arXiv subjects

S. R. Hassan

Publications and source records attributed to S. R. Hassan.

At least 37 records · Page 2Linked to original sources

arXiv2017

Thermal transport across a continuous metal-insulator transition

The celebrated Wiedemann-Franz (WF) law is believed to be robust in metals as long as interactions between electrons preserve their fermion-quasiparticle character. We study thermal transport and the fate of the WF law close to a continuous metal-insulator transition (MIT) in the Falicov-Kimball model (FKM) using cluster-dynamical mean-field theory (CDMFT). Surprisingly, as for electrical transport, we find robust and novel quantum critical scaling in thermal transport across the MIT. We unearth the deeper reasons for these novel findings in terms of (i) the specific structure of energy-current correlations for the FKM and (ii) the microscopic electronic processes which facil- itate energy transport while simultaneously blocking charge transport close to the MIT. However, within (C)DMFT, we also find that the WF law survives at T=0 in the incoherent metal right up to the MIT, even in absence of Landau quasiparticles.

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arXiv2017

Quantum critical magneto-transport at a continuous metal-insulator transition

In contrast to the seminal weak localization prediction of a non-critical Hall constant ($R_{H}$) at the Anderson metal-insulator transition (MIT), $R_{H}$ in quite a few real disordered systems exhibits both, a strong $T$-dependence and critical scaling near their MIT. Here, we investigate these issues in detail within a non-perturbative "strong localization" regime using cluster-dynamical mean field theory (CDMFT). We uncover $(i)$ clear and unconventional quantum-critical scaling of the $γ$-function, finding that $γ(g_{xy})\simeq$ log$(g_{xy})$ over a wide range spanning the continuous MIT, very similar to that seen for the longitudinal conductivity, $(ii)$ strongly $T$-dependent and clear quantum critical scaling in both transverse conductivity and $R_{H}$ at the MIT. We find that these surprising results are in comprehensive and very good accord with signatures of a novel kind of localization in disordered NbN near the MIT, providing substantial support for our "strong" localization view.

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arXiv2017

Quantum critical transport at a continuous metal-insulator transition

In contrast to the first-order correlation-driven Mott metal-insulator transition (MIT), contin- uous disorder-driven transitions are intrinsically quantum critical. Here, we investigate transport quantum criticality in the Falicov-Kimball model, a representative of the latter class in the "strong disorder" category. Employing cluster-dynamical mean-field theory (CDMFT), we find clear and anomalous quantum critical scaling behavior manifesting as perfect mirror symmetry of scaling curves on both sides of the MIT. Surprisingly, we find that the beta-function, \b{eta}(g), scales like log(g) deep into the bad-metallic phase as well, providing sound unified basis for these findings. We argue that such "strong localization" quantum criticality may manifest in real three-dimensional systems where disorder effects are more important than electron-electron interactions.

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arXiv2017

Real-space cluster dynamical mean-field approach to the Falicov-Kimball model: An alloy-analogy approach

It is long known that the best single-site coherent potential approximation (CPA) falls short of describing Anderson localization (AL). Here, we study a binary alloy disorder (or equivalently, a spinless Falicov-Kimball (FK)) model and construct a dominantly analytic cluster extension that treats intra-cluster ($1/d$, $d$=spatial dimension) correlations exactly. We find that, in general, the irreducible two-particle vertex exhibits clear non-analyticities before the band-splitting transition of the Hubbard type occurs, signaling onset of an unusual type of localization at strong coupling. Using time-dependent response to a sudden local quench as a diagnostic, we find that the long-time wave function overlap changes from a power-law to an anomalous form at strong coupling, lending additional support to this idea. Our results also imply such novel "strong" localization in the equivalent FK model, the simplest interacting fermion system.

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arXiv2017

Translational symmetry breaking and the disintegration of the Hofstadter butterfly

We study the effect of interactions on the Hofstadter butterfly of the honeycomb lattice. We show that the interactions induce charge ordering that breaks the translational and rotational symmetries of the system. These phase transitions are prolific and occur at many values of the flux and particle density. The breaking of the translational symmetry introduces a new length scale in the problem and this affects the energy band diagram resulting in the disintegration of the fractal structure in the energy flux plot, the Hofstadter butterfly. This disintegration increases with increase in the interaction strength. Many of these phase transitions are accompanied with change in the Hall conductivity. Consequently, the disintegration of the Hofstadter butterfly is manifested in the Landau fan diagram also.

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arXiv2016

Realization of a "Two Relaxation Rates" in the Hubbard-Falicov-Kimball Model

A single transport relaxation rate governs the decay of both, longitudinal and Hall currents in Landau Fermi Liquids (LFL). Breakdown of this fundamental feature, first observed in cuprates and subsequently in other three-dimensional correlated systems close to (partial or complete) Mott metal-insulator transitions, played a pivotal role in emergence of a non-Landau Fermi liquid paradigm in higher dimensions $D(>1)$. Motivated hereby, we explore the emergence of this "two relaxation rates" scenario in the Hubbard-Falicov-Kimball model (HFKM) using the dynamical mean-field theory (DMFT). Specializing to $D=3$, we find, beyond a critical FK interaction, that two distinct relaxation rates governing distinct temperature ($T$) dependence of the longitudinal and Hall currents naturally emerges in the non-LFL metal. We rationalize this surprising finding by an analytical analysis of the structure of charge and spin correlations in the underlying impurity problem, and point out good accord with observations in the famed case of V$_{2-y}$O$_3$ near the MIT.

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arXiv2016

Exploring Novel Quantum Criticality in Strained Graphene

Strain tuning is increasingly being recognized as a clean tuning parameter to induce novel behavior in quantum matter. Motivated by the possibility of straining graphene up to $20$ percent, we investigate novel quantum criticality due to interplay between strain-induced anisotropic band structure and critical antiferromagnetic spin fluctuations (AFSF) in this setting. We detail how this interplay drives $(i)$ a quantum phase transition (QPT) between the Dirac-semimetal-incoherent pseudogapped metal-correlated insulator as a function of strain ($ε$), and $(ii)$ critical AFSF-driven divergent nematic susceptibility near critical strain ($ε_{c}$) manifesting as critical singularities in magneto-thermal expansion and Grüneisen co-efficients. The correlated band insulator at large strain affords realization of a two-dimensional dimerized spin-singlet state due to this interplay, and we argue how doping such an insulator can lead to a spin-charge separated metal, leading to anomalous metallicity and possible unconventional superconductivity. On a wider front, our work serves to illustrate the range of novel states realizable by strain-tuning quantum materials.

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arXiv2016

Spin liquid like Raman signatures in hyperkagome iridate Na$_4$Ir$_3$O$_8$

Combining Raman scattering measurements with mean field calculations of the Raman response we show that Kitaev-like magnetic exchange is dominant in the hyperkagome iridate Na$_4$Ir$_3$O$_8$. In the measurements we observe a broad Raman band at $\sim$~3500 cm$^{-1}$ with a band-width $\sim 1700$~cm$^{-1}$. Calculations of the Raman response of the Kitaev-Heisenberg model on the hyperkagome lattice shows that the experimental observations are consistent with calculated Raman response where Kitaev exchange interaction ($J_K$) is much larger than the Heisenberg term J$_1$ ($J_1/J_K \sim 0.1$). A comparison with the theoretical model gives an estimate of the Kitaev exchange interaction parameter.

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arXiv2016

Effects of Interaction in the Hofstadter regime of the honeycomb lattice

We investigate phases of spinless fermions on the honeycomb lattice with nearest neighbor interaction in the Hofstadter regime. The interaction induces incompressible nematic and ferri-electric phases with broken translation symmetry. Some of the transitions are accompanied by changes in the Hall conductivity. We study pair correlations and show that the quantum metric, averaged over the Brillouin zone, characterizes the shape of the pair correlation function.

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arXiv2016

Raman Signatures of Strong Kitaev Exchange Correlations in (Na$_{1-x}$Li$_x$)$_2$IrO$_3$ : Experiments and Theory

Inelastic light scattering studies on single crystals of (Na$_{1-x}$Li$_x$)$_2$IrO$_3$ ($x = 0, 0.05$ and $0.15$) show a polarization independent broad band at $\sim $~2750 cm$^{-1}$ with a large band-width $\sim 1800$~cm$^{-1}$. For Na$_2$IrO$_3$ the broad band is seen for temperatures $ \leq 200$~K and persists inside the magnetically ordered state. For Li doped samples, the intensity of this mode increases, shifts to lower wave-numbers and persists to higher temperatures. Such a mode has recently been predicted (Knolle et.al.) as a signature of the Kitaev spin liquid. We assign the observation of the broad band to be a signature of strong Kitaev-exchange correlations. The fact that the broad band persists even inside the magnetically ordered state suggests that dynamically fluctuating moments survive even below $T_{N}$. This is further supported by our mean field calculations. The Raman response calculated in mean field theory shows that the broad band predicted for the spin liquid state survives in the magnetically ordered state near the zigzag-spin liquid phase boundary. A comparison with the theoretical model gives an estimate of the Kitaev exchange interaction parameter to be $J_K\approx 57$~meV.

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arXiv2015

Antiferromagnetism in the Hubbard model on the honeycomb lattice: a Two-Particle Self-Consistent study

The semimetal to antiferromagnet quantum phase transition of the Hubbard model on the honeycomb lattice has come to the forefront in the context of the proposal that a semimetal to spin liquid transition can occur before the transition to the antiferromagnetic phase. To study the semimetal to antiferromagnet transition, we generalize the two-particle self-consistent (TPSC) approach to the honeycomb lattice (a structure that can be realized in graphene for example). We show that the critical interaction strength where the transition occurs is $U_c/t=3.79\pm 0.01$ quite close to the value $U_c/t=3.869 \pm 0.013$ reported using large-scale quantum Monte Carlo simulations. This reinforces the conclusion that the semimetal to spin liquid transition is pre-empted by the transition to the antiferromagnet. Since TPSC satisfies the Mermin-Wagner theorem, we find temperature-dependent results for the antiferromagnetic and ferromagnetic correlation lengths as well as the dependence of double occupancy and of the renormalized spin and charge interactions on the bare interaction strength. We also estimate the value of the crossover temperature to the renormalized classical regime as a function of interaction strength.

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arXiv2015

Topological phases of the Kitaev-Hubbard Model at half-filling

The Kitaev-Hubbard model of interacting fermions is defined on the honeycomb lattice and, at strong coupling, interpolates between the Heisenberg model and the Kitaev model. It is basically a Hubbard model with ordinary hopping $t$ and spin-dependent hopping $t'$. We study this model in the weak to intermediate coupling regime, at half-filling, using the Cellular Dynamical Impurity Approximation (CDIA), an approach related to Dynamical Mean Field Theory but based on Potthoff's variational principle. We identify four phases in the $(U,t')$ plane: two semi-metallic phases with different numbers of Dirac points, an antiferromagnetic insulator, and an algebraic spin liquid. The last two are separated by a first-order transition. These four phases all meet at a single point and could be realized in cold atom systems.

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arXiv2015

First order Quantum Hall Transitions in Hofstadter Butterfly in the Honeycomb Lattice

We analyze the effects of nearest neighbor repulsive interactions in the Hofstadter system in a honeycomb lattice. At low fillings, we show that, as the interaction strength is increased there are two first order transitions, a Landau transition with translational and rotational symmetries broken, followed by a topological transition with a jump in the quantized Hall conductivity. We therefore predict that in physical realizations where the interaction effects are strong, there would be translation symmetry broken states with quantized Hall conductivities that differ from those predicted by the non-interacting theory.

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arXiv2015

$d$-wave superconductivity in coupled ladders

We study the one-band Hubbard model on the trellis lattice, a two-dimensional frustrated lattice of coupled two-leg ladders, with hopping amplitude $t$ within ladders and $t'$ between ladders. For large $U/t$ this is a model for the cuprate Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$. We investigate the phase diagram as a function of doping for $U=10t$ using two quantum cluster methods: The variational cluster approximation (VCA), with clusters of sizes 8 and 12, and Cellular dynamical mean field theory (CDMFT), both at zero temperature. Both methods predict a superconducting dome, ending at roughly 20\% doping in VCA and 15\% in CDMFT. In VCA, the superconducting order parameter is complex in a range of doping centered around 10\%, corresponding to bulk chiral, $T$-violating superconductivity. However, the CDMFT solution is not chiral. We find evidence for a migration of the Cooper pairs from the inter-ladder region towards the plaquettes as doping is increased.

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arXiv2013

Quarter-filled Kitaev-Hubbard Model: A Quantum Hall State in an Optical Lattice

We analyze the Physics of cold atoms in honeycomb optical lattices with on-site repulsion and spin-orbit couplings that break time reversal symmetry. Such systems, at half filling and large on-site repulsion, have been proposed as a possible realization of the Kitaev model. The spin-orbit couplings break the spin degeneracy and, if strong-enough, lead to four non-overlapping bands in the non-interacting limit. These bands carry non-zero Chern number and therefore the non-interacting system has non-zero angular momentum and chiral edge states at 1/4 and 3/4 filling. We have investigated the effect of interactions using the variational cluster perturbation theory and conclude that the chiral edge states exist in finite range of interaction and hopping parameter space.

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arXiv2013

Topological transitions in a model with Particle-Hole symmetry, Pancharatnam-Berry Curvature and Dirac Points

We study the topology and geometry of a fermionic model on the honeycomb lattice with spin-dependent hopping which breaks the time-reversal and charge-conjugation symmetries but preserves their composition. We show that in such a case the Zak phases are topological invariants that characterize the semi-metallic state at half-filling and determine the edge state structure. As the strength of the spin-dependent hopping varies, the model shows several Lifshitz transitions corresponding to creation and merging of multiple Dirac points. We discuss the possible realization of this model in cold atom systems and propose experimental signals of detecting the Dirac points and Pancharathnam-Berry curvature of the bands.

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arXiv2013

Absence of spin liquid in non-frustrated correlated systems

The question of the existence of a spin liquid state in the half-filled Hubbard model on the honeycomb (aka graphene) lattice is revisited. The Variational Cluster Approximation (VCA), the Cluster Dynamical Mean Field Theory (CDMFT) and the Cluster Dynamical Impurity Approximation (CDIA) are applied to various cluster systems. Assuming that the spin liquid phase coincides with the Mott insulating phase in this non-frustrated system, we find that the Mott transition is pre-empted by a magnetic transition occuring at a lower value of the interaction $U$, and therefore the spin liquid phase does not occur. This conclusion is obtained using clusters with two bath orbitals connected to each boundary cluster site. We argue that using a single bath orbital per boundary site is insufficient and leads to the erroneous conclusion that the system is gapped for all nonzero values of $U$.

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arXiv2013

Topological aspects of an exactly solvable spin chain

We analyse a spin-1/2 chain with two-spin interactions which shown to exactly solvable by Lieb, Schultz and Mattis. We show that the model can be viewed as a generalised Kitaev model that is analytically solvable for all defect sectors. We present an alternate proof that the defect free sector is the ground state, which is valid for a larger parameter range. We show that the defect sectors have degenerate ground states corresponding to unpaired Majorana fermion modes and that the degeneracy is topologically protected against disorder in the spin-spin couplings. The unpaired Majorana fermions can be manipulated by tuning the model parameters and can hence be used for topological quantum computation.

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