# NEWS: The **CQM Distinguished Lecture series** has been established in the Fall of 2015 to bring to Stony Brook University the renown experts in the physics of quantum matter.

## October 2017 – February 2018

Speaker: Sriram Ganeshan

Simons Center, Stony Brook University

Title: Lyapunov Exponent and Out-of-Time-Ordered Correlator’s Growth Rate in a Chaotic System

Abstract:

One of the central goals in the study of quantum chaos is to establish a correspondence principle between classical chaos and quantum dynamics. Due to the singular nature of the \hbar→ 0 limit, it has been a long-standing problem to recover key fingerprints of classical chaos such as the Lyapunov exponent starting from a microscopic quantum calculation. It was recently proposed that the out-of-time-ordered four-point correlator (OTOC) might serve as a useful characteristic of quantum-chaotic behavior because, in the semi-classical limit, its rate of exponential growth resembles the classical Lyapunov exponent. In this talk, I will present OTOC as a tool to unify the classical, quantum chaotic and weak localization regime for the quantum kicked rotor model–a textbook model of quantum chaos. Through OTOC, I will demonstrate how chaos develops in the quantum chaotic regime and is subsequently destroyed by the quantum interference effects that result in dynamical localization. We also make a quantitative comparison between the growth rate of OTOC and the classical Lyapunov exponent. Time permitting, I will introduce an integrable version of a linear rotor model with interactions that serve as a solvable model for many body localization in Floquet systems.

Speaker:** Jing Tao**,** BNL**

Abstract:

The optimal functionalities of materials often appear at phase transitions involving simultaneous changes in the electronic structure and the symmetry of the underlying lattice. It is experimentally challenging to disentangle which of the two effects––electronic or structural––is the driving force for the phase transition and to use the mechanism to control material properties. In this talk, we present a concurrent pumping and probing of Cu2S nanoplates using an electron beam to directly manipulate the transition between two phases with distinctly different crystal symmetries and charge-carrier concentrations, and show that the transition is the result of charge generation for one phase and charge depletion for the other. We demonstrate that this manipulation is fully reversible and nonthermal in nature. Our observations reveal a phase-transition pathway in materials, where electron-induced changes in the electronic structure can lead to a macroscopic reconstruction of the crystal structure. This control method is in contrast to conventional chemical doping, which is irreversible and often introduces unwanted lattice distortions.

We discuss the formulation the coarse equations of fluctuating nonlinear

hydrodynamics (FNH) in terms of density and current fluctuations . The self consistent formulation

of the renormalized dynamics and calculation of the correlation functions using

MSR Field theories are outlined. The possibility of a ergodic to nonergodic transition is presented.

The structure of the liquid is the input in the dynamical models considered here.

We discuss how the structure described in terms of equal time correlation function

is linked to density functional description of the classical liquid with

localized particles in a nonergodic state.

In this respect we consider the collective and single particle dynamics in terms of the

corresponding correlation functions of the liquid and examine the approximation which leads to the

vanishing of the self diffusion.

For a binary mixture this formulation of the FNH equations demonstrates the dependence of the

mass ratio of the two species on the asymptotic dynamics. The equations of the FNH formulated

along similar lines also apply to the flocking of active matter.

**Daniel Mittleman**, Brown University

**Abstract:**

The study of materials using terahertz emission spectroscopy – a process in which optical excitation leads to the generation of low-frequency (rectified) emission as a signature of ultrafast charge carrier dynamics – has become a standard tool in the nonlinear optics toolbox. This versatile optical technique can provide valuable information about the initial phases of carrier motion immediately following photoexcitation, and has been applied to many different material systems, including both bulk and surface dynamics in semiconductors, as well as new materials such as graphene and strongly correlated materials such as high-Tc oxides and topological insulators. These studies have all been limited in their spatial resolution by the diffraction-limited focusing of the input optical beam. In this talk, we discuss the adaptation of this emission spectroscopy technique to the nanoscale. Inspired by recent results in scattering-type near-field terahertz imaging and spectroscopy, we have constructed a new microscope for performing terahertz emission spectroscopy with nanometer spatial resolution. We demonstrate that the nonlinear process giving rise to terahertz emission is confined to a tip-size limited spatial region, on the order of 20 nm. This development offers the exciting new possibility of performing emission spectroscopy on individual nanoparticles.

**Bio:**

Daniel Mittleman received his PhD from the University of California Berkeley in 1994. After two years as a post-doctoral member of the technical staff at Bell Laboratories, he joined the faculty of the Electrical and Computer Engineering Department at Rice University in 1996. He moved to the School of Engineering at Brown University in 2015, where he continues to pursue research in the science and technology of the terahertz range. Dr. Mittleman is a Fellow of the OSA, the APS, and the IEEE. He is currently serving a three-year term as the Chair of the International Society for Infrared Millimeter and Terahertz Waves.

Thermal motions of atoms is an ever-present phenomenon in all of solid state physics. Under normal conditions phonons are the dominant mechanism that govern transport and the largest contribution to entropy. The inherent disorder in thermal motions makes theoretical predictions challenging.

We present methodological developments in finite temperature first principles simulations. We use Born-Oppenheimer molecular dynamics to construct effective Hamiltonians that explicitly depend on temperature. Results and examples include phonon spectral functions, thermodynamics and transport properties with non-trivial temperature dependencies.

Emergence is a ubiquitous feature of quantum condensed matter systems: the collective low-energy behavior of an interacting quantum many-body system oftentimes exhibits behavior profoundly different from that of the constituent degrees of freedom. In this talk, I will present a survey of recent results on one- and two-dimensional quantum systems which dramatically demonstrate this concept. In the first part of the talk, I will focus on a set of problems in which we are able to *uncover* — through both computational and analytical lines of attack — novel and striking emergent behavior in two paradigmatic many-body systems: a quantum antiferromagnet on the kagome lattice and a 2D electron gas in a strong perpendicular magnetic field at filling factor nu=1/2 (i.e., the half-filled Landau level). In the second part of the talk, I will switch gears and discuss how we can *exploit* such emergence for technological gain. In particular, I will discuss how Majorana fermions can emerge as zero-energy features of certain superconducting wires and how these “Majorana zero modes” can in principle be used to build superior quantum computing hardware: In this so-called topological approach to quantum computation, Majorana-based qubits remarkably allow perfect insensitivity to local noise as well as implementation of perfect quantum gates. Focusing on the former property, I will discuss our recent proposals for verifying topological (“perfect”) protection of quantum information in present-day devices being pursued vigorously by experimental groups at Microsoft and elsewhere. I will conclude by discussing several future directions of research in these areas.

The past decade’s apparent success in predicting and experimentally discovering distinct classes of topological insulators (TIs) and semimetals masks a fundamental shortcoming: out of 200,000 stoichiometric compounds extant in material databases, only several hundred of them are topologically nontrivial. Are TIs that esoteric, or does this reflect a fundamental problem with the current piecemeal approach to finding them? To address this, we propose a new and complete electronic band theory that highlights the link between topology and local chemical bonding, and combines this with the conventional band theory of electrons. We classify the possible band structures for all 230 crystal symmetry groups that arise from local atomic orbitals, and show which are topologically nontrivial. We show how our topological band theory sheds new light on known TIs, and demonstrate the power of our method to predict new TIs.

The coupling between lattice and electronic degrees of freedom in materials is at the heart of a variety of phenomena, including superconductivity, heat and charge transport, indirect optical absorption, and the temperature dependence of electronic structure. Density functional theory (DFT) calculations of electron-phonon coupling have proven to be powerful tools for predicting and elucidating these phenomena. We have developed new DFT-based implementations for calculating electron-phonon coupling relevant to two novel applications. The first is the calculation of Shockley-Read-Hall (SRH) recombination of carriers at point defects. SRH is a detrimental, efficiency-lowering process in light-emitting diodes and solar cells; it is often mediated by phonons, so electron-phonon coupling at point defects must be treated. The second application is for determining flexoelectric coefficients. Flexoelectricity refers to the polarization induced in a material by the application of a strain gradient. It is a universal effect in all insulators, and has implications for electronic devices. Computing the flexoelectric response of a material is also an electron-phonon coupling problem, since strain gradients can be treated as very-long-wavelength acoustic phonons. I will describe our first-principles methodologies for calculating flexoelectricity and SRH recombination, and give examples of calculations for technologically interesting materials.

Optics and photonics today enjoy unprecedented freedom. The ability to synthesize arbitrary light fields (through wavefront shaping) and the ability to design structures at the subwavelength scale (through nanofabrication) enable us to realize exciting new phenomena that were not accessible in the past. In this talk, I will present several such experiments, all guided by numerical simulations and theory. A) Conventional textbook wisdom is that waves cannot be perfectly confined within the continuum spectrum of an open system. Exceptions called “bound states in the continuum” [1] were hypothesized by von Neumann and Wigner. I will describe the first realization of such unusual states [2] and their manifestation as polarization vortices protected by topologically conserved “charges” [3]. B) I will show that by tailoring the radiation of optical modes, we can realize non-Hermitian photonic band structures with no counterpart in closed Hermitian systems, such as rings of exceptional points [4] and pairs of exceptional points connected by bulk Fermi arcs [5]. C) Strong disorder in naturally occurring light-scattering media allows us to study mesoscopic physics in a new arena. I will describe the control of optical transport via wavefront shaping, and how the long-range correlations between multiply scattered photons enable us to simultaneously control orders of magnitudes more degrees of freedom than what was previously thought to be possible [6,7].

[1] C. W. Hsu*, B. Zhen* *et al.,* *Nature Reviews Materials* 1, 16048 (2016).

[2] C. W. Hsu*, B. Zhen* *et al*., *Nature* 499, 188 (2013).

[3] B. Zhen*, C. W. Hsu* *et al.*, *Phys. Rev. Lett.* 113, 257401 (2014).

[4] B. Zhen*, C. W. Hsu* *et al*., *Nature* 525, 354 (2015).

[5] H. Zhou *et al.,* *Science*, eaap9859 (2018).

[6] C. W. Hsu *et al*., *Phys. Rev. Lett.* 115, 223901 (2015).

[7] C. W. Hsu *et al*., *Nature Physics* 13, 497 (2017).

One of the most interesting predictions resulting from quantum physics, is the violation of classical symmetries, collectively referred to as anomalies. A remarkable class of anomalies occurs when the continuous scale symmetry of a scale free quantum system is broken into a discrete scale symmetry for a critical value of a control parameter. This is an example of a (zero temperature) quantum phase transition. Such an anomaly takes place for the quantum inverse square potential known to describe ’Efimov physics’. Broken continuous scale symmetry into discrete scale symmetry also appears for a charged and massless Dirac fermion in an attractive 1/r Coulomb potential. The purpose of this talk is to demonstrate the universality of this quantum phase transition and to present convincing experimental evidence of its existence for a charged and massless fermion in an attractive Coulomb potential as realised in graphene.