arXiv subjects

Bitan Roy

Publications and source records attributed to Bitan Roy.

At least 55 records · Page 3Linked to original sources

arXiv2023

Emergent metallicity at the grain boundaries of higher-order topological insulators

Topological lattice defects, such as dislocations and grain boundaries (GBs), are ubiquitously present in the bulk of quantum materials and externally tunable in metamaterials. In terms of robust modes, localized near the defect cores, they are instrumental in identifying topological crystals, featuring the hallmark band inversion at a finite momentum (translationally active type). Here we show that GB superlattices in both two-dimensional and three-dimensional translationally active higher-order topological insulators harbor a myriad of dispersive modes that are typically placed at finite energies, but always well-separated from the bulk states. However, when the Burgers vector of the constituting edge dislocations points toward the gapless corners or hinges, both second-order and third-order topological insulators accommodate self-organized emergent topological metals near the zero energy (half-filling) in the GB mini Brillouin zone. We discuss possible material platforms where our proposed scenarios can be realized through the band-structure and defect engineering.

cond-mat.mes-hall↗

arXiv2023

Topologically distinct atomic insulators

Topological classification of quantum solids often (if not always) groups all trivial atomic or normal insulators (NIs) into the same featureless family. As we argue here, this is not necessarily the case always. In particular, when the global phase diagram of electronic crystals harbors topological insulators with the band inversion at various time-reversal invariant momenta ${\bf K}^{\rm TI}_{\rm inv}$ in the Brillouin zone, their proximal NIs display noninverted band-gap minima at ${\bf K}^{\rm NI}_{\rm min}={\bf K}^{\rm TI}_{\rm inv}$. In such systems, once topological superconductors nucleate from NIs, the inversion of the Bogoliubov de Gennes bands takes place at ${\bf K}^{\rm BdG}_{\rm inv}={\bf K}^{\rm NI}_{\rm min}$, inheriting from the parent state. We showcase this (possibly general) proposal for two-dimensional time-reversal symmetry-breaking insulators. Then distinct quantized thermal Hall conductivity and responses to dislocation lattice defects inside the paired states (tied with ${\bf K}^{\rm BdG}_{\rm inv}$ or ${\bf K}^{\rm NI}_{\rm min}$), in turn unambiguously identify different parent atomic NIs.

cond-mat.mes-hall↗

arXiv2023

Correlated Fractional Dirac Materials

Fractional Dirac materials (FDMs) feature a fractional energy-momentum relation $E(\vec{k}) \sim |\vec{k}|^α$, where $α\; (<1)$ is a real noninteger number, in contrast to that in conventional Dirac materials with $α=1$. Here we analyze the effects of short- and long-range Coulomb repulsions in two- and three-dimensional FDMs. Only a strong short-range interaction causes nucleation of a correlated insulator that takes place through a quantum critical point. The universality class of the associated quantum phase transition is determined by the correlation length exponent $ν^{-1}=d-α$ and dynamic scaling exponent $z=α$, set by the band curvature. On the other hand, the fractional dispersion is protected against long-range interaction due to its nonanalytic structure. Rather, a linear Dirac dispersion gets generated under coarse graining, and the associated Fermi velocity increases logarithmically in the infrared regime, thereby yielding a two-fluid system. Altogether, correlated FDMs unfold a rich landscape accommodating unconventional emergent many-body phenomena.

cond-mat.str-el↗

arXiv2023

Polar hairs of mixed-parity nodal superconductors in Rarita-Schwinger-Weyl metals

Linearly dispersing Rarita-Schwinger-Weyl (RSW) fermions featuring two Fermi velocities are the key constituents of itinerant spin-3/2 quantum materials. When doped, RSW metals sustain two Fermi surfaces (FSs), around which one fully gapped $s$-wave and five \emph{mixed-parity} local pairings can take place. The intraband components of four mixed-parity pairings support point nodes at the poles of two FSs, only around which long-lived quasiparticles live. For weak (strong) pairing amplitudes ($Δ$), gapless north and south poles belonging to the same (different) FS(s) get connected by \emph{polar hairs}, one-dimensional line nodes occupying the region between two FSs. The remaining one, by contrast, supports four nodal rings in between two FSs, symmetrically placed about their equators, but only when $Δ$ is small. For large $Δ$, this paired state becomes fully gapped. The transition temperature and pairing amplitudes follow the BCS scaling. We explicitly showcase these outcomes for a rotationally symmetric RSW metal, and contrast our findings when the system possesses an enlarged Lorentz symmetry and with those in spin-3/2 Luttinger materials.

cond-mat.supr-con↗

arXiv2023

Inner Skin Effects on Non-Hermitian Topological Fractals

Non-Hermitian (NH) crystals, quasicrystals and amorphous network display an accumulation of a macroscopic number of states near one of its specific interfaces with vacuum, such as edge, surface, hinge or corner. This phenomenon is known as the NH skin effect, which can only be observed with open boundary condition. In this regard self-similar fractals, manifesting inner boundaries in the interior of the system, harbor a novel phenomenon, the \emph{inner skin effect} (ISE). Then the NH skin effect appears at the inner boundaries of the fractal lattice with periodic boundary condition. We showcase this observation by implementing prominent models for NH insulators and superconductors on representative planar Sierpinski carpet fractal lattices. They accommodate both first-order and second-order ISEs at inner edges and corners, respectively, for charged as well as neutral Majorana fermions. Furthermore, over extended parameter regimes ISEs are tied with nontrivial bulk topological invariants, yielding intrinsic ISEs. With the recent success in engineering NH topological phases on highly tunable metamaterial platforms, such as photonic and phononic lattices, as well as topolectric circuits, the proposed ISEs can be observed experimentally at least on fractal metamaterials with periodic boundary condition.

cond-mat.mes-hall↗

arXiv2022

Projected Topological Branes

Nature harbors crystals of dimensionality ($d$) only up to three. Here we introduce the notion of \emph{projected topological branes} (PTBs): Lower-dimensional branes embedded in higher-dimensional parent topological crystals, constructed via a geometric cut-and-project procedure on the Hilbert space of the parent lattice Hamiltonian. When such a brane is inclined at a rational or an irrational slope, either a new lattice periodicity or a quasicrystal emerges. The latter gives birth to topoquasicrystals within the landscape of PTBs. As such PTBs are shown to inherit the hallmarks, such as the bulk-boundary, bulk-dislocation correspondences and topological invariant, of the parent topological crystals. We exemplify these outcomes by focusing on two-dimensional parent Chern insulators, leaving its signatures on projected one-dimensional (1D) topological branes in terms of localized endpoint, dislocation modes and the local Chern number. Finally, by stacking 1D projected Chern insulators, we showcase the imprints of three-dimensional Weyl semimetals in $d=2$, namely the Fermi arc surface states and bulk chiral zeroth Landau level, responsible for the chiral anomaly. Altogether, the proposed PTBs open a realistic avenue to harness higher-dimensional ($d>3$) topological phases in laboratory.

cond-mat.mes-hall↗

arXiv2022

Non-Hermitian dislocation modes: Stability and melting across exceptional points

The traditional bulk-boundary correspondence assuring robust gapless modes at the edges and surfaces of insulating and nodal topological materials gets masked in non-Hermitian (NH) systems by the skin effect, manifesting an accumulation of a macroscopic number of states near such interfaces. Here we show that dislocation lattice defects are immune to such skin effect or at most display a \emph{weak} skin effect (depending on its relative orientation with the Burgers vector), and as such they support robust topological modes in the bulk of a NH system, specifically when the parent Hermitian phase features band inversion at a finite momentum. However, the dislocation modes gradually lose their support at their core when the system approaches an exceptional point, and finally melt into the boundary of the system across the NH band gap closing. We explicitly demonstrate these findings for a two-dimensional NH Chern insulator, thereby establishing that dislocation lattice defects can be instrumental to experimentally probe pristine NH topology.

cond-mat.mes-hall↗

arXiv2022

Higher-order topological phases on fractal lattices

Electronic materials harbor a plethora of exotic quantum phases, ranging from unconventional superconductors to non-Fermi liquids, and, more recently, topological phases of matter. While these quantum phases in integer dimensions are well characterized by now, their presence in fractional dimensions remains vastly unexplored. Here, we theoretically show that a special class of crystalline phases, namely, higher-order topological phases that via an extended bulk-boundary correspondence feature robust gapless modes on lower dimensional boundaries, such as corners and hinges, can be found on a representative family of fractional materials: \emph{quantum fractals}. To anchor this general proposal, we demonstrate realizations of second-order topological insulators and superconductors, supporting charged and neutral Majorana corner modes, on planar Sierpiński carpet and triangle fractals, respectively. These predictions can be experimentally tested on designer electronic fractal materials, as well as on various highly tunable metamaterial platforms, such as photonic and acoustic lattices.

cond-mat.mes-hall↗

arXiv2022

Competing orders and cascade of degeneracy lifting in doped Bernal bilayer graphene

Motivated by recent experiments [H. Zhou, \emph{et al.}, Science {\bf 375}, 774 (2022) and S. C. de la Barrera, \emph{et al.}, arXiv:2110.13907], here we propose a general mechanism for valley and/or spin degeneracy lifting of the electronic bands in doped Bernal bilayer graphene, subject to electric displacement ($D$) fields. A $D$-field induced layer polarization (LP), when accompanied by Hubbard repulsion driven layer antiferromagnet (LAF) and next-nearest-neighbor repulsion driven quantum anomalous Hall (QAH) orders, lifts the four-fold degeneracy of electronic bands, yielding a quarter metal for small doping, as also observed in ABC trilayer graphene. With the disappearance of the QAH order, electronic bands recover two-fold valley degeneracy, thereby forming a conventional or compensated (with majority and minority carriers) half-metal at moderate doping, depending on the relative strength of LP and LAF. At even higher doping and for weak $D$-field only LAF survives and the Fermi surface recovers four-fold degeneracy. We also show that a pure repulsive electronic interaction mediated triplet $f$-wave pairing emerges from a parent correlated nematic liquid or compensated half-metal when an in-plane magnetic field is applied to the system.

cond-mat.mes-hall↗

arXiv2022

Metals, fractional metals, and superconductivity in rhombohedral trilayer graphene

Combining mean-field and renormalization group analyses, here we unveil the nature of recently observed superconductivity and parent metallic states in chemically doped rhombohedral trilayer graphene, subject to external electric displacement fields ($D$) [H. Zhou, \emph{et al.}, Nature (London) {\bf 598}, 434 (2021)]. We argue that close to the charge neutrality, on site Hubbard repulsion favors layer antiferromagnet, which when combined with the $D$-field induced layer polarization, produces a spin-polarized, but valley-unpolarized half-metal, conducive to the nucleation of spin-triplet $f$-wave pairing (SC2). At larger doping valence bond order emerges as a prominent candidate for isospin coherent paramagent, boosting condensation of spin-singlet Cooper pairs in the $s$-wave channel (SC1), manifesting a "selection rule" among competing orders. Responses of these paired states to displacement and in-plane magnetic fields show qualitative similarities with experimental observation. With the onset of the quantum anomalous Hall order, the valley degeneracy of half-metal gets lifted, forming a quarter-metal at lower doping [H. Zhou, \emph{et al.}, Nature (London) {\bf 598}, 429 (2021)].

cond-mat.str-el↗

arXiv2021

Mixed-parity octupolar pairing and corner Majorana modes in three dimensions

We identify time-reversal symmetry breaking mixed-parity superconducting states that feature eight Majorana corner modes in properly cleaved three-dimensional cubic crystals. Namely, when an odd-parity isotropic $p$-wave pairing coexists with cubic symmetry preserving even-parity octupolar $d_{x^2-y^2}+i d_{3z^2-r^2}$ pairing, the gapless surface Majorana modes of the former get localized at the eight corners, thus yielding an \emph{intrinsic} third-order topological superconductor (TOTSC). A cousin $d_{xy}+id_{3z^2-r^2}$ pairing also accommodating eight corner Majorana modes, by virtue of breaking the cubic symmetry, in contrast, yields an \emph{extrinsic} TOTSC. We identify a doped octupolar (topological or trivial) Dirac insulator as a suitable platform to sustain such unconventional superconductors, realized from an intraunit cell pairing. Finally, we argue that the proposed TOTSC can be experimentally realizable in NaCl and other structurally similar compounds under high pressure.

cond-mat.supr-con↗

arXiv2021

Dislocation as a bulk probe of higher-order topological insulators

Topological materials occupy the central stage in the modern condensed matter physics because of their robust metallic edge or surface states protected by the topological invariant, characterizing the electronic band structure in the bulk. Higher-order topological (HOT) states extend this usual bulk-boundary correspondence, so they host the modes localized at lower-dimensional boundaries, such as corners and hinges. Here we theoretically demonstrate that dislocations, ubiquitous defects in crystalline materials, can probe higher-order topology, recently realized in various platforms. We uncover that HOT insulators respond to dislocations through symmetry protected finite-energy in-gap electronic modes, localized at the defect core, which originate from an interplay between the orientation of the HOT mass domain wall and the Burgers vector of the dislocation. As such, these modes become gapless only when the Burgers vector points toward lower-dimensional gapless boundaries. Our findings are consequential for the systematic probing of the extended bulk-boundary correspondence in a broad range of HOT crystals, and photonic and phononic or mechanical metamaterials through the bulk topological lattice defects.

cond-mat.mes-hall↗

arXiv2021

Anomalous and normal dislocation modes in Floquet topological insulators

Electronic bands featuring nontrivial bulk topological invariant manifest through robust gapless modes at the boundaries, e.g., edges and surfaces. As such this bulk-boundary correspondence is also operative in driven quantum materials. For example, a suitable periodic drive can convert a trivial insulator into a Floquet topological insulator (FTI) that accommodates nondissipative dynamic gapless modes at the interfaces with vacuum. Here we theoretically demonstrate that dislocations, ubiquitous lattice defects in crystals, can probe FTIs as well as unconventional $π$-trivial insulator in the bulk of driven quantum systems by supporting normal and anomalous modes, localized near the defect core. Respectively, normal and anomalous dislocation modes reside at the Floquet zone center and boundaries. We exemplify these outcomes specifically for two-dimensional (2D) Floquet Chern insulator and $p_x+ip_y$ superconductor, where the dislocation modes are respectively constituted by charged and neutral Majorana fermions. Our findings should be therefore instrumental in probing Floquet topological phases in the state-of-the-art experiments in driven quantum crystals, cold atomic setups, and photonic and phononic metamaterials through bulk topological lattice defects.

cond-mat.mes-hall↗

arXiv2021

Competing magnetic orders and multipolar Weyl fermions in 227 pyrochlore iridates

Owing to comparably strong spin-orbit coupling and Hubbard interaction, iridium based 227 pyrochlore oxides harbor a rich confluence of competing magnetic orders and emergent multipolar Weyl quasiparticles. Here we show that this family of materials is predominantly susceptible toward the nucleation of electronic noncoplanar all-in all-out (AIAO) and three-in one-out (3I1O) orders, respectively transforming under the singlet $A_{2u}$ and triplet $T_{1u}$ representations, supporting octupolar and dipolar Weyl fermions, and favored by strong on-site Hubbard and nearest-neighbor ferromagnetic interaction. Furthermore, a coplanar magnetic order generically appears as an intermediate phase between them. This order transforms under the triplet $T_{2u}$ representation and also hosts octupolar Weyl fermions. With the AIAO and 3I1O phases possibly being realized in (Nd$_{1-x}$Pr$_{x}$)$_2$Ir$_2$O$_7$ when $x=0$ and 1, respectively, the intervening $T_{2u}$ order can in principle be found at an intermediate doping ($0<x<1$) or in pressured (hydrostatic) Nd$_2$Ir$_2$O$_7$.

cond-mat.str-el↗

arXiv2021

Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders

Performing a leading-order renormalization group analysis, here we compute the effects of generic local or short-range electronic interactions in monolayer and Bernal bilayer graphene. Respectively in these two systems chiral quasiparticles display linear and biquadratic band touching, leading to linearly vanishing and constant DOS. Consequently, the former system remains stable for weak enough local interactions, and supports a variety of ordered phases only beyond a critical strength of interactions. By contrast, ordered phases can nucleate for sufficiently weak interactions in bilayer graphene. By tuning the strength of all symmetry allowed local interactions, we construct various cuts of the phase diagram at zero and finite temperature and chemical doping. Typically, at zero doping insulating phases (such as charge-density-wave, antiferromagnet, quantum anomalous and spin Hall insulators) prevail at the lowest temperature, while gapless nematic or smectic liquids stabilize at higher temperatures. On the other hand, at finite doping the lowest temperature ordered phase is occupied by a superconductor. Besides anchoring such an organizing principle among the candidate ordered phases, we also establish a selection rule between them and the interaction channel responsible for the breakdown of linear or biquadrtic chiral nodal Fermi liquid. In addition, we also demonstrate the role of the normal state band structure in selecting the pattern of symmetry breaking from a soup of preselected incipient competing orders. As a direct consequence of the selection rule, while an antiferromagnetic phase develops in undoped monolayer and bilayer graphene, the linear (biquadratic) band dispersion favors condensation of a spin-singlet nematic (translational symmetry breaking Kekulé) superconductor in doped monolayer (bilayer) graphene, when the on site Hubbard repulsion dominates in these systems.

cond-mat.str-el↗

arXiv2021

Interacting spin-3/2 fermions in a Luttinger semimetal: Competing phases and their selection in the global phase diagram

We compute the effects of electronic interactions on gapless spin-3/2 excitations that in a noninteracting system emerge at a bi-quadratic touching of Kramers degenerate valence and conduction bands, known as Luttinger semimetal. This model can describe the low-energy physics of HgTe, gray-Sn, 227 pyrochlore iridates and half-Heuslers. For the sake of concreteness we only consider the short-range components of the Coulomb interaction. By combining mean-field analysis with a renormalization group (RG) calculation, we construct multiple cuts of the global phase diagram of interacting spin-3/2 fermions at zero and finite temperature and chemical doping. Such phase diagrams display a rich confluence of competing orders, among which rotational symmetry breaking nematic insulators and time reversal symmetry breaking magnetic orders are the prominent excitonic phases. We also show that even repulsive interactions can be conducive for both s-wave and d-wave pairings. The reconstructed band structure inside the ordered phases allows us to organize them according to the energy (entropy) gain in the following (reverse) order: s-wave pairing, nematic phases, magnetic orders and d-wave pairings, at zero chemical doping. But, the paired states are always energetically superior over the excitonic ones for finite doping. The phase diagrams obtained from the RG analysis show that an ordered phase with higher energy (entropy) gain is realized at low (high) temperature. In addition, we establish a "selection rule" between the interaction channels and the resulting ordered phases, suggesting that repulsive interactions in the magnetic (nematic) channels are conducive for the nucleation of d-wave (s-wave) pairing. The proposed methodology can shed light on the global phase diagram of other strongly interacting multi-band systems, such as doped Dirac semimetal, topological insulators and the like.

cond-mat.str-el↗

arXiv2021

Topolectric circuits: Theory and construction

We highlight a general theory to engineer arbitrary Hermitian tight-binding lattice models in electrical LC circuits, where the lattice sites are replaced by the electrical nodes, connected to its neighbors and to the ground by capacitors and inductors. In particular, by supplementing each node with $n$ subnodes, where the phases of the current and voltage are the $n$ distinct roots of \emph{unity}, one can in principle realize arbitrary hopping amplitude between the sites or nodes via the \emph{shift capacitor coupling} between them. This general principle is then implemented to construct a plethora of topological models in electrical circuits, \emph{topolectric circuits}, where the robust zero-energy topological boundary modes manifest through a large boundary impedance, when the circuit is tuned to the resonance frequency. The simplicity of our circuit constructions is based on the fact that the existence of the boundary modes relies only on the Clifford algebra of the corresponding Hermitian matrices entering the Hamiltonian and not on their particular representation. This in turn enables us to implement a wide class of topological models through rather simple topolectric circuits with nodes consisting of only two subnodes. We anchor these outcomes from the numerical computation of the on-resonance impedance in circuit realizations of first-order ($m=1$), such as Chern and quantum spin Hall insulators, and second- ($m=2$) and third- ($m=3$) order topological insulators in different dimensions, featuring sharp localization on boundaries of codimensionality $d_c=m$. Finally, we subscribe to the \emph{stacked topolectric circuit} construction to engineer three-dimensional Weyl, nodal-loop, quadrupolar Dirac and Weyl semimetals, respectively displaying surface and hinge localized impedance.

cond-mat.mes-hall↗

arXiv2021

Hierarchy of higher-order Floquet topological phases in three dimensions

Following a general protocol of periodically driving static first-order topological phases (supporting surface states) with suitable discrete symmetry breaking Wilson-Dirac masses, here we construct a hierarchy of higher-order Floquet topological phases in three dimensions. In particular, we demonstrate realizations of both second-order and third-order Floquet topological states, respectively supporting dynamic hinge and corner modes at zero quasienergy, by periodically driving their static first-order parent states with one and two discrete symmetry breaking Wilson-Dirac mass(es). While the static surface states are characterized by codimension $d_c=1$, the resulting dynamic hinge (corner) modes, protected by \emph{antiunitary} spectral or particle-hole symmetries, live on the boundaries with $d_c=2$ $(3)$. We exemplify these outcomes for three-dimensional topological insulators and Dirac semimetals, with the latter ones following an arbitrary spin-$j$ representation.

cond-mat.mes-hall↗