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Abstract The quantum geometric Berry curvature results in an anomalous correction to the band velocity of crystal electrons with a corresponding transverse (thermo)electric conductivity. However, time‐reversal symmetry typically constrains the direct observation and exploitation of anomalous transport to magnetic compounds. Here, it is demonstrated the anomalous Hall and Nernst conductivities are essential for describing the optoelectronic transport in thin films of the non‐magnetic, weakly gapped semimetal HfTe5 subject to an external magnetic field. A focused photoexcitation adresses the symmetries of the local Nernst conductivity, which unveils a hitherto hidden, anomalous photo‐Nernst effect of three‐dimensional (3D) massive Dirac fermions. The experimental temperature and density dependencies are compared with a semiclassical Boltzmann transport model. For HfTe5 thin films with the Fermi level close to the gap, the model suggests that the anomalous photo‐Nernst currents originate from an intrinsic Berry curvature mechanism, where the Zeeman interaction effectively breaks time‐reversal symmetry of the massive Dirac fermions already at moderate external magnetic fields.

We study black and white hole analogs in Weyl semimetals with inhomogeneous nodal tilts. We study how the presence of a microscopic lattice, giving rise to low-energy fermion doubler states at large momenta that are not present for elementary particles, affects the analogy between Weyl Hamiltonians and general relativity. Using a microscopic tight-binding lattice model, we find the doubler states to give rise to Hawking fragmentation and Hawking attenuation of wave packets by the analog event horizon. These phenomena depend on an analog Hawking temperature and can be measured in metamaterials and solids, as we confirm by numerical simulations.

We investigate the Hall conductance of a two-dimensional Chern insulator coupled to an environment causing gain and loss. Introducing a biorthogonal linear response theory, we show that sufficiently strong gain and loss lead to a characteristic nonanalytical contribution to the Hall conductance. Near its onset, this contribution exhibits a universal power law with a power 3/2 as a function of Dirac mass, chemical potential, and gain strength. Our results pave the way for the study of non-Hermitian topology in fermionic transport experiments.

We construct an exactly solvable lattice model of a fractional Weyl semimetal. The low-energy theory of this strongly interacting state is that of a Weyl semimetal built out of fractionally charged fermions. We show the existence of a universally quantized and fractional circular photogalvanic effect and a violation of the Wiedemann-Franz law in the system. Together with a spectral gap in the single-particle electronic Green's function, they provide strong experimental signatures for this exotic gapless state of matter.

We study a carbon-nanotube quantum dot embedded in a superconducting-quantum-interference-device loop in order to investigate the competition of strong electron correlations with a proximity effect. Depending on whether local pairing or local magnetism prevails, a superconducting quantum dot will exhibit a positive or a negative supercurrent, referred to as a 0 or π Josephson junction, respectively. In the regime of a strong Coulomb blockade, the 0-to-π transition is typically controlled by a change in the discrete charge state of the dot, from even to odd. In contrast, at a larger tunneling amplitude, the Kondo effect develops for an odd-charge (magnetic) dot in the normal state, and quenches magnetism. In this situation, we find that a first-order 0-to-π quantum phase transition can be triggered at a fixed valence when superconductivity is brought in, due to the competition of the superconducting gap and the Kondo temperature. The superconducting-quantum-interference-device geometry together with the tunability of our device allows the exploration of the associated phase diagram predicted by recent theories. We also report on the observation of anharmonic behavior of the current-phase relation in the transition regime, which we associate with the two accessible superconducting states. Our results finally demonstrate that the spin-singlet nature of the Kondo state helps to enhance the stability of the 0 phase far from the mixed-valence regime in odd-charge superconducting quantum dots.

We study electronic transport in Weyl semimetals with spatially varying nodal tilt profiles. We find that the flow of electrons can be guided precisely by judiciously chosen tilt profiles. In a broad regime of parameters, we show that electron flow is described well by semiclassical equations of motion similar to the ones governing gravitational attraction. This analogy provides a physically transparent tool for designing tiltronic devices like electronic lenses. The analogy to gravity circumvents the notoriously difficult full-fledged description of inhomogeneous solids. A comparison to microscopic lattice simulations shows that it is only valid for trajectories sufficiently far from analogue black holes. We finally comment on the Berry curvature-driven transverse motion and relate the latter to spin precession physics.

Real-world topological semimetals typically exhibit Dirac and Weyl nodes that coexist with trivial Fermi pockets. This tends to mask the physics of the relativistic quasiparticles. Using the example of ZrTe$_5$, we show that strain provides a powerful tool for in-situ tuning of the band structure such that all trivial pockets are pushed far away from the Fermi energy, but only for a certain range of Van der Waals gaps. Our results naturally reconcile contradicting reports on the presence or absence of additional pockets in ZrTe$_5$, and provide a clear map of where to find a pure three-dimensional Dirac semimetallic phase in the structural parameter space of the material.

An approach to bound states based on unitary transformations of Hamiltonians is presented. The method is applied to study the interaction between electrons in a BCS $s$-wave superconductor and a quantum spin. It is shown that known results from the t-matrix method and numerical studies are reproduced by this new method. As a main advantage, the method can straightforwardly be extended to study the topological properties of combined bound states in chains of many magnetic impurities. It also provides a uniform picture of the interplay between the Yu-Shiba-Rusinov (YSR) bound states and the Kondo singlet state.

We investigate transport in type-I/type-II Weyl semimetal heterostructures that realize effective black- or white-hole event horizons. We provide an exact solution to the scattering problem at normal incidence and low energies, both for a sharp and a slowly-varying Weyl cone tilt profile. In the latter case, we find two channels with transmission amplitudes analogue to those of Hawking radiation. Whereas the Hawking-like signatures of these two channels cancel in equilibrium, we demonstrate that one can favor the contribution of either channel using a non-equilibrium state, either by irradiating the type-II region or by coupling it to a magnetic lead. This in turn gives rise to a peak in the two-terminal differential conductance which can serve as an experimental indicator of the artificial event horizon.

We study Majorana fermions bound to vortex cores in a chiral $p$-wave superconductor at temperatures non-negligible compared to the superconducting gap. Thermal occupation of Caroli de Gennes-Matricon states, below the full gap, causes the free energy difference between the two fermionic parity sectors to decay algebraically with increasing temperature. The power law acquires an additional factor of $T^{-1}$ for each bound state thermally excited. The zero-temperature result is exponentially recovered well below the minigap (lowest-lying CdGM level). Our results suggest that temperatures larger than the minigap may not be disastrous for topological quantum computation. We discuss the prospect of precision measurements of pinning forces on vortices as a readout scheme for Majorana qubits.

We derive the low-energy theory of semi-quantized quantum Hall states, a recently observed class of gapless bilayer fractional quantum Hall states. Our theory shows these states to feature gapless quasiparticles of fractional charge coupled to an emergent Chern-Simons gauge field. These gapless quasiparticles can be understood as composites of electrons and Laughlin-like quasiparticles. We show that semi-quantized quantum Hall states exhibit perfect interlayer drag, host non-Fermi liquid physics, and serve as versatile parent states for fully gapped topological phases hosting anyonic excitations.