We compute the two-particle quantities relevant for superconducting correlations in the two-dimen... more We compute the two-particle quantities relevant for superconducting correlations in the two-dimensional Hubbard model within the dynamical cluster approximation. In the normal state we identify the parameter regime in density, interaction, and second-nearest-neighbor hopping strength that maximizes the d_{x^{2}-y^{2}} superconducting transition temperature. We find in all cases that the optimal transition temperature occurs at intermediate coupling strength, and is suppressed at strong and weak interaction strengths. Similarly, superconducting fluctuations are strongest at intermediate doping and suppressed towards large doping and half filling. We find a change in sign of the vertex contributions to d_{xy} superconductivity from repulsive near half filling to attractive at large doping. p-wave superconductivity is not found at the parameters we study, and s-wave contributions are always repulsive. For negative second-nearest-neighbor hopping the optimal transition temperature shift...
Inspired by phenomenological models for the pseudogap state, for example, the model of Yang, Rice... more Inspired by phenomenological models for the pseudogap state, for example, the model of Yang, Rice and Zhang[1], we have calculated the specific heat for the underdoped cuprate superconductors. Results will be shown for both the pseudogap and superconducting ...
We propose a hybridization phenomenology to describe the pseudogap state of the underdoped cuprat... more We propose a hybridization phenomenology to describe the pseudogap state of the underdoped cuprates. We show how a momentum independent pseudogap opens asymmetrically from the Fermi-surface but symmetric to the zeroes of the hybridized bonding dispersion, which results in false d-wave characteristics of the pseudogap at the Fermi level. By comparing against a d-wave form factor we illustrate the difficulty in identifying a momentum independent order in momentum averaged quantities such as the electronic Raman response. We identify a suppression in the single-particle density of states which produces a hump feature which should be observable experimentally in tunnelling dI/dV spectra and distinguishes the s-wave and d-wave ordering scenarios.
In this work we introduce the possibility of unparticle mediated superconductivity. We discuss a
... more In this work we introduce the possibility of unparticle mediated superconductivity. We discuss a
theoretical scenario where it can emerge and show that a superconducting state is allowed by deriving
and solving the gap equation for s-wave pairing of electrons interacting through the unparticle
generalization of the Coulomb interaction. The dependence of the gap equation on the unparticle
energy scale ΛU and the unparticle scaling dimension dU enables us to find a richer set of solutions
compared to those of the conventional BCS paradigm. We discuss unconventional features within
this construction, including the resulting insensitivity of pairing to the density of states at the Fermi
energy for dU = 3/2 of the superconducting gap and suggest possible experimental scenarios for this
mechanism.
Hexagonal warping provides an anisotropy to the dispersion curves of the helical Dirac fermions t... more Hexagonal warping provides an anisotropy to the dispersion curves of the helical Dirac fermions that exist at the surface of a topological insulator. A sub-dominant quadratic in momentum term leads to an asymmetry between conduction and valence band. A gap can also be opened through magnetic doping. We show how these various modifications to the Dirac spectrum change the polarization function of the surface states and employ our results to discuss their effect on the plasmons. In the long wavelength limit, the plasmon dispersion retains its square root dependence on its momentum, $\boldsymbol{q}$, but its slope is modified and it can acquire a weak dependence on the direction of $\boldsymbol{q}$. Further, we find the existence of several plasmon branches, one which is damped for all values of $\boldsymbol{q}$, and extract the plasmon scattering rate for a representative case.
The phenomenological Green’s function developed in the works of Yang, Rice, and Zhang has been ve... more The phenomenological Green’s function developed in the works of Yang, Rice, and Zhang has been very successful in understanding many of the anomalous superconducting properties of the deeply underdoped cuprates. It is based on considerations of the resonating valence bond spin liquid approximation and is designed to describe the underdoped regime of the cuprates. Here, we emphasize the region of doping, x, just below the quantum critical point at which the pseudogap develops. In addition to Luttinger hole pockets centered around the nodal direction, there are electron pockets near the antinodes which are connected to the hole pockets by gapped bridging contours. We determine the contours of nearest approach as would be measured in angular resolved photoemission experiments and emphasize signatures of the Fermi surface reconstruction from the large Fermi contour of Fermi liquid theory (which contains 1+x hole states) to the Luttinger pocket (which contains x hole states). We find that the quasiparticle effective mass renormalization increases strongly toward the edge of the Luttinger pockets beyond which it diverges.
We compute the two-particle quantities relevant for superconducting correlations in the two-dimen... more We compute the two-particle quantities relevant for superconducting correlations in the two-dimensional Hubbard model within the dynamical cluster approximation. In the normal state we identify the parameter regime in density, interaction, and second-nearest-neighbor hopping strength that maximizes the d_{x^{2}-y^{2}} superconducting transition temperature. We find in all cases that the optimal transition temperature occurs at intermediate coupling strength, and is suppressed at strong and weak interaction strengths. Similarly, superconducting fluctuations are strongest at intermediate doping and suppressed towards large doping and half filling. We find a change in sign of the vertex contributions to d_{xy} superconductivity from repulsive near half filling to attractive at large doping. p-wave superconductivity is not found at the parameters we study, and s-wave contributions are always repulsive. For negative second-nearest-neighbor hopping the optimal transition temperature shift...
Inspired by phenomenological models for the pseudogap state, for example, the model of Yang, Rice... more Inspired by phenomenological models for the pseudogap state, for example, the model of Yang, Rice and Zhang[1], we have calculated the specific heat for the underdoped cuprate superconductors. Results will be shown for both the pseudogap and superconducting ...
We propose a hybridization phenomenology to describe the pseudogap state of the underdoped cuprat... more We propose a hybridization phenomenology to describe the pseudogap state of the underdoped cuprates. We show how a momentum independent pseudogap opens asymmetrically from the Fermi-surface but symmetric to the zeroes of the hybridized bonding dispersion, which results in false d-wave characteristics of the pseudogap at the Fermi level. By comparing against a d-wave form factor we illustrate the difficulty in identifying a momentum independent order in momentum averaged quantities such as the electronic Raman response. We identify a suppression in the single-particle density of states which produces a hump feature which should be observable experimentally in tunnelling dI/dV spectra and distinguishes the s-wave and d-wave ordering scenarios.
In this work we introduce the possibility of unparticle mediated superconductivity. We discuss a
... more In this work we introduce the possibility of unparticle mediated superconductivity. We discuss a
theoretical scenario where it can emerge and show that a superconducting state is allowed by deriving
and solving the gap equation for s-wave pairing of electrons interacting through the unparticle
generalization of the Coulomb interaction. The dependence of the gap equation on the unparticle
energy scale ΛU and the unparticle scaling dimension dU enables us to find a richer set of solutions
compared to those of the conventional BCS paradigm. We discuss unconventional features within
this construction, including the resulting insensitivity of pairing to the density of states at the Fermi
energy for dU = 3/2 of the superconducting gap and suggest possible experimental scenarios for this
mechanism.
Hexagonal warping provides an anisotropy to the dispersion curves of the helical Dirac fermions t... more Hexagonal warping provides an anisotropy to the dispersion curves of the helical Dirac fermions that exist at the surface of a topological insulator. A sub-dominant quadratic in momentum term leads to an asymmetry between conduction and valence band. A gap can also be opened through magnetic doping. We show how these various modifications to the Dirac spectrum change the polarization function of the surface states and employ our results to discuss their effect on the plasmons. In the long wavelength limit, the plasmon dispersion retains its square root dependence on its momentum, $\boldsymbol{q}$, but its slope is modified and it can acquire a weak dependence on the direction of $\boldsymbol{q}$. Further, we find the existence of several plasmon branches, one which is damped for all values of $\boldsymbol{q}$, and extract the plasmon scattering rate for a representative case.
The phenomenological Green’s function developed in the works of Yang, Rice, and Zhang has been ve... more The phenomenological Green’s function developed in the works of Yang, Rice, and Zhang has been very successful in understanding many of the anomalous superconducting properties of the deeply underdoped cuprates. It is based on considerations of the resonating valence bond spin liquid approximation and is designed to describe the underdoped regime of the cuprates. Here, we emphasize the region of doping, x, just below the quantum critical point at which the pseudogap develops. In addition to Luttinger hole pockets centered around the nodal direction, there are electron pockets near the antinodes which are connected to the hole pockets by gapped bridging contours. We determine the contours of nearest approach as would be measured in angular resolved photoemission experiments and emphasize signatures of the Fermi surface reconstruction from the large Fermi contour of Fermi liquid theory (which contains 1+x hole states) to the Luttinger pocket (which contains x hole states). We find that the quasiparticle effective mass renormalization increases strongly toward the edge of the Luttinger pockets beyond which it diverges.
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theoretical scenario where it can emerge and show that a superconducting state is allowed by deriving
and solving the gap equation for s-wave pairing of electrons interacting through the unparticle
generalization of the Coulomb interaction. The dependence of the gap equation on the unparticle
energy scale ΛU and the unparticle scaling dimension dU enables us to find a richer set of solutions
compared to those of the conventional BCS paradigm. We discuss unconventional features within
this construction, including the resulting insensitivity of pairing to the density of states at the Fermi
energy for dU = 3/2 of the superconducting gap and suggest possible experimental scenarios for this
mechanism.
theoretical scenario where it can emerge and show that a superconducting state is allowed by deriving
and solving the gap equation for s-wave pairing of electrons interacting through the unparticle
generalization of the Coulomb interaction. The dependence of the gap equation on the unparticle
energy scale ΛU and the unparticle scaling dimension dU enables us to find a richer set of solutions
compared to those of the conventional BCS paradigm. We discuss unconventional features within
this construction, including the resulting insensitivity of pairing to the density of states at the Fermi
energy for dU = 3/2 of the superconducting gap and suggest possible experimental scenarios for this
mechanism.