arXiv subjects

Bitan Roy

Publications and source records attributed to Bitan Roy.

At least 37 records · Page 2Linked to original sources

arXiv2025

Hybrid symmetry class topological insulators

Traditional topological materials belong to different Altland-Zirnbauer symmetry classes (AZSCs) depending on their non-spatial symmetries. Here we introduce the notion of hybrid symmetry class topological insulators (HSCTIs): A fusion of two different AZSC topological insulators (TIs) such that they occupy orthogonal Cartesian hyperplanes and their universal massive Dirac Hamiltonian mutually anticommute, a mathematical procedure we name hybridization. The boundaries of HSCTIs can also harbor TIs, typically affiliated with an AZSC that is different from the ones for the parent two TIs. As such, a fusion or hybridization between planar class AII quantum spin Hall and vertical class BDI Su-Schrieffer-Heeger insulators gives birth to a three-dimensional class A HSCTI, accommodating quantum anomalous Hall insulators (class A) of opposite Chern numbers and quantized Hall conductivity of opposite signs on the top and bottom surfaces. Such a response is shown to be stable against weak disorder. We extend this construction to encompass crystalline HSCTI and topological superconductors (featuring half-quantized thermal Hall conductivity of opposite sings on the top and bottom surfaces), and beyond three spatial dimensions. Non-trivial responses of three-dimensional HSCTIs to crystal defects (namely edge dislocations) in terms of mid-gap bound states at zero energy around its core only on the top and bottom surfaces are presented. Possible (meta)material platforms to harness and engineer HSCTIs are discussed.

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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

From local spin nematicity to altermagnets: Footprints of band topology

Altermagnets are crystallographic rotational symmetry breaking spin-ordered states, possessing a net zero magnetization despite manifesting Kramer's non-degenerate bands. Here, we show that momentum-independent local spin nematic orders in monolayer, Bernal bilayer, and rhombohedral trilayer graphene give rise to $p$-wave, $d$-wave, and $f$-wave altermagnets, respectively, thereby inheriting the topology of linear, quadratic and cubic free fermion band dispersions that are also described in terms of angular momentum $\ell=1,\; 2$, and $3$ harmonics in the reciprocal space. The same conclusions also hold inside a spin-triplet nematic superconductor, featuring Majorana altermagnets. Altogether, these findings highlight the importance of electronic band structure in identifying such exotic magnetic orders in quantum materials. We depict the effects of in-plane magnetic fields on altermagnets, and propose spin-disordered alter-valley magnets in these systems.

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arXiv2025

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 $ε=2-d_M$ 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.

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arXiv2025

Dynamic mass generation on two-dimensional electronic hyperbolic lattices

Free electrons hopping on hyperbolic lattices embedded on a negatively curved space can foster (a) Dirac liquids, (b) Fermi liquids, and (c) flat bands, respectively characterized by a vanishing, constant, and divergent density of states near the half filling. From numerical self-consistent mean-field Hartree analyses, we show that nearest-neighbor Coulomb and on-site Hubbard repulsions respectively give rise to charge-density-wave and antiferromagnetic orders featuring staggered patterns of average electronic density and magnetization in all these systems, when the hyperbolic tessellation is accomplished by periodic arrangements of even $p$-gons. Both quantum orders dynamically open mass gaps near the charge neutrality point via spontaneous symmetry breaking. Only on hyperbolic Dirac materials these orderings take place via quantum phase transitions (QPTs) beyond critical interactions, which however decrease with increasing curvature, showcasing curvature-induced weak-coupling QPTs. We present scaling of these masses with the corresponding interaction strengths.

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arXiv2025

Yukawa-Lorentz symmetry of interacting non-Hermitian birefringent Dirac fermions

The energy spectra of linearly dispersing gapless spin-3/2 Dirac fermions display birefringence, featuring two effective Fermi velocities, thus breaking the space-time Lorentz symmetry. Here, we consider a non-Hermitian (NH) generalization of this scenario by introducing a masslike anti-Hermitian birefringent Dirac operator to its Hermitian counterpart. At the microscopic level, a generalized $π$-flux square lattice model with imbalance in the hopping amplitudes in the opposite directions among spinless fermions between the nearest-neighbor sites gives rise to pseudospin-3/2 NH Dirac fermions in terms of internal, namely sublattice, degrees of freedom. The resulting NH operator shows real eigenvalue spectra over an extended NH parameter regime, and a combination of non-spatial and discrete rotational symmetries protects the gapless nature of such quasiparticles. However, at the brink of dynamic mass generation, triggered by Hubbardlike local interactions, the birefringent parameter always vanishes under coarse grain due to the Yukawa-type interactions with scalar bosonic order-parameter fluctuations. The resulting quantum critical state is, therefore, described by two decoupled copies of spin-1/2 Dirac fermions with a unique terminal Fermi velocity, which is equal to the bosonic order-parameter velocity, thereby fostering an emergent space-time Lorentz symmetry. Furthermore, depending on the internal algebra between the anti-Hermitian birefringent Dirac operator and the candidate mass order, the system achieves the emergent Yukawa-Lorentz symmetry either by maintaining its non-Hermiticity or by recovering a full Hermiticity. We discuss the resulting quantum critical phenomena and possible microscopic realizations of the proposed scenarios.

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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.

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arXiv2025

Dispersive nodal fermions along grain boundaries in Floquet topological crystals

Driven quantum materials often feature emergent topology, otherwise absent in static crystals. Dynamic bulk-boundary correspondence, encoded by nondissipative gapless modes residing near the Floquet zone center and/or boundaries, is its most prominent example. Here we show that topologically robust gapless dispersive modes appear along the grain boundaries, embedded in the interior of Floquet topological crystals, when the Floquet-Bloch band inversion occurring at a finite momentum (${\bf K}^{\rm Flq}_{\rm inv}$) and the Burgers vector (${\bf b}$) of the constituting array of dislocations satisfy ${\bf K}^{\rm Flq}_{\rm inv} \cdot {\bf b}=π$ (modulo $2 π$). Such nondissipative gapless states can be found near the center and/or edges of the Floquet Brillouin zone, irrespective of the drive protocol. We showcase these general outcomes for two-dimensional driven time-reversal symmetry breaking insulators. Promising experimental platforms hosting such dynamic topological dispersive bands in real materials are discussed.

cond-mat.mes-hall↗

arXiv2024

Topological insulators on fractal lattices: A general principle of construction

Fractal lattices, featuring the self-similarity symmetry, are often geometric descents of parent crystals, possessing all their discrete symmetries (such as rotations and reflections) except the translational ones. Here, we formulate three different general approaches to construct real space Hamiltonian on a fractal lattice starting from the Bloch Hamiltonian on the parent crystal, fostering for example strong and crystalline topological insulators resulting from the interplay between the nontrivial geometry of the underlying electronic wave functions and the crystal symmetries. As a demonstrative example, we consider a generalized square lattice Chern insulator model and within the framework of all three methods we successfully showcase incarnations of strong and crystalline Chern insulators on the Sierpiński carpet fractal lattices. The proposed theoretical framework thus lays a generic foundation to build a tower of topological phases on the landscape of fractal lattices.

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arXiv2024

Magnetic catalysis in weakly interacting hyperbolic Dirac materials

Due to the linearly vanishing density of states, emergent massless Dirac quasiparticles resulting from the free fermion motion in a family of two-dimensional half-filled bipartite hyperbolic lattices feature dynamic mass generation through quantum phase transitions only for sufficiently strong finite-range Coulomb repulsion. As such, strong nearest-neighbor Coulomb repulsion ($V$) favors the nucleation of a charge-density-wave (CDW) order with a staggered pattern of average fermionic density between two sublattices of bipartite hyperbolic lattices. Considering a collection of spinless fermions (for simplicity), here we show that application of strong external magnetic fields by virtue of producing a \emph{finite} density of states near the zero energy triggers the condensation of the CDW order even for \emph{infinitesimal} $V$. The proposed curved space magnetic catalysis mechanism is operative for uniform and inhomogeneous (bell-shaped) magnetic fields. We present scaling of the CDW order with the total flux enclosed by hyperbolic Dirac materials for a wide range of (especially subcritical) $V$.

cond-mat.str-el↗

arXiv2024

Quantized electrical, thermal, and spin transports of non-Hermitian clean and dirty two-dimensional topological insulators and superconductors

From lattice-regularized models, devoid of any non-Hermitian (NH) skin effects, here we compute the electrical ($σ_{xy}$), thermal ($κ_{xy}$), and spin ($σ^{sp}_{xy}$) Hall, and the electrical ($G_{xx}$) and thermal ($G^{th}_{xx}$) longitudinal conductivities for appropriate NH planar topological insulators and superconductors related to all five non-trivial Altland-Zirbauer symmetry classes in their Hermitian limits. These models feature real eigenvalues over an extended NH parameter regime, only where the associated topological invariants remain quantized. In this regime, the NH quantum anomalous and spin Hall insulators show quantized $σ_{xy}$ and $G_{xx}$, respectively, the NH $p+ip$ ($p \pm ip$) pairing shows half-quantized $κ_{xy}$ ($G^{th}_{xx}$), while the NH $d+id$ pairing shows quantized $κ_{xy}$ and $σ^{sp}_{xy}$ in the clean and weak disorder (due to random pointlike charge impurities) regimes. We compute these quantities in experimentally realizable suitable six-terminal setups using the Kwant software package. But, in the strong disorder regime, all these topological responses vanish and with the increasing non-Hermiticity in the system this generic phenomenon occurs at weaker disorder.

cond-mat.mes-hall↗

arXiv2024

Superconductivity in three-dimensional interacting doped topological insulators

Three-dimensional doped Dirac insulators foster simply connected (in both topological and trivial regimes) and annular (deep inside the topological regime) Fermi surfaces (FSs) in the normal state, and allow on-site repulsions among fermions with opposite spin ($U_1$) and parity ($U_2$) eigenvalues. From an unbiased leading-order (one-loop) renormalization group analysis, controlled by a suitable $ε$ expansion, we show that this system develops a strong propensity toward the nucleation of scalar $s$-wave and odd-parity pseudoscalar $p$-wave pairings, favored by repulsive $U_1$ and $U_2$ interactions, respectively, irrespective of the underlying FS topology. Our results can be pertinent for the observed superconductivity in various doped narrow gap semiconductors, and the theoretical foundation can readily be applied to investigate similar phenomenon in various doped topological materials.

cond-mat.mes-hall↗

arXiv2024

Yukawa-Lorentz Symmetry in Non-Hermitian Dirac Materials

Lorentz spacetime symmetry represents a unifying feature of the fundamental forces, typically manifest at sufficiently high energies, while in quantum materials it emerges in the deep low-energy regime. However, its fate in quantum materials coupled to an environment thus far remained unexplored. We here introduce a general framework of constructing symmetry-protected Lorentz invariant non-Hermitian (NH) Dirac semimetals (DSMs), realized by invoking masslike anti-Hermitian Dirac operators to its Hermitian counterpart. Such NH DSMs feature purely real or imaginary isotropic linear band dispersion, yielding a vanishing density of states. Dynamic mass orderings in NH DSMs thus take place for strong Hubbardlike local interactions through a quantum phase transition, hosting a non-Fermi liquid, beyond which the system becomes an insulator. We show that depending on the internal Clifford algebra between the NH Dirac operator and candidate mass order-parameter, the resulting quantum-critical fluid either remains coupled with the environment or recovers full Hermiticity by decoupling from the bath, while always enjoying an emergent Yukawa-Lorentz symmetry in terms of a unique terminal velocity. We showcase the competition between such mass orderings, their hallmarks on quasiparticle spectra in the ordered phases, and the relevance of our findings for correlated designer NH Dirac materials.

cond-mat.str-el↗

arXiv2024

Noncrystalline topological superconductors

Topological insulators, featuring bulk-boundary correspondence, have been realized on a large number of noncrystalline materials, among which amorphous network, quasicrystals and fractal lattices are the most prominent ones. By contrast, topological superconductors beyond the realm of quantum crystals are yet to be harnessed, as their nucleation takes place around a well-defined Fermi surface with a Fermi momentum, the existence of which rests on the underlying translational symmetry. Here we identify a family of noncrystalline Dirac materials, devoid of time-reversal (${\mathcal T}$) and translational symmetries, on which a suitable local or on-site pairing yields topological superconductors. We showcase this outcome on all the above mentioned noncrystalline platforms embedded in a two-dimensional flat space. The resulting noncrystalline topological superconductors possess quantized topological invariants (Bott index and local Chern marker) and harbor robust one-dimensional Majorana edge modes, analogs of ${\mathcal T}$-odd $p+ip$ pairing in noncrystalline materials.

cond-mat.supr-con↗

arXiv2024

Quantized thermal and spin transports of dirty planar topological superconductors

Nontrivial bulk topological invariants of quantum materials can leave their signatures on charge, thermal and spin transports. In two dimensions, their imprints can be experimentally measured from well-developed multiterminal Hall bar arrangements. Here, we numerically compute the low temperature ($T$) thermal ($κ_{xy}$) and zero temperature spin ($σ^{sp}_{xy}$) Hall conductivities, and longitudinal thermal conductance ($G^{th}_{xx}$) of various prominent two-dimensional fully gapped topological superconductors, belonging to distinct Altland-Zirnbauer symmetry classes, namely $p+ip$ (class D), $d+id$ (class C) and $p \pm ip$ (class DIII) paired states, in mesoscopic six-terminal Hall bar setups from the scattering matrix formalism using Kwant. In both clean and weak disorder limits, the time-reversal symmetry breaking $p+ip$ and $d+id$ pairings show half-quantized and quantized $κ_{xy}$ [in units of $κ_0=π^2 k^2_B T/(3h)$], respectively, while the latter one in addition accommodates a quantized $σ^{sp}_{xy}$ [in units of $σ^{sp}_0=\hbar/(8 π)$]. By contrast, the time-reversal invariant $p \pm ip$ pairing only displays a quantized $G^{th}_{xx}$ at low $T$ up to a moderate strength of disorder. In the strong disorder regime, all these topological responses ($κ_{xy}$, $σ^{sp}_{xy}$, and $G^{th}_{xx}$) vanish. Possible material platforms hosting such paired states and manifesting these robust topological thermal and spin responses are discussed.

cond-mat.mes-hall↗

arXiv2024

Quantum Electrodynamics of Non-Hermitian Dirac Fermions

We develop an effective quantum electrodynamics for non-Hermitian (NH) Dirac materials interacting with photons. These systems are described by nonspatial symmetry protected Lorentz invariant NH Dirac operators, featuring two velocity parameters $v_{_{\rm H}}$ and $v_{_{\rm NH}}$ associated with the standard Hermitian and a masslike anti-Hermitian Dirac operators, respectively. They display linear energy-momentum relation, however, in terms of an effective Fermi velocity $v_{_{\rm F}}=\sqrt{v^2_{_{\rm H}}-v^2_{_{\rm NH}}}$ of NH Dirac fermions. Interaction with the fluctuating electromagnetic radiation then gives birth to an emergent Lorentz symmetry in this family of NH Dirac materials in the deep infrared regime, where the system possesses a unique terminal velocity $v_{_{\rm F}}=c$, with $c$ being the speed of light. While in two dimensions such a terminal velocity is set by the speed of light in the free space, dynamic screening in three spatial dimensions permits its nonuniversal values. Manifestations of such an emergent spacetime symmetry on the scale dependence of various physical observables in correlated NH Dirac materials are discussed.

cond-mat.str-el↗

arXiv2023

Dynamic melting and condensation of topological dislocation modes

Bulk dislocation lattice defects are instrumental in identifying translationally active topological insulators (TATIs), featuring band inversion at a finite momentum (${\bf K}_{\rm inv}$). As such, TATIs host robust gapless modes around the dislocation core, when the associated Burgers vector ${\bf b}$ satisfies ${\bf K}_{\rm inv} \cdot {\bf b}=π$ (modulo $2 π$). From the time evolution of appropriate density matrices, we show that when a TATI via a real time ramp enters into a trivial or translationally inert topological insulating phase, devoid of gapless dislocation modes, the signatures of the preramp defect modes survive for a long time. More intriguingly, as the system ramps into a TATI phase from any translationally inert insulator, signature of the dislocation mode dynamically builds up near its core, which is prominent for slow ramps. We exemplify these generic outcomes for two-dimensional time-reversal symmetry breaking insulators. Proposed dynamic responses at the dislocation core can be experimentally observed in quantum crystals, optical lattices and metamaterials with time a tunable band gap.

cond-mat.mes-hall↗

arXiv2023

Transport in strained graphene: Interplay of Abelian and axial magnetic fields

Immersed in external magnetic fields ($B$), buckled graphene constitutes an ideal tabletop setup, manifesting a confluence of time-reversal symmetry (${\mathcal T}$) breaking Abelian ($B$) and ${\mathcal T}$-preserving strain-induced internal axial ($b$) magnetic fields. In such a system, here we numerically compute two-terminal conductance ($G$), and four- as well as six-terminal Hall conductivity ($σ_{xy}$) for spinless fermions. On a flat graphene ($b=0$), the $B$ field produces quantized plateaus at $G=\pm |σ_{xy}|=(2n+1) e^2/h$, where $n=0,1,2, \cdots$. The strain induced $b$ field lifts the two-fold valley degeneracy of higher Landau levels and leads to the formation of additional even-integer plateaus at $G=\pm |σ_{xy}|= (2,4,\cdots)e^2/h$, when $B>b$. While the same sequence of plateaus is observed for $G$ when $b>B$, the numerical computation of $σ_{xy}$ in Hall bar geometries in this regime becomes unstable. A plateau at $G=σ_{xy}=0$ always appears with the onset of a charge-density-wave order, causing a staggered pattern of fermionic density between two sublattices of the honeycomb lattice.

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