Recent Progress on High Tc Superconductivity and Related Problems

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Conference Date:

Monday, July 6, 2015 (All day) to Friday, July 10, 2015 (All day)

Pirsa Collection:

Scientific Areas:

Quantum Matter

Quantum Gravity

Quantum Information

High Tc superconductivity in cuprates has engaged us for over 25 years. An apparent quantum complexityn arising from strong electron correlations and Mott physics, in the form of new experimental results, continues to challenge theorists. Intense efforts from theory has brought in a good and deep understanding of the optimal doped region of the phase diagram, particularly the superconducting phase. However, anomalous normal state in the optimal and under doped regime has defied simple theoretical understanding, partly because of nearly degenerate competing phases, differing structures and quantum chemistry among members of the cuprate family. But a standard model for the description of the winning superconducting phase is definitely there. There are also signals for some simplicity and new physic behind the complexity.

G. Baskaran, The Institute of Mathematica Sciences Chennai
Juan Carlos Campuzano, University of Illinois at Chicago
Zheng-Cheng Gu, Perimeter Institute
David Hawthorn, University of Waterloo
Jiang-Ping Hu, Purdue University
Sung-Sik Lee, Perimeter Institute & McMaster University
Jia-Wei Mei, Perimeter Institute
Yang Qi, Tsinghua University
Subir Sachdev, Perimeter Institue & Harvard University
Xiao-Gang Wen, Perimeter Institue and Massachusetts Institute of Technology
Zheng-Yu Weng, Tsinghua University

Monday, July 6, 2015

Time	Event	Location
10:00 – 11:00am	G. Baskaran, The Institute of Mathematica Sciences Chennai Anderson-Haldane Liquid State in the Pseudogap Phase of Under Doped Cuprates and Two Leg t-J Ladder	Sky Room
11:00 – 12:00pm	Zheng-Yu Weng, Tsinghua University A wave function approach to the t-J type models	Sky Room

Tuesday, July 7, 2015

Time	Event	Location
10:00 – 11:00am	Subir Sachdev, Perimeter Institute & Harvard University The non-superconducting states of the cuprates	Sky Room
11:00 – 12:00pm	Zheng-Cheng Gu, Perimeter Institute A tensor product state approach to spin-1/2 square J1-J2 Heisenberg model: spin liquid vs. deconfined quantum criticality	Sky Room

Wednesday, July 8, 2015

Time	Event	Location
10:00 – 11:00am	David Hawthorn, University of Waterloo Nematicity and charge density wave order in stripe ordered cuprates probed via resonant x-ray scattering	Sky Room
11:00 – 12:00pm	Jiang-Ping Hu, Purdue University Search the Genes of Unconventional High Temperature Superconductors	Sky Room
2:00 – 3:30pm	Colloquium: Juan Carlos Campusano, University of Chicago at Illinois The strange “normal” state of high temperature superconductors, heavy fermion, and charge density wave materials.	Theater

Thursday, July 9, 2015

Time	Event	Location
10:00 – 11:00am	Xiao-Gang Wen, Perimeter Institute & Massachusetts Institute of Technology Supperconductivity in t1-t2-J1-J2 model on Honeycomb lattice	Sky Room
11:00 – 12:00pm	Yang Qi, Tsinghua University Coexistence of Antiferromagnetism and Superconductivity on Honeycomb Lattice	Sky Room

Friday, July 10, 2015

Time	Event	Location
10:00 – 11:00am	Sung-Sik Lee, Perimeter Institute & McMaster University Anisotropic Non-Fermi Liquids	Sky Room
11:00 – 12:00pm	Jia-Wei Mei, Perimeter Institute Fractional spin-wave continuum in spin liquid states on the kagome lattice	Sky Room

Ganapathy Baskaran, The Institute of Mathematical Sciences Chennai

Anderson-Haldane Liquid State in the Pseudogap Phase of Under Doped Cuprates and Two Leg t-J Ladder

In a lightly doped Mott insulator, after AFM order disappears, bond singlets become manifest and a short range RVB state containing a small density of doped holes emerge. In this featureless RVB state a doped hole, instead of creating a deconfined holon and a spinon, becomes a `spin-charge locked' composite of a holon and a spinon, weakly bound by RVB gauge fields. In this RVB state incompressibility of bond singlet fluid and non-orthogonality of valence bond states leads to a Haldane exclusion statistics 1 for holon and 1/2 for spinon. We have suggested earlier [1] that the doped hole, now a composite, has a net exclusion statistics 3/2. One can formally build a small fermi sea using this composite fermion holes. Its Luttinger volume is 3/2 times more than expected in fermi liquid theory and Luttinger count in a folded zone. This novel quantum spin liquid [1], that bears charge quasi particles obeying a nontrivial Haldane exclusion statistics 3/2, will be called Anderson-Haldane liquid.

The above semi microscopic description could explain small fermi pockets seen in quantum oscillation experiments, an associated fermi volume anomaly, absence of quasi particles in ARPES and presence of competing orders. We also suggest that lightly doped two leg t-J ladder is a simple example of Anderson-Haldane liquid. Certain remarkable anomalous spectral features recently obtained by Zheng Zhu and Zheng Yu Weng [2] in a study of one hole in a two leg t-J ladder is interpreted as signal for emergence of Anderson-Haldane liquid.

Juan Carlos Campuzano, University of Illinois at Chicago

The strange “normal” state of high temperature superconductors, heavy fermion, and charge density wave materials.

In describing condensed matter, some well established paradigms have allowed much progress to be made in understanding and using materials. But in the last 15 - 20 years, new materials, such as heavy fermions, high temperature superconductors, and now charge density wave-supporting materials, have been shown to require new paradigms in describing them. While much progress has been achieved in that time, we still do not have a widely accepted theoretical description of the nature of their electronic excitations.

Zheng-Cheng Gu, Perimeter Institute

A tensor product state approach to spin-1/2 square J1-J2 Heisenberg model: spin liquid vs. deconfined quantum criticality

The ground state phase diagram of spin-1/2 J1-J2 antiferromagnetic Heisenberg model on square lattice around the maximally frustrated regime (J2~0.5J1) has been debated for decades. I will discuss some progresses on this old problem based on recent numerical results from density matrix renormalization group(DMRG) and tensor product states algorithms.

David Hawthorn, University of Waterloo

Nematicity and charge density wave order in stripe ordered cuprates probed via resonant x-ray scattering

In underdoped cuprate superconductors, a rich competition occurs between superconductivity and charge density wave order (CDW). Under debate, however, is whether rotational symmetry breaking (nematicity) also plays a central role -- whether it occurs intrinsically and generically or merely as a consequence of other orders. Here we employ resonant x-ray scattering in stripe-ordered (La,X)2CuO4 to probe the relationship between electronic nematicity of the Cu 3d orbitals, structural orthorhombicity of the (La,X)2O4 layers and CDW order. We find distinct temperature dependences of the structural orthorhombicity and the electronic nematicity, with the electronic nematicity, but no structural orthorhombicity enhancement below the onset of CDW order. These results indicate electronic nematicity is an order parameter that is distinct from a purely structural order parameter in underdoped cuprates.

Jiang-Ping Hu, Purdue University

Search the Genes of Unconventional High Temperature Superconductors

We discuss two basic principles to unify the understanding of both cuprates and iron-based superconductors: (1) the correspondence principle— the short range magnetic exchange interactions and the Fermi surfaces act collaboratively to achieve high Tc superconductivity and determine pairing symmetries; (2) the selective magnetic pairing rule: the superconductivity is only induced by the magnetic exchange couplings from the superexchange mechanism through cation-anion-cation chemical bondings but not those from direct exchange couplings resulted from the direct cation's d-d chemical bondings. These two principles provide a unified explanation why the d-wave pairing symmetry and the s-wave pairing symmetry are robust respectively in cuprates and iron-based superconductors. In the meanwhile, the above two principles can serve as direct guiding rules to search new unconventional high Tc superconductors. We propose that the third classes of unconventional high Tc superconducting candidates in compounds formed by cation-anion trigonal bipyramidal complexes with a d7 filling configuration on the cation ions. Their superconducting states are expected to be dominated by the d+id pairing symmetry. Synthesizing these compounds and verifying the prediction can convincingly establish the high Tc superconducting mechanism and pave a way to design new high Tc superconductors

Sung-Sik Lee, Perimeter Institute & McMaster University

Anisotropic Non-Fermi Liquids

We study non-Fermi liquids that arise at the quantum critical points associated with the spin and charge density wave transitions in metals with the C2 symmetry. We use the dimensional regularization scheme, where a one-dimensional Fermi surface is embedded in 3 − epsilon dimensional momentum space. In three dimensions, marginal Fermi liquids arise at the spin and charge density wave critical points. Below three dimensions, a perturbative anisotropic non-Fermi liquid is realized at the spin density wave critical point, where not only time but also different spatial coordinates develop distinct anomalous dimensions. On the other hand, the perturbative expansion breaks down at the charge density wave critical point immediately below three dimensions.

Jia-Wei Mei, Perimeter Institute

Fractional spin-wave continuum in spin liquid states on the kagome lattice

Motivated by spin-wave continuum (SWC) observed in recent neutron scattering experiments in Herbertsmithite, we use Gutzwiller-projected wave functions to study dynamic spin structure factor of spin liquid states on the kagome lattice. As their ground state, spin-1 excited states for spin liquids are represented by Gutzwiller-projected two-spinon excited wave functions. We investigate three different spin liquid candidates, spinon Fermi-surface spin liquid (FSL), Dirac spin liquid (DSL) and random-flux spin liquid (RSL). We find that DSL has no explicit contradiction with experiments. Besides a fractionalized spin moment, DSL has a fractionalized crystal momentum which is also detectable directly in the neutron scattering measurements.

Yang Qi, Tsinghua University

Coexistence of Antiferromagnetism and Superconductivity on Honeycomb Lattice

Motivated by results of DMRG and tensor network simulations on doped $t$-$J$ model on honeycomb lattice, we study superconductivity of singlet and triplet pairing in this model. We show that a superconducting state with coexisting spin-singlet and spin-triplet pairings is induced by the antiferromagnetic order near half-filling. The superconducting state we obtain has a topological phase transition that separates a topologically trivial state and a non-trivial state with Chern number two.

Subir Sachdev, Perimeter Institue & Harvard University

The non-superconducting states of the cuprates

The most interesting states of the cuprate compounds are not the superconductors with high critical temperatures. Instead, the novelty lies primarily in the higher temperature metallic “normal” states from which the superconductors descend, and in competing low temperature states with density wave order. I will review recent experimental and theoretical progress in understanding these states. The experimental evidence is compatible with the presence of a metal with topological order in the ‘pseudogap’ regime of low carrier density.

Xiao-Gang Wen, Perimeter Institue & Massachusetts Institute of Technology

Supperconductivity in t1-t2-J1-J2 model on Honeycomb lattice

We studied t1-t2-J1-J2 model on Honeycomb lattice at finite doping. We find that

when t_1 is very small, the t1-t2-J1-J2 model on Honeycomb lattice may be in a supperconducting phase. Such a supperconducting phase is not driven by the pairing, but by entanglement.

Tuesday Jul 07, 2015

Speaker(s):

Subir Sachdev

Scientific Organizer:

Zheng-Cheng Gu, Perimeter Institute