ABSTRACT We study the electronic contribution to the thermal conductivity and the thermopower of ... more ABSTRACT We study the electronic contribution to the thermal conductivity and the thermopower of Weyl and Dirac semimetals using a semiclassical Boltzmann approach. We investigate the effect of various relaxation processes including disorder and interactions on the thermoelectric properties, and also consider doping away from the Weyl or Dirac point. We find that the thermal conductivity and thermopower have an interesting dependence on the chemical potential that is characteristic of the linear electronic dispersion, and that the electron-electron interactions modify the Lorenz number. For the interacting system, we also use the Kubo formalism to obtain the transport coefficients. We find exact agreement between the Kubo and Boltzmann approaches at high tem- peratures. We also consider the effect of electric and magnetic fields on the thermal conductivity in various orientations with respect to the temperature gradient. Notably, when the temperature gradient and magnetic field are parallel, we find a large contribution to the longitudinal thermal conductivity that is quadratic in the magnetic field strength, similar to the magnetic field dependence of the longitudinal electrical conductivity due to the presence of the chiral anomaly when no thermal gradient is present.
ABSTRACT We study the phase diagram of layered perovskite (Li,Na)2IrO3 with an underlying honeyco... more ABSTRACT We study the phase diagram of layered perovskite (Li,Na)2IrO3 with an underlying honeycomb lattice structure in the strongly interacting limit. Because of the strong spin-orbit coupling of iridium, the effective spin exchange model is highly anisotropic and frustrated. We use the Schwinger fermion approach to map out the phase diagram of the model. At the mean field level several spin liquid phases are found: a gapless spin liquid , a chiral spin liquid, and a helical spin liquid phase. Moreover, in the strong exchange coupling limit we obtain a dimerized phase. The gapless spin liquid phase is characterized by Dirac nodes. In the chiral phase the Dirac nodes are gapped in the bulk, and the system possess a nonzero Chern number signifying existence of chiral modes along the boundary of the system. The helical phase preserves time reversal symmetry, has a bulk gap, and features helical gapless edge modes along boundary analogous to those in topological insulators with a nontrivial invariant. We further investigate the nature of the spin liquid phase by considering the gauge fluctuations above the mean field solution. The chiral spin liquid phase is stable as it breaks time reversal symmetry and acquires a nonzero Chern-Simon term in the effective low energy theory.
The flow of liquids in confined geometries has been much studied, especially in connection with w... more The flow of liquids in confined geometries has been much studied, especially in connection with work on liquid He. It is thus surprising that some basic aspects of this problem remain unresolved. In particular, deviations from Poiseuille's law for the simple, laminar flow of a classical liquid have recently been reported.( W. Urbanek, J. N. Zemel, and H. H. Bau, J. Micromech. Microeng. 3), 206 (1993). These deviations are especially striking since the transverse dimensions of the flow channels used in the experiments were typically ~ μ m or larger in size, which is much greater than any intrinsic length scales of the liquids (e.g., 2-propanol) which were employed. This unexpected result has prompted us to reexamine this problem. We describe our efforts to develop a simple yet versatile lithographic approach for fabricating micron and submicron scale flow channels, along with preliminary results of new tests of Poiseuille's law. Such flow channels should be useful for a variety of studies, including flow behavior at extremely small Reynolds numbers, and at nm size scales.
We theoretically investigate the Coulomb drag between the edge states of two quantum spin Hall sy... more We theoretically investigate the Coulomb drag between the edge states of two quantum spin Hall systems. Using an interacting theory of the one-dimensional helical edge modes, we show that the drag vanishes at second order in the inter-edge interaction, where it is typically finite in other systems, due to the absence of backscattering within the edges. However, in the presence of a small external magnetic field, the drag is finite and scales as the fourth power of the magnetic field, a behavior that sharply distinguishes it from other systems. We obtain the temperature dependence of the drag for regimes of both linear and quadratic edge dispersion in the presence of a finite field. This work was financially supported by ARO under Grant No. W911NF-09-1-0527. V. A. Zyuzin and G. A. Fiete, Phys. Rev. B 82, 113305 (2010).
We theoretically study the spatially anisotropic spin-1/2 kagome antiferromagnet with a Dzyaloshi... more We theoretically study the spatially anisotropic spin-1/2 kagome antiferromagnet with a Dzyaloshinskii-Moriya (DM) interaction using a renormalization-group analysis in the quasi-one-dimensional limit. We identify the various temperature and energy scales for ordering in the system. For a very weak DM interaction, we find a low-temperature spiral phase with the plane of the spiral selected by the DM interaction. This phase is similar to a previously identified phase in the absence of the DM interaction. However, above a critical DM interaction strength we find a transition to a phase with coexisting antiferromagnetic and dimer order, reminiscent of one-dimensional antiferromagnetic systems with a uniform DM interaction. Our results help shed light on the fate of two-dimensional systems with both strong interactions and significant spin-orbit coupling.
Physical Review B Condensed Matter and Materials Physics, Mar 1, 2010
We study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall... more We study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state. We focus on the physics of level degeneracy with electron number on the dot. The physics of such a resonant level is governed by a k-channel Kondo model when the quantum Hall state is a Read-Rezayi state at filling fraction ν=2+k/(k+2) or its particle-hole conjugate at ν=2+2/(k+2). The k-channel Kondo model is channel symmetric even without fine tuning any couplings in the former state; in the latter, it is generically channel asymmetric. The two limits exhibit non-Fermi liquid and Fermi liquid properties, respectively, and therefore may be distinguished. By exploiting the mapping between the resonant level model and the multichannel Kondo model, we discuss the thermodynamic and transport properties of the system. In the special case of k=2, our results provide a novel venue to distinguish between the Pfaffian and anti-Pfaffian states at filling fraction ν=5/2. Transport through a double-point contact geometry is possibly governed by an unusual fixed point. arXiv:0911.1799
In this work we investigate the phase diagram of heavy (4d and 5d) transition metal oxides on the... more In this work we investigate the phase diagram of heavy (4d and 5d) transition metal oxides on the pyrochlore lattice, such as those of the form $\mathrm{A_2M_2O_7}$, where A is a rare earth element and M is a transition metal element. We focus on the competition between Coulomb interaction, spin-orbit coupling, and lattice distortion when these energy scales are comparable. Strong spin-orbit coupling entangles the spin and the $t_{2g}$ $d$-orbitals giving rise to doublet $j=1/2$ and quadruplet $j=3/2$ states. In contrast to previous works which focused on the doublet manifold, we also discuss the quadruplet manifold which is relevant for several pyrochlore oxides. The Coulomb interaction is taken into account by use of the slave-rotor mean field theory and different classes of lattice distortions which further split the levels of the quadruplet $j=3/2$ manifold are studied. Various topological phases are predicted, including exotic strong and weak topological Mott insulating phases. We discuss the general structure of the phase diagram for several values of $d$-shell filling and various symmetry classes of lattice distortions. Our results are relevant to the search for exotic topological insulators and quantum spin liquids in strongly correlated materials with strong spin-orbit coupling.
We theoretically study topological phase transitions in four generalized versions of the Kane-Mel... more We theoretically study topological phase transitions in four generalized versions of the Kane-Mele-Hubbard model with up to $2\times 18^2$ sites. All models are free of the fermion-sign problem allowing numerically exact quantum Monte Carlo (QMC) calculations to be performed to extremely low temperatures. We numerically compute the $\mathbb{Z}_2$ invariant and spin Chern number $C_\sigma$ directly from the zero-frequency single-particle Green's functions, and study the topological phase transitions driven by the tight-binding parameters at different on-site interaction strengths. The $\mathbb{Z}_2$ invariant and spin Chern number, which are complementary to each another, characterize the topological phases and identify the critical points of topological phase transitions. Although the numerically determined phase boundaries are nearly identical for different system sizes, we find strong system-size dependence of the spin Chern number, where quantized values are only expected upon approaching the thermodynamic limit. For the Hubbard models we considered, the QMC results show that correlation effects lead to shifts in the phase boundaries relative to those in the non-interacting limit, without any spontaneously symmetry breaking. The interaction-induced shift is non-perturbative in the interactions and cannot be captured within a "simple" self-consistent calculation either, such as Hartree-Fock. Furthermore, our QMC calculations suggest that quantum fluctuations from interactions stabilize topological phases in systems where the one-body terms preserve the $D_3$ symmetry of the lattice, and destabilize topological phases when the one-body terms break the $D_3$ symmetry.
The many-body wave-function of an interacting one-dimensional electron system is probed, fo- cusi... more The many-body wave-function of an interacting one-dimensional electron system is probed, fo- cusing on the low-density, strong interaction regime. The properties of the wave-function are determined using tunneling between two long, clean, parallel quantum wires in a GaAs/AlGaAs heterostructure, allowing for gate-controlled electron density. As electron density is lowered to a critical value the many-body state abruptly changes from an
Collective ferromagnetic motion in a conducting medium is damped by the transfer of the magnetic ... more Collective ferromagnetic motion in a conducting medium is damped by the transfer of the magnetic moment and energy to the itinerant carriers. We present a calculation of the corresponding magnetization relaxation as a linear-response problem for the carrier dynamics in the effective exchange field of the ferromagnet. In electron systems with little intrinsic spin-orbit interaction, a uniform magnetization motion can
Proceedings of the National Academy of Sciences, 2015
Considerable evidence suggests that variations in the properties of topological insulators (TIs) ... more Considerable evidence suggests that variations in the properties of topological insulators (TIs) at the nanoscale and at interfaces can strongly affect the physics of topological materials. Therefore, a detailed understanding of surface states and interface coupling is crucial to the search for and applications of new topological phases of matter. Currently, no methods can provide depth profiling near surfaces or at interfaces of topologically inequivalent materials. Such a method could advance the study of interactions. Herein, we present a noninvasive depth-profiling technique based on β-detected NMR (β-NMR) spectroscopy of radioactive (8)Li(+) ions that can provide "one-dimensional imaging" in films of fixed thickness and generates nanoscale views of the electronic wavefunctions and magnetic order at topological surfaces and interfaces. By mapping the (8)Li nuclear resonance near the surface and 10-nm deep into the bulk of pure and Cr-doped bismuth antimony telluride films, we provide signatures related to the TI properties and their topological nontrivial characteristics that affect the electron-nuclear hyperfine field, the metallic shift, and magnetic order. These nanoscale variations in β-NMR parameters reflect the unconventional properties of the topological materials under study, and understanding the role of heterogeneities is expected to lead to the discovery of novel phenomena involving quantum materials.
While the theoretical and experimental study of topological phases of matter has experienced rapi... more While the theoretical and experimental study of topological phases of matter has experienced rapid growth over the last few years, there remain a relatively small number of material classes that have been experimentally shown to host these phases. Most of these materials contain bismuth, and none so far are oxides. In this work we make materials-specific predictions for topological phases using density functional theory combined with Hartree-Fock theory that includes the full orbital structure of the relevant iridium d-orbitals and the strong but finite spin-orbit coupling strength. We find Y2Ir2O7 bilayer and trilayer films grown along the [111] direction can support topological metallic phases with a direct gap of up to 0.05 eV, which could potentially bring transition metal oxides to the fore as a new class of topological materials with potential applications in oxide electronics.
Motivated by recent scanning tunneling microscope (STM) experiments on cobalt clusters adsorbed o... more Motivated by recent scanning tunneling microscope (STM) experiments on cobalt clusters adsorbed on single wall metallic nanotubes [Odom {\em et al.}, Science {\bf 290}, 1549 (2000)], we study theoretically the size dependence of STM spectra and spin-flip scattering of electrons from finite size ferromagnetic clusters adsorbed on metallic surfaces. We study two models of nanometer size ferromagnets: (i) An itinerant
We study the momentum space entanglement spectra of bosonic and fermionic formulations of the spi... more We study the momentum space entanglement spectra of bosonic and fermionic formulations of the spin-1/2 XXZ chain with analytical methods and exact diagonalization. We investigate the behavior of the entanglement gaps, present in both formulations, across quantum phase transitions in the XXZ chain. In both cases, finite size scaling suggests that the entanglement gap closure does not occur at the physical transition points. For bosons, we find that the entanglement gap observed in Thomale et al. [Phys. Rev. Lett. 105, 116805 (2010)] depends on the scaling dimension of the conformal field theory as varied by the XXZ anisotropy. For fermions, the infinite entanglement gap present at the XX point persists well past the phase transition at the Heisenberg point. We elaborate on how these shifted transition points in the entanglement spectra may support the numerical study of phase transitions in the momentum space density matrix renormalization group.
Using the hierarchy picture of the fractional quantum Hall effect, we study the ground-state peri... more Using the hierarchy picture of the fractional quantum Hall effect, we study the ground-state periodicity of a finite size quantum Hall droplet in a quantum Hall fluid of a different filling factor. The droplet edge charge is periodically modulated with flux through the droplet and will lead to a periodic variation in the conductance of a nearby point contact, such as occurs in some quantum Hall interferometers. Our model is consistent with experiment and predicts that superperiods can be observed in geometries where no interfering trajectories occur. The model may also provide an experimentally feasible method of detecting elusive neutral modes and otherwise obtaining information about the microscopic edge structure in fractional quantum Hall states.
We investigated topological phases in several decorated lattices such as the square- octagon and ... more We investigated topological phases in several decorated lattices such as the square- octagon and spin ruby lattices. The underlying models can be potentially simulated in optical lattices or in multi-orbital transition metal oxides. In the square-octagon lattice we apply a set of non-Abelian gauge fields to modulate the hopping between sites. Inversion symmetric fields open a gap and the model
In this work we investigate the phase diagram of 5d transition metal oxides on the pyrochlore lat... more In this work we investigate the phase diagram of 5d transition metal oxides on the pyrochlore lattice. In particular, the competition between Coulomb interaction, spin-orbit coupling and distortion are discussed. Spin-orbit coupling entangles the spin and t2g orbitals giving rise to doublet j=1/2 and quadruplet j=3/2 states. While most pervious works discussed the doublet manifold, we focus on the quadruplet
We study the nu=2k+2 quantum Hall states which are particle-hole conjugates of the nu=kk+2 Read-R... more We study the nu=2k+2 quantum Hall states which are particle-hole conjugates of the nu=kk+2 Read-Rezayi states. We find that equilibration between the different modes at the edge of such a state leads to an emergent SU(2)k algebra in the counter-propagating neutral sector. Heat flow along the edges of these states will be in the opposite direction of charge flow. In
We study the nu=(2)/(k+2) quantum Hall states which are particle-hole conjugates of the nu=(2)/(k... more We study the nu=(2)/(k+2) quantum Hall states which are particle-hole conjugates of the nu=(2)/(k+2) Read-Rezayi states. We find that equilibration between the different modes at the edge of such a state leads to an emergent SU(2)k algebra in the counter-propagating neutral sector. Heat flow along the edges of these states will be in the opposite direction of charge flow. In
ABSTRACT We study the electronic contribution to the thermal conductivity and the thermopower of ... more ABSTRACT We study the electronic contribution to the thermal conductivity and the thermopower of Weyl and Dirac semimetals using a semiclassical Boltzmann approach. We investigate the effect of various relaxation processes including disorder and interactions on the thermoelectric properties, and also consider doping away from the Weyl or Dirac point. We find that the thermal conductivity and thermopower have an interesting dependence on the chemical potential that is characteristic of the linear electronic dispersion, and that the electron-electron interactions modify the Lorenz number. For the interacting system, we also use the Kubo formalism to obtain the transport coefficients. We find exact agreement between the Kubo and Boltzmann approaches at high tem- peratures. We also consider the effect of electric and magnetic fields on the thermal conductivity in various orientations with respect to the temperature gradient. Notably, when the temperature gradient and magnetic field are parallel, we find a large contribution to the longitudinal thermal conductivity that is quadratic in the magnetic field strength, similar to the magnetic field dependence of the longitudinal electrical conductivity due to the presence of the chiral anomaly when no thermal gradient is present.
ABSTRACT We study the phase diagram of layered perovskite (Li,Na)2IrO3 with an underlying honeyco... more ABSTRACT We study the phase diagram of layered perovskite (Li,Na)2IrO3 with an underlying honeycomb lattice structure in the strongly interacting limit. Because of the strong spin-orbit coupling of iridium, the effective spin exchange model is highly anisotropic and frustrated. We use the Schwinger fermion approach to map out the phase diagram of the model. At the mean field level several spin liquid phases are found: a gapless spin liquid , a chiral spin liquid, and a helical spin liquid phase. Moreover, in the strong exchange coupling limit we obtain a dimerized phase. The gapless spin liquid phase is characterized by Dirac nodes. In the chiral phase the Dirac nodes are gapped in the bulk, and the system possess a nonzero Chern number signifying existence of chiral modes along the boundary of the system. The helical phase preserves time reversal symmetry, has a bulk gap, and features helical gapless edge modes along boundary analogous to those in topological insulators with a nontrivial invariant. We further investigate the nature of the spin liquid phase by considering the gauge fluctuations above the mean field solution. The chiral spin liquid phase is stable as it breaks time reversal symmetry and acquires a nonzero Chern-Simon term in the effective low energy theory.
The flow of liquids in confined geometries has been much studied, especially in connection with w... more The flow of liquids in confined geometries has been much studied, especially in connection with work on liquid He. It is thus surprising that some basic aspects of this problem remain unresolved. In particular, deviations from Poiseuille's law for the simple, laminar flow of a classical liquid have recently been reported.( W. Urbanek, J. N. Zemel, and H. H. Bau, J. Micromech. Microeng. 3), 206 (1993). These deviations are especially striking since the transverse dimensions of the flow channels used in the experiments were typically ~ μ m or larger in size, which is much greater than any intrinsic length scales of the liquids (e.g., 2-propanol) which were employed. This unexpected result has prompted us to reexamine this problem. We describe our efforts to develop a simple yet versatile lithographic approach for fabricating micron and submicron scale flow channels, along with preliminary results of new tests of Poiseuille's law. Such flow channels should be useful for a variety of studies, including flow behavior at extremely small Reynolds numbers, and at nm size scales.
We theoretically investigate the Coulomb drag between the edge states of two quantum spin Hall sy... more We theoretically investigate the Coulomb drag between the edge states of two quantum spin Hall systems. Using an interacting theory of the one-dimensional helical edge modes, we show that the drag vanishes at second order in the inter-edge interaction, where it is typically finite in other systems, due to the absence of backscattering within the edges. However, in the presence of a small external magnetic field, the drag is finite and scales as the fourth power of the magnetic field, a behavior that sharply distinguishes it from other systems. We obtain the temperature dependence of the drag for regimes of both linear and quadratic edge dispersion in the presence of a finite field. This work was financially supported by ARO under Grant No. W911NF-09-1-0527. V. A. Zyuzin and G. A. Fiete, Phys. Rev. B 82, 113305 (2010).
We theoretically study the spatially anisotropic spin-1/2 kagome antiferromagnet with a Dzyaloshi... more We theoretically study the spatially anisotropic spin-1/2 kagome antiferromagnet with a Dzyaloshinskii-Moriya (DM) interaction using a renormalization-group analysis in the quasi-one-dimensional limit. We identify the various temperature and energy scales for ordering in the system. For a very weak DM interaction, we find a low-temperature spiral phase with the plane of the spiral selected by the DM interaction. This phase is similar to a previously identified phase in the absence of the DM interaction. However, above a critical DM interaction strength we find a transition to a phase with coexisting antiferromagnetic and dimer order, reminiscent of one-dimensional antiferromagnetic systems with a uniform DM interaction. Our results help shed light on the fate of two-dimensional systems with both strong interactions and significant spin-orbit coupling.
Physical Review B Condensed Matter and Materials Physics, Mar 1, 2010
We study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall... more We study the coupling between a quantum dot and the edge of a non-Abelian fractional quantum Hall state. We focus on the physics of level degeneracy with electron number on the dot. The physics of such a resonant level is governed by a k-channel Kondo model when the quantum Hall state is a Read-Rezayi state at filling fraction ν=2+k/(k+2) or its particle-hole conjugate at ν=2+2/(k+2). The k-channel Kondo model is channel symmetric even without fine tuning any couplings in the former state; in the latter, it is generically channel asymmetric. The two limits exhibit non-Fermi liquid and Fermi liquid properties, respectively, and therefore may be distinguished. By exploiting the mapping between the resonant level model and the multichannel Kondo model, we discuss the thermodynamic and transport properties of the system. In the special case of k=2, our results provide a novel venue to distinguish between the Pfaffian and anti-Pfaffian states at filling fraction ν=5/2. Transport through a double-point contact geometry is possibly governed by an unusual fixed point. arXiv:0911.1799
In this work we investigate the phase diagram of heavy (4d and 5d) transition metal oxides on the... more In this work we investigate the phase diagram of heavy (4d and 5d) transition metal oxides on the pyrochlore lattice, such as those of the form $\mathrm{A_2M_2O_7}$, where A is a rare earth element and M is a transition metal element. We focus on the competition between Coulomb interaction, spin-orbit coupling, and lattice distortion when these energy scales are comparable. Strong spin-orbit coupling entangles the spin and the $t_{2g}$ $d$-orbitals giving rise to doublet $j=1/2$ and quadruplet $j=3/2$ states. In contrast to previous works which focused on the doublet manifold, we also discuss the quadruplet manifold which is relevant for several pyrochlore oxides. The Coulomb interaction is taken into account by use of the slave-rotor mean field theory and different classes of lattice distortions which further split the levels of the quadruplet $j=3/2$ manifold are studied. Various topological phases are predicted, including exotic strong and weak topological Mott insulating phases. We discuss the general structure of the phase diagram for several values of $d$-shell filling and various symmetry classes of lattice distortions. Our results are relevant to the search for exotic topological insulators and quantum spin liquids in strongly correlated materials with strong spin-orbit coupling.
We theoretically study topological phase transitions in four generalized versions of the Kane-Mel... more We theoretically study topological phase transitions in four generalized versions of the Kane-Mele-Hubbard model with up to $2\times 18^2$ sites. All models are free of the fermion-sign problem allowing numerically exact quantum Monte Carlo (QMC) calculations to be performed to extremely low temperatures. We numerically compute the $\mathbb{Z}_2$ invariant and spin Chern number $C_\sigma$ directly from the zero-frequency single-particle Green's functions, and study the topological phase transitions driven by the tight-binding parameters at different on-site interaction strengths. The $\mathbb{Z}_2$ invariant and spin Chern number, which are complementary to each another, characterize the topological phases and identify the critical points of topological phase transitions. Although the numerically determined phase boundaries are nearly identical for different system sizes, we find strong system-size dependence of the spin Chern number, where quantized values are only expected upon approaching the thermodynamic limit. For the Hubbard models we considered, the QMC results show that correlation effects lead to shifts in the phase boundaries relative to those in the non-interacting limit, without any spontaneously symmetry breaking. The interaction-induced shift is non-perturbative in the interactions and cannot be captured within a "simple" self-consistent calculation either, such as Hartree-Fock. Furthermore, our QMC calculations suggest that quantum fluctuations from interactions stabilize topological phases in systems where the one-body terms preserve the $D_3$ symmetry of the lattice, and destabilize topological phases when the one-body terms break the $D_3$ symmetry.
The many-body wave-function of an interacting one-dimensional electron system is probed, fo- cusi... more The many-body wave-function of an interacting one-dimensional electron system is probed, fo- cusing on the low-density, strong interaction regime. The properties of the wave-function are determined using tunneling between two long, clean, parallel quantum wires in a GaAs/AlGaAs heterostructure, allowing for gate-controlled electron density. As electron density is lowered to a critical value the many-body state abruptly changes from an
Collective ferromagnetic motion in a conducting medium is damped by the transfer of the magnetic ... more Collective ferromagnetic motion in a conducting medium is damped by the transfer of the magnetic moment and energy to the itinerant carriers. We present a calculation of the corresponding magnetization relaxation as a linear-response problem for the carrier dynamics in the effective exchange field of the ferromagnet. In electron systems with little intrinsic spin-orbit interaction, a uniform magnetization motion can
Proceedings of the National Academy of Sciences, 2015
Considerable evidence suggests that variations in the properties of topological insulators (TIs) ... more Considerable evidence suggests that variations in the properties of topological insulators (TIs) at the nanoscale and at interfaces can strongly affect the physics of topological materials. Therefore, a detailed understanding of surface states and interface coupling is crucial to the search for and applications of new topological phases of matter. Currently, no methods can provide depth profiling near surfaces or at interfaces of topologically inequivalent materials. Such a method could advance the study of interactions. Herein, we present a noninvasive depth-profiling technique based on β-detected NMR (β-NMR) spectroscopy of radioactive (8)Li(+) ions that can provide "one-dimensional imaging" in films of fixed thickness and generates nanoscale views of the electronic wavefunctions and magnetic order at topological surfaces and interfaces. By mapping the (8)Li nuclear resonance near the surface and 10-nm deep into the bulk of pure and Cr-doped bismuth antimony telluride films, we provide signatures related to the TI properties and their topological nontrivial characteristics that affect the electron-nuclear hyperfine field, the metallic shift, and magnetic order. These nanoscale variations in β-NMR parameters reflect the unconventional properties of the topological materials under study, and understanding the role of heterogeneities is expected to lead to the discovery of novel phenomena involving quantum materials.
While the theoretical and experimental study of topological phases of matter has experienced rapi... more While the theoretical and experimental study of topological phases of matter has experienced rapid growth over the last few years, there remain a relatively small number of material classes that have been experimentally shown to host these phases. Most of these materials contain bismuth, and none so far are oxides. In this work we make materials-specific predictions for topological phases using density functional theory combined with Hartree-Fock theory that includes the full orbital structure of the relevant iridium d-orbitals and the strong but finite spin-orbit coupling strength. We find Y2Ir2O7 bilayer and trilayer films grown along the [111] direction can support topological metallic phases with a direct gap of up to 0.05 eV, which could potentially bring transition metal oxides to the fore as a new class of topological materials with potential applications in oxide electronics.
Motivated by recent scanning tunneling microscope (STM) experiments on cobalt clusters adsorbed o... more Motivated by recent scanning tunneling microscope (STM) experiments on cobalt clusters adsorbed on single wall metallic nanotubes [Odom {\em et al.}, Science {\bf 290}, 1549 (2000)], we study theoretically the size dependence of STM spectra and spin-flip scattering of electrons from finite size ferromagnetic clusters adsorbed on metallic surfaces. We study two models of nanometer size ferromagnets: (i) An itinerant
We study the momentum space entanglement spectra of bosonic and fermionic formulations of the spi... more We study the momentum space entanglement spectra of bosonic and fermionic formulations of the spin-1/2 XXZ chain with analytical methods and exact diagonalization. We investigate the behavior of the entanglement gaps, present in both formulations, across quantum phase transitions in the XXZ chain. In both cases, finite size scaling suggests that the entanglement gap closure does not occur at the physical transition points. For bosons, we find that the entanglement gap observed in Thomale et al. [Phys. Rev. Lett. 105, 116805 (2010)] depends on the scaling dimension of the conformal field theory as varied by the XXZ anisotropy. For fermions, the infinite entanglement gap present at the XX point persists well past the phase transition at the Heisenberg point. We elaborate on how these shifted transition points in the entanglement spectra may support the numerical study of phase transitions in the momentum space density matrix renormalization group.
Using the hierarchy picture of the fractional quantum Hall effect, we study the ground-state peri... more Using the hierarchy picture of the fractional quantum Hall effect, we study the ground-state periodicity of a finite size quantum Hall droplet in a quantum Hall fluid of a different filling factor. The droplet edge charge is periodically modulated with flux through the droplet and will lead to a periodic variation in the conductance of a nearby point contact, such as occurs in some quantum Hall interferometers. Our model is consistent with experiment and predicts that superperiods can be observed in geometries where no interfering trajectories occur. The model may also provide an experimentally feasible method of detecting elusive neutral modes and otherwise obtaining information about the microscopic edge structure in fractional quantum Hall states.
We investigated topological phases in several decorated lattices such as the square- octagon and ... more We investigated topological phases in several decorated lattices such as the square- octagon and spin ruby lattices. The underlying models can be potentially simulated in optical lattices or in multi-orbital transition metal oxides. In the square-octagon lattice we apply a set of non-Abelian gauge fields to modulate the hopping between sites. Inversion symmetric fields open a gap and the model
In this work we investigate the phase diagram of 5d transition metal oxides on the pyrochlore lat... more In this work we investigate the phase diagram of 5d transition metal oxides on the pyrochlore lattice. In particular, the competition between Coulomb interaction, spin-orbit coupling and distortion are discussed. Spin-orbit coupling entangles the spin and t2g orbitals giving rise to doublet j=1/2 and quadruplet j=3/2 states. While most pervious works discussed the doublet manifold, we focus on the quadruplet
We study the nu=2k+2 quantum Hall states which are particle-hole conjugates of the nu=kk+2 Read-R... more We study the nu=2k+2 quantum Hall states which are particle-hole conjugates of the nu=kk+2 Read-Rezayi states. We find that equilibration between the different modes at the edge of such a state leads to an emergent SU(2)k algebra in the counter-propagating neutral sector. Heat flow along the edges of these states will be in the opposite direction of charge flow. In
We study the nu=(2)/(k+2) quantum Hall states which are particle-hole conjugates of the nu=(2)/(k... more We study the nu=(2)/(k+2) quantum Hall states which are particle-hole conjugates of the nu=(2)/(k+2) Read-Rezayi states. We find that equilibration between the different modes at the edge of such a state leads to an emergent SU(2)k algebra in the counter-propagating neutral sector. Heat flow along the edges of these states will be in the opposite direction of charge flow. In
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