological regime. By considering all symmetry allowed repulsive local four-fermion interactions, we show that the nature of the resulting superconducting states at low temperature follows certain Clifford algebraic selection rules, irrespective of the underlying Fermi surface topology. Within the framework of a microscopic Hubbard model, on-site repulsion among fermions with opposite orbitals (spin projections) typically favors topological $p$-wave (conventional $s$-wave) pairing. Theoretically predicted superconductivity can in principle be observed in experiments once the promising candidate materials for quantum anomalous and spin Hall insulators are doped to foster Fermi surfaces.

cond-mat.supr-con↗

arXiv2025

Non-unitary time dynamics of topological modes in open planar quantum systems

Nontrivial topological invariant of bulk electronic wavefunctions in two-dimensional quantum crystals leaves its footprints on the edge, dislocation, and corner modes. Here we investigate non-unitary time dynamics of these topological modes in square lattice-based open quantum systems in which the time-dependent Hamiltonian smoothly interpolates between topologically distinct insulators across band gap closing quantum critical points. The temporal dynamics of these modes is described by a Lindblad equation in which the instantaneous Hamiltonian plays the role of the Lindblad operator, thereby allowing the environment to couple with the system through the energy channels (weak measurement protocol). We show that in the presence of such a real time ramp, the survival probability of these modes decreases (increases) in short (long) time scale where the dephasing (quantum Zeno) effect dominates with the increasing amplitude of the system-to-environment coupling, for both slow and fast ramps from a topological to a normal insulating state. For a reverse course of the time evolution, the revival or condensation probability of nucleating such topological modes, otherwise absent in the initial system, increases for stronger system-to-environment coupling. This phenomenon can be attributed to the strong decoherence of the initial mixed state among all the energy eigenstates of the final Hamiltonian which also includes the topological modes, causing their enhanced condensation probability. Our findings can be germane to real open topological materials with time-tunable band gap, and should be applicable to open topological crystals of arbitrary dimension and belonging to any symmetry class.

cond-mat.mes-hall↗

arXiv2025

Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices

Depending on the lattice geometry, the nearest-neighbor (NN) tight-binding model for free fermions gives rise to particle-hole symmetric emergent Dirac liquid, Fermi liquid, and flat bands near the half-filling or zero-energy on bipartite Euclidean and hyperbolic lattices, respectively embedded on the flat and negatively curved spaces. Such noninteracting electronic fluids are characterized by a vanishing, a finite, and a diverging density of states near half-filling, respectively. A non-Hermitian generalization of this scenario resulting from an imbalance of the hopping amplitudes in the opposite directions between any pair of NN sites continues to accommodate a real eigenvalue spectrum over an extended non-Hermitian parameter regime. Most importantly, it reduces the band width without altering the characteristic scaling of the density of states close to the zero-energy. Here, we show that on two-dimensional bipartite Euclidean and hyperbolic lattices such a non-Hermiticity catalyzes the formation of both charge-density-wave and spin-density-wave orders at weaker (in comparison to the counterparts in conventional or Hermitian systems) NN Coulomb and on-site Hubbard repulsions, respectively. These two ordered states correspond to staggered patterns of average electronic density and spin between the NN sites, respectively, and both cause insulation in half-filled systems. We arrive at these conclusions by combining biorthogonal quantum mechanics and lattice-based self-consistent numerical mean-field analysis in the Hartree channel. We discuss the scaling of the associated mass gaps near the zero-energy with the non-Hermitian parameter, and also address the finite size scaling of the order parameters specifically on hyperbolic lattices with open boundary conditions. A robust general mathematical criterion for the proposed non-Hermitian catalysis mechanism for ordered phases is showcased.

cond-mat.str-el↗

arXiv2024

Axionic quantum criticality of generalized Weyl semimetals

We formulate a field-theoretic description for $d$-dimensional interacting nodal semimetals, featuring dispersion that scales with the linear and $n$th power of momentum along $d_L$ and $d_M$ mutually orthogonal directions around a few isolated points in the reciprocal space, respectively, with $d_L+d_M=d$, and residing at the brink of isotropic insulation, described by $N_b$-component bosonic order parameter fields. The resulting renormalization group (RG) procedure, tailored to capture the associated quantum critical phenomena, is controlled by a ``small" parameter $\epsilon=2-d_M$ and $1/N_f$, where $N_f$ is the number of identical fermion copies (flavor number) when in conjunction $d_L=1$. When applied to three-dimensional interacting general Weyl semimetals ($d_L=1$ and $d_M=2$), characterized by the Abelian monopole charge $n>1$, living at the shore of the axionic insulation ($N_b=2$), a leading-order RG analysis suggests the Gaussian nature of the underlying quantum phase transition, around which the critical exponents assume mean-field values. A traditional field-theoretic RG analysis yields the same outcomes for simple Weyl semimetals ($n=1$, $d_L=3$, and $d_M=0$). Consequently, emergent marginal Fermi liquids showcase only logarithmic corrections to physical observables at intermediate scales of measurements.

cond-mat.str-el↗