Abstract: Nonreciprocal interactions in which the influence of A on B differs from that of B on A are abundant in physical, chemical, biological, and ecological systems, and are known to give rise to oscillatory states. Yet, it remains unclear whether these states represent true phases of matter: Can they maintain long-range order in spatially extended, noisy environments in the thermodynamic limit? And what kinds of phase transitions do they exhibit? To address these questions, we introduce a minimal generalization of the Ising model with two species having opposing goals. We demonstrate that oscillatory phases are stable in three dimensions but not in two, and that nonreciprocity changes the critical exponents from those of the Ising model to those of the XY model. We further develop a Harris-like criterion that determines when nonreciprocity fundamentally alters universal behavior. Finally, we apply these insights to a recent model of biomolecular condensates, predicting exotic dynamical phases and suggesting experimental tests.

Abstract: The electronic wavefunction is at the heart of physical phenomena, defining the frontiers of quantum materials research. While the amplitude of the electron wavefunction in crystals can be measured with state-of-the-art probes in unprecedented resolution, its phase has remained largely inaccessible, obscuring rich electronic information. In this talk I will discuss our development of a quantum-path electron interferometer based on time- and angle-resolved photoemission spectroscopy (trARPES), enabling the reconstruction of the phase of electronic states in quantum materials – with energy and momentum resolution. We demonstrate the scheme by resolving the phase along the Dirac electronic band of a prototypical topological insulator and observe a resonance-associated phase jump as well as a momentum and phase synchronized inversion revealing the helicity of the Dirac cone. This photo-electron-interferometer scheme can be extended to a variety of materials, opening up the phase dimension in quantum materials research.

arXiv:2511.09560

Abstract: We consider fermions interacting with an external, in general non-Abelian, gauge field in an essentially inhomogeneous background: the Dirac operator Q(x,−iD) may be of arbitrary order in covariant derivatives and may depend explicitly on coordinates through background fields. For this setting we develop a covariant Wigner–Weyl calculus, in which the Wigner transform of the two-point Green function transforms as in the adjoint (two-index) representation of the gauge group. We derive the inverse transform, the star product in terms of a triangular Wilson loop, its differential representation and its expansion in powers of the field strength, and solve
the generalized Groenewold equation iteratively. The formalism is applied in two directions. (i) Non-dissipative transport: the responses of the vector and axial
currents to the non-Abelian field strength are expressed through topological invariants composed of Wigner-transformed Green functions; this gives the non-Abelian versions of the chiral separation effect and of the quantum Hall effect. (ii) The chiral anomaly: using point-splitting regularization and the Atiyah–Singer
theorem, we show that the anomaly factorizes into the instanton number times the momentum-space invariant N3 responsible for the stability of Fermi points, the same invariant that governs the chiral separation effect.

Following Phys. Rev. D 112, 056035 (2025) and Phys. Lett. B 871, 140021 (2025) [PLB]

Abstract: TBA

Abstract: I define altermagnetism and introduce the two-dimensional Lieb lattice as the simplest realization of this novel magnetic phase. The anomalous Hall effect arising from altermagnetic order and spin–orbit interaction is illustrated with several examples. A comparison between the magnetic point-group and spin-space-group formulations is presented, demonstrating that the Berry-curvature singularity at nodal lines gives rise to a linear, non-analytic scaling of the intrinsic Hall conductivity with spin–orbit coupling. Extrinsic Hall is shown to be substantial in roughly half of altermagnets, namely featuring the Dzyaloshinskii-Moriya interaction.

The non-relativistic piezomagnetism is classified next as linear, quadratic and cubic in strain in g-, h- and i-wave altermagnets, respectively.

Finally I will discuss the odd-parity magnets as the zero spin-orbit realization of ising superconductors.

Abstract: TBA