From the Aharonov-Bohm effect to general relativity, geometry plays a central role in modern physics. In quantum mechanics, many physical processes depend on the Berry curvature. However, recent advances in quantum information theory have highlighted the role of its symmetric counterpart, the quantum metric tensor. In this paper, we perform a detailed analysis of the ground state Riemannian geometry induced by the metric tensor, using the quantum $XY$ chain in a transverse field as our primary example. We focus on a particular geometric invariant, the Gaussian curvature, and show how both integrals of the curvature within a given phase and singularities of the curvature near phase transitions are protected by critical scaling theory. For cases where the curvature is integrable, we show that the integrated curvature provides a new geometric invariant, which like the Chern number characterizes individual phases of matter. For cases where the curvature is singular, we classify three types (integrable, conical, and curvature singularities) and detail situations where each type of singularity should arise. Finally, to connect this abstract geometry to experiment, we discuss three different methods for measuring the metric tensor: via integrating a properly weighted noise spectral function or by using leading-order responses of the work distribution to ramps and quenches in quantum many-body systems.

We study the influence of the band structure on the symmetry and superconducting transition temperature in the (solvable) weak-coupling limit of the repulsive Hubbard model. Among other results we find that (1) as a function of increasing nematicity, starting from the square-lattice (zero nematicity) limit where a nodal $d$-wave state is strongly preferred, there is a smooth evolution to the quasi-1D limit, where a striking near-degeneracy is found between a $p$-wave- and a $d$-wave-type paired states with accidental nodes on the quasi-one-dimensional Fermi surfaces—a situation that may be relevant to the Bechgaard salts. (2) In a bilayer system, we find a phase transition as a function of increasing bilayer coupling from a $d$-wave to an $s_{\pm }$-wave state reminiscent of the iron-based superconductors. (3) When an antinodal gap is produced by charge-density-wave order, not only is the pairing scale reduced, but the symmetry of the pairs switches from $d_{x^2-y^2}$ to $d_{xy}$; in the context of the cuprates, this suggests that were the pseudogap entirely due to a competing CDW order, this would likely cause a corresponding symmetry change of the superconducting order (which is not seen in experiment).

We investigate the ultrafast response of the bismuth (111) surface by means of time-resolved photoemission spectroscopy. The direct visualization of the electronic structure allows us to gain insights on electron-electron and electron-phonon interaction. Concerning electron-electron interaction, it is found that electron thermalization is fluence dependent and can take as much as several hundreds of femtoseconds at low fluences. This behavior is in qualitative agreement with Landau's theory of Fermi liquids, but the data show deviations from the behavior of a common three-dimensional degenerate electron gas. Concerning electron-phonon interaction, our data allows us to directly observe the coupling of Bloch states to the coherent $A_{1g}$ mode. It is found that surface states are much less coupled to this mode when compared to bulk states. This is confirmed by ab initio calculations of surface and bulk bismuth.

A new method is presented for measuring terms in the elastoresistivity tensor $m_{ij}$ of single crystal samples with tetragonal symmetry. The technique is applied to a representative underdoped Fe-arsenide, Ba(Fe${}_{0.975}$Co${}_{0.025}$)${}_2$As${}_2$, revealing an anomalously large and anisotropic elastoresistance in comparison to simple metals. The $m_{66}$ coefficient follows a Curie-Weiss temperature dependence, providing direct evidence that the tetragonal-to-orthorhombic structural phase transition that occurs at $T_s=97.5$ K in this material is not the result of a true-proper ferroelastic transition. Rather, the material suffers a pseudoproper transition for which the lattice strain is not the primary order parameter.

A determination of the superconducting (SC) electron pairing symmetry forms the basis for establishing a microscopic mechanism for superconductivity. For iron pnictide superconductors, the $s^{\pm }$-pairing symmetry theory predicts the presence of a sharp neutron spin resonance at an energy below the sum of hole and electron SC gap energies ($E\le 2\Delta$) below $T_c$. On the other hand, the $s^{++}$-pairing symmetry expects a broad spin excitation enhancement at an energy above $2\Delta$ below $T_c$. Although the resonance has been observed in iron pnictide superconductors at an energy below $2\Delta$ consistent with the $s^{\pm }$-pairing symmetry, the mode has also been interpreted as arising from the $s^{++}$-pairing symmetry with $E\ge 2\Delta$ due to its broad energy width and the large uncertainty in determining the SC gaps. Here we use inelastic neutron scattering to reveal a sharp resonance at $E=7$ meV in SC NaFe${}_{0.935}$Co${}_{0.045}$As ($T_c=18$ K). On warming towards $T_c$, the mode energy hardly softens while its energy width increases rapidly. By comparing with calculated spin-excitation spectra within the $s^{\pm }$ and $s^{++}$-pairing symmetries, we conclude that the ground-state resonance in NaFe${}_{0.935}$Co${}_{0.045}$As is only consistent with the $s^{\pm }$ pairing, and is inconsistent with the $s^{++}$-pairing symmetry.

By direct calculations of the spin gap in the frustrated Heisenberg model on the square lattice, with nearest- ($J_1$) and next-nearest-neighbor ($J_2$) super-exchange couplings, we provide a solid evidence that the spin-liquid phase in the frustrated regime $0.45\lesssim J_2/J_1\lesssim 0.6$ is gapless. Our numerical method is based on a variational wave function that is systematically improved by the application of few Lanczos steps and allows us to obtain reliable extrapolations in the thermodynamic limit. The peculiar nature of the nonmagnetic state is unveiled by the existence of $S=1$ gapless excitations at $k=(\pi ,0)$ and $(0,\pi )$. The magnetic transition can be described and interpreted by a variational state that is built from Abrikosov fermions having a $Z_2$ gauge structure and four Dirac points in the spinon spectrum.

I consider refrigeration and heat engine circuits based on the nonlinear thermoelectric response of point contacts at pinch off, allowing for electrostatic interaction effects. I show that a refrigerator can cool to much lower temperatures than predicted by the thermoelectric figure of merit $ZT$ (which is based on linear-response arguments). The lowest achievable temperature has a discontinuity, called a fold catastrophe in mathematics, at a critical driving current $I=I_{\mathrm{c}}$. For $I>I_{\mathrm{c}}$ one can in principle cool to absolute zero, when for $I<I_{\mathrm{c}}$ the lowest temperature is about half the ambient temperature. Heat backflow due to phonons and photons stops cooling at a temperature above absolute zero, and above a certain threshold turns the discontinuity into a sharp cusp. I also give a heuristic condition for when an arbitrary system's nonlinear response means that its $ZT$ ceases to indicate (even qualitatively) the lowest temperature to which the system can refrigerate.

We present detailed magnetometry and muon-spin rotation data on polycrystalline samples of overdoped, nonsuperconducting LiFe${}_{1-x}$Ni${}_x$As ($x=0.1,0.2$) and Li${}_{1-y}$Fe${}_{1+y}$As ($0\le y\le 0.04$) as well as superconducting LiFeAs. While LiFe${}_{1-x}$Ni${}_x$As exhibits weak antiferromagnetic fluctuations down to $1.5\mathrm{K}$, Li${}_{1-y}$Fe${}_{1+y}$As samples, which have a much smaller deviation from the $1:1:1$ stoichiometry, show a crossover from ferromagnetic to antiferromagnetic fluctuations on cooling and a freezing of dynamically fluctuating moments at low temperatures. We do not find any signatures of time-reversal symmetry breaking in stoichiometric LiFeAs that would support recent predictions of triplet pairing.

By measuring time-dependent optical birefringence with 4-femtosecond (fs) laser pulses, we determine the time scale for photoinduced melting of orbital order in the single-layer manganite La${}_{0.5}$Sr${}_{1.5}$MnO${}_4$. Such high time resolution is required to distinguish atomic motions that control the Jahn-Teller distortion from even faster electronic rearrangements. The experiment reveals an 18 fs bottleneck for the loss of orbital order, corresponding to about one-quarter period of the in-plane Jahn-Teller mode. Furthermore, we observe coherent oscillations of this Jahn-Teller mode. Both their amplitude and the birefringence drop exhibit a threshold in their fluence dependence, indicating cooperativity in the lattice response.

We report nuclear magnetic resonance Knight shift data in the heavy-fermion material CeIrIn${}_5$ at fields up to 30 T. The Knight shift of the In displays a strong anomaly, and we analyze the results using two interpretations. We find that the Kondo lattice coherence temperature and the effective mass of the heavy electrons remain largely unaffected by the magnetic field, despite the fact that the Zeeman energy is of the order of the coherence temperature.

We have observed the Autler-Townes doublet in a superconducting Al/AlO${}_X$/Al transmon qubit that acts as an artificial atom embedded in a three-dimensional Cu microwave cavity at a temperature of 22 mK. Using pulsed microwave spectroscopy, the three lowest transmon levels are isolated, eliminating unwanted effects of higher qubit modes and cavity modes. The long coherence time ($\sim$$40\mu \text{s}$) of the transmon enables us to observe a clear Autler-Townes splitting at drive amplitudes much smaller than the transmon level anharmonicity (177 MHz). Three-level density matrix simulations with no free parameters provide excellent fits to the data. At maximum separation, the fidelity of a dark state achieved in this experiment is estimated to be $99.6\%–99.9\%$.

We demonstrate that the volume of the Fermi surface, measured very precisely using de Haas-van Alphen oscillations, can be used to probe changes in the nature and occupancy of localized electronic states. In systems with unconventional ordered states, this allows an underlying electronic order parameter to be followed to very low temperatures. We describe this effect in the field-induced antiferroquadrupolar (AFQ) ordered phase of PrOs${}_4$Sb${}_{12}$, a heavy fermion intermetallic compound. We find that the phase of de Haas-van Alphen oscillations is sensitively coupled, through the Fermi volume, to the configuration of the Pr $f$-electron states that are responsible for AFQ order. In particular, the $\beta$ sheet of the Fermi surface expands or shrinks as the occupancy of two competing localized Pr crystal field states changes. Our results are in good agreement with previous measurements, above 300 mK, of the AFQ order parameter by other methods. In addition, the low-temperature sensitivity of our measurement technique reveals a strong and previously unrecognized influence of hyperfine coupling on the order parameter below 300 mK within the AFQ phase. Such hyperfine couplings could provide insight into the nature of hidden order states in other systems.

The dynamic responses of a rhodium catalyst and a graphene sheet are investigated upon random excitation with 80 kV electrons. An extraordinary electron microscope stability and resolution allow studying temporary atom displacements from their equilibrium lattice sites into metastable sites across projected distances as short as 60 pm. In the rhodium catalyst, directed and reversible atom displacements emerge from excitations into metastable interstitial sites and surface states that can be explained by single atom trajectories. Calculated energy barriers of 0.13 eV and 1.05 eV allow capturing single atom trapping events at video rates that are stabilized by the Rh [110] surface corrugation. Molecular dynamics simulations reveal that randomly delivered electrons can also reversibly enhance the $s{p}^3$ and the $s{p}^1$ characters of the $s{p}^2$-bonded carbon atoms in graphene. The underlying collective atom motion can dynamically stabilize characteristic atom displacements that are unpredictable by single atom trajectories. We detect three specific displacements and use two of them to propose a path for the irreversible phase transformation of a graphene nanoribbon into carbene. Collectively stabilized atom displacements greatly exceed the thermal vibration amplitudes described by Debye-Waller factors and their measured dose rate dependence is attributed to tunable phonon contributions to the internal energy of the systems. Our experiments suggest operating electron microscopes with beam currents as small as zepto-amperes/nm${}^2$ in a weak-excitation approach to improve on sample integrity and allow for time-resolved studies of conformational object changes that probe for functional behavior of catalytic surfaces or molecules.

We establish a physically meaningful representation of a quantum energy density for use in quantum Monte Carlo calculations. The energy density operator, defined in terms of Hamiltonian components and density operators, returns the correct Hamiltonian when integrated over a volume containing a cluster of particles. This property is demonstrated for a helium-neon “gas,” showing that atomic energies obtained from the energy density correspond to eigenvalues of isolated systems. The formation energies of defects or interfaces are typically calculated as total-energy differences. Using a model of $\delta$-doped silicon (where dopant atoms form a thin plane) we show how interfacial energies can be calculated more efficiently with the energy density, since the region of interest is small. We also demonstrate how the energy density correctly transitions to the bulk limit away from the interface where the correct energy is obtainable from a separate total-energy calculation.

We study the time evolution and steady state of the charge current in a single-impurity Anderson model, using matrix product states techniques. A nonequilibrium situation is imposed by applying a bias voltage across one-dimensional tight-binding leads. Focusing on particle-hole symmetry, we extract current-voltage characteristics from universal low-bias up to high-bias regimes, where band effects start to play a dominant role. We discuss three quenches, which after strongly quench-dependent transients yield the same steady-state current. Among these quenches we identify those favorable for extracting steady-state observables. The period of short-time oscillations is shown to compare well to real-time renormalization group results for a simpler model of spinless fermions. We find indications that many-body effects play an important role at high-bias voltage and finite bandwidth of the metallic leads. The growth of entanglement entropy after a certain time scale $\propto {\Delta }^{-1}$ is the major limiting factor for calculating the time evolution. We show that the magnitude of the steady-state current positively correlates with entanglement entropy. The role of high-energy states for the steady-state current is explored by considering a damping term in the time evolution.

We present $GW$ calculations of the topological insulators Bi${}_2$Se${}_3$, Bi${}_2$Te${}_3$, and Sb${}_2$Te${}_3$ within the all-electron full-potential linearized augmented-plane-wave formalism. Quasiparticle effects produce significant qualitative changes in the band structures of these materials when compared to density functional theory (DFT), especially at the $\Gamma$ point, where band inversion takes place. There, the widely used perturbative one-shot $GW$ approach can produce unphysical band dispersions, as the quasiparticle wave functions are forced to be identical to the noninteracting single-particle states. We show that a treatment beyond the perturbative approach, which incorporates the off-diagonal $GW$ matrix elements and thus enables many-body hybridization to be effective in the quasiparticle wave functions, is crucial in these cases to describe the characteristics of the band inversion around the $\Gamma$ point in an appropriate way. In addition, this beyond one-shot $GW$ approach allows us to calculate the values of the $Z_2$ topological invariants and compare them with those previously obtained within DFT.

We investigate, assess, and suggest possibilities for a measurement of the local spin susceptibility of a conducting low-dimensional electron system. The basic setup of the experiment we envisage is a source-probe one. Locally induced spin density (e.g., by a magnetized atomic force microscope tip) extends in the medium according to its spin susceptibility. The induced magnetization can be detected as a dipolar magnetic field, for instance, by an ultrasensitive nitrogen-vacancy center based detector, from which the spatial structure of the spin susceptibility can be deduced. We find that one-dimensional systems, such as semiconducting nanowires or carbon nanotubes, are expected to yield a measurable signal. The signal in a two-dimensional electron gas is weaker, though materials with a high enough $g$-factor (such as InGaAs) seem promising for successful measurements.

We study the interaction of electromagnetic waves with two nested parallel metallic wire arrays, such that the unit cell of the structure has two inequivalent parallel wires. We develop a formalism to solve scattering problems using effective medium methods and prove that the electromagnetic coupling of the two sets of wires may result in the emergence of sharp Fano resonances.

We consider states of bosons in two dimensions that do not support anyons in the bulk, but nevertheless have stable chiral edge modes that are protected even without any symmetry. Such states must have edge modes with central charge $c=8k$ for integer $k$. While there is a single such state with $c=8$, there are, naively, two such states with $c=16$, corresponding to the two distinct even unimodular lattices in 16 dimensions. However, we show that these two phases are the same in the bulk, which is a consequence of the uniqueness of signature $(8k+n,n)$ even unimodular lattices. The bulk phases are stably equivalent, in a sense that we make precise. However, there are two different phases of the edge corresponding to these two lattices, thereby realizing a novel form of the bulk-edge correspondence. Two distinct fully chiral edge phases are associated with the same bulk phase, which is consistent with the uniqueness of the bulk since the transition between them, which is generically first order, can occur purely at the edge. Our construction is closely related to $T$ duality of toroidally compactified heterotic strings. We discuss generalizations of these results.

In tetragonal ${\mathrm{SrCo}}_2{\mathrm{As}}_2$ single crystals, inelastic neutron scattering measurements demonstrated that strong stripe-type antiferromagnetic (AFM) correlations occur at a temperature $T=5$ K [Jayasekara et al., arXiv:1306.5174] that are the same as in the isostructural $A{\mathrm{Fe}}_2{\mathrm{As}}_2$ ($A$ $=$ Ca, Sr, Ba) parent compounds of high-$T_{\mathrm{c}}$ superconductors. This surprising discovery suggests that ${\mathrm{SrCo}}_2{\mathrm{As}}_2$ may also be a good parent compound for high-$T_{\mathrm{c}}$ superconductivity. Here structural and thermal expansion, electrical resistivity $\rho$, angle-resolved photoemission spectroscopy (ARPES), heat capacity $C_{\mathrm{p}}$, magnetic susceptibility $\chi$, ${}^{75}$As NMR, and neutron diffraction measurements of ${\mathrm{SrCo}}_2{\mathrm{As}}_2$ crystals are reported together with LDA band structure calculations that shed further light on this fascinating material. The $c$-axis thermal expansion coefficient ${\alpha }_c$ is negative from 7 to 300 K, whereas ${\alpha }_a$ (the $a$-axis thermal expansion coefficient) is positive over this $T$ range. The $\rho \left(T\right)$ shows metallic character. The ARPES measurements and band theory confirm the metallic character and in addition show the presence of a flat band near the Fermi energy $E_{\mathrm{F}}$. The band calculations exhibit an extremely sharp peak in the density of states $\mathcal{D}(E\approx E_{\mathrm{F}})$ arising from a flat $d_{x^2-y^2}$ band, where the $x$ and $y$ axes are along the $a$ and $b$ axes of the Co square lattice, respectively. A comparison of the Sommerfeld coefficient of the electronic specific heat with $\chi (T\to 0)$ suggests the presence of strong ferromagnetic itinerant spin correlations, which on the basis of the Stoner criterion predicts that ${\mathrm{SrCo}}_2{\mathrm{As}}_2$ should be an itinerant ferromagnet, in conflict with the magnetization data. The $\chi \left(T\right)$ does have a large magnitude, but also exhibits a broad maximum at $\approx 115$ K suggestive of dynamic short-range AFM spin correlations, in agreement with the neutron scattering data. The measurements show no evidence for any type of phase transition between 1.3 and 300 K and we suggest that metallic ${\mathrm{SrCo}}_2{\mathrm{As}}_2$ has a gapless quantum spin-liquid ground state.