Crowded-field photometry from HST-imaging

We present a thorough investigation of stellar photometry based on HST imaging of crowded fields at 85 and 10 arcsec from the centre of the high-surface brightness elliptical M32. The Principal Investigators of the present archive data have elsewhere presented an impressive colour-magnitude diagram of the field at 85 arcsec. Based on the same data we enlarge on their photometric analysis and supplement with error estimators that more clearly show the implications of severe image crowding on the stellar photometry. We show that the faintest stars (I>25.0, V>26.0) are found too bright by several tens of a magnitude. For the field at 10 arcsec we conclude that it is not possible to obtain reliable stellar photometry, standard deviations being larger than 0.4 mag. Artificial-star experiments show that only very few of the brightest stars of the luminosity function can be expected to represent single objects, the majority being either spurious or not as bright as measured.Comment: 7 pages, to be published in Astronomy and Astrophysic

Nonlinear Hall Acceleration and the Quantum Rectification Sum Rule

Electrons moving in a Bloch band are known to acquire an anomalous Hall velocity proportional to the Berry curvature of the band which is responsible for the intrinsic linear Hall effect in materials with broken time-reversal symmetry. Here, we demonstrate that there is also an anomalous correction to the electron acceleration which is proportional to the Berry curvature dipole and is responsible for the nonlinear Hall effect recently discovered in materials with broken inversion symmetry. This allows us to uncover a deeper meaning of the Berry curvature dipole as a nonlinear version of the Drude weight that serves as a measurable order parameter for broken inversion symmetry in metals. We also derive a quantum rectification sum rule in time reversal invariant materials by showing that the integral over frequency of the rectification conductivity depends solely on the Berry connection and not on the band energies. The intraband spectral weight of this sum rule is exhausted by the Berry curvature dipole Drude-like peak, and the interband weight is also entirely controlled by the Berry connection. This sum rule opens a door to search for alternative photovoltaic technologies based on the Berry geometry of bands. We also describe the rectification properties of Weyl semimetals which are a promising platform to investigate these effects

Mixed-valence insulators with neutral Fermi surfaces

Samarium hexaboride is a classic three-dimensional mixed valence system with a high-temperature metallic phase that evolves into a paramagnetic charge insulator below 40 kelvin. A number of recent experiments have suggested the possibility that the low-temperature insulating bulk hosts electrically neutral gapless fermionic excitations. Here we show that a possible ground state of strongly correlated mixed valence insulators - composite exciton Fermi liquid - hosts a three dimensional Fermi surface of a neutral fermion, that we name the "composite exciton". We describe the mechanism responsible for the formation of such excitons, discuss the phenomenology of the composite exciton Fermi liquids and make comparison to experiments in SmB$_6$.Comment: Final published versio

Cyclotron resonance inside the Mott gap: a fingerprint of emergent neutral fermions

A major obstacle to identify exotic quantum phases of matter featuring spin-charge separation above one-dimension is the lack of tailored probes allowing to establish their presence in correlated materials. Here we propose an optoelectronic response that could allow to pinpoint the presence of certain spin-charge separated states with emergent neutral gapless fermions in two and three-dimensional materials. We show that even though these states behave like insulators under static electric fields, they can display clear cyclotron resonance peaks in their light absorption spectrum under static magnetic fields, but typically the principal Kohn mode will be missing in comparison to ordinary metals. This distinctive phenomena could be tested in materials such as triangular lattice organics, three-dimensional mixed valence insulators YbB$_{12}$ and SmB$_6$, and transition metal dichalcogenides 1T-TaS$_2$ and 1T-TaSe$_2$

Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials

It is well-known that a non-vanishing Hall conductivity requires time-reversal symmetry breaking. However, in this work, we demonstrate that a Hall-like transverse current can occur in second-order response to an external electric field in a wide class of time-reversal invariant and inversion breaking materials, at both zero and twice the optical frequency. This nonlinear Hall effect has a quantum origin arising from the dipole moment of the Berry curvature in momentum space, which generates a net anomalous velocity when the system is in a current-carrying state. We show that the nonlinear Hall coefficient is a rank-two pseudo-tensor, whose form is determined by point group symmetry. We discus optimal conditions to observe this effect and propose candidate two- and three-dimensional materials, including topological crystalline insulators, transition metal dichalcogenides and Weyl semimetals.Comment: 5 pages, 1 figur

Quantum oscillations in insulators with neutral Fermi surfaces

We develop a theory of quantum oscillations in insulators with an emergent fermi sea of neutral fermions minimally coupled to an emergent $U(1)$ gauge field. As pointed out by Motrunich (Phys. Rev. B 73, 155115 (2006)), in the presence of a physical magnetic field the emergent magnetic field develops a non-zero value leading to Landau quantization for the neutral fermions. We focus on the magnetic field and temperature dependence of the analogue of the de Haas-van Alphen effect in two- and three-dimensions. At temperatures above the effective cyclotron energy, the magnetization oscillations behave similarly to those of an ordinary metal, albeit in a field of a strength that differs from the physical magnetic field. At low temperatures the oscillations evolve into a series of phase transitions. We provide analytical expressions for the amplitude and period of the oscillations in both of these regimes and simple extrapolations that capture well their crossover. We also describe oscillations in the electrical resistivity of these systems that are expected to be superimposed with the activated temperature behavior characteristic of their insulating nature and discuss suitable experimental conditions for the observation of these effects in mixed-valence insulators and triangular lattice organic materials.Comment: 20 pages, 9 figures, 1 tabl