Bulletin of the American Physical Society, Mar 8, 2007
94720-We show that the Majorana fermion zero modes in the cores of odd winding number vortices of... more 94720-We show that the Majorana fermion zero modes in the cores of odd winding number vortices of a 2D p x + ip y-paired superconductor is due to an index theorem. This theorem is analogous to that proven by Jackiw and Rebbi for the existence of localized Dirac fermion zero modes on the mass domain walls of a 1D Dirac theory. The important difference is that, in our case, the theorem is proven for a two component fermion field theory where the first and second components are related by parity reversal and hermitian conjugation. The vortices with Majorana zero modes can be used, in principle, to build a topological quantum computer.
In this paper, we demonstrate that in frustrated magnets when several conventional (i.e., symmetr... more In this paper, we demonstrate that in frustrated magnets when several conventional (i.e., symmetry-breaking) orders compete, and are "intertwined" by a Wess-Zumino-Witten (WZW) term, the possibility of spin liquid arises. The resulting spin liquid could have excitations which carry fractional spins and obey non-trivial self/mutual statistics. As a concrete example, we consider the case where the competing orders are the Néel and valence-bond solid (VBS) order on square lattice. Examining different scenarios of vortex condensation from the VBS side, we show that the intermediate phases, including spin liquids, between the Néel and VBS order always break certain symmetry. Remarkably, our starting theory, without fractionalized particles (partons) and guage field, predicts results agreeing with those derived from a parton theory. This suggests that the missing link between the Ginzberg-Landau-Wilson action of competing order and the physics of spin liquid is the WZW term.
In this paper, we generalize Witten's non-abelian bosonization in (1+1)-D to two and three spatia... more In this paper, we generalize Witten's non-abelian bosonization in (1+1)-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. We apply the bosonization results to the SU (2) gauge theory of the π-flux phase, critical spin liquids in 1,2,3 spatial dimensions, and twisted bilayer graphene.
Transition metal dichalcogenides are ideal compounds to investigate dimensionality effect since t... more Transition metal dichalcogenides are ideal compounds to investigate dimensionality effect since the weak coupling between layers enables to study single-layer material which removes interlayer interactions and introduces quantum confinement. We investigate dimensionality effect of NbSe 2 in which the bulk phase shows charge density wave (CDW) (T CDW =33 K) and superconductivity (T c =7.2 K). We report electronic band structure of MBE grown monolayer NbSe 2 measured by Angel-resolved photoemission spectroscopy compared with bulk. We find the number of bands crossing the Fermi energy reduces from three (bulk) to one (monolayer). Based on the significant suppression of superconducting T c =0.65 K with robust CDW in monolayer NbSe 2 , our results imply the band remained at the Fermi level in monolayer NbSe 2 may play a crucial role in CDW formation and the disappeared bands are possibly in charge of superconductivity.
We study the effects of Cu substitution in Fe1.1Te, the non-superconducting parent compound of th... more We study the effects of Cu substitution in Fe1.1Te, the non-superconducting parent compound of the iron-based superconductor, Fe1+yTe1−xSex, utilizing neutron scattering techniques. It is found that the structural and magnetic transitions, which occur at ∼ 60 K without Cu, are monotonically depressed with increasing Cu content. By 10% Cu for Fe, the structural transition is hardly detectable, and the system becomes a spin glass below 22 K, with a slightly incommensurate ordering wave vector of (0.5-δ, 0, 0.5) with δ being the incommensurability of 0.02, and correlation length of 12Å along the a axis and 9Å along the c axis. With 4% Cu, both transition temperatures are at 41 K, though short-range incommensurate order at (0.42, 0, 0.5) is present at 60 K. With further cooling, the incommensurability decreases linearly with temperature down to 37 K, below which there is a first order transition to a long-range almost-commensurate antiferromagnetic structure. A spin anisotropy gap of 4.5 meV is also observed in this compound. Our results show that the weakly magnetic Cu has large effects on the magnetic correlations; it is suggested that this is caused by the frustration of the exchange interactions between the coupled Fe spins.
Recently Chakravarty, Laughlin, Morr and Nayak made an interesting proposal that the cuprate supe... more Recently Chakravarty, Laughlin, Morr and Nayak made an interesting proposal that the cuprate superconductors possess a hidden "d-density wave" order. We study the implication of this proposal for the superfluid density ρs. We find that it predicts a temperature gradient |dρs/dT |T =0 that is strongly doping dependent near the critical doping at which the superconducting gap vanishes.
To elucidate the superconductor to metal transition at the end of superconducting dome, the overd... more To elucidate the superconductor to metal transition at the end of superconducting dome, the overdoped regime has stepped onto the center stage of cuprate research recently. Here, we use scanning tunneling microscopy to investigate the atomic-scale electronic structure of overdoped trilayer and bilayer Bi2Sr2Can−1CunO2n+4+ cuprates. At low energies the spectroscopic maps are well described by dispersive quasiparticle interference patterns. However, as the bias increases to the superconducting coherence peak energy, a virtually nondispersive pattern with √2 × √2 periodicity emerges. Remarkably, the position of the coherence peaks exhibits evident particle-hole asymmetry which also modulates with the same period. We propose that this is an extreme quasiparticle interference phenomenon, caused by pairing-breaking scattering between flat anti-nodal Bogoliubov bands, which is ultimately responsible for the superconductor to metal transition.
We show that the plateau transitions in the quantum Hall effect is the same as the dimerization t... more We show that the plateau transitions in the quantum Hall effect is the same as the dimerization transition of a half-filled, one dimensional, U(2n) Hubbard model at n = 0. We address the properties of the latter by a combination of perturbative renormalization group and Monte Carlo simulations. Results on both critical and off-critical properties are presented.
... the spin gap Ao develops. "I'his is most easily done via the non-Abelian bosonizati... more ... the spin gap Ao develops. "I'his is most easily done via the non-Abelian bosonization [12], according to which a-',_i "-'*(_z, + £R)+ i(-1) i × const ×tr [(g,- g+)_] . (5) The expression for ¢ is identical with s _ _rand g, _ g,. In the above g, and g, are the ...
Bulletin of the American Physical Society, Mar 13, 2006
We present a theory of a superconducting wire dissipatively coupled to an environment. We show th... more We present a theory of a superconducting wire dissipatively coupled to an environment. We show that due to the finite extent of the wire, in the absence of dissipation quantum phase slips always destroy superconductivity, even at zero temperature. Dissipation stabilizes the superconducting phase. We apply this theory to understand the "anti-proximity effect" recently seen by Tian et. al. [Phys. Rev. Lett. 95, 076802 (2005)] in Zinc nanowires.
Bulletin of the American Physical Society, Mar 13, 2006
Orientational ordering, which originates from broken rotational symmetry, is a central feature of... more Orientational ordering, which originates from broken rotational symmetry, is a central feature of a broad range of materials including liquid crystals, quantum magnets, and some biological systems. By doping C 60 monolayers with alkali impurities, the symmetry of C 60 molecules can be broken, opening up the possibility for unique twodimensional molecular orientational ordering. Here we present a scanning tunneling microscopy/spectroscopy study of K x C 60 monolayers on Au(111), x ≥4. We find novel orientational orderings in the C 60 monolayers at different doping levels, which coincide with strong variations in the monolayer local density of states. This demonstrates the importance of the interplay between Coulomb repulsion, electron-phonon coupling, electronic quadrupolar interactions, and direct orbital overlap in determining the behavior of fullerene nanostructures.
We study the superconductivity of strongly coupled electron-phonon systems where the geometry of ... more We study the superconductivity of strongly coupled electron-phonon systems where the geometry of the lattice frustrates the charge order by the sign-problem-free Quantum Monte Carlo(QMC) method. The results suggest that with charge order frustrated, the superconductivity can benefit from strong electron-phonon interaction in a wide range of coupling strengths.
Under periodic boundary condition in the transverse direction, we calculate the averaged zero-tem... more Under periodic boundary condition in the transverse direction, we calculate the averaged zero-temperature two-terminal conductance (< G >) and its statistical fluctuations (< (δG) 2n > for n ≤ 4) at the critical point of integer quantum Hall plateau transitions. We find universal values for < G >= (0.58 ± 0.03) e 2 h , and < (δG) 2n >= (e 2 h) 2n A 2n , where A 2,4,6,8 = 0.081 ± 0.005; 0.013±0.003; 0.0026±0.005; and (8±2)×10 −4 respectively. We also determine the leading finite size scaling corrections to these observables. Comparisons with experiments will be made.
Superconductivity in doped quantum paramagnets has been a subject of long theoretical inquiry. In... more Superconductivity in doped quantum paramagnets has been a subject of long theoretical inquiry. In this work, we report a density matrix renormalization group study of lightly doped t-J models on the finite-width square lattice (doped hole densities δ = 1/12 and 1/8) with parameters for which previous studies have suggested that the undoped system in 2D is either a quantum spin liquid or a valence bond crystal. Our studies are performed on cylinders with width up to 8. Ground-state correlations are found to be nearly identical for the "doped quantum spin liquid" and "doped valence bond crystal." Upon increasing the cylinder widths from 4 to 8, we observed a significant strengthening of the quasi-long-range superconducting correlations and a dramatic suppression of any "competing" charge density wave order. Extrapolating from the observed behavior of the width eight cylinders, we speculate that the system has a nodeless d-wave superconducting ground state in the 2D limit.
Applying the method of [Nucl. Phys. B 972, 115565 (2021)], which bosonizes massless relativistic ... more Applying the method of [Nucl. Phys. B 972, 115565 (2021)], which bosonizes massless relativistic free fermions, we derive the (non-Abelian) bosonized theory for free fermion topological insulators and superconductors that have, in addition to the U(1) charge, time reversal and charge conjugation symmetries and flavor symmetries. For the case we consider, the flavor symmetries render the topological classification Z. The results are nonlinear σ models with the topological θ term. In addition, we present the theory of a class of bosonic symmetry-protected topological states, whose boundaries are critical spin liquids.
We show that in (3+1)-D space-time dimensions, the O(6) non-linear sigma model, with a level-1 We... more We show that in (3+1)-D space-time dimensions, the O(6) non-linear sigma model, with a level-1 Wess-Zumino-Witten term, exhibits the electromagnetic duality. If we name the six components of the sigma field as the Neel and valence-bond-solid (VBS) order parameters, the hedgehogs of the Neel and VBS order play the role of monopole and charge. The duality corresponds to the exchange of monopole and charge hence the exchange of the Neel and VBS order. The condensation of monopole can trigger a direct Neel ↔ VBS phase transition. We conjecture that the critical point is self-dual, which is a generalization of the deconfined quantum critical point in (2+1)-D. In this theory, there exist two deconfined phases where the Neel/VBS hedgehogs are massive but cost finite energy. This leads to two fractionalized phases with particles carrying fractional spin or VBS quantum numbers and gapless gauge bosons.
Bulletin of the American Physical Society, Mar 8, 2007
94720-We show that the Majorana fermion zero modes in the cores of odd winding number vortices of... more 94720-We show that the Majorana fermion zero modes in the cores of odd winding number vortices of a 2D p x + ip y-paired superconductor is due to an index theorem. This theorem is analogous to that proven by Jackiw and Rebbi for the existence of localized Dirac fermion zero modes on the mass domain walls of a 1D Dirac theory. The important difference is that, in our case, the theorem is proven for a two component fermion field theory where the first and second components are related by parity reversal and hermitian conjugation. The vortices with Majorana zero modes can be used, in principle, to build a topological quantum computer.
In this paper, we demonstrate that in frustrated magnets when several conventional (i.e., symmetr... more In this paper, we demonstrate that in frustrated magnets when several conventional (i.e., symmetry-breaking) orders compete, and are "intertwined" by a Wess-Zumino-Witten (WZW) term, the possibility of spin liquid arises. The resulting spin liquid could have excitations which carry fractional spins and obey non-trivial self/mutual statistics. As a concrete example, we consider the case where the competing orders are the Néel and valence-bond solid (VBS) order on square lattice. Examining different scenarios of vortex condensation from the VBS side, we show that the intermediate phases, including spin liquids, between the Néel and VBS order always break certain symmetry. Remarkably, our starting theory, without fractionalized particles (partons) and guage field, predicts results agreeing with those derived from a parton theory. This suggests that the missing link between the Ginzberg-Landau-Wilson action of competing order and the physics of spin liquid is the WZW term.
In this paper, we generalize Witten's non-abelian bosonization in (1+1)-D to two and three spatia... more In this paper, we generalize Witten's non-abelian bosonization in (1+1)-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. We apply the bosonization results to the SU (2) gauge theory of the π-flux phase, critical spin liquids in 1,2,3 spatial dimensions, and twisted bilayer graphene.
Transition metal dichalcogenides are ideal compounds to investigate dimensionality effect since t... more Transition metal dichalcogenides are ideal compounds to investigate dimensionality effect since the weak coupling between layers enables to study single-layer material which removes interlayer interactions and introduces quantum confinement. We investigate dimensionality effect of NbSe 2 in which the bulk phase shows charge density wave (CDW) (T CDW =33 K) and superconductivity (T c =7.2 K). We report electronic band structure of MBE grown monolayer NbSe 2 measured by Angel-resolved photoemission spectroscopy compared with bulk. We find the number of bands crossing the Fermi energy reduces from three (bulk) to one (monolayer). Based on the significant suppression of superconducting T c =0.65 K with robust CDW in monolayer NbSe 2 , our results imply the band remained at the Fermi level in monolayer NbSe 2 may play a crucial role in CDW formation and the disappeared bands are possibly in charge of superconductivity.
We study the effects of Cu substitution in Fe1.1Te, the non-superconducting parent compound of th... more We study the effects of Cu substitution in Fe1.1Te, the non-superconducting parent compound of the iron-based superconductor, Fe1+yTe1−xSex, utilizing neutron scattering techniques. It is found that the structural and magnetic transitions, which occur at ∼ 60 K without Cu, are monotonically depressed with increasing Cu content. By 10% Cu for Fe, the structural transition is hardly detectable, and the system becomes a spin glass below 22 K, with a slightly incommensurate ordering wave vector of (0.5-δ, 0, 0.5) with δ being the incommensurability of 0.02, and correlation length of 12Å along the a axis and 9Å along the c axis. With 4% Cu, both transition temperatures are at 41 K, though short-range incommensurate order at (0.42, 0, 0.5) is present at 60 K. With further cooling, the incommensurability decreases linearly with temperature down to 37 K, below which there is a first order transition to a long-range almost-commensurate antiferromagnetic structure. A spin anisotropy gap of 4.5 meV is also observed in this compound. Our results show that the weakly magnetic Cu has large effects on the magnetic correlations; it is suggested that this is caused by the frustration of the exchange interactions between the coupled Fe spins.
Recently Chakravarty, Laughlin, Morr and Nayak made an interesting proposal that the cuprate supe... more Recently Chakravarty, Laughlin, Morr and Nayak made an interesting proposal that the cuprate superconductors possess a hidden "d-density wave" order. We study the implication of this proposal for the superfluid density ρs. We find that it predicts a temperature gradient |dρs/dT |T =0 that is strongly doping dependent near the critical doping at which the superconducting gap vanishes.
To elucidate the superconductor to metal transition at the end of superconducting dome, the overd... more To elucidate the superconductor to metal transition at the end of superconducting dome, the overdoped regime has stepped onto the center stage of cuprate research recently. Here, we use scanning tunneling microscopy to investigate the atomic-scale electronic structure of overdoped trilayer and bilayer Bi2Sr2Can−1CunO2n+4+ cuprates. At low energies the spectroscopic maps are well described by dispersive quasiparticle interference patterns. However, as the bias increases to the superconducting coherence peak energy, a virtually nondispersive pattern with √2 × √2 periodicity emerges. Remarkably, the position of the coherence peaks exhibits evident particle-hole asymmetry which also modulates with the same period. We propose that this is an extreme quasiparticle interference phenomenon, caused by pairing-breaking scattering between flat anti-nodal Bogoliubov bands, which is ultimately responsible for the superconductor to metal transition.
We show that the plateau transitions in the quantum Hall effect is the same as the dimerization t... more We show that the plateau transitions in the quantum Hall effect is the same as the dimerization transition of a half-filled, one dimensional, U(2n) Hubbard model at n = 0. We address the properties of the latter by a combination of perturbative renormalization group and Monte Carlo simulations. Results on both critical and off-critical properties are presented.
... the spin gap Ao develops. "I'his is most easily done via the non-Abelian bosonizati... more ... the spin gap Ao develops. "I'his is most easily done via the non-Abelian bosonization [12], according to which a-',_i "-'*(_z, + £R)+ i(-1) i × const ×tr [(g,- g+)_] . (5) The expression for ¢ is identical with s _ _rand g, _ g,. In the above g, and g, are the ...
Bulletin of the American Physical Society, Mar 13, 2006
We present a theory of a superconducting wire dissipatively coupled to an environment. We show th... more We present a theory of a superconducting wire dissipatively coupled to an environment. We show that due to the finite extent of the wire, in the absence of dissipation quantum phase slips always destroy superconductivity, even at zero temperature. Dissipation stabilizes the superconducting phase. We apply this theory to understand the "anti-proximity effect" recently seen by Tian et. al. [Phys. Rev. Lett. 95, 076802 (2005)] in Zinc nanowires.
Bulletin of the American Physical Society, Mar 13, 2006
Orientational ordering, which originates from broken rotational symmetry, is a central feature of... more Orientational ordering, which originates from broken rotational symmetry, is a central feature of a broad range of materials including liquid crystals, quantum magnets, and some biological systems. By doping C 60 monolayers with alkali impurities, the symmetry of C 60 molecules can be broken, opening up the possibility for unique twodimensional molecular orientational ordering. Here we present a scanning tunneling microscopy/spectroscopy study of K x C 60 monolayers on Au(111), x ≥4. We find novel orientational orderings in the C 60 monolayers at different doping levels, which coincide with strong variations in the monolayer local density of states. This demonstrates the importance of the interplay between Coulomb repulsion, electron-phonon coupling, electronic quadrupolar interactions, and direct orbital overlap in determining the behavior of fullerene nanostructures.
We study the superconductivity of strongly coupled electron-phonon systems where the geometry of ... more We study the superconductivity of strongly coupled electron-phonon systems where the geometry of the lattice frustrates the charge order by the sign-problem-free Quantum Monte Carlo(QMC) method. The results suggest that with charge order frustrated, the superconductivity can benefit from strong electron-phonon interaction in a wide range of coupling strengths.
Under periodic boundary condition in the transverse direction, we calculate the averaged zero-tem... more Under periodic boundary condition in the transverse direction, we calculate the averaged zero-temperature two-terminal conductance (< G >) and its statistical fluctuations (< (δG) 2n > for n ≤ 4) at the critical point of integer quantum Hall plateau transitions. We find universal values for < G >= (0.58 ± 0.03) e 2 h , and < (δG) 2n >= (e 2 h) 2n A 2n , where A 2,4,6,8 = 0.081 ± 0.005; 0.013±0.003; 0.0026±0.005; and (8±2)×10 −4 respectively. We also determine the leading finite size scaling corrections to these observables. Comparisons with experiments will be made.
Superconductivity in doped quantum paramagnets has been a subject of long theoretical inquiry. In... more Superconductivity in doped quantum paramagnets has been a subject of long theoretical inquiry. In this work, we report a density matrix renormalization group study of lightly doped t-J models on the finite-width square lattice (doped hole densities δ = 1/12 and 1/8) with parameters for which previous studies have suggested that the undoped system in 2D is either a quantum spin liquid or a valence bond crystal. Our studies are performed on cylinders with width up to 8. Ground-state correlations are found to be nearly identical for the "doped quantum spin liquid" and "doped valence bond crystal." Upon increasing the cylinder widths from 4 to 8, we observed a significant strengthening of the quasi-long-range superconducting correlations and a dramatic suppression of any "competing" charge density wave order. Extrapolating from the observed behavior of the width eight cylinders, we speculate that the system has a nodeless d-wave superconducting ground state in the 2D limit.
Applying the method of [Nucl. Phys. B 972, 115565 (2021)], which bosonizes massless relativistic ... more Applying the method of [Nucl. Phys. B 972, 115565 (2021)], which bosonizes massless relativistic free fermions, we derive the (non-Abelian) bosonized theory for free fermion topological insulators and superconductors that have, in addition to the U(1) charge, time reversal and charge conjugation symmetries and flavor symmetries. For the case we consider, the flavor symmetries render the topological classification Z. The results are nonlinear σ models with the topological θ term. In addition, we present the theory of a class of bosonic symmetry-protected topological states, whose boundaries are critical spin liquids.
We show that in (3+1)-D space-time dimensions, the O(6) non-linear sigma model, with a level-1 We... more We show that in (3+1)-D space-time dimensions, the O(6) non-linear sigma model, with a level-1 Wess-Zumino-Witten term, exhibits the electromagnetic duality. If we name the six components of the sigma field as the Neel and valence-bond-solid (VBS) order parameters, the hedgehogs of the Neel and VBS order play the role of monopole and charge. The duality corresponds to the exchange of monopole and charge hence the exchange of the Neel and VBS order. The condensation of monopole can trigger a direct Neel ↔ VBS phase transition. We conjecture that the critical point is self-dual, which is a generalization of the deconfined quantum critical point in (2+1)-D. In this theory, there exist two deconfined phases where the Neel/VBS hedgehogs are massive but cost finite energy. This leads to two fractionalized phases with particles carrying fractional spin or VBS quantum numbers and gapless gauge bosons.
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Papers by Dung-hai Lee