APS March meeting talks rehearsal

Dr. Daniel Kaplan, Rutgers University

Quantum geometry in nonlinear response

The question of electronic transport in solids has been actively reexamined in light of quantum geometry, that is the effects of band topology and wavefunction structure on electronic properties.

In linear response, these signatures are most famously connected with the Berry curvature which is associated with an anomalous Hall effect. Here, I will show a panoply of responses that emerges at nonlinear order, entirely defined by quantum geometric properties of electronic wavefunctions. I will present the general theory of nonlinear response and photoconductivity, focusing on second order effects, and specifically current rectification and second harmonic generation. Related to Moir’e materials, I will discuss a dc current generated by higher momentum correlations of the electronic wavefunction, which is strongly enhanced by flat band to flat band transitions. I will also present a unique nonlinear current, directly related to the dipole of the quantum metric, which sets on when time-reversal symmetry (TRS) is broken. This current dominates transport in scenario where the Berry curvature is strictly zero (by symmetry), such as in PT-symmetric systems or recently investigated altermagnets. This current also serves as a probe of crystal symmetries and the magnetic order of the system; I will present recent experiments on the magnetic topological insulator (and candidate axionic insulator) MnBi2Te4 which have uncovered this novel nonlinear transport effect. I will conclude with a general overview of quantum geometry in nonlinear signals, showing applications to polarization generation (in non-polar media), symmetry breaking in superconductors and light-induced sliding ferroelectricity.

Dr. John Sous, Yale University

Bipolaronic high transition-temperature superconductivity

A model for phonon-mediated high-Tc superconductivity based on superfluidity of light bipolarons is presented. I present numerically exact results obtained using a sign-problem-free quantum Monte Carlo approach for bipolaron binding energies, masses and radii for both Holstein (density-coupled) and Peierls/Su-Schrieffer-Heeger (bond-modulated) models of electron-phonon coupling, with and without both short- and long-range Coulomb interactions. The bond-modulated mechanism is shown to give rise to small-size, yet light-mass bipolarons, which condense at temperatures that generically and significantly exceed typical upper bounds on Tc of phonon-mediated superconductivity based on Migdal-Eliashberg theory. Using a semi-classical instanton approach, an upper bound on Tc for the bond bipolaronic superconductivity is shown to parametrically exceed the upper based on Holstein bipolaron superconductivity.

Dr. Yu He, Yale University

Electronic pseudogap from fluctuations in low dimensional materials

Most metal-to-insulator and metal-to-superconductor transitions are so dramatic that certain symmetries are also concurrently broken, and an energy gap opens in lockstep with this process. But there are electronic systems that develop energy gaps without any broken symmetry, most notably the “pseudogap” in cuprate superconductors. In this talk, I will show two examples of electronic pseudogap in unexpected places: the heavily hole-doped cuprates [1], and an excitonic insulator candidate Ta2NiSe5 [2]. The former is supposedly a good metal where mean-field BCS is thought to apply, and the latter is a structural symmetry-breaking system with strong electron-phonon coupling. Via angle-resolved photoemission spectroscopy and x-ray scattering, we show the electronic gap to persist well above the transition temperature in both systems. With insights from controlled numerical calculations, we show that fluctuation is an important factor when describing the properties of low dimensional material systems. Finally, I will discuss a few new directions in the study of fluctuations.

[1] Phys Rev X 11, 031068 (2021); Nat Mater 22, 671 (2023)

[2] Phys Rev Research 5, 043089 (2023); Nat Commun 14, 7512 (2023)

Dr. Shafique Adam, Washington University in St. Louis

A narrow magic window for ultraflat bands and emergent heavy fermions near the magic angle in twisted bilayer graphene

The notion of a single “magic angle” in twisted bilayer graphene has evolved into a fascinating array of magic angles and ranges each describing different facets of the material’s behavior.  While the original continuum model predicted a nominal magic angle, its simplicity ignored the intricate interplay of different physical phenomena.  For example, lattice relaxation [1] near the magic angle shifts its value upward, only to be counteracted by pseudomagnetic fields.  Including a symmetry allowed relaxation parameter changes this magic angle to a magic range.  Yet another magic angle emerges from the coupling to phonons when the Fermi velocity equals the phonon sound velocity.  Building upon this rich tapestry of magical effects, we will discuss our recent work on the convergence of lattice relaxation and Hartree interaction near the magic angle [2]. We unveil a previously unreported Lifshitz transition to a Fermi surface topology that supports a “heavy fermion” pocket and an ultraflat band pinned to the Fermi energy. Analytical and numerical insights shed light on the narrow “magic angle range” where the “heavy fermion” is stable and make predictions for its experimental observation.  We believe that the bands presented here are accurate  at high temperature and provide a good starting point to understand the myriad of complex behavior observed in this system.

[1] “Analytical Model for Atomic Relaxation in Twisted Moiré Materials” by MMA Ezzi, GN Pallewela, C De Beule, EJ Mele, and S Adam, arXiv:2401.00498 (2024)

[2] “A self-consistent Hartree theory for lattice-relaxed magic-angle twisted bilayer graphene” by MMA Ezzi, L Peng, Z Liu, JHZ Chao, GN Pallewela, D Foo, and S Adam arXiv:2404.17638 (2024)

Dr. Tien Tien Yeh, NORDITA and UConn

Structured Light and Induced Vorticity in Superconductors

Questions of controlling the quantum states of matter via light have been at the forefront of research on driven phases. We demonstrate the effects of imprinted vorticity on superconducting coherent states using structured light. Within the framework of the generalized time-dependent Ginzburg-Landau equation, we show the induction of coherent vortex pairs moving in phase with electromagnetic wave oscillation. The structured light, generated by a Laguerre-Gaussian beam, provides light sources with various quantum properties, such as spin angular momentum and orbital angular momentum. This state of light is also well known as an optical vortex, characterized by a twisted phase front. In the current work, we investigate the optically induced dynamics of superconducting coherent states using both normal light sources and optical vortices. These results uncover rich hydrodynamics of superconducting states and suggest new optical applications for imprinting quantum states on superconducting materials.

Prof. Nikolay Prokofiev, UMass Amherst

Bi-polaron superconductivity in the low density limit

It has been assumed for decades that high values of Tc from the electron-phonon coupling are impossible. At weak-to-intermediate coupling strength this result follows from the Migdal-Eliashberg theory, while at strong coupling, when bipolarons form, the transition temperatures are low because of the exponential effective mass enhancement. However, the latter conclusion was based on numerical solutions of the Holstein model. I will discuss a different model with coupling based on the displacement modulated hopping of electrons and argue that much larger values of the bipolaron Tc can be achieved in this setup. Non-locality of the problem gives rise to small-size, yet relatively light bipolarons, which can be studied by an exact sign-problem-free quantum Monte Carlo approach even in the presence of strong Hubbard and Coulomb potentials. We find that Tc in this model generically and significantly exceeds typical upper bounds based on Migdal-Eliashberg theory or superfluidity of Holstein bipolarons, and, thus, offers a route towards the design of high-Tc superconductors via functional material engineering. Finally, there are indications for even better prospects in systems with non-linear electron-phonon coupling.

Prof. Claudio Chamon, Boston University

Circuit complexity and functionality: a thermodynamic perspective

We explore a link between complexity and physics for circuits of given functionality. Taking advantage of the connection between circuit counting problems and the derivation of ensembles in statistical mechanics, we tie the entropy of circuits of a given functionality and fixed number of gates to circuit complexity. We use thermodynamic relations to connect the quantity analogous to the equilibrium temperature to the exponent describing the exponential growth of the number of distinct functionalities as a function of complexity. This connection is intimately related to the finite compressibility of typical circuits. Finally, we use the thermodynamic approach to formulate a framework for the obfuscation of programs of arbitrary length – an important problem in cryptography – as thermalization through recursive mixing of neighboring sections of a circuit, which can viewed as the mixing of two containers with “gases of gates”. This recursive process equilibrates the average complexity and leads to the saturation of the circuit entropy, while preserving functionality of the overall circuit. The thermodynamic arguments hinge on ergodicity in the space of circuits which we conjecture is limited to disconnected ergodic sectors due to fragmentation. The notion of fragmentation has important implications for the problem of circuit obfuscation as it implies that there are circuits with same size and functionality that cannot be connected via local moves. Furthermore, we argue that fragmentation is unavoidable unless the complexity classes NP and coNP coincide.

Dr. Paul M. Eugenio, University of Connecticut

Tunable moire sublattices in twisted square homobilayers: exploiting fundamental principles for new technologies

Stacking and twisting atomically thin bilayers at small angles produces an approximate periodic pattern, due to the overlap of the crystal layers. These devices, dubbed “moire” bilayers, exhibit a high degree of tunability and variability: through choice of twist angle, constituent layers, and gating. To date, a number of such devices have been built which have demonstrated a plethora of novel phases, including non-trivial topology and Mott physics. Despite this explosion in moire research, moire bilayers have been almost exclusively formed from layers with triangular/hexagonal crystal geometry, and where the valence bands are centered on the Gamma or K/K’ high symmetry points. Here we theoretically demonstrate that moire devices formed from square bilayers can be used to simulate the ground state of the Hubbard model, but where the ratio of the nearest-neighbor (t) and next-to-nearest neighbor (t’) tunneling can be tuned between zero and infinity, in situ via an electric field. If experimentally realized, such a device would be the first of its kind, and would open a pathway toward the testing of a number of proposed exotic phases, such as a spin-liquid and d+id superconductivity. Most importantly, the square Hubbard model is a quintessential model for high-Tc in cuprates, where numerics has demonstrated the absence of superconductivity when t’=0.