arXiv subjects

Pallab Goswami

Publications and source records attributed to Pallab Goswami.

At least 37 records · Page 2Linked to original sources

arXiv2017

Two dimensional metallic phases from disordered QED$_3$

Metallic phases have been observed in several disordered two dimensional (2d) systems, including thin films near superconductor-insulator transitions and quantum Hall systems near plateau transitions. The existence of 2d metallic phases at zero temperature generally requires an interplay of disorder and interaction effects. Consequently, experimental observations of 2d metallic behavior have largely defied explanation. We formulate a general stability criterion for strongly interacting, massless Dirac fermions against disorder, which describe metallic ground states with vanishing density of states. We show that (2+1)-dimensional quantum electrodynamics (QED$_3$) with a large, even number of fermion flavors remains metallic in the presence of weak scalar potential disorder due to the dynamic screening of disorder by gauge fluctuations. We also show that QED$_3$ with weak mass disorder exhibits a stable, dirty metallic phase in which both interactions and disorder play important roles.

cond-mat.str-el↗

arXiv2017

Single particle excitations in disordered Weyl fluids

We theoretically study the single particle Green function of a three dimensional disordered Weyl semimetal using a combination of techniques. These include analytic $T$-matrix and renormalization group methods with complementary regimes of validity, and an exact numerical approach based on the kernel polynomial technique. We show that at any nonzero disorder, Weyl excitations are not ballistic: they instead have a nonzero linewidth that for weak short-range disorder arises from non-perturbative resonant impurity scattering. Perturbative approaches find a quantum critical point between a semimetal and a metal at a finite disorder strength, but this transition is avoided due to nonperturbative effects. At moderate disorder strength and intermediate energies the avoided quantum critical point renormalizes the scaling of single particle properties. In this regime we compute numerically the anomalous dimension of the fermion field and find $η= 0.13 \pm 0.04$, which agrees well with a renormalization group analysis ($η= 0.125$). Our predictions can be directly tested by ARPES and STM measurements in samples dominated by neutral impurities.

cond-mat.dis-nn↗

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↗

arXiv2017

Superuniversality of topological quantum phase transition and global phase diagram of dirty topological systems in three dimensions

The quantum phase transition between two clean, non interacting topologically distinct gapped states in three dimensions is governed by a massless Dirac fermion fixed point, irrespective of the underlying symmetry class, and this constitutes a remarkably simple example of superuniversality. For a sufficiently weak disorder strength, we show that the massless Dirac fixed point is at the heart of the robustness of superuniversality. We establish this by considering both perturbative and nonperturbative effects of disorder. The superuniversality breaks down at a critical strength of disorder, beyond which the topologically distinct localized phases become separated by a delocalized diffusive phase. In the global phase diagram, the disorder controlled fixed point where superuniversality is lost, serves as a multicritical point, where the delocalized diffusive and two topologically distinct localized phases meet and the nature of the localization-delocalization transition depends on the underlying symmetry class. Based on these features we construct the global phase diagrams of noninteracting, dirty topological systems in three dimensions. We also establish a similar structure of the phase diagram and the superuniversality for weak disorder in higher spatial dimensions. By noting that $1/r^2$ power-law correlated disorder acts as a marginal perturbation for massless Dirac fermion in any spatial dimension $d$, we have established a general renormalization group framework for addressing disorder driven critical phenomena for fixed spatial dimension $d > 2$.

cond-mat.dis-nn↗

arXiv2016

Quantum phases of disordered three-dimensional Majorana-Weyl fermions

The gapless Bogoliubov-de Gennes (BdG) quasiparticles of a clean three dimensional spinless $p_x+ip_y$ superconductor provide an intriguing example of a thermal Hall semimetal (ThSM) phase of Majorana-Weyl fermions in class D of the Altland-Zirnbauer symmetry classification; such a phase can support a large anomalous thermal Hall conductivity and protected surface Majorana-Fermi arcs at zero energy. We study the effect of quenched disorder on such a topological phase with both numerical and analytical methods. Using the kernel polynomial method, we compute the average and typical density of states for the BdG quasiparticles; based on this, we construct the disordered phase diagram. We show for infinitesimal disorder, the ThSM is converted into a diffusive thermal Hall metal (ThDM) due to rare statistical fluctuations. Consequently, the phase diagram of the disordered model only consists of ThDM and thermal insulating phases. Nonetheless, there is a cross-over at finite energies from a ThSM regime to a ThDM regime, and we establish the scaling properties of the avoided quantum critical point which marks this cross-over. Additionally, we show the existence of two types of thermal insulators: (i) a trivial thermal band insulator (ThBI) [or BEC phase] supporting only exponentially localized Lifshitz states (at low energy), and (ii) a thermal Anderson insulator (AI) at large disorder strengths. We determine the nature of the two distinct localization transitions between these two types of insulators and ThDM.We also discuss the experimental relevance of our results for three dimensional, time reversal symmetry breaking, triplet superconducting states.

cond-mat.dis-nn↗

arXiv2016

Dynamic zero modes of Dirac fermions and competing singlet phases of antiferromagnetic order

In quantum spin systems, singlet phases often develop in the vicinity of an antiferromagnetic order. Typical settings for such problems arise when itinerant fermions are also present. In this work, we develop a theoretical framework for addressing such competing orders in an itinerant system, described by Dirac fermions strongly coupled to an O(3) nonlinear sigma model. We focus on two spatial dimensions, where upon disordering the antiferromagnetic order by quantum fluctuations the singular tunneling events also known as (anti)hedgehogs can nucleate competing singlet orders in the paramagnetic phase. In the presence of an isolated hedgehog configuration of the nonlinear sigma model field, we show that the fermion determinant vanishes as the dynamic Euclidean Dirac operator supports fermion zero modes of definite chirality. This provides a topological mechanism for suppressing the tunneling events. Using the methodology of quantum chromodynamics, we evaluate the fermion determinant in the close proximity of magnetic quantum phase transition, when the antiferromagnetic order parameter field can be described by a dilute gas of hedgehogs and antihedgehogs. We show how the precise nature of emergent singlet order is determined by the overlap between dynamic fermion zero modes of opposite chirality, localized on the hedgehogs and antihedgehogs. For a Kondo-Heisenberg model on the honeycomb lattice, we demonstrate the competition between spin Peierls order and Kondo singlet formation, thereby elucidating its global phase diagram. We also discuss other physical problems that can be addressed within this general framework.

cond-mat.str-el↗

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↗

arXiv2016

A calculation for polar Kerr effect in high temperature cuprate superconductors

A mechanism is proposed for the tantalizing evidence of polar Kerr effect in a class of high temperature superconductors--the signs of the Kerr angle from two opposite faces of the same sample are identical and magnetic field training is non-existent. The mechanism does not break global time reversal symmetry, as in an antiferromagnet, and results in zero Faraday effect. It is best understood in a phenomenological model of bilayer cuprates, such as YBCO, in which intra-bilayer tunneling nucleates a chiral d-density wave such that the individual layers have opposite chirality. Although specific to the chiral d-density wave, the mechanism may be more general to any quasi-two-dimensional orbital antiferromagnet in which time reversal symmetry is broken in each plane, but not when averaged macroscopically.

cond-mat.str-el↗

arXiv2016

Disorder driven itinerant quantum criticality of three dimensional massless Dirac fermions

Progress in the understanding of quantum critical properties of itinerant electrons has been hindered by the lack of effective models which are amenable to controlled analytical and numerically exact calculations. Here we establish that the disorder driven semimetal to metal quantum phase transition of three dimensional massless Dirac fermions could serve as a paradigmatic toy model for studying itinerant quantum criticality, which is solved in this work by exact numerical and approximate field theoretic calculations. As a result, we establish the robust existence of a non-Gaussian universality class, and also construct the relevant low energy effective field theory that could guide the understanding of quantum critical scaling for many strange metals. Using the kernel polynomial method (KPM), we provide numerical results for the calculated dynamical exponent ($z$) and correlation length exponent ($ν$) for the disorder-driven semimetal (SM) to diffusive metal (DM) quantum phase transition at the Dirac point for several types of disorder, establishing its universal nature and obtaining the numerical scaling functions in agreement with our field theoretical analysis.

cond-mat.dis-nn↗

arXiv2015

Nernst and magneto-thermal conductivity in a lattice model of Weyl fermions

Weyl semimetals (WSM) are topologically protected three dimensional materials whose low energy excitations are linearly dispersing massless Dirac fermions, possessing a non-trivial Berry curvature. Using semi-classical Boltzmann dynamics in the relaxation time approximation for a lattice model of time reversal (TR) symmetry broken WSM, we compute both magnetic field dependent and anomalous contributions to the Nernst coefficient. In addition to the magnetic field dependent Nernst response, which is present in both Dirac and Weyl semimetals, we show that, contrary to previous reports, the TR-broken WSM also has an anomalous Nernst response due to a non-vanishing Berry curvature. We also compute the thermal conductivities of a WSM in the Nernst (${\nabla T} \perp \mathbf{B}$) and the longitudinal (${\nabla T} \parallel \mathbf{B}$) set-up and confirm from our lattice model that in the parallel set-up, the Wiedemann-Franz law is violated between the longitudinal thermal and electrical conductivities due to chiral anomaly.

cond-mat.str-el↗

arXiv2015

Topological Weyl Superconductor to Diffusive Thermal Hall Metal Crossover in the B-Phase of UPt$_3$

The recent phase sensitive measurements in the superconducting $B$-phase of UPt$_3$ provide strong evidence for the triplet, chiral $k_z(k_x \pm ik_y)^2$ pairing symmetries, which endow the Cooper pairs with orbital angular momentum projections $L _z= \pm 2$ along the $c$-axis. In the absence of disorder such pairing can support both line and point nodes, and both types of nodal quasiparticles exhibit nontrivial topology in the momentum space. The point nodes, located at the intersections of the closed Fermi surfaces with the $c$-axis, act as the double monopoles and the antimonopoles of the Berry curvature, and generalize the notion of Weyl quasiparticles. Consequently, the $B$ phase should support an anomalous thermal Hall effect, the polar Kerr effect, in addition to the protected Fermi arcs on the (1,0,0) and the (0,1,0) surfaces. The line node at the Fermi surface equator acts as a vortex loop in the momentum space and gives rise to the zero energy, dispersionless Andreev bound states on the (0,0,1) surface. At the transition from the $B$-phase to the $A$-phase, the time reversal symmetry is restored, and only the line node survives inside the $A$-phase. As both line and double-Weyl point nodes possess linearly vanishing density of states, we show that weak disorder acts as a marginally relevant perturbation. Consequently, an infinitesimal amount of disorder destroys the ballistic quasiparticle pole, while giving rise to a diffusive phase with a finite density of states at the zero energy. The resulting diffusive phase exhibits $T$-linear specific heat, and an anomalous thermal Hall effect. We predict that the low temperature thermodynamic and transport properties display a crossover between a ballistic thermal Hall semimetal and a diffusive thermal Hall metal.

cond-mat.supr-con↗

arXiv2015

Optical gyrotropy as a test for dynamic chiral magnetic effect of Weyl semimetals

Recent angle resolved photoemission spectroscopy measurements have identified an inversion symmetry breaking Weyl semimetal phase in TaAs and NbAs. In an inversion symmetry breaking Weyl semimetal the left and the right handed Weyl points can occur at different energies and the energy mismatch between the Weyl points of opposite chirality is known as the chiral chemical potential. In the presence of the chiral chemical potential, the nontrivial Berry curvature of the Weyl fermions gives rise to the \emph{dynamic} chiral magnetic effect. This describes how a time dependent magnetic field leads to an electrical current along the applied field direction, which is also proportional to the field strength. We derive a general formula for the dynamic chiral magnetic conductivity of the inversion symmetry breaking Weyl semimetal. We show that the measurement of the natural optical activity or rotary power provides a direct confirmation of the existence of the dynamic chiral magnetic effect in inversion symmetry breaking Weyl semimetals.

cond-mat.str-el↗

arXiv2015

Axial anomaly and longitudinal magnetoresistance of a generic three dimensional metal

We show that the emergence of the axial anomaly is a universal phenomenon for a generic three dimensional metal in the presence of parallel electric ($E$) and magnetic ($B$) fields. In contrast to the expectations of the classical theory of magnetotransport, this intrinsically quantum mechanical phenomenon gives rise to the longitudinal magnetoresistance for any three dimensional metal. However, the emergence of the axial anomaly does not guarantee the existence of negative longitudinal magnetoresistance. We show this through an explicit calculation of the longitudinal magnetoconductivity in the quantum limit using the Boltzmann equation, for both short-range neutral and long-range ionic impurity scattering processes. We demonstrate that the ionic scattering contributes a large positive magnetoconductivity $\propto B^2$ in the quantum limit, which can cause a strong negative magnetoresistance for any three dimensional or quasi-two dimensional metal. In contrast, the finite range neutral impurities and zero range point impurities can lead to both positive and negative longitudinal magnetoresistance depending on the underlying band structure. In the presence of both neutral and ionic impurities, the longitudinal magnetoresistance of a generic metal in the quantum limit initially becomes negative, and ultimately becomes positive after passing through a minimum. We discuss in detail the qualitative agreement between our theory and recent observations of negative longitudinal magnetoresistance in Weyl semimetals TaAs and TaP, Dirac semimetals Na$_3$Bi, Bi$_{1-x}$Sb$_x$, and ZrTe$_5$, and quasi-two dimensional metals PdCoO$_2$, $α$-(BEDT-TTF)$_2$I$_3$ which do not possess any bulk three dimensional Dirac or Weyl quasiparticles.

cond-mat.mes-hall↗

arXiv2015

Anderson localization and the quantum phase diagram of three dimensional disordered Dirac semimetals

We study the quantum phase diagram of a three dimensional non-interacting Dirac semimetal in the presence of either quenched axial or scalar potential disorder, by calculating the average and the typical density of states as well as the inverse participation ratio using numerically exact methods. We show that as a function of the disorder strength a half-filled (i.e. undoped) Dirac semimetal displays three distinct ground states, namely an incompressible semimetal, a compressible diffusive metal, and a localized Anderson insulator, in stark contrast to a conventional dirty metal that only supports the latter two phases. We establish the existence of two distinct quantum critical points, which respectively govern the semimetal-metal and the metal-insulator quantum phase transitions and also reveal their underlying multifractal nature. Away from half-filling the (doped) system behaves as a diffusive metal that can undergo Anderson localization only, which is shown by determining the mobility edge and the phase diagram in terms of energy and disorder.

cond-mat.dis-nn↗

arXiv2014

Disordered and interacting parabolic semimetals in two and three dimensions

A clean noninteracting parabolic semimetal is characterized by quadratic band touching between the conduction and the valence bands at isolated diabolic points in the Brillouin zone and describes a fermionic quantum critical system with dynamic exponent z=2. We consider the stability of such a semimetal against electronic interaction and quenched disorder using a perturbative renormalization group analysis for two and three spatial dimensions. For the noninteracting problem infinitesimally weak disorder leads to an Anderson insulator and a diffusive metal respectively in two and three dimensions. On the other hand, the long range Coulomb interaction causes an excitonic instability for the clean interacting problem towards a broken symmetry ground state in both dimensions. Our weak coupling analysis of the combined effects of disorder and interaction suggests the competition between a broken symmetry and a disorder controlled metallic or insulating states, but is inadequate for describing the quantum phase transitions among them. We discuss the relevance of our results for bilayer graphene and some 227 iridate compounds, and identify these materials as promising candidates for exploring novel disorder and interaction controlled quantum critical phenomena.

cond-mat.str-el↗

arXiv2014

Axionic superconductivity in three dimensional doped narrow gap semiconductors

We consider the competition between the conventional s-wave and the triplet Balian-Werthamer or the B-phase pairings in the doped three dimensional narrow gap semiconductors, such as $\mathrm{Cu}_x\mathrm{Bi}_2\mathrm{Se}_3$ and $\mathrm{Sn}_{1-x}\mathrm{In}_x\mathrm{Te}$. When the coupling constants of the two contending channels are comparable, we find a simultaneously time-reversal and parity violating $p + is$ state at low temperatures, which provides an example of dynamic axionic state of matter. In contradistinction to the time-reversal invariant, topological B-phase, the $p + is$ state possesses gapped Majorana fermions as the surface Andreev bound states, which give rise to an anomalous surface thermal Hall effect. The anomalous gravitational and electrodynamic responses of the $p+is$ state can be described by the $θ$ vacuum structure, where $θ\neq 0$ or $π$.

cond-mat.supr-con↗

arXiv2014

$Z_2$ index for gapless fermionic modes in the vortex core of three dimensional paired Dirac fermions

We consider the gapless modes along the vortex line of the fully gapped, momentum independent paired states of three-dimensional Dirac fermions. For this, we require the solution of fermion zero modes of the corresponding two-dimensional problem in the presence of a point vortex, in the plane perpendicular to the vortex line. Based on the spectral symmetry requirement for the existence of the zero mode, we identify the appropriate generalized Jackiw-Rossi Hamiltonians for different paired states. A four-dimensional generalized Jackiw-Rossi Hamiltonian possesses spectral symmetry with respect to an antiunitary operator, and gives rise to a single zero mode only for the {\em odd vorticity}, which is formally described by a $Z_2$ index. In the presence of generic perturbations such as chemical potential, Dirac mass, and Zeeman couplings, the associated two-dimensional problem for the odd parity topological superconducting state maps onto {\em two} copies of generalized Jackiw-Rossi Hamiltonian, and consequently an odd vortex binds two Majorana fermions. In contrast, there are no zero energy states for the topologically trivial $s$-wave superconductor in the presence of any chiral symmetry breaking perturbation in the particle-hole channel, such as regular Dirac mass. We show that the number of one-dimensional dispersive modes along the vortex line is also determined by the index of the associated two-dimensional problem. For an axial superfluid state in the presence of various perturbations, we discuss the consequences of the $Z_2$ index on the anomaly equations.

cond-mat.mes-hall↗