# 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.

## February – April 2018

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.

Interplay between multiple degrees of freedom — spin, orbital, and lattice — is a promising way to achieve novel phases of matter and functional materials. Development of recent electronic structure tools, such as density-functional theory (DFT) or dynamical mean-field theory (DMFT), has enabled ab-initio study of such phenomena in real materials, and here I will talk about a couple of such examples where electron correlations and spin-orbit coupling take an essential role. In the first example, a deficient spinel chalcogenide GaV_4S_8, I will show that spin-states of V_4 clusters and the crystal structure are closely coupled to each other based on our cluster DMFT calculation results employing molecular orbital bases. In the second example, I will talk about a possible solid-state realization of the Haldane model in a Fe-based honeycomb layered honeycomb compound from the cooperation of spin-orbit coupling and the on-site Coulomb interaction within the Fe d-orbitals.

Speaker: **Liang Wu**, Univ. of Calif. Berkeley and Univ. of Pennsylvania

B-131 Physics, Stony Brook University

**abstract**:

^{(2)}(ω) has been a focus of basic research and technological development for decades as it is both a probe of inversion symmetry breaking in media and the basis for generating coherent light from far-infrared to ultraviolet wavelengths. Here, we focus on the relation between band geometry and nonlinear optics. We measured second harmonic generation (SHG) with incident photon energy from 0.4 eV – 1.6 eV on a polar semimetal TaAs with a sharp resonant peak detected, that is larger than previously measured in any crystal. Our discovery of a giant anisotropic σ

^{(2)}(ω) in TaAs raises the following questions: what is special about TaAs and/or polar metals that accounts for large resonant optical nonlinearity, and, is there a fundamental upper bound on σ

^{(2)}(ω) in such inversion breaking crystals? I will describe a simple model based on the band-geometric theory of nonlinear optical response that addresses these questions.

**Matt Reuter**, Stony Brook Applied Math and IACS

B131 Physics, Stony Brook University

**Abstract**

Exploiting the structure of a quantum mechanical Hamiltonian often leads to fast algorithms for computational simulations involving the system. For instance, sparsity of the Hamiltonian can lead to efficient algorithms for obtaining the Green’s function. But can this structure also provide physical insights? In this talk we will discuss the types of structure that can hide in a Hamiltonian by examining the Hamiltonian’s information content. We then apply this idea to two systems. First, we will investigate the complex band structure of an almost-crystalline system, showing that complex band structure is the minimal, intrinsic material information for describing the system [1]. Second, we will tie this hidden Hamiltonian structure to complete destructive interference effects in electron transport through molecules [2, 3].

[1] M. G. Reuter. J. Phys.: Condens. Matter 29, 053001 (2017).

[2] M. G. Reuter, T. Hansen. J. Chem. Phys. 141, 181103 (2014).

[3] P. Sam-ang, M. G. Reuter. New J. Phys. 19, 053002 (2017).

Speaker: **Jiadong Zang**, Univ. of New Hampshire

B-131 Physics, Stony Brook University