Topological phase transition and texture inversion in a tunable topological insulator

The recently discovered three-dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit interaction or the crystal lattice, driving the system through a topological quantum phase transition. By directly measuring the topological quantum numbers and invariants, we report the observation of a phase transition in a tunable spin-orbit system, BiTl(S(1-δ)Se(δ))(2), in which the topological state formation is visualized. In the topological state, vortex-like polarization states are observed to exhibit three-dimensional vectorial textures, which collectively feature a chirality transition as the spin momentum-locked electrons on the surface go through the zero carrier density point. Such phase transition and texture inversion can be the physical basis for observing fractional charge (±e/2) and other fractional topological phenomena.     

Quantum spin hall insulator state in HgTe quantum wells

Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density and high mobility in which we could tune, through an external gate voltage, the carrier conduction from n-type to p-type, passing through an insulating regime. For thin quantum wells with well width d < 6.3 nanometers, the insulating regime showed the conventional behavior of vanishingly small conductance at low temperature. However, for thicker quantum wells (d > 6.3 nanometers), the nominally insulating regime showed a plateau of residual conductance close to 2e(2)/h, where e is the electron charge and h is Planck's constant. The residual conductance was independent of the sample width, indicating that it is caused by edge states. Furthermore, the residual conductance was destroyed by a small external magnetic field. The quantum phase transition at the critical thickness, d = 6.3 nanometers, was also independently determined from the magnetic field-induced insulator-to-metal transition. These observations provide experimental evidence of the quantum spin Hall effect.     

Quantum phase extraction in isospectral electronic nanostructures

Quantum phase is not directly observable and is usually determined by interferometric methods. We present a method to map complete electron wave functions, including internal quantum phase information, from measured single-state probability densities. We harness the mathematical discovery of drum-like manifolds bearing different shapes but identical resonances, and construct quantum isospectral nanostructures with matching electronic structure but divergent physical structure. Quantum measurement (scanning tunneling microscopy) of these "quantum drums"-degenerate two-dimensional electron states on the copper(111) surface confined by individually positioned carbon monoxide molecules-reveals that isospectrality provides an extra topological degree of freedom enabling robust quantum state transplantation and phase extraction.     

Actinide topological insulator materials with strong interaction

Topological band insulators have recently been discovered in spin-orbit coupled two-and three-dimensional systems. We theoretically predict a class of topological insulators where interaction effects play a dominant role. In actinide elements, simple rocksalt compounds formed by Pu and Am lie on the boundary between metals and insulators. We show that interaction drives a quantum phase transition to a topological insulator phase with a single Dirac cone on the surface. These putative topological insulators may provide a setting for both applied and fundamental investigation.     

Quantum phase interference and parity effects in magnetic molecular clusters

An experimental method based on the Landau-Zener model was developed to measure very small tunnel splittings in molecular clusters of eight iron atoms, which at low temperature behave like a nanomagnet with a spin ground state of S = 10. The observed oscillations of the tunnel splittings as a function of the magnetic field applied along the hard anisotropy axis are due to topological quantum interference of two tunnel paths of opposite windings. Transitions between quantum numbers M = -S and (S - n), with n even or odd, revealed a parity effect that is analogous to the suppression of tunneling predicted for half-integer spins. This observation is direct evidence of the topological part of the quantum spin phase (Berry phase) in a magnetic system.     

Deconfined quantum critical points

The theory of second-order phase transitions is one of the foundations of modern statistical mechanics and condensed-matter theory. A central concept is the observable order parameter, whose nonzero average value characterizes one or more phases. At large distances and long times, fluctuations of the order parameter(s) are described by a continuum field theory, and these dominate the physics near such phase transitions. We show that near second-order quantum phase transitions, subtle quantum interference effects can invalidate this paradigm, and we present a theory of quantum critical points in a variety of experimentally relevant two-dimensional antiferromagnets. The critical points separate phases characterized by conventional "confining" order parameters. Nevertheless, the critical theory contains an emergent gauge field and "deconfined" degrees of freedom associated with fractionalization of the order parameters. We propose that this paradigm for quantum criticality may be the key to resolving a number of experimental puzzles in correlated electron systems and offer a new perspective on the properties of complex materials.     

The Resonating Valence Bond State in La2CuO4 and Superconductivity

The oxide superconductors, particularly those recently discovered that are based on La(2)CuO(4), have a set of peculiarities that suggest a common, unique mechanism: they tend in every case to occur near a metal-insulator transition into an odd-electron insulator with peculiar magnetic properties. This insulating phase is proposed to be the long-sought "resonating-valence-bond" state or "quantum spin liquid" hypothesized in 1973. This insulating magnetic phase is favored by low spin, low dimensionality, and magnetic frustration. The preexisting magnetic singlet pairs of the insulating state become charged superconducting pairs when the insulator is doped sufficiently strongly. The mechanism for superconductivity is hence predominantly electronic and magnetic, although weak phonon interactions may favor the state. Many unusual properties are predicted, especially of the insulating state.     

Quasi-particle properties from tunneling in the v = 5/2 fractional quantum Hall state

Quasi-particles with fractional charge and statistics, as well as modified Coulomb interactions, exist in a two-dimensional electron system in the fractional quantum Hall (FQH) regime. Theoretical models of the FQH state at filling fraction v = 5/2 make the further prediction that the wave function can encode the interchange of two quasi-particles, making this state relevant for topological quantum computing. We show that bias-dependent tunneling across a narrow constriction at v = 5/2 exhibits temperature scaling and, from fits to the theoretical scaling form, extract values for the effective charge and the interaction parameter of the quasi-particles. Ranges of values obtained are consistent with those predicted by certain models of the 5/2 state.     

Metal-insulator transition in disordered two-dimensional electron systems

We present a theory of the metal-insulator transition in a disordered two-dimensional electron gas. A quantum critical point, separating the metallic phase, which is stabilized by electronic interactions, from the insulating phase, where disorder prevails over the electronic interactions, has been identified. The existence of the quantum critical point leads to a divergence in the density of states of the underlying collective modes at the transition, causing the thermodynamic properties to behave critically as the transition is approached. We show that the interplay of electron-electron interactions and disorder can explain the observed transport properties and the anomalous enhancement of the spin susceptibility near the metal-insulator transition.     

Divergent nematic susceptibility in an iron arsenide superconductor

Within the Landau paradigm of continuous phase transitions, ordered states of matter are characterized by a broken symmetry. Although the broken symmetry is usually evident, determining the driving force behind the phase transition can be complicated by coupling between distinct order parameters. We show how measurement of the divergent nematic susceptibility of the iron pnictide superconductor Ba(Fe(1-x)Co(x))(2)As(2) distinguishes an electronic nematic phase transition from a simple ferroelastic distortion. These measurements also indicate an electronic nematic quantum phase transition near the composition with optimal superconducting transition temperature.     

The coexistence of superconductivity and topological order in the Bi₂Se₃ thin films

Three-dimensional topological insulators (TIs) are characterized by their nontrivial surface states, in which electrons have their spin locked at a right angle to their momentum under the protection of time-reversal symmetry. The topologically ordered phase in TIs does not break any symmetry. The interplay between topological order and symmetry breaking, such as that observed in superconductivity, can lead to new quantum phenomena and devices. We fabricated a superconducting TI/superconductor heterostructure by growing dibismuth triselenide (Bi(2)Se(3)) thin films on superconductor niobium diselenide substrate. Using scanning tunneling microscopy and angle-resolved photoemission spectroscopy, we observed the superconducting gap at the Bi(2)Se(3) surface in the regime of Bi(2)Se(3) film thickness where topological surface states form. This observation lays the groundwork for experimentally realizing Majorana fermions in condensed matter physics.     

Topological transitions in metamaterials

Light-matter interactions can be controlled by manipulating the photonic environment. We uncovered an optical topological transition in strongly anisotropic metamaterials that results in a dramatic increase in the photon density of states-an effect that can be used to engineer this interaction. We describe a transition in the topology of the iso-frequency surface from a closed ellipsoid to an open hyperboloid by use of artificially nanostructured metamaterials. We show that this topological transition manifests itself in increased rates of spontaneous emission of emitters positioned near the metamaterial. Altering the topology of the iso-frequency surface by using metamaterials provides a fundamentally new route to manipulating light-matter interactions.     

Holes in a Quantum Spin Liquid

Magnetic neutron scattering provides evidence for nucleation of antiferromagnetic droplets around impurities in a doped nickel oxide-based quantum magnet. The undoped parent compound contains a spin liquid with a cooperative singlet ground state and a gap in the magnetic excitation spectrum. Calcium doping creates excitations below the gap with an incommensurate structure factor. We show that weakly interacting antiferromagnetic droplets with a central phase shift of pi and a size controlled by the correlation length of the quantum liquid can account for the data. The experiment provides a quantitative impression of the magnetic polarization cloud associated with holes in a doped transition metal oxide.     

Universal signatures of fractionalized quantum critical points

Ground states of certain materials can support exotic excitations with a charge equal to a fraction of the fundamental electron charge. The condensation of these fractionalized particles has been predicted to drive unusual quantum phase transitions. Through numerical and theoretical analysis of a physical model of interacting lattice bosons, we establish the existence of such an exotic critical point, called XY*. We measure a highly nonclassical critical exponent η = 1.493 and construct a universal scaling function of winding number distributions that directly demonstrates the distinct topological sectors of an emergent Z(2) gauge field. The universal quantities used to establish this exotic transition can be used to detect other fractionalized quantum critical points in future model and material systems.     

Observation of quantum criticality with ultracold atoms in optical lattices

Quantum criticality emerges when a many-body system is in the proximity of a continuous phase transition that is driven by quantum fluctuations. In the quantum critical regime, exotic, yet universal properties are anticipated; ultracold atoms provide a clean system to test these predictions. We report the observation of quantum criticality with two-dimensional Bose gases in optical lattices. On the basis of in situ density measurements, we observe scaling behavior of the equation of state at low temperatures, locate the quantum critical point, and constrain the critical exponents. We observe a finite critical entropy per particle that carries a weak dependence on the atomic interaction strength. Our experiment provides a prototypical method to study quantum criticality with ultracold atoms.     

Theoretical study of geometric phase effects in the hydrogen-exchange reaction

The crossing of two electronic potential surfaces (a conical intersection) should result in geometric phase effects even for molecular processes confined to the lower surface. However, recent quantum simulations of the hydrogen exchange reaction (H + H2 --> H2 + H) have predicted a cancellation in such effects when product distributions are integrated over all scattering angles. We used a simple topological argument to extract reaction paths with different senses from a nuclear wave function that encircles a conical intersection. In the hydrogen-exchange reaction, these senses correspond to paths that cross one or two transition states. These two sets of paths scatter their products into different regions of space, which causes the cancellation in geometric phase effects. The analysis should generalize to other direct reactions.     

Is the fragility of a liquid embedded in the properties of its glass?

When a liquid is cooled below its melting temperature, it usually crystallizes. However, if the quenching rate is fast enough, the system may remain in a disordered state, progressively losing its fluidity upon further cooling. When the time needed for the rearrangement of the local atomic structure reaches approximately 100 seconds, the system becomes "solid" for any practical purpose, and this defines the glass transition temperature Tg. Approaching this transition from the liquid side, different systems show qualitatively different temperature dependencies of the viscosity, and accordingly they have been classified by introducing the concept of "fragility." We report experimental observations that relate the microscopic properties of the glassy phase to the fragility. We find that the vibrational properties of the glass well below Tg are correlated with the fragility value. Consequently, we extend the fragility concept to the glassy state and indicate how to determine the fragility uniquely from glass properties well below Tg.     

Dipolar antiferromagnetism and quantum criticality in LiErF₄

Magnetism has been predicted to occur in systems in which dipolar interactions dominate exchange. We present neutron scattering, specific heat, and magnetic susceptibility data for LiErF(4), establishing it as a model dipolar-coupled antiferromagnet with planar spin-anisotropy and a quantum phase transition in applied field H(c|| = 4.0 ± 0.1 kilo-oersteds. We discovered non-mean-field critical scaling for the classical phase transition at the antiferromagnetic transition temperature that is consistent with the two-dimensional XY/h(4) universality class; in accord with this, the quantum phase transition at H(c) exhibits three-dimensional classical behavior. The effective dimensional reduction may be a consequence of the intrinsic frustrated nature of the dipolar interaction, which strengthens the role of fluctuations.     

Magnetic superstructure in the two-dimensional quantum antiferromagnet SrCu2(BO3)2

We report the observation of magnetic superstructure in a magnetization plateau state of SrCu2(BO3)2, a frustrated quasi-two-dimensional quantum spin system. The Cu and B nuclear magnetic resonance (NMR) spectra at 35 millikelvin indicate an apparently discontinuous phase transition from uniform magnetization to a modulated superstructure near 27 tesla, above which a magnetization plateau at 1/8 of the full saturation has been observed. Comparison of the Cu NMR spectrum and the theoretical analysis of a Heisenberg spin model demonstrates the crystallization of itinerant triplets in the plateau phase within a large rhomboid unit cell (16 spins per layer) showing oscillations of the spin polarization. Thus, we are now in possession of an interesting model system to study a localization transition of strongly interacting quantum particles.     

Magnetic field-induced superconductivity in the ferromagnet URhGe

In several metals, including URhGe, superconductivity has recently been observed to appear and coexist with ferromagnetism at temperatures well below that at which the ferromagnetic state forms. However, the material characteristics leading to such a state of coexistence have not yet been fully elucidated. We report that in URhGe there is a magnetic transition where the direction of the spin axis changes when a magnetic field of 12 tesla is applied parallel to the crystal b axis. We also report that a second pocket of superconductivity occurs at low temperature for a range of fields enveloping this magnetic transition, well above the field of 2 tesla at which superconductivity is first destroyed. Our findings strongly suggest that excitations in which the spins rotate stimulate superconductivity in the neighborhood of a quantum phase transition under high magnetic field.