## Abstracts for Condensed Matter Seminars

### Hong Ding, July 10, 2014, Abstract:

Iron-based superconductors (Fe-SCs), with their highest transition temperature (Tc) at 57K, have been added since 2008 to the family of high-Tc superconductors which has been solely occupied by copper-based superconductors (Cu-SCs) for more than 20 years. Both Fe-SCs and Cu-SCs, with a transition element playing crucial roles in their superconductivity, share a similar phase diagram where the superconducting phase is adjacent to a magnetic order phase, and are clearly beyond of the scope of BCS superconductors. In this talk I will report our extensive and some new ARPES results on Fe-SCs, which demonstrate unequivocally that a strong pairing gap is determined by its location in the momentum space, basically following a coskxcosky function which is likely determined by the local next-nearest-neighboring antiferromagnetic exchange J2, in much the same way that the d-wave gap of cuprates is caused by its nearest-neighboring exchange J1. In an example of Li(Fe,Co)As, the low-energy spin fluctuations, while sensitive to the Fermi surface nesting condition, are found not directly tie to its superconductivity. We conclude that a same pairing mechanism, at least phenomenologically if not microscopically, must be in work for both Fe- and Cu-SCs.

### Peng Cai, September 22, 2014, Abstract

One of the key issues regarding the cuprate high temperature superconductors is the evolution of the electronic structure when charge carriers are doped into the parent Mott insulator. We have performed scanning tunneling microscopy studies on the parent Ca2CuO2Cl2 Mott insulator and severely underdoped Bi2Sr2-xLaxCuO6 in the antiferromagnetic insulating state. The large energy window covered by the tunneling spectroscopy allows us to simultaneously capture the features of the full charge transfer gap and the low energy electronic state at the atomic scale. We show that with increasing hole doping, the high energy spectral weight of the upper Hubbard band is systematically transferred to the low energy electronic states within the charge transfer gap. When sufficient amount of holes are introduced, a V-shaped energy gap forms near the Fermi level and in the meantime a short-range charge ordering emerges. The implications of these results on the pseudogap phase and charge density order in the cuprates will be discussed.

### Patrick Lee, October 27, 2014 Abstract:

The pseudo-gap phase has long been considered a central piece of the high Tc puzzle. I shall review some of the data and show why they are difficult to explain. I then show that by postulating a novel form of pair fluctuation, much of the data can be accounted for. Experiments to test this idea will be discussed.

### John Martinis, November 10, 2014, Abstract

Superconducting quantum computing is now at an important crossroad, where “proof of concept” experiments involving small numbers of qubits can be transitioned to more challenging and systematic approaches that could actually lead to building a quantum computer. Our optimism is based on two recent developments: a new hardware architecture for error detection based on “surface codes”, and recent improvements in the coherence of superconducting qubits. I will explain how the surface code is a major advance for quantum computing, as it allows one to use qubits with realistic fidelities, and has a connection architecture that is compatible with integrated circuit technology. We have also recently demonstrated a universal set of logic gates in a superconducting Xmon qubit that achieves single-qubit gate fidelity of 99.92% and a two-qubit gate fidelity up to 99.4%. This places Josephson quantum computing at the fault-tolerant threshold for surface code error correction. Our quantum processor is a first step towards the surface code, using five qubits arranged in a linear array with nearest-neighbor coupling. Using this device we have further demonstrated generation of the five-qubit Greenberger-Horne-Zeilinger (GHZ) state using the complete circuit and full set of gates, giving a state fidelity of 82% and a Bell state (2 qubit) fidelity of 99.5%. These results demonstrate that Josephson quantum computing is a high-fidelity technology, with a clear path to scaling up to large-scale, fault-tolerant quantum circuits.

### Barry Bradlyn, November 11, 2014, Abstract:

One hallmark of topological phases with broken time reversal symmetry is the appearance of quantized non-dissipative transport coefficients, the archetypical example being the quantized Hall conductivity in quantum Hall states. Here I will talk about two other non-dissipative transport coefficients that appear in such systems - the Hall viscosity and the thermal Hall conductivity. In the first part of the talk, I will start by reviewing previous results concerning the Hall viscosity, including its relation to a topological invariant known as the shift. Next, I will show how the Hall viscosity can be computed from a Kubo formula. For Galilean invariant systems, the Kubo formula implies a relationship between the viscosity and conductivity tensors which may have relevance for experiment. In the second part of the talk, I will discuss the thermal Hall conductivity, its relation to the central charge of the edge theory, and in particular the absence of a bulk contribution to the thermal Hall current. I will do this by constructing a low-energy effective theory in a curved non-relativistic background, allowing for torsion. I will show that the bulk contribution to the thermal current takes the form of an "energy magnetization" current, and hence show that it does not contribute to heat transport.

### Debaleena Nandi, November 13, 2014, Abstract:

Bose-Einstein condensation of excitons is realized in a quantum Hall bilayer at vT=1 when the total electron density in the two quantum wells matches the degeneracy of a single spin split Landau level. By decreasing equally the electron density in the two quantum wells and thereby decreasing the effective inter-layer separation between electrons, the system exhibits a phase transition between two independent quantum Hall layers and a phase coherent bilayer. Earlier studies in Hall bar geometry revealed remarkable signatures of the exciton condensate in tunneling and Coulomb drag experiments. The tunneling is reminiscent of the dc Josephson effect [1] and a quantized Hall drag [2] is also observed. However, whether exciton transport is a bulk or edge phenomenon cannot be distinguished in these Hall bar experiments.

Our experiments in Corbino geometry [3,4,5] reveal both tunneling and Coulomb drag as happening throughout the bulk of the vT=1 bilayer. Just like all quantum hall states, charge transport through the bulk is activated and suppressed by a quantum hall gap. But the bulk is transparent to the exciton mode of transport. Also, the transmission of bulk excitons is found to be nearly dissipationless. This is consistent with exciton condensation.

To probe the analogy between tunneling in bilayers and the dc-Josephson effect further, we are looking for Shapiro-like steps in the tunneling when the tunnel junction is coupled to microwave radiation. We will briefly also report progress in this effort.

References

[1] I. B. Spielman, J. P. Eisenstein, L. N. Pfeiffer, & K. W. West, Physical Review Letters, 84, 5808 (2000).

[2] M. Kellogg, J. P.Eisenstein, L. N. Pfeiffer, & K. W. West, Physical Review Letters, 93, 036801 (2004).

[3] A.D.K. Finck, J.P. Eisenstein, L. N. Pfeiffer, & K. W. West, Physical Review Letters, 106, 236807 (2011).

[4] D. Nandi, A. D. K. Finck, J. P. Eisenstein, L. N. Pfeiffer, & K. W. West, Nature, 488, 481(2012).

[5] D. Nandi, T. Khaire, A. D. K. Finck, J. P. Eisenstein, L. N. Pfeiffer, & K. W. West, , Physical Review B, 88, 165308 (2013).

### Anatoli Polkovnikov, November 17, 2014, Abstract:

I will overview relations between the non-adiabatic response and the geometric tensor. In particular, I will show how the Berry curvature (imaginary part of the geometric tensor) and the topological phase transitions can be engineered and measured using non-adiabatic response and discuss recent experiments in superconducting qubits. The real part of the geometric tensor (Fubini-Study metric) can be measured through noise or imaginary part of the linear response susceptibility. In turn this metric can be used to construct new geometric and topological invariants based on the Euler characteristic. In the last part of the talk I will show that the Newtonian or Hamiltonian dynamics is emergent from the non-adiabatic response and that the notion of the mass is closely related to the metric tensor. I will discuss leading corrections beyond the Hamiltonian dynamics. I will demonstrate general results using simple examples of particles or photons confined to a cavity.

### Adolpho Grushin, November 19, 2014, Abstract:

Chern insulators (CI) and fractional Chern insulators (FCI) are zero field lattice analogues of the integer and fractional quantum Hall effects respectively. In this talk we will address the important problem of when and how they are induced by interactions. For the former, we will focus on the existing disagreement between mean field theory results and exact diagonalization/infinite density matrix renormalization group (iDMRG) studies regarding the emergence of the CI state from a semi-metal via short range interactions. For the FCI state I will exemplify its full numerical characterization with the help of iDMRG, a method which will allows us to address, amongst other things, the character of the Metal-FCI phase transition, a possible benchmark for future experiments.

References:

arXiv:1407.6985

Phys. Rev. B 88, 245123 (2013)

Phys. Rev. B 87, 085136 (2013)

### Chen Chiu, November 24, 2014, Abstract:

We present a new scheme to engineer the energy-momentum dispersion of atoms in optical lattices. By hybridizing bands, we identify a novel quantum phase transition from the emergence of superfluid domains with ferromagnetic interactions. Bragg spectroscopy within one domain reveals the appearance of roton excitations, which strongly suppress superfluidity near the quantum critical point.

### James Analytis, December 1, 2015, Abstact:

The physics of quantum critical phase transitions connects to some of the most difficult problems in condensed matter physics, including metal-insulator transitions, frustrated magnetism and high temperature superconductivity. Near a quantum critical point (QCP) a new kind of metal emerges, whose thermodynamic and transport properties do not fit into the unified phenomenology with which we understand conventional metals - the Landau Fermi liquid (FL) theory - characterized by a low temperature limiting T-linear specific heat and a T^2 resistivity. Studying the evolution of the T¬ dependence of these observables as a function of a control parameter leads to the identification both of the presence and the nature of the quantum phase transition in candidate systems. In this study we measure the transport properties of BaFe2(As1-xPx)2, at T<T_c by suppressing superconductivity with high magnetic fields. We find an anomalous magnetic field dependence that suggests that not only does magnetic field directly affect the scattering rate (which is unusual for metals), but it does so in a way that is identical to temperature. We suggest that there is a universal phenomenology of scattering near a quantum critical point.

### Nicolas Regnault, December 8, 2014, Abstract:

The understanding and simulation of quantum many-body states in one space dimension has experienced revolutionary progress with the advent of the density matrix renormalization group. In modern language, this method can be viewed as a variational optimization over the set of matrix product states (MPS). Due to their perimeter law entanglement, 2-D systems such as the fractional quantum Hall effect are harder to simulate by MPS.

We will show that many fractional quantum Hall states have an exact infinite MPS representation. We will discuss how a controlled truncation can be performed on this representation and we will give a natural interpretation from the entanglement spectrum perspective. Through the MPS, We will give evidences why certain model states related to non-unitary conformal field theories, are pathological. We will also show the direct characterization of the Read-Rezayi quasihole excitations from their MPS description.

### Donna Sheng, December 10, 2014, Abstract

The kagome spin-1/2 model with dominant nearest neighboring (J1) antiferromagnetic coupling

had been proposed to host an exotic gapped Z2 spin liquid based on density matrix renormalization group study. Here we report a new finding that small perturbations from the second (J2) and third neighboring (J3) exchange couplings will lead to a time reversal symmetry breaking chiral spin liquid. Searching for the microscopic understanding of the emerging and collapsing of these phases, we study the quantum phase diagram and the interplay of J1-J2-J3 couplings in the kagome lattice model.

For SU2 invariant model, we establish a rich phase diagram where a chiral spin liquid phase emerges between the magnetically ordered antiferromagnetic phase known as $q=(0,0)$ state and a complex non-coplanar ordered state with spins forming the vertices of a cuboctahedron known as a cuboc1 phase. We characterize the spontaneous time-reversal symmetry breaking chiral spin liquid as the Laughlin nu=1/2 bosonic fractional quantum Hall state proposed 20 years ago, based on topological Chern number and modular matrices of the state. The robustness of the chiral spin liquid persists into spin anisotropic model, including the pure XY model (where all the spin exchange interactions are XY interactions).

We explore the nature of quantum phase transitions from chiral spin liquid to time-reversal invariant spin liquid and other magnetic ordered phases, and point to the possibility of the novel continuous transitions in such systems.

We also reveal that there may be a gapless spin liquid state for nearest neighboring dominant spin anisotropic model, with the low energy singlet excitations as magneto-roton minimum of the system. We will also discuss the possible indications of the theoretical results to the experimental relevant frustrated kagome magnets.

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