Probing Fermi Sea Topology by Andreev State Transport.

We show that the topology of the Fermi sea of a two-dimensional electron gas (2DEG) is reflected in the ballistic Landauer transport along a long and narrow Josephson π junction that proximitizes the 2DEG. The low-energy Andreev states bound to the junction are shown to exhibit a dispersion that is sensitive to the Euler characteristic of the Fermi sea (χ_{F}). We highlight two important relations: one connects the electron or hole nature of Andreev states to the convex or concave nature of Fermi surface critical points, and one relates these critical points to χ_{F}. We then argue that the transport of Andreev states leads to a quantized conductance that probes χ_{F}. An experiment is proposed to measure this effect, from which we predict an I-V characteristic that not only captures the topology of the Fermi sea in metals, but also resembles the rectification effect in diodes. Finally, we evaluate the feasibility of measuring this quantized response in graphene, InAs and HgTe 2DEGs.

Observation of the Superconducting Proximity Effect from Surface States in SmB_{6}/YB_{6} Thin Film Heterostructures via Terahertz Spectroscopy.

The ac conduction of epitaxially grown SmB_{6} thin films and superconducting heterostructures of SmB_{6}/YB_{6} are investigated via time-domain terahertz spectroscopy. A two-channel model of thickness-dependent bulk states and thickness-independent surface states accurately describes the measured conductance of bare SmB_{6} thin films, demonstrating the presence of surface states in SmB_{6}. While the observed reductions in the simultaneously measured superconducting gap, transition temperature, and superfluid density of SmB_{6}/YB_{6} heterostructures relative to bare YB_{6} indicate the penetration of proximity-induced superconductivity into the SmB_{6} overlayer; the corresponding SmB_{6}-thickness independence between different heterostructures indicates that the induced superconductivity is predominantly confined to the interface surface state of the SmB_{6}. This study demonstrates the ability of terahertz spectroscopy to probe proximity-induced superconductivity at an interface buried within a heterostructure, and our results show that SmB_{6} behaves as a predominantly insulating bulk surrounded by conducting surface states in both the normal and induced-superconducting states in both terahertz and dc responses, which is consistent with the topological Kondo insulator picture.

Direct Imaging of Antiferromagnetic Domains and Anomalous Layer-Dependent Mirror Symmetry Breaking in Atomically Thin MnPS_{3}.

We have developed a sensitive cryogenic second-harmonic generation microscopy to study a van der Waals antiferromagnet MnPS_{3}. We find that long-range Néel antiferromagnetic order develops from the bulk crystal down to the bilayer, while it is absent in the monolayer. Before entering the long-range antiferromagnetic ordered phase in all samples, an upturn of the second harmonic generation below 200 K indicates the formation of the short-range order and magnetoelastic coupling. We also directly image the two antiphase (180°) antiferromagnetic domains and thermally induced domain switching down to bilayer. An anomalous mirror symmetry breaking shows up in samples thinner than ten layers for the temperature both above and below the Néel temperature, which indicates a structural change in few-layer samples. Minimal change of the second harmonic generation polar patterns in strain tuning experiments indicate that the symmetry crossover at ten layers is most likely an intrinsic property of MnPS_{3} instead of an extrinsic origin of substrate-induced strain. Our results show that second harmonic generation microscopy is a direct tool for studying antiferromagnetic domains in atomically thin materials, and opens a new way to study two-dimensional antiferromagnets.

Spatially dispersive circular photogalvanic effect in a Weyl semimetal.

Weyl semimetals (WSMs) are gapless topological states of matter with broken inversion and/or time reversal symmetry. WSMs can support a circulating photocurrent when illuminated by circularly polarized light at normal incidence. Here, we report a spatially dispersive circular photogalvanic effect (s-CPGE) in a WSM that occurs with a spatially varying beam profile. Our analysis shows that the s-CPGE is controlled by a symmetry selection rule combined with asymmetric carrier excitation and relaxation dynamics. By evaluating the s-CPGE for a minimal model of a WSM, a frequency-dependent scaling behaviour of the photocurrent is obtained. Wavelength-dependent measurements from the visible to mid-infrared range show evidence of Berry curvature singularities and band inversion in the s-CPGE response. We present the s-CPGE as a promising spectroscopic probe for topological band properties, with the potential for controlling photoresponse by patterning optical fields on topological materials to store, manipulate and transmit information.

Dirac Semimetals in Two Dimensions.

Graphene is famous for being a host of 2D Dirac fermions. However, spin-orbit coupling introduces a small gap, so that graphene is formally a quantum spin Hall insulator. Here we present symmetry-protected 2D Dirac semimetals, which feature Dirac cones at high-symmetry points that are not gapped by spin-orbit interactions and exhibit behavior distinct from both graphene and 3D Dirac semimetals. Using a two-site tight-binding model, we construct representatives of three possible distinct Dirac semimetal phases and show that single symmetry-protected Dirac points are impossible in two dimensions. An essential role is played by the presence of nonsymmorphic space group symmetries. We argue that these symmetries tune the system to the boundary between a 2D topological and trivial insulator. By breaking the symmetries we are able to access trivial and topological insulators as well as Weyl semimetal phases.

Absence of Luttinger's theorem due to zeros in the single-particle Green function.

We show exactly with an SU(N) interacting model that even if the ambiguity associated with the placement of the chemical potential, µ, for a T=0 gapped system is removed by using the unique value µ(T→0), Luttinger's sum rule is violated even if the ground-state degeneracy is lifted by an infinitesimal hopping. The failure stems from the nonexistence of the Luttinger-Ward functional for a system in which the self-energy diverges. Since it is the existence of the Luttinger-Ward functional that is the basis for Luttinger's theorem which relates the charge density to sign changes of the single-particle Green function, no such theorem exists. Experimental data on the cuprates are presented which show a systematic deviation from the Luttinger count, implying a breakdown of the electron quasiparticle picture in strongly correlated electron matter.

Interface between topological and superconducting qubits.

We propose and analyze an interface between a topological qubit and a superconducting flux qubit. In our scheme, the interaction between Majorana fermions in a topological insulator is coherently controlled by a superconducting phase that depends on the quantum state of the flux qubit. A controlled-phase gate, achieved by pulsing this interaction on and off, can transfer quantum information between the topological qubit and the superconducting qubit.