Topological Solitons in Helical Strings

The low-energy physics of (quasi)degenerate one-dimensional systems is typically understood as the particle-like dynamics of kinks between stable, ordered structures. Such dynamics, we show, becomes highly non-trivial when the ground states are topologically constrained: a dynamics of the domains rather than on the domains which the kinks separate. Motivated by recently reported observations of charged polymers physisorbed on nanotubes, we study kinks between helical structures of a string wrapping around a cylinder. While their motion cannot be disentangled from domain dynamics, and energy and momentum is not concentrated in the solitons, the dynamics of the domains can be folded back into a one-particle picture.Comment: 5 pages 4 figures. Supplementary materials (animation): S1.mov, S2.mov, S3.mo

Superconductivity at low density near a ferroelectric quantum critical point: doped SrTiO

Recent experiments on electron- or hole-doped SrTiO$_{3}$ have revealed a hitherto unknown form of superconductivity, where the Fermi energy of the paired electrons is much lower than the energies of the bosonic excitations thought to be responsible for the attractive interaction. We show that this situation requires a fresh look at the problem calling for (i) a systematic modeling of the dynamical screening of the Coulomb interaction by ionic and electronic charges, (ii) a transverse optical phonon mediated pair interaction and (iii) a determination of the energy range over which the pairing takes place. We argue that the latter is essentially given by the limiting energy beyond which quasiparticles cease to be well defined. The model allows to find the transition temperature as a function of both, the doping concentration and the dielectric properties of the host system, in good agreement with experimental data. The additional interaction mediated by the transverse optical soft phonon is shown to be essential in explaining the observed anomalous isotope effect. The model allows to capture the effect of the incipient (or real) ferroelectric phase in pure, or oxygen isotope substituted SrTiO$_{3}$ .Comment: 7 pages, 2 figs, revised version, Phys rev B to be publishe

Cracking the Supersolid

We prepresent an overview of the status of experiment and theory on the supersolid state of matter.Comment: Extended version of Science Perspective with more reference

Complexity and geometry of quantum state manifolds

We show that the Hilbert space spanned by a continuously parametrized wavefunction family---i.e., a quantum state manifold---is dominated by a subspace, onto which all member states have close to unity projection weight. Its characteristic dimensionality $D_P$ is much smaller than the full Hilbert space dimension, and is equivalent to a statistical complexity measure $e^{S_2}$, where $S_2$ is the $2^{nd}$ Renyi entropy of the manifold. In the thermodynamic limit, $D_P$ closely approximates the quantum geometric volume of the manifold under the Fubini-Study metric, revealing an intriguing connection between information and geometry. This connection persists in compact manifolds such as a twisted boundary phase, where the corresponding geometric circumference is lower bounded by a term proportional to its topological index, reminiscent of entanglement entropy.Comment: 8 pages including supplementar

Odd-frequency Superconductivity in Driven Systems

We show that Berezinskii's classification of the symmetries of Cooper pair amplitudes holds for driven systems even in the absence of translation invariance. We then consider a model Hamiltonian for a superconductor coupled to an external driving potential and, treating the driving potential as a perturbation, we investigate the corrections to the anomalous Green's function, density of states, and spectral function. We find that in the presence of an external drive the anomalous Green's function develops terms that are odd in frequency and that the same mechanism responsible for these odd-frequency terms generates additional features in the density of states and spectral function.Comment: 10 pages, 3 figure

Dynamical quantum phase transitions: Role of topological nodes in wavefunction overlaps

A sudden quantum quench of a Bloch band from one topological phase toward another has been shown to exhibit an intimate connection with the notion of a dynamical quantum phase transition (DQPT), where the returning probability of the quenched state to the initial state---i.e. the Loschmidt echo---vanishes at critical times $\{t^{*}\}$. Analytical results so far are limited to two-band models, leaving the exact relation between topology and DQPT unclear. In this work, we show that for a general multi-band system, a robust DQPT relies on the existence of nodes (i.e. zeros) in the wavefunction overlap between the initial band and the post-quench energy eigenstates. These nodes are topologically protected if the two participating wavefunctions have distinctive topological indices. We demonstrate these ideas in detail for both one and two spatial dimensions using a three-band generalized Hofstadter model. We also discuss possible experimental observations.Comment: 5 pages, 2 figures, plus supplementary. v2: fixed typos, updated references, added a new appendix on a 1D 3-band model exhibiting symmetry-protected DQPT. To appear in Phys. Rev. Let

Visualizing the particle-hole dualism in high-temperature superconductors

Recent Scanning Tunneling Microscope (STM) experiments offer a unique insight into the inner workings of the superconducting state of high-Tc superconductors. Deliberately placed inside the material impurities perturb the coherent state and produce additional excitations. Superconducting excitations - quasiparticles - are the quantum mechanical mixture of negatively charged electron (-e) and positively charged hole (+e). Depending on the applied voltage bias in STM one can sample the particle and hole content of a superconducting excitation. We argue that the complimentary cross-shaped patterns observed on the positive and negative biases are the manifestation of the particle-hole dualism of the quasiparticles.Comment: 4 pages, 4 eps figure

Excitonic instability in optically-pumped three-dimensional Dirac materials

Recently it was suggested that transient excitonic instability can be realized in optically-pumped two-dimensional (2D) Dirac materials (DMs), such as graphene and topological insulator surface states. Here we discuss the possibility of achieving a transient excitonic condensate in optically-pumped three-dimensional (3D) DMs, such as Dirac and Weyl semimetals, described by non-equilibrium chemical potentials for photoexcited electrons and holes. Similar to the equilibrium case with long-range interactions, we find that for pumped 3D DMs with screened Coulomb potential two possible excitonic phases exist, an excitonic insulator phase and the charge density wave phase originating from intranodal and internodal interactions, respectively. In the pumped case, the critical coupling for excitonic instability vanishes; therefore, the two phases coexist for arbitrarily weak coupling strengths. The excitonic gap in the charge density wave phase is always the largest one. The competition between screening effects and the increase of the density of states with optical pumping results in a reach phase diagram for the transient excitonic condensate. Based on the static theory of screening, we find that under certain conditions for the value of the dimensionless coupling constant screening in 3D DMs can be weaker than in 2D DMs. Furthermore, we identify the signatures of the transient excitonic condensate that could be probed by scanning tunneling spectroscopy, photoemission and optical conductivity measurements. Finally, we provide estimates of critical temperatures and excitonic gaps for existing and hypothetical 3D DMs.Comment: 23 pages, 14 figures, 5 appendice

Pair symmetry conversion in driven multiband superconductors

It was recently shown that odd-frequency superconducting pair amplitudes can be induced in conventional superconductors subjected to a spatially-nonuniform time-dependent drive. It has also been shown that, in the presence of interband scattering, multiband superconductors will possess bulk odd-frequency superconducting pair amplitudes. In this work we build on these previous results to demonstrate that by subjecting a multiband superconductor with interband scattering to a time-dependent drive even-frequency pair amplitudes can be converted to odd-frequency pair amplitudes and vice versa. We will discuss the physical conditions under which these pair symmetry conversions can be achieved and possible experimental signatures of their presence.Comment: 14 pages, 5 figure

Odd Frequency Density Waves

A new type of hidden order in many body systems is explored. This order appears in states which are analogues to charge density waves, or spin density waves, but involve anomalous particle-hole correlations that are odd in relative time and frequency. These states are shown to be inherently different from the usual states of density waves. We discuss two methods to experimentally observe the new type of pairing where a clear distinction between odd and even correlations can be detected: (i) by measuring the density-density correlation, both in time and space and (ii) via the conductivity which, according to the Kubo formula, is given by the current-current correlation. An order parameter for these states is defined and calculated for a simple model, illuminating the physical nature of this order.Comment: 5 pages, 1 figur