arXiv subjects

Bitan Roy

Publications and source records attributed to Bitan Roy.

At least 91 records · Page 5Linked to original sources

arXiv2018

From Birefringent Electrons to a Marginal or Non-Fermi Liquid of Relativistic Spin-1/2 Fermions: An Emergent Superuniversality

We present the quantum critical theory of an interacting nodal Fermi-liquid of quasi-relativisitc pseudo-spin-3/2 fermions that have a non-interacting birefringent spectrum with two distinct Fermi velocities. When such quasiparticles interact with gapless bosonic degrees of freedom that mediate either the long-range Coulomb interaction or its short range component (responsible for spontaneous symmetry breaking), in the deep infrared or quantum critical regime in two dimensions the system is respectively described by a marginal- or a non-Fermi liquid of relativistic spin-1/2 fermions (possessing a unique velocity), and is always a marginal Fermi liquid in three dimensions. We consider a possible generalization of these scenarios to fermions with an arbitrary half-odd-integer spin, and conjecture that critical spin-1/2 excitations represent a superuniversal description of the entire family of interacting quasi-relativistic fermions.

cond-mat.mes-hall↗

arXiv2018

Collisionless Transport Close to a Fermionic Quantum Critical Point in Dirac Materials

Quantum transport close to a critical point is a fundamental, but enigmatic problem due to fluctuations, persisting at all length scales. We report the scaling of optical conductivity (OC) in the \emph{collisionless} regime ($\hbar ω\gg k_B T$) in the vicinity of a relativistic quantum critical point, separating two-dimensional ($d=2$) massless Dirac fermions from a fully gapped insulator or superconductor. Close to such critical point gapless fermionic and bosonic excitations are strongly coupled, leading to a \emph{universal} suppression of the inter-band OC as well as of the Drude peak (while maintaining its delta function profile) inside the critical regime, which we compute to the leading order in $1/N_f$- and $ε$-expansions, where $N_f$ counts fermion flavor number and $ε=3-d$. Correction to the OC at such a non-Gaussian critical point due to the long-range Coulomb interaction and generalizations of these scenarios to a strongly interacting three-dimensional Dirac or Weyl liquid are also presented, which can be tested numerically and possibly from non-pertubative gauge-gravity duality, for example.

cond-mat.mes-hall↗

arXiv2018

Incompressible Even Denominator Fractional Quantum Hall States in the Zeroth Landau Level of Monolayer Graphene

Incompressible even denominator fractional quantum Hall states at fillings $ν= \pm \frac{1}{2}$ and $ν= \pm \frac{1}{4}$ have been recently observed in monolayer graphene. We use a Chern-Simons description of multi-component fractional quantum Hall states in graphene to investigate the properties of these states and suggest variational wavefunctions that may describe them. We find that the experimentally observed even denominator fractions and standard odd fractions (such as $ν=1/3, 2/5$, etc.) can be accommodated within the same flux attachment scheme and argue that they may arise from sublattice or chiral symmetry breaking orders (such as charge-density-wave and antiferromagnetism) of composite Dirac fermions, a phenomenon unifying integer and fractional quantum Hall physics for relativistic fermions. We also discuss possible experimental probes that can narrow down the candidate broken symmetry phases for the fractional quantum Hall states in the zeroth Landau level of monolayer graphene.

cond-mat.str-el↗

arXiv2018

Global Phase Diagram of a Dirty Weyl Liquid and Emergent Superuniversality

Pursuing complementary field-theoretic and numerical methods, we here paint the global phase diagram of a three-dimensional dirty Weyl system. The generalized Harris criterion, augmented by a perturbative renormalization-group (RG) analysis shows that weak disorder is an irrelevant perturbation at the Weyl semimetal(WSM)-insulator quantum critical point (QCP). But, a metallic phase sets in through a quantum phase transition (QPT) at strong disorder across a multicritical point (MCP). The field theoretic predictions for the correlation length exponent $ν=2$ and dynamic scaling exponent $z=5/4$ at this MCP are in good agreement with the ones extracted numerically, yielding $ν=1.98 \pm 0.10$ and $z=1.26 \pm 0.05$, from the scaling of the average density of states (DOS). Deep inside the WSM phase, generic disorder is also an irrelevant perturbation, while a metallic phase appears at strong disorder through a QPT. We here demonstrate that in the presence of generic, but strong disorder the WSM-metal QPT is ultimately always characterized by the exponents $ν=1$ and $z=3/2$ (to one-loop order), originating from intra-node or chiral symmetric (e.g., regular and axial potential) disorder. We here anchor such emergent \emph{chiral superuniversality} through complementary RG calculations, controlled via $ε$-expansions, and numerical analysis of average DOS across WSM-metal QPT. In addition, we also discuss a subsequent QPT (at even stronger disorder) of a Weyl metal into an Anderson insulator by numerically computing the typical DOS at zero energy. The scaling behavior of various physical observables, such as residue of quasiparticle pole, dynamic conductivity, specific heat, Gr$\ddot{\mbox{u}}$neisen ratio, inside various phases as well as across various QPTs in the global phase diagram of a dirty Weyl liquid are discussed.

cond-mat.mes-hall↗

arXiv2018

Itinerant quantum multi-criticality of two dimensional Dirac fermions

We analyze emergent quantum multi-criticality for strongly interacting, massless Dirac fermions in two spatial dimensions ($d=2$) within the framework of Gross-Neveu-Yukawa models, by considering the competing order parameters that give rise to fully gapped (insulating or superconducting) ground states. We focus only on those competing orders, which can be rotated into each other by generators of an exact or emergent chiral symmetry of massless Dirac fermions, and break $O(S_1)$ and $O(S_2)$ symmetries in the ordered phase. Performing a renormalization group analysis by using the $ε=(3-d)$ expansion scheme, we show that all the coupling constants in the critical hyperplane flow toward a new attractive fixed point, supporting an \emph{enlarged} $O(S_1+S_2)$ chiral symmetry. Such a fixed point acts as an exotic quantum multi-critical point (MCP), governing the \emph{continuous} semimetal-insulator as well as insulator-insulator (for example antiferromagnet to valence bond solid) quantum phase transitions. In comparison with the lower symmetric semimetal-insulator quantum critical points, possessing either $O(S_1)$ or $O(S_2)$ chiral symmetry, the MCP displays enhanced correlation length exponents, and anomalous scaling dimensions for both fermionic and bosonic fields. We discuss the scaling properties of the ratio of bosonic and fermionic masses, and the increased dc resistivity at the MCP. By computing the scaling dimensions of different local fermion bilinears in the particle-hole channel, we establish that most of the four fermion operators or generalized density-density correlation functions display faster power law decays at the MCP compared to the free fermion and lower symmetric itinerant quantum critical points. Possible generalization of this scenario to higher dimensional Dirac fermions is also outlined.

cond-mat.str-el↗

arXiv2018

Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension

We compute the effects of generic short-range interactions on gapless electrons residing at the quantum critical point separating a two-dimensional Dirac semimetal (DSM) and a symmetry-preserving band insulator (BI). The electronic dispersion at this critical point is anisotropic ($E_{\mathbf k}=\pm \sqrt{v^2 k^2_x + b^2 k^{2n}_y}$ with $n=2$), which results in unconventional scaling of physical observables. Due to the vanishing density of states ($\varrho(E) \sim |E|^{1/n}$), this anisotropic semimetal (ASM) is stable against weak short-range interactions. However, for stronger interactions the direct DSM-BI transition can either $(i)$ become a first-order transition, or $(ii)$ get avoided by an intervening broken-symmetry phase (BSP). We perform a renormalization group analysis by perturbing away from the one-dimensional limit with the small parameter $ε= 1/n$, augmented with a $1/n$ expansion (parametrically suppressing quantum fluctuations in higher dimension). We identify charge density wave (CDW), antiferromagnet (AFM) and singlet s-wave superconductor as the three dominant candidates for the BSP. The onset of any such order at strong coupling $(\sim ε)$ takes place through a continuous quantum phase transition across multicritical point. We also present the phase diagram of an extended Hubbard model for the ASM, obtained via the controlled deformation of its counterpart in one dimension. The latter displays spin-charge separation and instabilities to CDW, spin density wave, and Luther-Emery liquid phases at arbitrarily weak coupling. The spin density wave and Luther-Emery liquid phases deform into pseudospin SU(2)-symmetric quantum critical points separating the ASM from the AFM and superconducting orders, respectively. Our results can be germane for a uniaxially strained honeycomb lattice or organic compound $α$-(BEDT-TTF)$_2\text{I}_3$.

cond-mat.str-el↗

arXiv2017

Dissolution of topological Fermi arcs in a dirty Weyl semimetal

Weyl semimetals (WSMs) have recently attracted a great deal of attention as they provide condensed matter realization of chiral anomaly, feature topologically protected Fermi arc surface states and sustain sharp chiral Weyl quasiparticles up to a critical disorder at which a continuous quantum phase transition (QPT) drives the system into a metallic phase. We here numerically demonstrate that with increasing strength of disorder the Fermi arc gradually looses its sharpness, and close to the WSM-metal QPT it completely dissolves into the metallic bath of the bulk. Predicted topological nature of the WSM-metal QPT and the resulting bulk-boundary correspondence across this transition can directly be observed in angle-resolved-photo-emmision-spectroscopy (ARPES) and Fourier transformed scanning-tunneling-microscopy (STM) measurements by following the continuous deformation of the Fermi arcs with increasing disorder in recently discovered Weyl materials.

cond-mat.mes-hall↗

arXiv2017

Optical conductivity of an interacting Weyl liquid in the collisionless regime

Optical conductivity (OC) can serve as a measure of correlation effects in a wide range of condensed matter systems. We here show that the long-range tail of the Coulomb interaction yields a universal correction to the OC in a three-dimensional Weyl semimetal $σ(Ω)=σ_0(Ω)\left[ 1+\frac{1}{N+1} \right]$, where of $σ_0(Ω)=Ne^2_0 Ω/(12 h v)$ is the OC in the non-interacting system, with $v$ as the actual (renormalized) Fermi velocity of Weyl quasiparticles at frequency $Ω$, and $e_0$ is the electron charge in vacuum. Such universal enhancement of OC, which depends only on the number of Weyl nodes near the Fermi level ($N$), is a remarkable consequence of an intriguing conspiracy among the quantum-critical nature of an interacting Weyl liquid, marginal irrelevance of the long-range Coulomb interaction and the violation of hyperscaling in three dimensions, and can directly be measured in recently discovered Weyl as well as Dirac materials. By contrast, a local density-density interaction produces a non-universal correction to the OC, stemming from the non-renormalizable nature of the corresponding interacting field theory.

cond-mat.mes-hall↗

arXiv2017

Interacting line-node semimetal: Proximity effect and spontaneous symmetry breaking

Effects of short-range electronic interactions in a three-dimensional line-node semimetal that supports linearly dispersing quasiparticles around an isolated loop in the Brillouin zone are discussed. Due to vanishing density of states ($\varrho(E) \sim |E|$) various orderings in the bulk of the system, such as the antiferromagnet and charge-density-wave, set in for sufficiently strong onsite ($U$) and nearest-neighbor ($V$) repulsions, respectively. While onset of these two orderings from the semimetallic phase takes place through continuous quantum phase transitions, a first-order transition separates two ordered phases. By contrast, topologically protected drumhead shaped surface states can undergo charge or spin orderings, depending on relative strength of $U$ and $V$, even when they are sufficiently weak. Such surface orderings as well as weak long-range Coulomb interaction can be conducive to spontaneous symmetry breaking in the bulk for weaker interactions. We numerically establish such proximity effect driven spontaneous symmetry breaking in the bulk for subcritical strength of interactions due to flat surface band and also discuss possible superconducting orders in this system.

cond-mat.mes-hall↗

arXiv2017

Global phase diagram of a three dimensional dirty topological superconductor

We investigate the phase diagram of a three-dimensional, time-reversal symmetric topological superconductor in the presence of charge impurities and random $s$-wave pairing. Combining complimentary field theoretic and numerical methods, we show that the quantum phase transition between two topologically distinct paired states (or thermal insulators), described by thermal Dirac semimetal, remains unaffected in the presence of sufficiently weak generic randomness. At stronger disorder, however, these two phases are separated by an intervening thermal metallic phase of diffusive Majorana fermions. We show that across the insulator-insulator and metal-insulator transitions, normalized thermal conductance displays single parameter scaling, allowing us to numerically extract the critical exponents across them. The pertinence of our study in strong spin-orbit coupled, three-dimensional doped narrow gap semiconductors, such as Cu$_x$Bi$_2$Se$_3$, is discussed.

cond-mat.mes-hall↗

arXiv2017

Interacting Weyl fermions: Phases, phase transitions and global phase diagram

We study the effects of short-range interactions on a generalized three-dimensional Weyl semimetal, where the band touching points act as the (anti)monopoles of Abelian Berry curvature of strength $n$. We show that any local interaction has a \emph{negative} scaling dimension $-2/n$. Consequently all Weyl semimetals are stable against weak short-range interactions. For sufficiently strong interactions, we demonstrate that the Weyl semimetal either undergoes a first order transition into a band insulator or a continuous transition into a symmetry breaking phase. A translational symmetry breaking axion insulator and a rotational symmetry breaking semimetal are two prominent candidates for the broken symmetry phase. At the one-loop order, the correlation length exponent for continuous transitions is $ν=n/2$, indicating their non-Gaussian nature for any $n>1$. We also discuss the scaling of the thermodynamic and transport quantities in general Weyl semimetals as well as inside the broken symmetry phases.

cond-mat.str-el↗

arXiv2017

Competing orders and topology in the global phase diagram of pyrochlore iridates

Strong electronic interactions and spin orbit coupling can be conducive for realizing novel broken symmetry phases supporting quasiparticles with nontrivial band topology. 227 pyrochlore iridates provide a suitable material platform for studying such emergent phenomena where both topology and competing orders play important roles. In contrast to the most members of this material class, which are thought to display "all-in all-out" (AIAO) type magnetically ordered low-temperature insulating ground states, Pr$_2$Ir$_2$O$_7$ remains metallic while exhibiting "spin ice" (SI) correlations at low temperatures. Additionally, this is the only 227 iridate compound, which exhibits a large anomalous Hall effect (AHE) along [1,1,1] direction below 1.5 K, without possessing any measurable magnetic moment. By focusing on the normal state of 227 iridates, described by a parabolic semimetal with quadratic band touching, we use renormalization group analysis, mean-field theory, and phenomenological Landau theory as three complementary methods to construct a global phase diagram in the presence of generic local interactions among itinerant electrons of Ir ions. While the global phase diagram supports several competing multipolar orders, motivated by the phenomenology of 227 iridates we particularly emphasize the competition between AIAO and SI orders and how it can cause a mixed phase with "three-in one-out" (3I1O) spin configurations. In terms of topological properties of Weyl quasiparticles of the 3I1O state, we provide an explanation for the magnitude and the direction of the observed AHE in Pr$_2$Ir$_2$O$_7$. We propose a strain induced enhancement of the onset temperature for AHE in thin films of Pr$_2$Ir$_2$O$_7$ and additional experiments for studying competing orders in the vicinity of the metal-insulator transition.

cond-mat.str-el↗

arXiv2016

Weyl fermions with arbitrary monopole in magnetic fields: Landau levels, longitudinal magnetotransport, and density-wave ordering

We theoretically address the effects of strong magnetic fields in three-dimensional Weyl semimetals (WSMs) built out of Weyl nodes with a monopole charge $n$. For $n=1$, $2$, and $3$ we realize single, double, and triple WSM, respectively, and the monopole charge $n$ determines the integer topological invariant of the WSM. Within the linearized continuum description, the quasiparticle spectrum is then composed of Landau levels (LLs), containing exactly $n$ number of chiral zeroth Landau levels (ZLLs), irrespective of the orientation of the magnetic field. In the presence of strong backscattering, for example, (due to quenched disorder associated with random impurities), these systems generically give rise to longitudinal magnetotransport. Restricting ourselves to the quantum limit (and assuming only the subspace of the ZLLs to be partially filled) and mainly accounting for Gaussian impurities, we show that the longitudinal magnetoconductivity (LMC) in all members of the Weyl family displays a positive linear-$B$ scaling, when the field is applied along the axis that separates the Weyl nodes. But, in double and triple WSM, LMC displays a smooth crossover to a nonlinear $B$-dependence as the field is tilted away from such a high-symmetry direction. In addition, due to the enhanced density of states, the LL quantization can trigger instabilities toward the formation of translational symmetry breaking density-wave orderings for sufficiently weak interaction (BCS instability), which gaps out the ZLLs. Concomitantly as the temperature (magnetic field) is gradually decreased (increased) the LMC becomes negative. Thus WSMs with arbitrary monopole charge ($n$) can host an intriguing interplay of LL quantization, longitudinal magnetotransport (a possible manifestation of one-dimensional chiral or axial anomaly), and density-wave ordering, when placed in a strong magnetic field.

cond-mat.mtrl-sci↗

arXiv2016

Quantum phases of interacting electrons in three-dimensional dirty Dirac semimetals

We theoretically study the stability of three dimensional Dirac semimetals against short-range electron-electron interaction and quenched time-reversal symmetric disorder (but excluding mass disorder). First we focus on the clean interacting and the noninteracting dirty Dirac semimetal separately, and show that they support two distinct quantum critical points. Using renormalization group techniques, we find that while interaction driven quantum critical points are \emph{Gaussian} (mean-field) in nature, describing quantum phase transitions into various broken symmetry phases, the ones controlled by disorder are \emph{non-Gaussian}, capturing the transition to a metallic phase. We classify such diffusive quantum critical points based on the transformation of disorder vertices under a \emph{continuous} chiral rotation. Our wek coupling renormalization group analysis suggests that two distinct quantum critical points are stable in an interacting dirty Dirac semimetal (with chiral symmetric randomness), and a multicritical point (at finite interaction and disorder) results from their interplay. By contrast, the chiral symmetry breaking disorder driven critical point is unstable against weak interactions. Effects of weak disorder on the ordering tendencies in Dirac semimetal are analyzed. The clean interacting critical points, however, satisfy the \emph{Harris criterion}, and are therefore expected to be unstable against bond disorder. Although our weak coupling analysis is inadequate to establish the ultimate stability of these fixed points in the strong coupling regime (when both interaction and disorder are strong), they can still govern crossover behaviors in Dirac semimetals over a large length scale, when either interaction or randomness is sufficiently weak.

cond-mat.mes-hall↗

arXiv2016

Universal optical conductivity of a disordered Weyl semimetal

Topological Weyl semimetals, besides manifesting chiral anomaly, can also accommodate a disorder-driven unconventional quantum phase transition into a metallic phase. A fundamentally and practically important question in this regard concerns an experimentally measurable quantity that can clearly distinguish these two phases. We show that the optical conductivity while serving this purpose can also play the role of a bonafide order parameter across such disorder-driven semimetal-metal quantum phase transition by virtue of displaying distinct scaling behavior in semimetallic and metallic phases, as well as inside the quantum critical fan supporting a non-Fermi liquid. We demonstrate that the correction to dielectric constant and optical conductivity in a dirty Weyl semimetal due to weak disorder is independent of the actual nature of point-like impurity scatterers. Therefore, optical conductivity can be used as an experimentally measurable quantity to study the critical properties and to pin the universality class of the disorder-driven quantum phase transition in Weyl semimetals.

cond-mat.mes-hall↗

arXiv2016

Note on "Quantum superconducting criticality in graphene and topological insulators"

We correct our previous conclusion regarding the fate of a charged quantum critical point across the superconducting transition for two dimensional massless Dirac fermion. Within the leading order $ε$ expansion, we now find that the requisite number of four-component Dirac fermion flavors ($N_f$) for the continuous phase transition through a charged critical point is $N_f>18.2699$. For $N_f\geq1/2$, the critical number of bosonic flavors for this transition is significantly reduced as compared to the value determined in the absence of the Dirac fermions in the theory.

cond-mat.mes-hall↗

arXiv2016

Ferromagnetism and glassiness on the surface of topological insulators

We investigate the nature of the ordering among magnetic adatoms, randomly deposited on the surface of topological insulators. Restricting ourselves to dilute impurity and weak coupling (between itinerant fermion and magnetic impurities) limit, we show that for arbitrary amount of chemical doping away from the apex of the surface Dirac cone the magnetic impurities tend to arrange themselves in a spin-density-wave pattern, with the periodicity approximately $π/k_F$, where $k_F$ is the Fermi wave vector, when magnetic moment for impurity adatoms is isotropic. However, when magnetic moment possesses strong Ising or easy-axis anisotropy, pursuing both analytical and numerical approaches we show that the ground state is ferromagnetic for low to moderate chemical doping, despite the fragmentation of the system into multiple ferromagnetic islands. For high doping away from the Dirac point as well, the system appears to fragment into many ferromagnetic islands, but the magnetization in these islands is randomly distributed. Such magnetic ordering with net zero magnetization, is referred here as ferromagnetic spin glass, which is separated from the pure ferromagnet state by a first order phase transition. We generalize our analysis for cubic topological insulators (supporting three Dirac cones on a surface) and demonstrate that the nature of magnetic orderings and the transition between them remains qualitatively the same. We also discuss the possible relevance of our analysis to recent experiments.

cond-mat.mes-hall↗

arXiv2016

Continuous and discontinuous topological quantum phase transitions

The continuous quantum phase transition between noninteracting, time-reversal symmetric topological and trivial insulators in three dimensions is described by the massless Dirac fermion. We address the stability of this quantum critical point against short range electronic interactions by using renormalization group analysis and mean field theory. For sufficiently weak interactions, we show that the nature of the direct transition remains unchanged. Beyond a critical strength of interactions we find that either (i) there is a direct first order transition between two time reversal symmetric insulators or (ii) the direct transition is eliminated by an intervening time reversal and inversion odd "axionic" insulator. We also demonstrate the existence of an interaction driven first order quantum phase transition between topological and trivial gapped states in lower dimensions.

cond-mat.mes-hall↗