Existence of a Sm-C Grain Boundary Phase at the Chiral MAC Point
Molecular Crystals and Liquid Crystals, 1991
Based on a mean field analysis of the Chen-Lubensky model we extend an earlier discussion regardi... more Based on a mean field analysis of the Chen-Lubensky model we extend an earlier discussion regarding the effect of chirality on the region of the phase diagram where the Cholesteric, Smectic-A, and Smectic- C* phases meet (i.e., the N* AC* point). We show that, on the Sm-C* side of the phase diagram, a second twist grain boundary (or chiral smectic)
The structure of the edge excitations of a quantum Hall droplet, confined in a double quantum wel... more The structure of the edge excitations of a quantum Hall droplet, confined in a double quantum well, is studied using a generalized version of the Wen-Stone chiral boson action. As the interwell tunneling t is increased, one finds a "metal-insulator" transition from a phase where the optic edge mode is ungapped to a phase where the optic mode is gapped. The large-t phase exhibits edge quasiexcitons whose charge is half that of a quasiparticle-quasihole bound state. The critical behavior of the conductances, the exciton gap, and the excitonic order parameter is discussed.
Quantum dots in the fractional quantum Hall regime are studied using a Hartree formulation of the... more Quantum dots in the fractional quantum Hall regime are studied using a Hartree formulation of the composite fermion theory. Under appropriate conditions the chemical potential of the dots will oscillate periodically with B due to the transfer of composite fermions between quasi-Landau bands. This effect is analogous to the addition spectrum oscillations which occur in quantum dots in the integer quantum Hall regime. Period φ 0 oscillations are found in sharply confined dots with filling factors ν = 2/5 and ν = 2/3. Period 3φ 0 oscillations are found in a parabolically confined ν = 2/5 dot. More generally, we argue that the oscillation period of dots with band pinning should vary continuously with B whereas the period of dots without band pinning is φ 0. Finally, we discuss the possibility of detecting fractionally charged excitations using the observed period of addition spectrum oscillations.
The nematic-to-smectic-A transition in liquid crystals is analogous to the normal to superconduct... more The nematic-to-smectic-A transition in liquid crystals is analogous to the normal to superconducting transition in metals with the Frank director n in liquid crystals playing the role of the vector potential A in metals. The liquid-crystal analog of an external magnetic field is a field, arising, for example, from molecular chirality, leading to a nonzero V)& n in the equilibrium nematic phase. The cholesteric (twisted nematic) phase is the analog of a normal metal in an external magnetic field. In type-II superconductors in an external magnetic field, the Abrikosov flux lattice phase with partial flux penetration intervenes between the low-temperature Meissner phase and the hightemperature normal-metal phase. In this paper we study the analog in liquid crystals containing chiral molecules of the Abrikosov phase in superconductors. Using a covariant form of the de Gennes free energy, we find that in mean-field theory a state, which we call the twist-grainboundary (TGB) state, with regularly spaced grain boundaries consisting of parallel screw dislocations, intervenes between the smectic and cholesteric phases. We calculate the liquid-crystal analogs of the upper and lower critical fields H, 2 and H, l. The properties of the TGB phase depend on the angle 2n. a between axes of dislocations in adjacent grain boundaries. a can be rational or irrational. When a =p/q for mutually prime integers p and q, the TGB state has a q-fold screw axis and quasicrystalline symmetry for crystallographically forbidden q. Our calculations ignore exponentially small terms favoring lock in at rational a. We calculate the x-ray scattering intensities in the cholesteric phase near the TGB phase boundary and in the TGB phase for rational and irrational a. We also discuss experimental difficulties in observing the TGB state and the possible effects fluctuations not included in mean-field theory might have on its existence.
We investigate the edge reconstruction phenomenon believed to occur in quantum dots in the quantu... more We investigate the edge reconstruction phenomenon believed to occur in quantum dots in the quantum Hall regime when the filling fraction is ν < ∼ 1. Our approach involves the examination of large dots (≤ 40 electrons) using a partial diagonalization technique in which the occupancies of the deep interior orbitals are frozen. To interpret the results of this calculation, we evaluate the overlap between the diagonalized ground state and a set of trial wavefunctions which we call projected necklace (PN) states. A PN state is simply the angular momentum projection of a maximum density droplet surrounded by a ring of localized electrons. Our calculations reveal that PN states have up to 99% overlap with the diagonalized ground states, and are lower in energy than the states identified in Chamon and Wen's study of the edge reconstruction.
In this paper, we examine interwell tunneling between a pair of fractional quantum Hall liquids i... more In this paper, we examine interwell tunneling between a pair of fractional quantum Hall liquids in a double quantum well system in a tilted magnetic field. Using a variational Monte Carlo method, we calculate moments of the intra-Landau level tunneling spectrum as a function of in-plane field component B and interwell spacing d. This is done for variety of incompressible states including a pair of ν = 1/3 layers ([330]), pair of ν = 1/5 layers ([550]), and Halperin's [331] state. The results suggest a technique to extract interwell correlations from the tunneling spectral data.
We present the results of a series of Quantum Monte Carlo calculations of the temperature depende... more We present the results of a series of Quantum Monte Carlo calculations of the temperature dependent conductance of dissipative non-superconducting tunnel junctions. Finite size scaling methods are used to demonstrate the absence of coherent transport in Ohmic tunnel junctions. However, a quantum phase transition between coherent and incoherent behavior is found in sub-Ohmic tunnel junctions. The critical conductance is found to be temperature independent and the critical exponents, ν and η, are found to be in agreement with renormalization group results by Kosterlitz.
Bogoliubov theory of Coulomb-coupled [ m ↑ m ↓ 0] quantum Hall states
Physical Review B, 1994
Bogoliubov theory of Coulomb-coupled [m ↑ m ↓ 0] quantum Hall states. Daniel P. Arovas and Scot R... more Bogoliubov theory of Coulomb-coupled [m ↑ m ↓ 0] quantum Hall states. Daniel P. Arovas and Scot R. Renn Department of Physics, University of California at San Diego, La Jolla, California 92093. Received 4 May 1994 The ...
Non-linear current voltage characteristics of a disordered Luttinger liquid are calculated using ... more Non-linear current voltage characteristics of a disordered Luttinger liquid are calculated using a perturbative formalism. One finds non-universal power law characteristics of the form I(V) ∼ V 1/(2g−1) which is valid both in the superfluid phase when I is small and also in the insulator phase when I is large. Mesoscopic voltage fluctuations are also calculated. One finds Var(∆V) ∼ I 4g−3. Both the I(V) characteristic and the voltage fluctuations exhibit universal power law behavior at the superfluid insulator transition whereg = 3 2. The possible application of these results to the non-linear transport properties of gated Hall bars is discussed.
The Ueda-Guinea model of a dissipative tunnel junction is investigated. This model accounts for f... more The Ueda-Guinea model of a dissipative tunnel junction is investigated. This model accounts for final state effects associated with single-electron tunneling. A quantum phase transition emerges, marking a boundary between insulating (Coulomb blockade) and conducting phases. The system is analyzed by large-N techniques, self-consistent harmonic approximation, and Monte Carlo methods.
Recently, Inderees et al. have observed inverse-square-root behavior of specific heat of YBa2Cu30... more Recently, Inderees et al. have observed inverse-square-root behavior of specific heat of YBa2Cu307near T, corresponding to Gaussian Auctuations. We analyze their results using the most general Landau theories of superconductivity that are consistent with either orthorhombic or tetragonal crystal symmetry. In particular, we calculate the amplitude ratio C+/C-, where C(T) C~~T-T, [ 't2 and the coefficients Cy and Care associated with the behavior of C(T) above and below T"res pecti vely. We conclude that the value of the amplitude ratio observed experimentally is inconsistent with ordinary s-wave pairing. For an orthorhombic crystal only trip1et superconductivity is possible. Assuming tetragonal symmetry we find that either triplet pairing or some d-wave singlet states are allowed. The latter must have an order parameter transforming like d""d",. This singlet case lies within the experimental bounds only if the anisotropic gradient terms satisfy certain conditions, which we discuss in terms of microscopic models.
Evidence for anisotropic pairing in YBaâCuâOââ/sub delta/ from the Landau theory of fluctuation specific heat
Recently, Inderees et al. have observed inverse-square-root behavior of specific heat of YBaâCuâO... more Recently, Inderees et al. have observed inverse-square-root behavior of specific heat of YBaâCuâOââ/sub delta/ near T/sub c/ corresponding to Gaussian fluctuations. We analyze their results using the most general Landau theories of superconductivity that are consistent with either orthorhombic or tetragonal crystal symmetry. In particular we calculate the amplitude ratio C/sub +//Câ, where C(T) = C/sub +- /chemically bondT-T/sub c/chemically bondâ»Â¹Â² and the coefficients C/sub +/ and Câ are associated with the behavior of C(T) above and below T/sub c/, respectively. We conclude that the value of the amplitude ratio observed experimentally is inconsistent with ordinary s-wave pairing. For an orthorhombic crystal only triplet superconductivity is possible. Assuming tetragonal symmetry we find that either triplet pairing or some d-wave singlet states are allowed. The latter must have an order parameter transforming like d/sub x//sub z/,d/sub y//sub z/. This singlet case lies within ...
Non-Ohmic tunnel junctions are believed to occur in systems where the exciton and orthogonality c... more Non-Ohmic tunnel junctions are believed to occur in systems where the exciton and orthogonality catastrophe effects significantly modify tunneling rates. Here we present a simple non-perturbative treatment of the thermodynamic and transport properties of subOhmic and superOhmic tunnel junctions. The large-N approximation demonstrates the existence of a quantum phase transition in subOhmic but not superOhmic tunnel junctions. In addition, we find a pseudogap which vanishes continuously as the transition is approached.
We consider a model for electron tunneling between a pair of ultrasmall metallic grains. Under ap... more We consider a model for electron tunneling between a pair of ultrasmall metallic grains. Under appropriate circumstances, non-equilibrium final state effects can strongly enhance tunneling and produce electron-hole coherence between the grains. The model displays a quantum phase transition between a Coulomb blockaded state to a coherent state exhibiting subohmic tunneling conductance. The critical state of the junction exhibits a temperature independent resistance of order h/e 2. Finally we discuss the possible relevance to granular materials and quantum dots. In particular, similarities between the quantum transition in our model and the metal-insulator transition in granular wires observed by Herzog et al. are described in detail.
We present a simplified polymer model for twist-boundary phases in liquid crystals. The thermodyn... more We present a simplified polymer model for twist-boundary phases in liquid crystals. The thermodynamic phases of this model are characterized by an angle 2pialpha~. There are incommensurate phases with alpha~ an irrational number and commensurate phases with alpha~=P/Q, with P and Q relatively prime integers. The latter have quasicrystalline symmetry for Q=5 or Q>6. Equilibrium phases with all values of alpha~ can be produced by varying a control parameter alpha. The curve alpha~(alpha) is an incomplete devil's staircase with finite locking intervals about every rational alpha~.
%e propose a theory of shear-induced melting of colloidal crystals based on a nonequilibrium gene... more %e propose a theory of shear-induced melting of colloidal crystals based on a nonequilibrium generalization of first-order freezing theory. The results agree qualitatively with experiment.
Existence of a Sm-C Grain Boundary Phase at the Chiral MAC Point
Molecular Crystals and Liquid Crystals, 1991
Based on a mean field analysis of the Chen-Lubensky model we extend an earlier discussion regardi... more Based on a mean field analysis of the Chen-Lubensky model we extend an earlier discussion regarding the effect of chirality on the region of the phase diagram where the Cholesteric, Smectic-A, and Smectic- C* phases meet (i.e., the N* AC* point). We show that, on the Sm-C* side of the phase diagram, a second twist grain boundary (or chiral smectic)
The structure of the edge excitations of a quantum Hall droplet, confined in a double quantum wel... more The structure of the edge excitations of a quantum Hall droplet, confined in a double quantum well, is studied using a generalized version of the Wen-Stone chiral boson action. As the interwell tunneling t is increased, one finds a "metal-insulator" transition from a phase where the optic edge mode is ungapped to a phase where the optic mode is gapped. The large-t phase exhibits edge quasiexcitons whose charge is half that of a quasiparticle-quasihole bound state. The critical behavior of the conductances, the exciton gap, and the excitonic order parameter is discussed.
Quantum dots in the fractional quantum Hall regime are studied using a Hartree formulation of the... more Quantum dots in the fractional quantum Hall regime are studied using a Hartree formulation of the composite fermion theory. Under appropriate conditions the chemical potential of the dots will oscillate periodically with B due to the transfer of composite fermions between quasi-Landau bands. This effect is analogous to the addition spectrum oscillations which occur in quantum dots in the integer quantum Hall regime. Period φ 0 oscillations are found in sharply confined dots with filling factors ν = 2/5 and ν = 2/3. Period 3φ 0 oscillations are found in a parabolically confined ν = 2/5 dot. More generally, we argue that the oscillation period of dots with band pinning should vary continuously with B whereas the period of dots without band pinning is φ 0. Finally, we discuss the possibility of detecting fractionally charged excitations using the observed period of addition spectrum oscillations.
The nematic-to-smectic-A transition in liquid crystals is analogous to the normal to superconduct... more The nematic-to-smectic-A transition in liquid crystals is analogous to the normal to superconducting transition in metals with the Frank director n in liquid crystals playing the role of the vector potential A in metals. The liquid-crystal analog of an external magnetic field is a field, arising, for example, from molecular chirality, leading to a nonzero V)& n in the equilibrium nematic phase. The cholesteric (twisted nematic) phase is the analog of a normal metal in an external magnetic field. In type-II superconductors in an external magnetic field, the Abrikosov flux lattice phase with partial flux penetration intervenes between the low-temperature Meissner phase and the hightemperature normal-metal phase. In this paper we study the analog in liquid crystals containing chiral molecules of the Abrikosov phase in superconductors. Using a covariant form of the de Gennes free energy, we find that in mean-field theory a state, which we call the twist-grainboundary (TGB) state, with regularly spaced grain boundaries consisting of parallel screw dislocations, intervenes between the smectic and cholesteric phases. We calculate the liquid-crystal analogs of the upper and lower critical fields H, 2 and H, l. The properties of the TGB phase depend on the angle 2n. a between axes of dislocations in adjacent grain boundaries. a can be rational or irrational. When a =p/q for mutually prime integers p and q, the TGB state has a q-fold screw axis and quasicrystalline symmetry for crystallographically forbidden q. Our calculations ignore exponentially small terms favoring lock in at rational a. We calculate the x-ray scattering intensities in the cholesteric phase near the TGB phase boundary and in the TGB phase for rational and irrational a. We also discuss experimental difficulties in observing the TGB state and the possible effects fluctuations not included in mean-field theory might have on its existence.
We investigate the edge reconstruction phenomenon believed to occur in quantum dots in the quantu... more We investigate the edge reconstruction phenomenon believed to occur in quantum dots in the quantum Hall regime when the filling fraction is ν < ∼ 1. Our approach involves the examination of large dots (≤ 40 electrons) using a partial diagonalization technique in which the occupancies of the deep interior orbitals are frozen. To interpret the results of this calculation, we evaluate the overlap between the diagonalized ground state and a set of trial wavefunctions which we call projected necklace (PN) states. A PN state is simply the angular momentum projection of a maximum density droplet surrounded by a ring of localized electrons. Our calculations reveal that PN states have up to 99% overlap with the diagonalized ground states, and are lower in energy than the states identified in Chamon and Wen's study of the edge reconstruction.
In this paper, we examine interwell tunneling between a pair of fractional quantum Hall liquids i... more In this paper, we examine interwell tunneling between a pair of fractional quantum Hall liquids in a double quantum well system in a tilted magnetic field. Using a variational Monte Carlo method, we calculate moments of the intra-Landau level tunneling spectrum as a function of in-plane field component B and interwell spacing d. This is done for variety of incompressible states including a pair of ν = 1/3 layers ([330]), pair of ν = 1/5 layers ([550]), and Halperin's [331] state. The results suggest a technique to extract interwell correlations from the tunneling spectral data.
We present the results of a series of Quantum Monte Carlo calculations of the temperature depende... more We present the results of a series of Quantum Monte Carlo calculations of the temperature dependent conductance of dissipative non-superconducting tunnel junctions. Finite size scaling methods are used to demonstrate the absence of coherent transport in Ohmic tunnel junctions. However, a quantum phase transition between coherent and incoherent behavior is found in sub-Ohmic tunnel junctions. The critical conductance is found to be temperature independent and the critical exponents, ν and η, are found to be in agreement with renormalization group results by Kosterlitz.
Bogoliubov theory of Coulomb-coupled [ m ↑ m ↓ 0] quantum Hall states
Physical Review B, 1994
Bogoliubov theory of Coulomb-coupled [m ↑ m ↓ 0] quantum Hall states. Daniel P. Arovas and Scot R... more Bogoliubov theory of Coulomb-coupled [m ↑ m ↓ 0] quantum Hall states. Daniel P. Arovas and Scot R. Renn Department of Physics, University of California at San Diego, La Jolla, California 92093. Received 4 May 1994 The ...
Non-linear current voltage characteristics of a disordered Luttinger liquid are calculated using ... more Non-linear current voltage characteristics of a disordered Luttinger liquid are calculated using a perturbative formalism. One finds non-universal power law characteristics of the form I(V) ∼ V 1/(2g−1) which is valid both in the superfluid phase when I is small and also in the insulator phase when I is large. Mesoscopic voltage fluctuations are also calculated. One finds Var(∆V) ∼ I 4g−3. Both the I(V) characteristic and the voltage fluctuations exhibit universal power law behavior at the superfluid insulator transition whereg = 3 2. The possible application of these results to the non-linear transport properties of gated Hall bars is discussed.
The Ueda-Guinea model of a dissipative tunnel junction is investigated. This model accounts for f... more The Ueda-Guinea model of a dissipative tunnel junction is investigated. This model accounts for final state effects associated with single-electron tunneling. A quantum phase transition emerges, marking a boundary between insulating (Coulomb blockade) and conducting phases. The system is analyzed by large-N techniques, self-consistent harmonic approximation, and Monte Carlo methods.
Recently, Inderees et al. have observed inverse-square-root behavior of specific heat of YBa2Cu30... more Recently, Inderees et al. have observed inverse-square-root behavior of specific heat of YBa2Cu307near T, corresponding to Gaussian Auctuations. We analyze their results using the most general Landau theories of superconductivity that are consistent with either orthorhombic or tetragonal crystal symmetry. In particular, we calculate the amplitude ratio C+/C-, where C(T) C~~T-T, [ 't2 and the coefficients Cy and Care associated with the behavior of C(T) above and below T"res pecti vely. We conclude that the value of the amplitude ratio observed experimentally is inconsistent with ordinary s-wave pairing. For an orthorhombic crystal only trip1et superconductivity is possible. Assuming tetragonal symmetry we find that either triplet pairing or some d-wave singlet states are allowed. The latter must have an order parameter transforming like d""d",. This singlet case lies within the experimental bounds only if the anisotropic gradient terms satisfy certain conditions, which we discuss in terms of microscopic models.
Evidence for anisotropic pairing in YBaâCuâOââ/sub delta/ from the Landau theory of fluctuation specific heat
Recently, Inderees et al. have observed inverse-square-root behavior of specific heat of YBaâCuâO... more Recently, Inderees et al. have observed inverse-square-root behavior of specific heat of YBaâCuâOââ/sub delta/ near T/sub c/ corresponding to Gaussian fluctuations. We analyze their results using the most general Landau theories of superconductivity that are consistent with either orthorhombic or tetragonal crystal symmetry. In particular we calculate the amplitude ratio C/sub +//Câ, where C(T) = C/sub +- /chemically bondT-T/sub c/chemically bondâ»Â¹Â² and the coefficients C/sub +/ and Câ are associated with the behavior of C(T) above and below T/sub c/, respectively. We conclude that the value of the amplitude ratio observed experimentally is inconsistent with ordinary s-wave pairing. For an orthorhombic crystal only triplet superconductivity is possible. Assuming tetragonal symmetry we find that either triplet pairing or some d-wave singlet states are allowed. The latter must have an order parameter transforming like d/sub x//sub z/,d/sub y//sub z/. This singlet case lies within ...
Non-Ohmic tunnel junctions are believed to occur in systems where the exciton and orthogonality c... more Non-Ohmic tunnel junctions are believed to occur in systems where the exciton and orthogonality catastrophe effects significantly modify tunneling rates. Here we present a simple non-perturbative treatment of the thermodynamic and transport properties of subOhmic and superOhmic tunnel junctions. The large-N approximation demonstrates the existence of a quantum phase transition in subOhmic but not superOhmic tunnel junctions. In addition, we find a pseudogap which vanishes continuously as the transition is approached.
We consider a model for electron tunneling between a pair of ultrasmall metallic grains. Under ap... more We consider a model for electron tunneling between a pair of ultrasmall metallic grains. Under appropriate circumstances, non-equilibrium final state effects can strongly enhance tunneling and produce electron-hole coherence between the grains. The model displays a quantum phase transition between a Coulomb blockaded state to a coherent state exhibiting subohmic tunneling conductance. The critical state of the junction exhibits a temperature independent resistance of order h/e 2. Finally we discuss the possible relevance to granular materials and quantum dots. In particular, similarities between the quantum transition in our model and the metal-insulator transition in granular wires observed by Herzog et al. are described in detail.
We present a simplified polymer model for twist-boundary phases in liquid crystals. The thermodyn... more We present a simplified polymer model for twist-boundary phases in liquid crystals. The thermodynamic phases of this model are characterized by an angle 2pialpha~. There are incommensurate phases with alpha~ an irrational number and commensurate phases with alpha~=P/Q, with P and Q relatively prime integers. The latter have quasicrystalline symmetry for Q=5 or Q>6. Equilibrium phases with all values of alpha~ can be produced by varying a control parameter alpha. The curve alpha~(alpha) is an incomplete devil's staircase with finite locking intervals about every rational alpha~.
%e propose a theory of shear-induced melting of colloidal crystals based on a nonequilibrium gene... more %e propose a theory of shear-induced melting of colloidal crystals based on a nonequilibrium generalization of first-order freezing theory. The results agree qualitatively with experiment.
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