Impurity Induced Phase Competition and Supersolidity

Karmakar, Madhuparna; Ganesh, R.

doi:10.7566/jpsj.86.124719

Cited by 5 publications

(4 citation statements)

References 37 publications

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“…As the attractive Hubbard model of Eq. 1 has been shown 19,23 to map to an SO(3) theory that is closely analogous to the SO(5) theory, this result is also applicable here. We hypothesize that coupling in the CDW sector leads to an additional interaction between two vortices, given by…”

Section: Inter-vortex Interactionssupporting

confidence: 65%

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Vortex Core Ordering in Abrikosov Lattices

Karmakar

Ganesh

2018

J. Phys. Soc. Jpn.

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Vortex lattices, arising from repulsive inter-vortex interactions, are a canonical example of emergent phenomena. Recent studies on the cuprates have drawn attention to the appearance of competing correlations within vortex cores. This gives internal structure to each vortex and changes the nature of inter-vortex interactions, especially at short range. This can have significant consequences for vortex lattices wherein vortices are in close proximity to one another. We consider the attractive Hubbard model, a prototypical model for phase competition, with checkerboard charge density wave order appearing in vortex cores. We use next-nearest-neighbour hopping, t , to tune the strength of competing order in the core. Using Bogoliubov deGennes mean field simulations, we study the variation in quasiparticle gap, superfluid stiffness and shear stiffness, as the core order is tuned. The presence of competing order allows for a new defect: domain walls that separate regions with different types of charge order overlying the vortex-laden superfluid background. We find the energy cost of such domain walls. Our results indicate a stable intermediate supersolid region with coexisting superfluid and charge orders. At one end, this phase is unstable to melting of the vortex lattice into a purely charge ordered state, possibly via an intervening liquid-like state. At the other end, charge order becomes incoherent due to domain formation while superconducting order persists.

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Section: Inter-vortex Interactionssupporting

confidence: 65%

“…In an earlier study restricted to t = 0.2, we always found a robust gap 19 . The occurrence of zero energy states due to strong gradients is reminiscent of the effect of randomly placed impurities in the Hubbard model 23 .…”

Section: Quasiparticle Gapmentioning

confidence: 99%

Vortex Core Ordering in Abrikosov Lattices

Karmakar

Ganesh

2018

J. Phys. Soc. Jpn.

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“…Based on this observation, it was conjectured that these two models were equivalent. This conjecture was supported by further studies 29,30 . In this article, we establish this equivalence by way of a rigorous mapping.…”

Section: Introductionsupporting

confidence: 60%

The attractive Hubbard model as an $SO(3)$ system of competing phases: supersolid order and its thermal melting

Karmakar,

Ganesh

2020

Preprint

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Competition between superconductivity and charge order is a recurring theme in contemporary condensed matter physics. This is quintessentially captured in the attractive Hubbard model, a simple theoretical model where the competition can be directly tuned. In previous studies by the current authors, it has been suggested that the Hubbard model maps to an SO(3) non-linear sigma model, where the phase competition becomes manifest. In this article, we rigorously demonstrate this mapping and use it to study thermal disordering of a supersolid. Starting with the attractive Hubbard model in the presence of an orbital field, we take the limit of strong coupling where a pseudospin description emerges. The in-plane pseudospin components represent superconducting pairing while the out-of-plane component encodes charge density wave order. We obtain an effective spin-1/2 Hamiltonian with ferromagnetic in-plane couplings and antiferromagnetic z-z couplings. In addition, the orbital field gives rise to a textured Dzyaloshinskii-Moriya interaction that has the same periodicity as the magnetic unit cell. In order to examine the nature of ordering in this spin model, we consider it in the classical limit. We assume slowly varying fields, leading to the SO(3) non-linear sigma model description. As an application of these ideas, we study the nature of ordering using simulated annealing and classical Monte Carlo simulations. The ground state represents a supersolid with coexisting superconductivity and charge order. It can be viewed as a 'meron crystal', a regular arrangement of superconducting vortices with charge-ordered cores. The overlap of core regions gives rise to coherent long-ranged charge order. As the temperature is raised, this charge order is lost via a sharp phase transition in the Ising universality class.

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“…In place of a magnetic field, disorder can also be used to bring out competing order. A point-like impurity suffices to seed local CDW correlations over a superconducting background 31 .…”

Section: So(3) Theory Of Competing Ordermentioning

confidence: 99%

Skyrmion-like textures in superconductors with competing orders

2019

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Vortex cores in a superconductor can develop structure and manifest competing orders. In strong magnetic fields, the inter-vortex distance can become short enough for vortex cores to overlap, giving rise to long ranged textures. We show that spin orbit coupling (SOC) can modify the interaction between vortex cores to give rise to undulating competing order fields. We illustrate this using the SO(3) theory of competing orders, wherein superconductivity and a scalar order form a threecomponent vector field. We consider a spherical surface with a radial magnetic flux that creates two vortices. We find stationary solutions where both vortex cores develop competing order in (a) the same sense, and (b) opposite senses. The latter represents a topologically stable vector configuration analogous to a single skyrmion. Its free energy is lowered when SOC is introduced, making it the ground state beyond a threshold SOC strength. We study this physics on the two dimensional plane using the attractive Hubbard model with Rashba SOC. Here, charge density wave (CDW) order competes with superconductivity. We find phases with long ranged, but spatially modulated, CDW order where the average CDW moment vanishes. In a wide range of parameters, CDW loses its rigidity as SOC lowers the energy cost for domain wall formation. We discuss consequences for systems such as the cuprates where charge order develops without a sharp diffraction peak. arXiv:1903.11053v1 [cond-mat.supr-con]

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Impurity Induced Phase Competition and Supersolidity

Cited by 5 publications

References 37 publications

Vortex Core Ordering in Abrikosov Lattices

Vortex Core Ordering in Abrikosov Lattices

The attractive Hubbard model as an $SO(3)$ system of competing phases: supersolid order and its thermal melting

Skyrmion-like textures in superconductors with competing orders

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