Condensed Matter Physics/Biophysics

Condensed matter (CM) research at Notre Dame encompasses topics of research ranging from “hard” CM problems such as semiconductor or superconductor systems to “soft” CM problems such as studies of multicellular aggregates or the application of network theory to biological systems.

The Stavropolous Center for Complex Quantum Matter

The Stavropoulos center– led by Prof. Laszlo Forró – aims to discover and develop new material systems that will be technologically relevant for electronic, sensing and energy harvesting applications. The center brings together various groups specializing in material growth, electrical measurements in a magnetic field, spin resonance, near-field optics and ultralow temperatures. Members of the center have interests that span a broad range of emergent and functional materials.

Materials and systems.

Two-dimensional materials. Two-dimensional (2D) materials are another rapidly growing frontier of modern condensed matter physics research. Their reduced dimensionality allows us to prepare and access intriguing states of matter that may not be readily available in other materials. By stacking 2D layers vertically in a controlled way and tuning parameters such as charge density and stacking order, we are capable of creating artificial heterostructures with programmed properties. For example, we can design flat-band materials unraveling strongly correlated electron physics. At Notre Dame, we apply state-of-the-art methods to study and explore 2D materials with rigorous theoretical and experimental approaches. We work on probing optoelectronic properties through local probe characterization, high magnetic field studies and theoretical modeling of exotic quantum states in 2D materials. Groups involved in work on 2D materials: Hsu, Xiaolong Liu, Stepanov.

Topological materials. Topological materials are materials which host protected electronic states at their boundaries whose existence is guaranteed by a topological invariant, such as a band inversion. These states manifest themselves as gapless pseudo-relativistic electronic modes such as Dirac, Weyl or Majorana modes. Various groups at Notre Dame are studying semiconductors, superconductors and magnetic materials that intrinsically host topological states. The synthesis of these materials can be done on-site at the MBE lab. Groups involved in work on topological matter: Assaf, Hsu, Xiaolong Liu, Eskildsen.

Superconductors and vortex matter. Superconductivity remains a frontier subject, despite being discovered more than a century ago. Long standing questions on this topic include the mechanism driving superconductivity at high temperatures, the manipulation of vortices in established and novel classes of superconductivity, superconductivity in presence of Dirac or Weyl nodes, and triplet superconductivity. Groups involved in work on superconductivity: Assaf, Eskildsen, Forró, Hsu, Janko, Xiaolong Liu, Stepanov.

Magnetism. New magnetic materials unveil new forms of magnetic order, such as skyrmions, and non-collinear antiferromagnets. Recently discovered unconventional antiferromagnets host some properties of ferromagnets, without a net moment present. Several groups at Notre Dame are investigating novel routes to manipulate and detect the properties of magnetic materials. Groups involved in work on magnetism: Assaf, Eskildsen, Janko, Forró.

Quantum Systems. The Emergent Quantum Systems Laboratory (EQSL) led by Prof. Dafei Jin explores topics at the intersection of condensed matter physics and quantum information science. They combine nanoscale quantum electronic and photonic devices with macroscopic quantum liquids and solids to reveal exotic quantum phenomena and create transformative quantum technologies. Their research could lead to ideal platforms for quantum computing, networking, and sensing that will fundamentally change the way we think and live.

Semiconductors, nanostructures, and surfaces. Semiconductors and nanoscale materials, as well as their interfaces and surfaces, can be exploited for energy generation, catalytic activity, quantum sensing, and computation. Various groups are involved in this type of research at the frontier between fundamentals and application: Ptasinska, Janko, and concurrent faculty Kuno (Chemistry) and Hinkle (EE).


Scanning tunneling microscopy. Using scanning tunneling microscopes (STM), we measure quantum mechanical wave functions of solids with sub-atomic precision and sub-meV energy resolution. Such capabilities allow us to visualize and understand vexing problems in quantum matter that emerge in topological, superconducting, and magnetic materials. STM also enables the manipulation of single atoms/molecules and the assembly of them into designer structures. Quantum simulators and artificial lattices that cannot be found in nature can be created. (Xiaolong Liu)

Electron spin resonance (ESR). Transitions can be induced between spin states in a molecule in solution or a solid by applying a magnetic field and then supplying electromagnetic energy to the system in the microwave. We are equipped with a Bruker Elexsys II ESR (EPR) spectrometer with a super X-band microwave bridge (9.2-9.9 GHz) with power tunable 200nW-200 mW and a maximum magnetic field of 1.45 T. A He flow cryostat allows to measure at temperatures as low as 3.8 K and a high-temperature resonator allows us to go up to 1200 K. The spectrometer can be combined with various available lasers available (405 nm, 488 nm, 530 nm and 639 nm) enabling light-induced ESR measurements (Forró).

Near-field optical microscopy. Scanning near-field optical microscopy (SNOM) allows us to resolve optical properties of the materials many orders of magnitude below the Abbe diffraction limit. Nano-optical cavities formed to enhance and control the confined light are modified by the local electromagnetic environment underneath the tip. SNOM is widely used to probe optical plasmonic properties in 2D samples and study local thermodynamic properties in samples with modified electronic properties. SNOM techniques allow us to study light-matter interactions at the extreme confinement in insulating, superconducting, metallic and semiconducting devices. (Stepanov)

Optical spectroscopies. Photoluminescence takes place when photons stimulate the emission of a (different) photon. It is a result of the radiative recombination of the excited electrons participating in the process. We are equipped with a Horiba Jobin-Yvon Triax 320 spectrometer with a visible CCD detector. Various laser (405nm, 488nm, 530nm, 639nm), and a continuously variable halogen lamp with a built-in grating monochromator can be used as sources of excitation (Forró). Raman spectroscopy is based on the analysis of inelastically scattered light and can sense phonons, optical magnons, plasmons, or even electronic excitations. A WITec-made alpha300R Raman spectrometer with a 10cm-1 cutoff equipped with three excitation wavelengths (457 nm, 532 nm, and 633 nm) is available for measurements down to 4K. The spectrometer is also equipped with a wide variety of microscope objectives (Forró).

Electrical and optical measurements at high magnetic fields. Using superconducting coils cooled down to liquid helium temperatures, we can reach high magnetic fields to probe the electronic, magnetic, vibrational, and optical properties of solids. Three systems are available for such measurements, a Quantum Design PPMS allowing 14T and 1.8K (Forró), an MPMS allowing 7T and 2K and a custom Oxford Instruments cryostat allowing up to 16T and 1.5K coupled to an electrical rack and a broadband FTIR spectrometer (Assaf).

Small-angle neutron scattering (SANS). SANS is ideal for bulk studies of materials at mesoscopic length scales from tens to hundreds of nanometers, and thus well suited for studies of both magnetic skyrmions and superconducting vortices.  The SANS experiments are carried out at domestic and international facilities, and often push the boundaries of the technique.  This includes measurements in the presence of electrical or thermal currents, using strain to tune the electronic properties of a given material, and performing spatially resolved SANS measurements. (Eskildsen)

Molecular beam epitaxy (MBE). MBE allows the layer-by-layer synthesis of ultra-high purity materials, with atomic control of properties. Learn more about the MBE activity at Notre Dame though this link. (Assaf, Xinyu Liu)

Surface Science. Photoemission spectroscopy allows the characterization of chemical and electronic structures of surfaces and their interfaces. X-ray photoelectron spectroscopy (XPS) combined with ultraviolet photoelectron spectroscopy (UPS) measurements can be carried out at the Radiation Lab in the group of S. Ptasinska, including studies under UHV and near-ambient pressure conditions.

Theoretical Condensed Matter Physics

Topological superconductivity

Topological superconductors (Tsc) are exotic quantum phases of matter that exhibit Majorana boundary modes and are proposed to be promising platforms for topological quantum computation. Depending on the protecting symmetries, Tsc can host first- or higher-order band topology, which feature Majorana modes on different-dimensional boundaries. Theoretical research at Notre Dame focuses on various topics in first- and higher-order Tsc phases, including topological invariants, material predictions, and experimental signatures. Methods used are both analytical and numerical, including real- and momentum-space classification methods, renormalization group techniques, and Hartree-Fock method etc. (Hsu)

Correlated phases and unconventional superconductivity in few-layer VdW systems

Recent experimental breakthroughs in manipulating mono-layer and few-layer Van der Waals materials have led to new platforms that can be designed to realize rare exotic phases. In particular, the twist angle between adjacent layers is in fact a tuning knob that can tune the relative strengths between the kinetic energy and electronic interactions. At Notre Dame, we theoretically investigate how various interaction-driven phases could be favored by tuning twist angle and other experimental knobs in different VdW systems. (Hsu)

Quantum Dynamics

Isolated quantum many-body systems without heat bath can exhibit interesting eigenstate and dynamical properties in the presence of disorders and interactions. In particular, such systems do not reach thermal equilibrium and exhibit phases that can be well-described by statistical mechanics. At Notre Dame, we apply novel numerical approaches, such as Machine-learning methods tailored for such problems, to study entanglement, dynamical, and localization properties in these systems. Recently, we also focus on the localization and dynamics in non-Hermitian quantum systems. (Hsu)  

Confined vortex network of type-II superconductor

At Notre Dame, we study confined superconducting vortex matter, when Abrikosov vortices are confined into a mesoscopic container. When the container is large, the vortices are arranged in a triangular Abrikosov vortex lattice. In contrast, in a mesoscopic container, vortices are arranged in other geometries strongly influenced by the container symmetry. In order to systematically study the system of confined vortices, we use computer simulations for Abrikosov vortex on mesoscopic superconducting samples. The computational methods we used include: Molecular Dynamic (MD) simulation, Gradient Descent, Eigenvector Following, etc. We developed a network science approach to analyze and represent the complicated energy landscape of these systems. We developed original codes to effectively find local minima (metastable states) and first-order saddle points (transition states) of the energy function, which are then connected to construct a complex network representation of the energy landscape. With the transition barrier on each edge, this is a concise representation encoding the system dynamics. One of the topics we are particularly interested in is the “magic number” sequence in different containers, corresponding to extraordinary stable states at some specific numbers of vortices. We also investigate the effect of container symmetry and size on these magic number states and differentiate between the so-called angular melting and general melting transitions. Finally, we explore the influence of anisotropic vortex interactions on the structure of mesoscopic vortex matter (Janko).

Optical cooling of semiconductors

Development in cryocooler are critical for academic research and industry. The discoveries of unique phenomena at low temperature, including Bose–Einstein condensation, superconductivity,  superfluidity, and the fractional quantum Hall effect, are all based on the ability to reach low temperatures. It is also essential to numerous modern technologies such as visible and infrared photodetectors, which require low temperatures to suppress dark noise and improve device performance. Currently, minimum achievable temperatures for thermoelectric solid-state cryocoolers are around 170 K.  So a pressing need exists to develop new solid state cooling technologies suitable for future optoelectronic applications. The concept of condensed phase optical refrigeration has existed for several decades. In semiconductors, this entails first creating a cold population of free electrons and holes using a laser tuned to the semiconductor band edge. Subsequent phonon coupling results in carrier excitation and leads to emission with energies greater than those of the incident laser. This removes thermal energy from the system and sets the basis for optical cooling. Despite the conceptual simplicity of the process, realizing optical refrigeration requires exacting parameters from the condensed phase medium. This includes near-unity external quantum efficiencies (EQEs) and corresponding up-conversion efficiencies, both aimed at suppressing unwanted background heating. In this study, we are therefore investigating the potential laser cooling of CsPbBr3 nanocrystals as well as other high EQE nanostructures. The goal is to understand the origin of upconversion in these materials and to eventually demonstrate practical examples of condensed phase optical cooling. (Janko)

Superfluorescence from perovskite nanocrystal superlattices

Spontaneous emission is a basic quantum mechanical effect due to the coupling of an excited electronic state with the vacuum state of the electromagnetic field. In an ensemble of identical emitters, cooperative radiation emerges. Called superradiance (SR) by Dicke, who first proposed the phenomenon in 1954, this effect arises from the excitation of an ensemble of individual dipole emitters and results in an emissive, macroscopic quantum state. SR has been observed in a variety of systems, with some of the most recent examples being cold atomic clouds, photosynthetic antenna complexes, quantum dots and nitrogen vacancies in nanodiamonds. A special case of SR is superfluorescence (SF), where the initially prepared state is an incoherent ensemble of emitting dipoles that spontaneously self organizes through their mutual field to generate macroscopic coherence. In an exciting development, SF-like behavior has recently been observed at low temperature (6 K) in a solid state superlattice of CsPbBr3 perovskite nanocrystals (NCs) [Rainò G. et al. Nature 563, 671-675 (2018)]. These superlattices consist of millions of individual NCs self-assembled into ordered arrays with dimensions on the order of microns. Apparent SF distinguishes itself from the normal band edge emission of CsPbBr3 NCs in that it has a 2.7 times faster radiative lifetime.  Most importantly, the emission is coherent as seen through first- and second-order correlation measurements. We have now developed an open quantum model, based on the use of well-known non-Hermitian radiative Hamiltonians, to rationalize SF-like emission from NC superlattices in the weak excitation regime. Our model accounts for interactions between individual NCs and their common light field even for distances larger than the transition wavelength inside the material. Our aim is to rationalize the recent experimental observations of SF in these materials and to predict some experimental conditions that can allow a stronger, more robust SF. (Janko)


The department hosts an active program In biophysics, focusing on modeling the structure and development of various biological systems. A strong focus is on understanding the topological properties of cellular networks--the networks formed by the Interactions between metabolites, genes and proteins, modeling both their structure and dynamical behavior. Using techniques from statistical mechanics, models of “convergent extension” cell rearrangements have been developed as a way to understand one step in embryonic development. At a higher level, multicellular aggregates, such as embryonic and mature tissues, are modeled. These systems often share the properties of “excitable media” and “soft matter,” familiar to modern condensed matter physics and dynamical systems theory. Biological research is carried out in collaboration with other groups on the campus, involving faculty from biochemistry and biology, under the coordination of the Center for Biocomplexity.