arXiv subjects

Andrew C. Potter

Publications and source records attributed to Andrew C. Potter.

At least 91 records · Page 5Linked to original sources

arXiv2014

Boundary-law scaling of entanglement entropy in diffusive metals

Entanglement structure serves as a powerful way to characterize quantum many-body phases. This is particularly so for gapless quantum liquids, where entanglement-based tools provide one of the only means to systematically characterize these complicated phases. For example, the Fermi-surface structure of Fermi-liquids is revealed in entanglement entropy by a log-correction to the typical boundary-law scaling of simpler quantum ground-states. In this paper, I analyze the entanglement structure of a disordered, but delocalized diffusive metal. Using a combination of analytic arguments and numerical calculations, I show that, despite having the same number of extended gapless excitations as a clean Fermi-liquid, the diffusive metal exhibits only boundary-law entanglement scaling. This result pinpoints the sharp Fermi-surface structure, rather than the finite density of gapless excitations, as the origin of the log-correction in the Fermi-liquid entanglement scaling.

cond-mat.str-el↗

arXiv2014

Landau Quantization and Quasiparticle Interference in the Three-Dimensional Dirac Semimetal Cd3As2

Condensed matter systems provide a rich setting to realize Dirac and Majorana fermionic excitations and the possibility to manipulate them in materials for potential applications. Recently, it has been proposed that Weyl fermions, which are chiral, massless particles, can emerge in certain bulk materials or in topological insulator multilayers and can produce unusual transport properties, such as charge pumping driven by a chiral anomaly. A pair of Weyl fermions protected by crystalline symmetry, effectively forming a massless Dirac fermion, has been predicted to appear as low energy excitations in a number of candidate materials termed three-dimensional (3D) Dirac semimetals. Here we report scanning tunneling microscopy (STM) measurements at sub-Kelvin temperatures and high magnetic fields on one promising host material, the II-V semiconductor Cd3As2. Our study provides the first atomic scale probe of Cd3As2, showing that defects mostly influence the valence band, consistent with the observation of ultra-high mobility carriers in the conduction band. By combining Landau level spectroscopy and quasiparticle interference (QPI), we distinguish a large spin-splitting of the conduction band in a magnetic field and its extended Dirac-like dispersion above the expected regime. A model band structure consistent with our experimental findings suggests that for a specific orientation of the applied magnetic field, Weyl fermions are the low-energy excitations in Cd3As2.

cond-mat.mes-hall↗

arXiv2014

Marginal Anderson localization and many body delocalization

We consider d dimensional systems which are localized in the absence of interactions, but whose single particle (SP) localization length diverges near a discrete set of (single-particle) energies, with critical exponent ν. This class includes disordered systems with intrinsic- or symmetry-protected- topological bands, such as disordered integer quantum Hall insulators. In the absence of interactions, such marginally localized systems exhibit anomalous properties intermediate between localized and extended including: vanishing DC conductivity but sub-diffusive dynamics, and fractal entanglement (an entanglement entropy with a scaling intermediate between area and volume law). We investigate the stability of marginal localization in the presence of interactions, and argue that arbitrarily weak short range interactions trigger delocalization for partially filled bands at non-zero energy density if ν\ge 1/d. We use the Harris/Chayes bound ν\ge 2/d, to conclude that marginal localization is generically unstable in the presence of interactions. Our results suggest the impossibility of stabilizing quantized Hall conductance at non-zero energy density.

cond-mat.stat-mech↗

arXiv2014

Gapped Symmetry Preserving Surface-State for the Electron Topological Insulator

It is well known that the 3D electronic topological insulator (TI) with charge-conservation and time-reversal symmetry cannot have a trivial insulating surface that preserves symmetry. It is often implicitly assumed that if the TI surface preserves both symmetries then it must be gapless. Here we show that it is possible for the TI surface to be both gapped and symmetry-preserving, at the expense of having surface-topological order. In contrast to analogous bosonic topological insulators, this symmetric surface topological order is intrinsically non-Abelian. We show that the surface-topological order provides a complete non-perturbative definition of the electron TI that transcends a free-particle band-structure picture, and could provide a useful perspective for studying strongly correlated topological Mott insulators.

cond-mat.str-el↗

arXiv2014

Quantum Oscillations from Surface Fermi-Arcs in Weyl and Dirac Semi-Metals

The surface states of Weyl semi-metals (SM's) consist of disjointed Fermi-arcs. This unusual surface-Fermiology provides a fingerprint of the topological features of the bulk Weyl-phase. Using a combination of semiclassical and numerical methods, we show that, in contrast to naive expectation, there are closed magnetic orbits involving the open- surface Fermi-arcs. Below a critical field strength that depends on sample thickness, these orbits produce periodic quantum oscillations of the density of states in a magnetic field, enabling a variety of experimental probes of the unconventional Fermi-arc surface states. The orbits are also essential for reproducing the bulk chiral anomaly in a finite slab. These results are then extended to the closely related and recently discovered 3D Dirac SM materials, including Cd3As2 and Na3Bi, which are doubled copies of Weyl semi-metals protected by crystal symmetry. Despite the fact that the protecting crystal symmetry is broken by a surface, we show that Dirac materials can still host unconventional surface-states, which can be detected in quantum oscillations experiments.

cond-mat.mes-hall↗

arXiv2013

Classification of interacting electronic topological insulators in three dimensions

A fundamental open problem in condensed matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. We show that there are 6 new electronic topological insulators that have no non-interacting counterpart. Combined with the previously known band-insulators, these produce a total of 8 topologically distinct phases. Two of the new topological insulators have a simple physical description as Mott insulators in which the electron spins form spin analogs of the familiar topological band-insulator. The remaining are obtained as combinations of these two `topological paramagnets' and the topological band insulator. We prove that these 8 phases form a complete list of all possible interacting topological insulators, and are classified by a Z_2^3 group-structure. Experimental signatures are also discussed for these phases.

cond-mat.str-el↗

arXiv2013

Edge-Ferromagnetism from Majorana Flat-Bands: Application to Split Tunneling-Conductance Peaks in the High-Tc Cuprates

In mean-field descriptions of nodal d-wave superconductors, generic edges exhibit dispersionless Majorana fermion bands at zero-energy. These states give rise to an extensive ground-state degeneracy, and are protected by time-reversal (TR) symmetry. We argue that the infinite density of states of these flat-bands make them inherently unstable to interactions, and show that repulsive interactions lead to edge FM which splits the flat bands. This edge FM offers an explanation for the observation of splitting of zero-bias peaks in edge tunneling in High-Tc cuprate superconductors. We argue that this mechanism for splitting is more likely than previously proposed scenarios, and describe its experimental consequences.

cond-mat.supr-con↗

arXiv2013

Anomalous Supercurrent from Majorana States in Topological Insulator Josephson Junctions

We propose a Josephson junction setup based on a topological insulator (TI) thin film to detect Majorana states, which exploits the unique helical and extended nature of the TI surface state. When the magnetic flux through the junction is close to an integer number of flux quanta, Majorana states, present on both surfaces of the film, give rise to a narrow peak-dip structure in the current- phase relation by hybridizing at the edge of the junction. Moreover, the maximal Majorana-state contribution to Josephson current takes a (nearly) universal value, approximately equal to the supercurrent capacity of a single quantum-channel. These features provide a characteristic signature of Majorana states based entirely on supercurrent.

cond-mat.mes-hall↗

arXiv2013

Mechanisms for Sub-Gap Optical Conductivity in Herbertsmithite

Recent terahertz conductivity measurements observed low-power-law frequency dependence of optical conduction within the Mott gap of the Kagome lattice spin-liquid candidate Herbertsmithite. We investigate mechanisms for this observed sub-gap conductivity for two possible scenarios in which the ground-state is described by: 1) a U(1) Dirac spin-liquid with emergent fermionic spinons or 2) a nearly critical Z2 spin-liquid in the vicinity of a continuous quantum phase transition to magnetic order. We identify new mechanisms for optical-absorption via magneto-elastic effects and spin- orbit coupling. In addition, for the Dirac spin-liquid scenario, we establish an explicit microscopic origin for previously proposed absorption mechanisms based on slave-particle effective field theory descriptions.

cond-mat.str-el↗

arXiv2012

Hanbury-Brown and Twiss interference of anyons

We present a study of an Hanbury Brown and Twiss (HBT) interferometer realized with anyons. Such a device can directly probe entanglement and fractional statistics of initially uncorrelated particles. We calculate HBT cross-correlations of Abelian Laughlin anyons. The correlations we calculate exhibit partial bunching similar to bosons, indicating a substantial statistical transmuta- tion from the underlying electronic degrees of freedom. We also find qualitative differences between the anyonic signal and the corresponding bosonic or fermionic signals, indicating that anyons cannot be simply thought as intermediate between bosons and fermions.

cond-mat.mes-hall↗

arXiv2012

Zero-bias peaks in spin-orbit coupled superconducting wires with and without Majorana end-states

One of the simplest proposed experimental probes of a Majorana bound-state is a quantized (2e^2/h) value of zero-bias tunneling conductance. When temperature is somewhat larger than the intrinsic width of the Majorana peak, conductance is no longer quantized, but a zero-bias peak can remain. Such a non-quantized zero-bias peak has been recently reported for semiconducting nanowires with proximity induced superconductivity. In this paper we analyze the relation of the zero-bias peak to the presence of Majorana end-states, by simulating the tunneling conductance for multi-band wires with realistic amounts of disorder. We show that this system generically exhibits a (non-quantized) zero-bias peak even when the wire is topologically trivial and does not possess Majorana end-states. We make comparisons to recent experiments, and discuss the necessary requirements for confirming the existence of a Majorana state.

cond-mat.mes-hall↗

arXiv2012

Quantum spin liquids and the metal-insulator transition in doped semiconductors

We describe a new possible route to the metal-insulator transition in doped semiconductors such as Si:P or Si:B. We explore the possibility that the loss of metallic transport occurs through Mott localization of electrons into a quantum spin liquid state with diffusive charge neutral "spinon" excitations. Such a quantum spin liquid state can appear as an intermediate phase between the metal and the Anderson-Mott insulator. An immediate testable consequence is the presence of metallic thermal conductivity at low temperature in the electrical insulator near the metal-insulator transition. Further we show that though the transition is second order the zero temperature residual electrical conductivity will jump as the transition is approached from the metallic side. However the electrical conductivity will have a non-monotonic temperature dependence that may complicate the extrapolation to zero temperature. Signatures in other experiments and some comparisons with existing data are made.

cond-mat.str-el↗

arXiv2012

Superconductivity and Ferromagnetism in Oxide Interface Structures: Possibility of Finite Momentum Pairing

We introduce a model to explain the observed ferromagnetism and superconductivity in LAO/STO oxide interface structures. Due to the polar catastrophe mechanism, 1/2 charge per unit cell is transferred to the interface layer. We argue that this charge localizes and orders ferromagnetically via exchange with the conduction electrons. Ordinarily this ferromagnetism would destroy superconductivity, but due to strong spin-orbit coupling near the interface, the magnetism and superconductivity can coexist by forming an FFLO-type condensate of Cooper pairs at finite momentum, which is surprisingly robust in the presence of strong disorder.

cond-mat.supr-con↗

arXiv2012

Topological Superconductivity and Majorana Fermions in Metallic Surface-States

Heavy metals, such as Au, Ag, and Pb, often have sharp surface states that are split by strong Rashba spin-orbit coupling. The strong spin-orbit coupling and two-dimensional nature of these surface states make them ideal platforms for realizing topological superconductivity and Majorana fermions. In this paper, we further develop a proposal to realize Majorana fermions at the ends of quasi-one-dimensional metallic wires. We show how superconductivity can be induced on the metallic surface states by a combination of proximity effect, disorder, and interactions. Applying a magnetic field along the wire can drive the wire into a topologically non-trivial state with Majorana end-states. Unlike the case of a perpendicular field, where the chemical potential must be fined tuned near the Rashba-band crossing, the parallel field allows one to realize Majoranas for arbitrarily large chemical potential. We then show that, despite the presence of a large carrier density from the bulk metal, it is still possible to effectively control the chemical potential of the surface states by gating. The simplest version of our proposal, which involves only an Au(111) film deposited on a conventional superconductor, should be readily realizable.

cond-mat.mes-hall↗

arXiv2011

Erratum: Engineering a p+ip Superconductor: Comparison of Topological Insulator and Rashba Spin-Orbit Coupled Materials [Phys. Rev. B 83, 184520 (2011)]

In this erratum, we revisit the issue of bulk-disorder on proposals to realize an effective p+ip superconductor from spin-orbit coupled materials. Contrary to the claim in [Phys. Rev. B 83, 184520 (2011)], we show that the pair breaking effects of bulk-disorder are negligible, and that bulk disorder does not suppress the induced superconductivity. This argument does not apply to our conclusions regarding impurities residing in the spin-orbit coupled material or disorder at the interface to the bulk superconductor, both of which tend to suppress superconductivity unless spin-orbit coupling is large.

cond-mat.mes-hall↗

arXiv2011

Engineering a p+ip Superconductor: Comparison of Topological Insulator and Rashba Spin-Orbit Coupled Materials

We compare topological insulator materials and Rashba coupled surfaces as candidates for engineering p+ip superconductivity. Specifically, in each type of material we examine 1) the limitations to inducing superconductivity by proximity to an ordinary s-wave superconductor, and 2) the robustness of the resulting superconductivity against disorder. We find that topological insulators have strong advantages in both regards: there are no fundamental barriers to inducing superconductivity, and the induced superconductivity is immune to disorder. In contrast, for Rashba coupled quantum wires or surface states, the the achievable gap from induced superconductivity is limited unless the Rashba coupling is large. Furthermore, for small Rashba coupling the induced superconductivity is strongly susceptible to disorder. These features pose serious difficulties for realizing p+ip superconductors in semiconductor materials due to their weak spin-orbit coupling, and suggest the need to seek alternatives. Some candidate materials are discussed.

cond-mat.supr-con↗

arXiv2010

Majorana End-States in Multi-band Microstructures with Rashba Spin-Orbit Coupling

A recent work [1] demonstrated, for an ideal spinless p+ip superconductor, that Majorana end-states can be realized outside the strict one-dimensional limit, so long as: 1) the sample width does not greatly exceed the superconducting coherence length and 2) an odd number of transverse sub-bands are occupied. Here we extend this analysis to the case of an effective p+ip superconductor engineered from Rashba spin-orbit coupled surface with induced magnetization and superconductivity, and find a number of new features. Specifically, we find that finite size quantization allows Majorana end-states even when the chemical potential is outside of the induced Zeeman gap where the bulk material would not be topological. This is relevant to proposals utilizing semiconducting quantum wires, however, we also find that the bulk energy gap is substantially reduced if the induced magnetization is too large. We next consider a slightly different geometry, and show that Majorana end-states can be created at the ends of ferromagnetic domains. Finally, we consider the case of meandering edges and find, surprisingly, that the existence of well-defined transverse sub-bands is not necessary for the formation of robust Majorana end-states.

cond-mat.mes-hall↗

arXiv2010

Superfluidity and dimerization in a multilayered system of fermionic polar molecules

We consider a layered system of fermionic molecules with permanent dipole moments aligned by an external field. The dipole interactions between fermions in adjacent layers are attractive and induce inter-layer pairing. Due to competition for pairing among adjacent layers, the mean-field ground state of the layered system is a dimerized superfluid, with pairing only between every-other layer. We construct an effective Ising-XY lattice model that describes the interplay between dimerization and superfluid phase fluctuations. In addition to the dimerized superfluid ground state, and high temperature normal state, at intermediate temperature, we find an unusual dimerized "pseudogap" state with only short-range phase coherence. We propose light scattering experiments to detect dimerization.

cond-mat.quant-gas↗