Session Y25: Superconductivity in Cuprates (mostly): Theory II

Magnetic impurity induced states in superconducting Bi$_{2}$Sr$_{2}$CaCuO$_{8+\delta}$

We revisit the Ni impurity problem in superconducting Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (BSCCO-2212) using the Bogoliubov- de Gennes (BdG)-Wannier approach [1, 2]. We solve the self-consistent BdG equations on a square lattice and use first principle-based Wannier function to compute the local density of states (LDOS) with sub-atomic resolution in the vicinity of a magnetic impurity. We find two spin-resolved virtual bound states localized around the impurity position. The spatial LDOS patterns at the resonance energies are found to be in excellent agreement with STM experiment [3], and can be understood by accounting for the tails of Cu Wannier function.\\[4pt] [1] Peayush Choubey, T. Berlijn, A. Kreisel, C. Cao and P. J. Hirschfeld, Phys. Rev. B. 90, 134520 (2014).\\[0pt] [2] A. Kreisel, Peayush Choubey, T. Berlijn, B. M. Andersen and P. J. Hirschfeld, arxiv: 1407.1846 (2014).\\[0pt] [3] E. W. Hudson, K. M. Lang, V. Madhavan, S. H. Pan, H. Eisaki, S. Uchida and J. C. Davis, Nature, 411, 920 (2001).   

Mid-gap States and Upper Hubbard Band in Bi-2201 Cuprate Superconductor

A recent Scanning Tunneling Spectra (STS) measurement on underdoped Bi-2201 by Yayu Wang and collaborators, discovered mid-gap states between Oxygen band and upper Hubbard band (UHB) of Cu. There is a strong interplay between the spectral weights and energies of the UHB and these mid-gap states. We performed a variational calculation of the Hubbard model by constructing explicitly the mid-gap states and UHB states. The doping dependence of the energies and spectral weight transfer between UHB and the mid-gap state explains well the results of STS experiment.   

Fidelity Study of Superconductivity in Extended Hubbard Models

The role of strong electronic correlations on unconventional superconductivity remains an important open question. Here, we explore the influence of long-range Coulomb interactions, present in real material systems, through nearest and next-nearest neighbor extended Hubbard interactions in addition to the usual on-site terms. Utilizing large scale, numerical exact diagonalization, we analyze the signatures of superconductivity in the ground states through the fidelity metric of quantum information theory. We find that these extended interactions enhance charge fluctuations with various wave vectors. These suppress superconductivity in general, but in certain parameter regimes superconductivity is sustained. This has implications for tuning extended interactions in real materials.   

The Ground State Phase Diagram of the Two-Dimensional Hubbard Model on Square Lattice

We systematically study the 0K phase diagram of the two-dimensional Hubbard model on the square lattice using density matrix embedding theory (DMET) with broken spin and particle number symmetry. We explicitly treat clusters with up to 16 sites and extrapolate the energy and relevant order parameters to the thermodynamic limit. At half-filling, the energies from DMET are as accurate as results from the state-of-the-art auxiliary-field QMC and density matrix renormalisation group (DMRG), with similar error bars. When doped, however, these ``exact'' methods either suffer from the sign problem, or require too large systems to be tractable, while the DMET calculations remain accurate. We obtain a phase diagram similar to the generic phase diagram of the cuprates, and find very robust superconductivity in the ground-state. We also see inhomogeneous phases in the strong interaction regime. We find the negative next nearest neighbor hopping (t$^\prime$/t $<$ 0) enhances the spatially inhomogeneous phases while the positive t$^\prime$ stabilizes the antiferromagnetic order.   

Superconducting transition temperature in two-dimensional doped repulsive Hubbard model: DCA+ simulations with continuous momentum dependence

DCA+ algorithm extends the dynamical cluster approximation (DCA) with continuous lattice self-energy to ensure better convergence with cluster size and delay the occurrence of the severe sign problem. This new algorithm enables a systematic investigation of the phase diagram of 2D Hubbard model relevant to the high temperature superconductors. We calculate the superconducting transition temperature $T_{c}$ in the 2D repulsive Hubbard model on square lattice with nearest-neighbor hoppings for different doping levels, focussing on the intermediate correlation ($U/t=7$) regime.   

Phase fluctuation in overdoped cuprates? Superconducting dome due to Mott-ness of the tightly bound preformed pairs

In contrast to the current lore, we demonstrate that even the overdoped cuprates suffer from superconducting phase fluctuation in the strong binding limit. Specifically, the Mott-ness of the underlying doped holes dictates naturally a generic optimal doping around 15\% and nearly complete loss of phase coherence around 25\%, giving rise to a dome shape of superconducting transition temperature in excellent agreement with experimental observations of the cuprates. We verify this effect with a simple estimation using Gutzwiller approximation of the preformed pairs, obtained through variational Monte Carlo calculation. This realization suggests strongly the interesting possibility that the high-temperature superconductivity in the cuprates might be mostly described by Bose-Einstein condensation, without crossing over to amplitude fluctuating Cooper pairs.   

Exact phase diagram of multi-orbital spin-fermion model for hole doped cuprates

Recent experiments revealing the ubiquitous presence of spin and charge ordered states in hole-doped cuprates have placed the study of broken symmetry states at the center of high Tc~superconductivity research. Here we aim to understand the phase diagram of broken symmetry states using a simple model that captures the essence of hole doped cuprates [1]. The model consists of itinerant quantum holes on oxygen p-orbitals coupled to classical Cu spins. It is amenable to sign problem free Monte-Carlo simulation allowing us to study finite temperature properties as well as unbiased determination of ground state spin and charge configuration. As a function of system parameters, we obtain a rich phase diagram. Our analysis provides a transparent and unifying picture for various charge and spin ordered states as arising from frustration of antiferromagnetic order due to hole doping, through exact finite temperature phase diagram of the model. [1] M. H. Fischer, S. Wu, M. Lawler, A. Paramekanti, and E.-A. Kim, New J. Phys. 16, 093057 (2014).   

Enchancement of superconductivity in a three-dimensional hotspot model of competing orders in the cuprates

Recent experiments in the cuprates have seen evidence of a transient superconducting state upon optical excitation polarized along the c-axis. Motivated by these experiments we considered a hotspot model of competing superconductivity and bond density order in a system of stacked planes. We generically find an enhancement of superconductivity in the coexistent phase as a function of c-axis coupling strength. Furthermore, we propose a simple Floquet system which takes advantage of this enhancement.   

Collective modes in the hot spot model of cuprates

We study the collective modes of the possible order parameters of cuprate high-temperature superconductors. Observing and analyzing these modes provide insights into the nature of the ordered state. Using the hot spot model of cuprates, we explore the amplitude oscillations of both charge density wave (CDW) and superconducting states. Especially interesting is the region, in which CDW and superconductivity coexist, and in which the two amplitude oscillations become mixed in a single mode with energy inside the single-particle gap. We compare these results with the recent data extracted from reflectivity measurements.   

Can short-ranged orders enhance superconductivity of cuprates?

Recent advances in experiments established short-ranged orders associated with tendencies for spatial symmetry breaking as universal phenomena of underdoped cuprates. This brings the question of the relationship between these short-ranged orders and superconductivity to the forefront of the study of high Tc superconductivity. Here we study this issue paying special attention to the role form-factors play. Using both non-self-consistent and self-consistent Bogoliubov-de Gennes equation with real-space realization of short-range order we investigate how the short-ranged order affect the electronic structure as well as superconducting tendencies. Typically an inhomogeneous potential due to short-ranged ordering patterns will act as a scatterer that is detrimental to unconventional superconductor which is not protected through Anderson's theorem. However we find that that form factor of the short-ranged ordering form can make consequential differences in the way short-range order interact with superconductivity, with the possibility of enhancing superconductivity.   

Amplitude mode oscillations in pump-probe photoemission spectra of electron-phonon mediated superconductors

The amplitude, or Higgs mode is deeply intertwined with the historical development of the BCS theory of superconductivity. Although the presence of the Higgs mode is fundamental to superconductivity, it remained elusive for many decades, and its presence and observability is still under debate in many contexts. We present results for time-dependent photoemission spectra to directly probe the dynamics of the superconducting gap edge where the fingerprint of superconductivity is strongest. The pumping of a superconductor is simulated by solving the two-time Gor'kov equations of motion for the Migdal-Eliashberg model, which is a minimal gauge-invariant model for superconductivity with a pairing boson and dissipation. The Higgs mode can be directly detected without the requirement of any additional symmetry breaking and is clearly visible as oscillations of the gap edge spectra at twice the gap frequency, a hallmark of amplitude modes.   

Angle-dependent magnetoresistance and the presence of fluctuating hot spots on the Fermi surface of Tl2201

The normal-state transport properties of cuprate high-temperature superconductors are not well understood. While the Hall angle in such materials is typically proportional to $T^2$, the in-plane resistivity has a more complicated temperature dependence. This has led to many theories of the scattering processes in such materials, including several that posit the existence of two or more independent scattering lifetimes. Here, we propose a model that may explain the cuprates' complicated normal-state behavior without the need to invoke multiple scattering channels: fluctuating hot spots on the Fermi surface, a result of transient antiferromagnetic order. I will demonstrate that this model can accurately simulate angle-dependent magnetoresistance data from Tl$_2$Ba$_2$CuO$_{6+\delta}$, and discuss what additional calculations and experiments will be performed in order to further test this model.   

Polar Kerr effect from chiral-nematic charge order

We analyze the polar Kerr effect in an itinerant electron system on a square lattice in the presence of a composite charge order proposed for the pseudogap state in underdoped cuprates. This composite charge order preserves translational symmetries, and is ``chiral-nematic" in the sense that it breaks time-reversal symmetry, mirror symmetries in $x$ and $y$ directions, and $C_4$ lattice rotation symmetry. The Kerr angle $\theta_K$ in $C_4$-symmetric system is proportional to the antisymmetric component of the anomalous Hall conductivity $\sigma_{xy}-\sigma_{yx}$. We show that this result holds when $C_4$ symmetry is broken. We show that chiral-nematic charge order satisfies all symmetry requirements by a polar Kerr effect. We further show that to get a non-zero $\theta_K$ in a one-band spin-fluctuation scenario, in the absence of disorder, one has to extend the spin-mediated interaction to momenta away from $(\pi,\pi)$ and has to include particle-hole asymmetry. Alternatively, in the presence of disorder one can get a non-zero $\theta_K$ from impurity scattering: either due to skew scattering (with non-Gaussian disorder) or due to particle-hole asymmetry in case of Gaussian disorder. We finally discuss the effect of an external magnetic field on the Kerr signal.   

Finite T spectral function of a single carrier injected into an Ising chain: a comparison of 3 different models

When studying the properties of complex, magnetic materials it is often necessary to work with effective Hamiltonians. In many cases the effective Hamiltonian is obtained by mapping the full, multiband Hamiltonian onto a simpler, single band model. A prominent example is the use of Zhang-Rice singlets to map the multiband Emery model for cuprates onto the single band $t-J$-model. Such mappings are usually done at zero temperature (T) and it is implicitly assumed that they are justified at finite T, as well. We present results on 3 different models of a single charge carrier (electron or hole) injected into a ferromagnetic Ising chain. Model I is a two band, two sublattice model, Model II is a two band, single sublattice model, and Model III is a single band model, the so called $t-J_z$-model. Due to the absence of spin-flip terms, a numerically exact solution of all 3 Models is possible, even at finite T. At zero T a mapping between all 3 models results in the same low energy physics. However, this is no longer true at finite T. Here the low energy behavior of Model III is significantly different from that of Models I and II. The reasons for this discrepancy and its implications for more realistic models (higher dimension, inclusion of spin-flip terms) are discussed.