Majorana-fermion origin of the planar thermal Hall effect in the Kitaev magnet α-RuCl3.

The field-induced quantum-disordered state of layered honeycomb magnet α-RuCl3 is a prime candidate for Kitaev spin liquids hosting Majorana fermions and non-Abelian anyons. Recent observations of anomalous planar thermal Hall effect demonstrate a topological edge mode, but whether it originates from Majorana fermions or bosonic magnons remains controversial. Here, we distinguish these origins from combined low-temperature measurements of high-resolution specific heat and thermal Hall conductivity with rotating magnetic fields within the honeycomb plane. A distinct closure of the low-energy bulk gap is observed for the fields in the Ru-Ru bond direction, and the gap opens rapidly when the field is tilted. Notably, this change occurs concomitantly with the sign reversal of the Hall effect. General discussions of topological bands show that this is the hallmark of an angle rotation-induced topological transition of fermions, providing conclusive evidence for the Majorana-fermion origin of the thermal Hall effect in α-RuCl3.

Monolayer Kagome metals AV3Sb5.

Recently, layered kagome metals AV3Sb5 (A = K, Rb, and Cs) have emerged as a fertile platform for exploring frustrated geometry, correlations, and topology. Here, using first-principles and mean-field calculations, we demonstrate that AV3Sb5 can crystallize in a mono-layered form, revealing a range of properties that render the system unique. Most importantly, the two-dimensional monolayer preserves intrinsically different symmetries from the three-dimensional layered bulk, enforced by stoichiometry. Consequently, the van Hove singularities, logarithmic divergences of the electronic density of states, are enriched, leading to a variety of competing instabilities such as doublets of charge density waves and s- and d-wave superconductivity. We show that the competition between orders can be fine-tuned in the monolayer via electron-filling of the van Hove singularities. Thus, our results suggest the monolayer kagome metal AV3Sb5 as a promising platform for designer quantum phases.

Identification of a Kitaev quantum spin liquid by magnetic field angle dependence.

Quantum spin liquids realize massive entanglement and fractional quasiparticles from localized spins, proposed as an avenue for quantum science and technology. In particular, topological quantum computations are suggested in the non-abelian phase of Kitaev quantum spin liquid with Majorana fermions, and detection of Majorana fermions is one of the most outstanding problems in modern condensed matter physics. Here, we propose a concrete way to identify the non-abelian Kitaev quantum spin liquid by magnetic field angle dependence. Topologically protected critical lines exist on a plane of magnetic field angles, and their shapes are determined by microscopic spin interactions. A chirality operator plays a key role in demonstrating microscopic dependences of the critical lines. We also show that the chirality operator can be used to evaluate topological properties of the non-abelian Kitaev quantum spin liquid without relying on Majorana fermion descriptions. Experimental criteria for the non-abelian spin liquid state are provided for future experiments.

Band-selective gap opening by a C 4-symmetric order in a proximity-coupled heterostructure Sr2VO3FeAs.

Complex electronic phases in strongly correlated electron systems are manifested by broken symmetries in the low-energy electronic states. Some mysterious phases, however, exhibit intriguing energy gap opening without an apparent signature of symmetry breaking (e.g., high-TC cuprates and heavy fermion superconductors). Here, we report an unconventional gap opening in a heterostructured, iron-based superconductor Sr2VO3FeAs across a phase transition at T 0 ∼150 K. Using angle-resolved photoemission spectroscopy, we identify that a fully isotropic gap opens selectively on one of the Fermi surfaces with finite warping along the interlayer direction. This band selectivity is incompatible with conventional gap opening mechanisms associated with symmetry breaking. These findings, together with the unusual field-dependent magnetoresistance, suggest that the Kondo-type proximity coupling of itinerant Fe electrons to localized V spin plays a role in stabilizing the exotic phase, which may serve as a distinct precursor state for unconventional superconductivity.

Using Disorder to Identify Bogoliubov Fermi-Surface States.

We argue that a superconducting state with a Fermi surface of Bogoliubov quasiparticles, a Bogoliubov Fermi surface (BG-FS), can be identified by the dependence of physical quantities on disorder. In particular, we show that a linear dependence of the residual density of states at weak disorder distinguishes a BG-FS state from other nodal superconducting states. We further demonstrate the stability of supercurrent against impurities and a characteristic Drude-like behavior of the optical conductivity. Our results can be directly applied to electron irradiation experiments on candidate materials of BG-FSs, including Sr_{2}RuO_{4}, FeSe_{1-x}S_{x}, and UBe_{13}.

Vestiges of Topological Phase Transitions in Kitaev Quantum Spin Liquids.

We investigate signatures of topological quantum phase transitions (TQPTs) between the Z_{2} quantum spin liquids (QSLs). In two spatial dimensions, Z_{2} QSLs and their TQPTs are only well defined at zero temperature (T=0), and it is imperative to clarify their observable signatures under nonzero temperatures. Here, we present the vestiges of TQPTs between Z_{2} QSLs with Majorana fermions in terms of thermal Hall conductivity κ_{xy} at nonzero temperatures. The κ_{xy}/T shows characteristic temperature dependences around TQPTs. We argue that an exponential upturn near T=0 and the peak of κ_{xy}/T around massive excitation energy are observable smoking-gun signals of the TQPTs. Quantum critical fan-shape temperature dependences are uncovered across TQPTs. We also perform the parton mean-field analysis on a modified Kitaev model with next-nearest neighbor interactions finding TQPTs between the phases with different Chern numbers and their vestiges self-consistently. We discuss the implication of our results to the recent experiments in α-RuCl_{3}.

Multiscale Quantum Criticality Driven by Kondo Lattice Coupling in Pyrochlore Systems.

Pyrochlore systems (A_{2}B_{2}O_{7}) with A-site rare-earth local moments and B-site 5d conduction electrons offer excellent material platforms for the discovery of exotic quantum many-body ground states. Notable examples include U(1) quantum spin liquid of the local moments and semimetallic non-Fermi liquid of the conduction electrons. Here we investigate emergent quantum phases and their transitions driven by the Kondo lattice coupling between such highly entangled quantum ground states. Using the renormalization group method, it is shown that weak Kondo lattice coupling is irrelevant, leading to a fractionalized semimetal phase with decoupled local moments and conduction electrons. Upon increasing the Kondo lattice coupling, this phase is unstable to the formation of broken symmetry states. Particularly important is the opposing influence of the Kondo lattice coupling and long-range Coulomb interaction. The former prefers to break the particle-hole symmetry while the latter tends to restore it. The characteristic competition leads to possibly multiple phase transitions, first from a fractionalized semimetal phase to a fractionalized Fermi surface state with particle-hole pockets, followed by the second transition to a fractionalized ferromagnetic state. Multiscale quantum critical behaviors appear at nonzero temperatures and with external magnetic field near such quantum phase transitions. We discuss the implication of these results to the experiments on Pr_{2}Ir_{2}O_{7}.

Emergent Anisotropic Non-Fermi Liquid at a Topological Phase Transition in Three Dimensions.

Understanding correlation effects in topological phases and their transitions is a cutting-edge area of research in recent condensed matter physics. We study topological quantum phase transitions (TQPTs) between double-Weyl semimetals (DWSMs) and insulators, and argue that a novel class of quantum criticality appears at the TQPT characterized by emergent anisotropic non-Fermi-liquid behaviors, in which the interplay between the Coulomb interaction and electronic critical modes induces not only anisotropic renormalization of the Coulomb interaction but also strongly correlated electronic excitation in three spatial dimensions. Using the standard renormalization group methods, large N_{f} theory, and the ε=4-d method with a fermion flavor number N_{f} and spatial dimension d, we obtain the anomalous dimensions of electrons (η_{f}=0.366/N_{f}) in large N_{f} theory and the associated anisotropic scaling relations of various physical observables. Our results may be observed in candidate materials for DWSMs such as HgCr_{2}Se_{4} or SrSi_{2} when the system undergoes a TQPT.

Competing Orders and Anomalies.

A conservation law is one of the most fundamental properties in nature, but a certain class of conservation "laws" could be spoiled by intrinsic quantum mechanical effects, so-called quantum anomalies. Profound properties of the anomalies have deepened our understanding in quantum many body systems. Here, we investigate quantum anomaly effects in quantum phase transitions between competing orders and striking consequences of their presence. We explicitly calculate topological nature of anomalies of non-linear sigma models (NLSMs) with the Wess-Zumino-Witten (WZW) terms. The non-perturbative nature is directly related with the 't Hooft anomaly matching condition: anomalies are conserved in renormalization group flow. By applying the matching condition, we show massless excitations are enforced by the anomalies in a whole phase diagram in sharp contrast to the case of the Landau-Ginzburg-Wilson theory which only has massive excitations in symmetric phases. Furthermore, we find non-perturbative criteria to characterize quantum phase transitions between competing orders. For example, in 4D, we show the two competing order parameter theories, CP(1) and the NLSM with WZW, describe different universality class. Physical realizations and experimental implication of the anomalies are also discussed.

Novel Quantum Criticality in Two Dimensional Topological Phase transitions.

Topological quantum phase transitions intrinsically intertwine self-similarity and topology of many-electron wave-functions, and divining them is one of the most significant ways to advance understanding in condensed matter physics. Our focus is to investigate an unconventional class of the transitions between insulators and Dirac semimetals whose description is beyond conventional pseudo relativistic Dirac Hamiltonian. At the transition without the long-range Coulomb interaction, the electronic energy dispersion along one direction behaves like a relativistic particle, linear in momentum, but along the other direction it behaves like a non-relativistic particle, quadratic in momentum. Various physical systems ranging from TiO2-VO2 heterostructure to organic material α-(BEDT-TTF)2I3 under pressure have been proposed to have such anisotropic dispersion relation. Here, we discover a novel quantum criticality at the phase transition by incorporating the long range Coulomb interaction. Unique interplay between the Coulomb interaction and electronic critical modes enforces not only the anisotropic renormalization of the Coulomb interaction but also marginally modified electronic excitation. In connection with experiments, we investigate several striking effects in physical observables of our novel criticality.

Non-Fermi-liquid and topological states with strong spin-orbit coupling.

We argue that a class of strongly spin-orbit-coupled materials, including some pyrochlore iridates and the inverted band gap semiconductor HgTe, may be described by a minimal model consisting of the Luttinger Hamiltonian supplemented by Coulomb interactions, a problem studied by Abrikosov and collaborators. It contains twofold degenerate conduction and valence bands touching quadratically at the zone center. Using modern renormalization group methods, we update and extend Abrikosov's classic work and show that interactions induce a quantum critical non-Fermi-liquid phase, stable provided time-reversal and cubic symmetries are maintained. We determine the universal power-law exponents describing various observables in this Luttinger-Abrikosov-Beneslavskii state, which include conductivity, specific heat, nonlinear susceptibility, and the magnetic Gruneisen number. Furthermore, we determine the phase diagram in the presence of cubic and/or time-reversal symmetry breaking perturbations, which includes a topological insulator and Weyl semimetal phases. Many of these phases possess an extraordinarily large anomalous Hall effect, with the Hall conductivity scaling sublinearly with magnetization σ(xy)∼M0.51.

Theory of topological quantum phase transitions in 3D noncentrosymmetric systems.

We construct a general theory describing the topological quantum phase transitions in 3D systems with broken inversion symmetry. While the consideration of the system's codimension generally predicts the appearance of a stable metallic phase between the normal and topological insulators, it is shown that a direct topological phase transition between two insulators is also possible when an accidental band crossing occurs along directions with high crystalline symmetry. At the quantum critical point, the energy dispersion becomes quadratic along one direction while the dispersions along the other two orthogonal directions are linear, which manifests the zero chirality of the band touching point. Because of the anisotropic dispersion at quantum critical point, various thermodynamic and transport properties show unusual temperature dependence and anisotropic behaviors.

Superfluid-insulator transitions of the fermi gas with near-unitary interactions in a periodic potential.

We consider spin-1/2 fermions of mass m with interactions near the unitary limit. In an applied periodic potential of amplitude V and period a_{L}, and with a density of an even integer number of fermions per unit cell, there is a second-order quantum phase transition between superfluid and insulating ground states at a critical V=V_{c}. We compute the universal ratio V_{c}ma_{L};{2}/variant Planck's over 2pi;{2} at N=infinity in a model with Sp(2N) spin symmetry. The insulator interpolates between a band insulator of fermions and a Mott insulator of fermion pairs. We discuss implications for recent experiments.