arXiv subjects

Matthew J. Gilbert

Publications and source records attributed to Matthew J. Gilbert.

At least 37 records · Page 2Linked to original sources

arXiv2017

Fulde-Ferrell States in Inverse Proximity Coupled Magnetically-Doped Topological Heterostructures

We study the superconducting properties of the thin film BCS superconductor proximity coupled to a magnetically doped topological insulator(TI). Using the mean field theory, we show that Fulde-Ferrell(FF) pairing can be induced in the conventional superconductor by having inverse proximity effect(IPE). This occurs when the IPE of the TI to the superconductor is large enough that the normal band of the superconductor possesses a proximity induced spin-orbit coupling and magnetization. We find that the energetics of the different pairings are dependent on the coupling strength between the TI and the BCS superconductor and the thickness of the superconductor film. As the thickness of the superconductor film is increased, we find a crossover from the FF pairing to the BCS pairing phase. This is a consequence of the increased number of the superconducting bands, which favor the BCS pairing, implying that the FF phase can only be observed in the thin-film limit. In addition, we also propose transport experiments that show distinct signatures of the FF phase.

cond-mat.supr-con↗

arXiv2017

Topological crystalline superconductors with linearly and projectively represented $C_{n}$ symmetry

We study superconductors with $n$-fold rotational invariance both in the presence and in the absence of spin-orbit interactions. More specifically, we classify the non-interacting Hamiltonians by defining a series of $Z$-numbers for the Bogoliubov-de Gennes (BdG) symmetry classes of the Altland-Zimbauer classification of random matrices in $1$D, $2$D, and $3$D in the presence of discrete rotational invariance. Our analysis emphasizes the important role played by the angular momentum of the Cooper pairs in the system: for pairings of nonzero angular momentum, the rotation symmetry may be represented projectively, and a projective representation of rotation symmetry may have anomalous properties, including the anti-commutation with the time-reversal symmetry. In 1D and 3D, we show how an $n$-fold axis enhances the topological classification and give additional topological numbers; in 2D, we establish a relation between the Chern number (in class D and CI) and the eigenvalues of rotation symmetry at high-symmetry points. For each nontrivial class in 3D, we write down a minimal effective theory for the surface Majorana states.

cond-mat.supr-con↗

arXiv2016

Topological superconductivity in an ultrathin, magnetically-doped topological insulator proximity coupled to a conventional superconductor

As a promising candidate system to realize topological superconductivity, the system of a 3D topological insulator (TI) grown on top of the s-wave superconductor has been extensively studied. To access the topological superconductivity experimentally, the 3D TI sample must be thin enough to allow for Cooper pair tunneling to the exposed surface of TI. The use of magnetically ordered dopants to break time-reversal symmetry may allow the surface of a TI to host Majorana fermion, which are believed to be a signature of topological superconductivity. In this work, we study a magnetically-doped thin film TI-superconductor hybrid systems. Considering the proximity induced order parameter in thin film of TI, we analyze the gap closing points of the Hamiltonian and draw the phase diagram as a function of relevant parameters: the hybridization gap, Zeeman energy, and chemical potential of the TI system. Our findings provide a useful guide in choosing relevant parameters to facilitate the observation of topological superconductivity in thin film TI-superconductor hybrid systems. In addition, we further perform numerical analysis on a TI proximity coupled to a s-wave superconductor and find that, due to the spin-momentum locked nature of the surface states in TI, the induced s-wave order parameter of the surface states persists even at large magnitude of the Zeeman energy.

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arXiv2016

Performance of Topological Insulator Interconnects

The poor performance of copper interconnects at the nanometer scale calls for new material solutions for continued scaling of integrated circuits. We propose the use of three dimensional time-reversal-invariant topological insulators (TIs), which host backscattering-protected surface states, for this purpose. Using semiclassical methods, we demonstrate that nanoscale TI interconnects have a resistance 1-3 orders of magnitude lower than copper interconnects and graphene nanoribbons at the nanometer scale. We use the nonequilibrium Green function (NEGF) formalism to measure the change in conductance of nanoscale TI and metal interconnects caused by the presence of impurity disorder. We show that metal interconnects suffer a resistance increase, relative to the clean limit, in excess of 500% due to disorder while the TI's surface states increase less than 35% in the same regime.

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arXiv2016

Disorder Induced Phase Transitions of Type-II Weyl Semimetal

Weyl semimetals are a newly discovered class of materials that host relativistic massless Weyl fermions as their low-energy bulk excitations. Among this new class of materials, there exist two general types of semimetals that are of particular interest: type-I Weyl semimetals, that have broken inversion or time-reversal symmetry symmetry, and type-II Weyl semimetals, that additionally breaks Lorentz invariance. In this work, we use Born approximation to analytically demonstrate that the type-I Weyl semimetals may undergo a quantum phase transition to type-II Weyl semimetals in the presence of the finite charge and magnetic disorder when non-zero tilt exist. The phase transition occurs when the disorder renormalizes the topological mass, thereby reducing the Fermi velocity near the Weyl cone below the tilt of the cone. We also confirm the presence of the disorder induced phase transition in Weyl semimetals using exact diagonalization of a three-dimensional tight-binding model to calculate the resultant phase diagram of the type-I Weyl semimetal.

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arXiv2016

Probing unconventional superconductivity in inversion symmetric doped Weyl semimetal

Unconventional superconductivity has been predicted to arise in the topologically non-trivial Fermi surface of doped inversion symmetric Weyl semimetals (WSM). In particular, Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) and nodal BCS states are theoretically predicted to be possible superconductor pairing states in inversion symmetric doped WSM. In an effort to resolve preferred pairing state, we theoretically study two separate four terminal quantum transport methods that each exhibit a unique electrical signature in the presence of FFLO and nodal BCS states in doped WSMs. We first introduce a Josephson junction that consists of a doped WSM and an s-wave superconductor in which we show that the application of a transverse uniform current in s-wave superconductor effectively cancels the momentum carried by FFLO states in doped WSM. From our numerical analysis, we find a peak in Josephson current amplitude at finite uniform current in s-wave superconductor that serves as an indicator of FFLO states in doped WSMs. Furthermore, we show using a four terminal measurement configuration that the nodal points may be shifted by an application of transverse uniform current in doped WSM. We analyze the topological phase transitions induced by nodal pair annihilation in non-equilibrium by constructing the phase diagram and we find a characteristic decrease in the density of states that serves as a signature of the quantum critical point in the topological phase transition, thereby identifying nodal BCS states in doped WSM.

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arXiv2016

Modular Anomalies in (2+1) and (3+1)-D Edge Theories

The classification of topological phases of matter in the presence of interactions is an area of intense interest. One possible means of classification is via studying the partition function under modular transforms, as the presence of an anomalous phase arising in the edge theory of a D-dimensional system under modular transformation, or modular anomaly, signals the presence of a (D+1)-D non-trivial bulk. In this work, we discuss the modular transformations of conformal field theories along a (2+1)-D and a (3+1)-D edge. Using both analytical and numerical methods, we show that chiral complex free fermions in (2+1)-D and (3+1)-D are modular invariant. However, we show in (3+1)-D that when the edge theory is coupled to a background U(1) gauge field this results in the presence of a modular anomaly that is the manifestation of a quantum Hall effect in a (4+1)-D bulk. Using the modular anomaly, we find that the edge theory of (4+1)-D insulator with spacetime inversion symmetry(P*T) and fermion number parity symmetry for each spin becomes modular invariant when 8 copies of the edges exist.

cond-mat.str-el↗

arXiv2015

Parafermionic phases with symmetry-breaking and topological order

Parafermions are the simplest generalizations of Majorana fermions that realize topological order. We propose a less restrictive notion of topological order in 1D open chains, which generalizes the seminal work by Fendley [J. Stat. Mech., P11020 (2012)]. The first essential property is that the groundstates are mutually indistinguishable by local, symmetric probes, and the second is a generalized notion of zero edge modes which cyclically permute the groundstates. These two properties are shown to be topologically robust, and applicable to a wider family of topologically-ordered Hamiltonians than has been previously considered. An an application of these edge modes, we formulate a new notion of twisted boundary conditions on a closed chain, which guarantees that the closed-chain groundstate is topological, i.e., it originates from the topological manifold of degenerate states on the open chain. Finally, we generalize these ideas to describe symmetry-breaking phases with a parafermionic order parameter. These exotic phases are condensates of parafermion multiplets, which generalizes Cooper pairing in superconductors. The stability of these condensates are investigated on both open and closed chains.

cond-mat.str-el↗

arXiv2014

Voltage Induced Dynamical Quantum Phase Transitions in Exciton Condensates

We explore non-analytic quantum phase dynamics of dipolar exciton condensates formed in a system of 1D quantum layers subjected to voltage quenches. We map the exciton condensate physics on to the pseudospin ferromagnet model showing an additional oscillatory metastable and paramagnetic phase beyond the well-known ferromagnetic phase by utilizing a time-dependent, non-perturbative theoretical model. We explain the coherent phase of the exciton condensate in quantum Hall bilayers, observed for currents equal to and slightly larger than the critical current, as a stable time-dependent phase characterized by persistent charged meron flow in each of the individual layers with a characteristic AC Josephson frequency. As the magnitude of the voltage quench is further increased, we find that the time-dependent current oscillations associated with the charged meron flow decay, resulting in a transient pseudospin paramagnet phase characterized by partially coherent charge transfer between layers, before the state relaxes to incoherent charge transfer between the layers.

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arXiv2014

Momentum space imaging of Cooper pairing in a half-Dirac-gas topological superconductor (a helical 2D topological superconductor)

Superconductivity in Dirac electrons has recently been proposed as a new platform between novel concepts in high-energy and condensed matter physics. It has been proposed that supersymmetry and exotic quasiparticles, both of which remain elusive in particle physics, may be realized as emergent particles in superconducting Dirac electron systems. Using artificially fabricated topological insulator-superconductor heterostructures, we present direct spectroscopic evidence for the existence of Cooper pairing in a half Dirac gas 2D topological superconductor. Our studies reveal that superconductivity in a helical Dirac gas is distinctly different from that of in an ordinary two-dimensional superconductor while considering the spin degrees of freedom of electrons. We further show that the pairing of Dirac electrons can be suppressed by time-reversal symmetry breaking impurities removing the distinction. Our demonstration and momentum-space imaging of Cooper pairing in a half Dirac gas and its magnetic behavior taken together serve as a critically important 2D topological superconductor platform for future testing of novel fundamental physics predictions such as emergent supersymmetry and quantum criticality in topological systems.

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arXiv2014

Aharonov-Bohm Oscillations in a Quasi-Ballistic 3D Topological Insulator Nanowire

In three-dimensional topological insulators (3D TI) nanowires, transport occurs via gapless surface states where the spin is fixed perpendicular to the momentum[1-6]. Carriers encircling the surface thus acquire a πBerry phase, which is predicted to open up a gap in the lowest-energy 1D surface subband. Inserting a magnetic flux (Φ) of h/2e through the nanowire should cancel the Berry phase and restore the gapless 1D mode[7-8]. However, this signature has been missing in transport experiments reported to date[9-11]. Here, we report measurements of mechanically-exfoliated 3D TI nanowires which exhibit Aharonov-Bohm oscillations consistent with topological surface transport. The use of low-doped, quasi-ballistic devices allows us to observe a minimum conductance at Φ = 0 and a maximum conductance reaching e^2/h at Φ = h/2e near the lowest subband (i.e. the Dirac point), as well as the carrier density dependence of the transport.

cond-mat.mes-hall↗

arXiv2014

Spinless Topological Insulators without Time-Reversal Symmetry

We explore the 32 crystallographic point groups and identify topological phases of matter with robust surface modes. For n =3,4 and 6 of the C_{nv} groups, we find the first-known 3D topological insulators without spin-orbit coupling, and with surface modes that are protected only by point groups, i.e., not needing time-reversal symmetry. To describe these C_{nv} systems, we introduce the notions of (a) a halved mirror chirality: an integer invariant which characterizes half-mirror-planes in the 3D Brillouin zone, and (b) a bent Chern number: the traditional TKNN invariant generalized to bent 2D manifolds. We find that a Weyl semimetallic phase intermediates two gapped phases with distinct halved chiralities.

cond-mat.str-el↗

arXiv2014

New class of topological superconductors protected by magnetic group symmetries

We study a new type of three-dimensional topological superconductors that exhibit Majorana zero modes (MZM) protected by a magnetic group symmetry, a combined antiunitary symmetry composed of a mirror reflection and time-reversal. This new symmetry enhances the noninteracting topological classification of a superconducting vortex from $Z_2$ to $Z$, indicating that multiple MZMs can coexist at the end of one magnetic vortex of unit flux. Specially, we show that a vortex binding two MZMs can be realized on the $(001)$-surface of a topological crystalline insulator SnTe with proximity induced BCS Cooper pairing, or in bulk superconductor In$_x$Sn$_{1-x}$Te.

cond-mat.mes-hall↗

arXiv2014

Tri-Dirac Surface Modes in Topological Superconductors

We propose a new type of topological surface modes having cubic dispersion in three-dimensional topological superconductors. Lower order dispersions are prohibited by the threefold rotational symmetry and time-reversal symmetry. Cooper pairing in the bulk changes sign under improper rotations, akin to$^{3}$He-B. The surface manifestations are a divergent surface density of states at the Fermi level and isospins that rotate three times as they circle the origin in momentum space. We propose that Heusler alloys with band inversion are candidate materials to harbor the novel topological superconductivity.

cond-mat.mes-hall↗

arXiv2013

Theory of quasiparticle interference in mirror symmetric 2D systems and its application to surface states of topological crystalline insulators

We study symmetry protected features in the quasiparticle interference (QPI) pattern of 2D systems with mirror symmetries and time-reversal symmetry, around a single static point impurity. We show that, in the Fourier transformed local density of states (FT-LDOS), $ρ(\bq,ω)$, while the position of high intensity peaks generically depends on the geometric features of the iso-energy contour at energy $ω$, the \emph{absence} of certain peaks is guaranteed by the opposite mirror eigenvalues of the two Bloch states that are (i) on the mirror symmetric lines in the Brillouin zone (BZ) and (ii) separated by scattering vector $\bq$. We apply the general result to the QPI on the $ <{001} >$-surface of topological crystalline insulator Pb$_{1-x}$Sn$_x$Te and predict all vanishing peaks in $ρ(\bq,ω)$. The model-independent analysis is supported by numerical calculations using an effective four-band model derived from symmetry analysis.

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arXiv2013

Topological Insulators with Commensurate Antiferromagnetism

We study the topological features of non-interacting insulators subject to an antiferromangetic (AFM) Zeeman field, or AFM insulators, the period of which is commensurate with the lattice period. These insulators can be classified by the presence/absence of an emergent anti-unitary symmetry: the combined operation of time-reversal and a lattice translation by vector $\mathbf{D}$. For AFM insulators that preserve this combined symmetry, regardless of any details in lattice structure or magnetic structure, we show that (i) there is a new type of Kramers' degeneracy protected by the combined symmetry; (ii) a new $Z_2$ index may be defined for 3D AFM insulators, but not for those in lower dimensions and (iii) in 3D AFM insulators with a non-trivial $Z_2$ index, there are odd number of gapless surface modes if and only if the surface termination also preserves the combined symmetry, but the dispersion of surface states becomes highly anisotropic if the AFM propagation vector becomes small compared with the reciprocal lattice vectors. We numerically demonstrate the theory by calculating the spectral weight of the surface states of a 3D TI in the presence of AFM fields with different propagation vectors, which may be observed by ARPES in Bi$_2$Se$_3$ or Bi$_2$Te$_3$ with induced antiferromagnetism.

cond-mat.mes-hall↗

arXiv2013

Large Chern Number Quantum Anomalous Hall Effect In Thin-film Topological Crystalline Insulators

Quantum anomalous Hall (QAH) insulators are two-dimensional (2D) insulating states exhibiting properties similar to those of quantum Hall states but without external magnetic field. They have quantized Hall conductance $σ^H=Ce^2/h$, where integer $C$ is called the Chern number, and represents the number of gapless edge modes. Recent experiments demonstrated that chromium doped thin-film (Bi,Sb)$_2$Te$_3$ is a QAH insulator with Chern number $C=\pm1$. Here we theoretically predict that thin-film topological crystalline insulators (TCI) can host various QAH phases, when doped by ferromagnetically ordered dopants. Any Chern number between $\pm4$ can, in principle, be reached as a result of the interplay between (a) the induced Zeeman field, depending on the magnetic doping concentration, (b) the structural distortion, either intrinsic or induced by a piezoelectric material through proximity effect and (c) the thickness of the thin film. The tunable Chern numbers found in TCI possess significant potential for ultra-low power information processing applications.

cond-mat.mes-hall↗

arXiv2013

Weyl Phases in Point-Group Symmetric Superconductors

We study superconductivity in a Weyl semimetal with broken time-reversal symmetry and stabilized by a point-group symmetry. The resulting superconducting phase is characterized by topologically protected bulk nodes and surface states with Fermi arcs. The topological invariant governing the system is calculated using changes in eigenvalues of the point-group operator along high-symmetry momentum lines. We show that this invariant is determined by the Fermi surface topology of the Weyl semimetal. We discuss the effect of surface orientation and $C_4$-breaking strain as possible experimental consequences.

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