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.
Within the framework of the kinetic energy driven superconducting mechanism, we study the electro... more Within the framework of the kinetic energy driven superconducting mechanism, we study the electronic structure of cuprate superconductors. It is shown that the peak position at [π,0] point in the Brillouin zone moves to the Fermi energy with increasing the doping concentration, while the superconducting quasiparticles around the [π,0] point disperse very weakly with momentum, which are in agreement with the experimental results.
We present a particle-hole symmetric theory for a two-dimensional electron gas at filling factor ... more We present a particle-hole symmetric theory for a two-dimensional electron gas at filling factor one half. In this theory, elementary excitations are dipole-like fermions floating on top of the $\nu=1/2$ boson quantum Hall liquid. In the absence of disorder these dipoles can form a Fermi-liquid. Disorder can break them apart and drive the ground state into a quantum critical state.
We present a theory to describe the low energy physics of a two-dimensional electron gas at filli... more We present a theory to describe the low energy physics of a two-dimensional electron gas at filling factor ν = 1/2. In this theory the elementary excitations are dipole-like fermionic particles each made up of charge ±1/2 quasiparticles. These neutral fermions obey a constrained dynamics, do not respect time reversal symmetry, and do not form a conventional Fermi liquid. Sufficiently strong disorder breaks up the dipoles and causes the system to realize the critical state of the ν = 0→1 plateau transition. We argue that the present description is consistent with the particle-hole symmetry in the lowest Landau level. 73.50.Jt, 05.30.-d, 74.20.-z Typeset using REVTEX 1 The discovery of an anomaly in acoustic wave propagation attracted much interest in the physics of a two-dimensional electron gas (2DEG) near filling factor ν = 1/2 [1]. Shortly after the experimental discovery an intriguing idea, composite fermion theory, was put forward in an extensive paper by Halperin, Lee and Read ...
A major unsolved puzzle in cuprate superconductivity is that, despite accumulated evidence of mor... more A major unsolved puzzle in cuprate superconductivity is that, despite accumulated evidence of more conventional normal state properties over the last 30 years, the superconducting $T_c$ of the overdoped cuprates seems to be still controlled by phase coherence rather than the Cooper pair formation. So far, a microscopic understanding of this unexpected behavior is lacking. Here we report angle-resolved photoemission, magnetic and thermodynamic evidence that Cooper pairs form at temperatures more than 30% above $T_c$ in overdoped metallic Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212). More importantly, our data lead to a microscopic understanding where the phase fluctuation is enhanced by the flat dispersion near the Brillouin zone boundary. This proposal is tested by a sign-problem free quantum Monte Carlo simulation. Such a microscopic mechanism is likely to find applications in other flat band superconductors, such as twisted bilayer-bilayer graphene and NdNiO$_2$
The subject of this paper is the phase transition between symmetry protected topological states (... more The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, H d+1 (G, U(1)), contains at least one Z 2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z 2n or Z groups can be induced on the boundary of a (d + 1)-dimensional G × Z T 2-symmetric SPT by a Z T 2 symmetry breaking field. Moreover we show these boundary phase transitions can be "transplanted" to d dimensions and realized in lattice models as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase.
This work is motivated by a specific point of view: at short distances and high energies the undo... more This work is motivated by a specific point of view: at short distances and high energies the undoped and underdoped cuprates resemble the π-flux phase of the t-J model. The purpose of this paper is to present a mechanism by which pairing grows out of the doped π-flux phase. According to this mechanism pairing symmetry is determined by a parameter controlling the quantum tunneling of gauge flux quanta. For zero tunneling the symmetry is d x 2 −y 2 + idxy, while for large tunneling it is d x 2 −y 2. A zero-temperature critical point separates these two limits.
Ultrafast spectroscopy is an emerging technique with great promise in the study of quantum materi... more Ultrafast spectroscopy is an emerging technique with great promise in the study of quantum materials, as it makes it possible to track similarities and correlations that are not evident near equilibrium. Thus far, however, the way in which these processes modify the electron self-energy-a fundamental quantity describing many-body interactions in a material-has been little discussed. Here we use time-and angle-resolved photoemission to directly measure the ultrafast response of self-energy to near-infrared photoexcitation in hightemperature cuprate superconductor. Below the critical temperature of the superconductor, ultrafast excitations trigger a synchronous decrease of electron self-energy and superconducting gap, culminating in a saturation in the weakening of electron-boson coupling when the superconducting gap is fully quenched. In contrast, electron-boson coupling is unresponsive to ultrafast excitations above the critical temperature of the superconductor and in the metallic state of a related material. These findings open a new pathway for studying transient self-energy and correlation effects in solids.
Dissecting Cooper Pairs Angle-resolved photoemission spectroscopy (ARPES) is used in the study of... more Dissecting Cooper Pairs Angle-resolved photoemission spectroscopy (ARPES) is used in the study of the electronic structure of complex materials. Recently, time-resolved ARPES has become possible, where the state of the system is excited by a short “pump” pulse, and ARPES is performed using a second “probe” pulse applied after varying times. Smallwood et al. (p. 1137 ) used this technique to study the recombination of Cooper pairs—the fundamental charge carriers in superconductors—in a cuprate high-temperature superconductor.
We present theoretical models, in one and two space dimensions, that exhibit Mott insulating grou... more We present theoretical models, in one and two space dimensions, that exhibit Mott insulating ground states at fractional occupations without any symmetry breaking. The Hamiltonians of these models are non-local in configuration space, but local in phase space.
We study the effects of electron-electron interaction on the critical properties of the plateau t... more We study the effects of electron-electron interaction on the critical properties of the plateau transitions in the integer quantum Hall effect. We find the renormalization group dimension associated with short-range interactions to be −0.66 ± 0.04. Thus the non-interacting fixed point (characterized z = 2 and ν ≈ 2.3) is stable. For the Coulomb interaction, we find the correlation effect is a marginal perturbation at a Hartree-Fock fixed point (z = 1, ν ≈ 2.3) by dimension counting. Further calculations are needed to determine its stability upon loop corrections.
The current pattern in the mixed state of high-Tc superconductors is studied in the U(1) mean fie... more The current pattern in the mixed state of high-Tc superconductors is studied in the U(1) mean field theory of the t-J model. Our findings are the following. 1) In the absence of antiferromagnetism a robust staggered current pattern exists in the core of vortices if the doping is not too high. 2) At a fixed doping and with increasing magnetic field, the size of the staggered current core expands, and eventually percolates. 3) The polarity of the staggered current is pinned by the direction of the magnetic field. 4) Vortex cores locally modify the hole density-in a staggered (non-staggered) core, the excess charge is slightly negative (positive). 5) Gutzwiller projection does not wash out the staggered current. Finally we present two experimental predictions concerning neutron scattering and STM spectra that capture the signature of the staggered current induced by the vortices.
The surface of a topological insulator is a closed two dimensional manifold. The surface states a... more The surface of a topological insulator is a closed two dimensional manifold. The surface states are described by the Dirac Hamiltonian in curved two dimensional spaces. For a slab-like sample with a magnetic field perpendicular to its top and bottom surfaces, there are chiral states delocalized on the four side faces. These "chiral sheets" carry both charge and spin currents. In strong magnetic fields, the quantized charge Hall effect (σxy = (2n + 1)e 2 /h) will coexist with spin Hall effect.
We discuss how the braiding properties of Laughlin quasi-particles in quantum Hall states can be ... more We discuss how the braiding properties of Laughlin quasi-particles in quantum Hall states can be understood within a one-dimensional formalism we proposed earlier. In this formalism the twodimensional space of the Hall liquid is identified with the phase space of a one-dimensional lattice system, and localized Laughlin quasi-holes can be understood as coherent states of lattice solitons. The formalism makes comparatively little use of the detailed structure of Laughlin wavefunctions, and may offer ways to be generalized to non-abelian states.
We report the first variational Monte Carlo (VMC) study of the iron-based superconductors. We use... more We report the first variational Monte Carlo (VMC) study of the iron-based superconductors. We use realistic band structures, and the ordering instabilities/variational ansatzs are suggested by previous functional renormalization group calculations. We examine antiferromagnetism, superconducting pairing, normal state fermi surface distortion and orbital order in the antiferromagnetic state.
We address two important issues that arise in recent studies of iron-based superconductivity. (1)... more We address two important issues that arise in recent studies of iron-based superconductivity. (1) Why are the Tc of AxFe2−ySe2 and the single unit cell FeSe on SrTiO3 so high despite both only have electron pockets? (2) What (if any) are the effects of orbital order and orbital fluctuation on the Cooper pairing. Our conclusions are summarized in the third paragraph of the paper. The discovery of A x Fe 2−y Se 2 [1] (T max c = 48K, under pressure[2]) and single unit cell FeSe on SrTiO 3 (FeSe/STO)[3] (T max c =65K, determined by angle-resolved photoemission spectroscopy (ARPES)[4]), stirred up a new wave of excitement in iron-based superconductors (FeSCs) research. In ARPES studies it is found, at ambient pressure, both systems have no hole pocket[4, 5]. Because it is often perceived that the scattering between the electron and hole pockets are important for both antiferromagnetism and Cooper pairing[6], this becomes an issue.
We introduce and solve a semi-classical random walk (RW) model that describes the dynamics of spi... more We introduce and solve a semi-classical random walk (RW) model that describes the dynamics of spin polarization waves in zinc-blende semiconductor quantum wells. We derive the dispersion relations for these waves, including the Rashba, linear and cubic Dresselhaus spin-orbit interactions, as well as the effects of an electric field applied parallel to the spin polarization wave vector. In agreement with calculations based on quantum kinetic theory [P. Kleinert and V. V. Bryksin, Phys. Rev. B 76, 205326 (2007)], the RW approach predicts that spin waves acquire a phase velocity in the presence of the field that crosses zero at a nonzero wave vector, q 0. In addition, we show that the spin-wave decay rate is independent of field at q 0 but increases as (q − q 0) 2 for q = q 0. These predictions can be tested experimentally by suitable transient spin grating experiments.
We study the dependence of the ground state energy on an applied Aharonov-Bohm flux Φ for the Lut... more We study the dependence of the ground state energy on an applied Aharonov-Bohm flux Φ for the Luttinger model with large momentum scattering. Employing the method of finite size bosonization, we show that for systems with a spin gap but with gapless charge degrees of freedom, the ground state energy has an exact period of hc/2e, i. e. half a flux quantum, in the limit of large system size L. Finite size corrections are found to vanish exponentially in L. This behavior is contrasted to that of the spin gapless case, for both even and odd particle number. Generalizations to finite temperature are also discussed.
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.
Within the framework of the kinetic energy driven superconducting mechanism, we study the electro... more Within the framework of the kinetic energy driven superconducting mechanism, we study the electronic structure of cuprate superconductors. It is shown that the peak position at [π,0] point in the Brillouin zone moves to the Fermi energy with increasing the doping concentration, while the superconducting quasiparticles around the [π,0] point disperse very weakly with momentum, which are in agreement with the experimental results.
We present a particle-hole symmetric theory for a two-dimensional electron gas at filling factor ... more We present a particle-hole symmetric theory for a two-dimensional electron gas at filling factor one half. In this theory, elementary excitations are dipole-like fermions floating on top of the $\nu=1/2$ boson quantum Hall liquid. In the absence of disorder these dipoles can form a Fermi-liquid. Disorder can break them apart and drive the ground state into a quantum critical state.
We present a theory to describe the low energy physics of a two-dimensional electron gas at filli... more We present a theory to describe the low energy physics of a two-dimensional electron gas at filling factor ν = 1/2. In this theory the elementary excitations are dipole-like fermionic particles each made up of charge ±1/2 quasiparticles. These neutral fermions obey a constrained dynamics, do not respect time reversal symmetry, and do not form a conventional Fermi liquid. Sufficiently strong disorder breaks up the dipoles and causes the system to realize the critical state of the ν = 0→1 plateau transition. We argue that the present description is consistent with the particle-hole symmetry in the lowest Landau level. 73.50.Jt, 05.30.-d, 74.20.-z Typeset using REVTEX 1 The discovery of an anomaly in acoustic wave propagation attracted much interest in the physics of a two-dimensional electron gas (2DEG) near filling factor ν = 1/2 [1]. Shortly after the experimental discovery an intriguing idea, composite fermion theory, was put forward in an extensive paper by Halperin, Lee and Read ...
A major unsolved puzzle in cuprate superconductivity is that, despite accumulated evidence of mor... more A major unsolved puzzle in cuprate superconductivity is that, despite accumulated evidence of more conventional normal state properties over the last 30 years, the superconducting $T_c$ of the overdoped cuprates seems to be still controlled by phase coherence rather than the Cooper pair formation. So far, a microscopic understanding of this unexpected behavior is lacking. Here we report angle-resolved photoemission, magnetic and thermodynamic evidence that Cooper pairs form at temperatures more than 30% above $T_c$ in overdoped metallic Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (Bi-2212). More importantly, our data lead to a microscopic understanding where the phase fluctuation is enhanced by the flat dispersion near the Brillouin zone boundary. This proposal is tested by a sign-problem free quantum Monte Carlo simulation. Such a microscopic mechanism is likely to find applications in other flat band superconductors, such as twisted bilayer-bilayer graphene and NdNiO$_2$
The subject of this paper is the phase transition between symmetry protected topological states (... more The subject of this paper is the phase transition between symmetry protected topological states (SPTs). We consider spatial dimension d and symmetry group G so that the cohomology group, H d+1 (G, U(1)), contains at least one Z 2n or Z factor. We show that the phase transition between the trivial SPT and the root states that generate the Z 2n or Z groups can be induced on the boundary of a (d + 1)-dimensional G × Z T 2-symmetric SPT by a Z T 2 symmetry breaking field. Moreover we show these boundary phase transitions can be "transplanted" to d dimensions and realized in lattice models as a function of a tuning parameter. The price one pays is for the critical value of the tuning parameter there is an extra non-local (duality-like) symmetry. In the case where the phase transition is continuous, our theory predicts the presence of unusual (sometimes fractionalized) excitations corresponding to delocalized boundary excitations of the non-trivial SPT on one side of the transition. This theory also predicts other phase transition scenarios including first order transition and transition via an intermediate symmetry breaking phase.
This work is motivated by a specific point of view: at short distances and high energies the undo... more This work is motivated by a specific point of view: at short distances and high energies the undoped and underdoped cuprates resemble the π-flux phase of the t-J model. The purpose of this paper is to present a mechanism by which pairing grows out of the doped π-flux phase. According to this mechanism pairing symmetry is determined by a parameter controlling the quantum tunneling of gauge flux quanta. For zero tunneling the symmetry is d x 2 −y 2 + idxy, while for large tunneling it is d x 2 −y 2. A zero-temperature critical point separates these two limits.
Ultrafast spectroscopy is an emerging technique with great promise in the study of quantum materi... more Ultrafast spectroscopy is an emerging technique with great promise in the study of quantum materials, as it makes it possible to track similarities and correlations that are not evident near equilibrium. Thus far, however, the way in which these processes modify the electron self-energy-a fundamental quantity describing many-body interactions in a material-has been little discussed. Here we use time-and angle-resolved photoemission to directly measure the ultrafast response of self-energy to near-infrared photoexcitation in hightemperature cuprate superconductor. Below the critical temperature of the superconductor, ultrafast excitations trigger a synchronous decrease of electron self-energy and superconducting gap, culminating in a saturation in the weakening of electron-boson coupling when the superconducting gap is fully quenched. In contrast, electron-boson coupling is unresponsive to ultrafast excitations above the critical temperature of the superconductor and in the metallic state of a related material. These findings open a new pathway for studying transient self-energy and correlation effects in solids.
Dissecting Cooper Pairs Angle-resolved photoemission spectroscopy (ARPES) is used in the study of... more Dissecting Cooper Pairs Angle-resolved photoemission spectroscopy (ARPES) is used in the study of the electronic structure of complex materials. Recently, time-resolved ARPES has become possible, where the state of the system is excited by a short “pump” pulse, and ARPES is performed using a second “probe” pulse applied after varying times. Smallwood et al. (p. 1137 ) used this technique to study the recombination of Cooper pairs—the fundamental charge carriers in superconductors—in a cuprate high-temperature superconductor.
We present theoretical models, in one and two space dimensions, that exhibit Mott insulating grou... more We present theoretical models, in one and two space dimensions, that exhibit Mott insulating ground states at fractional occupations without any symmetry breaking. The Hamiltonians of these models are non-local in configuration space, but local in phase space.
We study the effects of electron-electron interaction on the critical properties of the plateau t... more We study the effects of electron-electron interaction on the critical properties of the plateau transitions in the integer quantum Hall effect. We find the renormalization group dimension associated with short-range interactions to be −0.66 ± 0.04. Thus the non-interacting fixed point (characterized z = 2 and ν ≈ 2.3) is stable. For the Coulomb interaction, we find the correlation effect is a marginal perturbation at a Hartree-Fock fixed point (z = 1, ν ≈ 2.3) by dimension counting. Further calculations are needed to determine its stability upon loop corrections.
The current pattern in the mixed state of high-Tc superconductors is studied in the U(1) mean fie... more The current pattern in the mixed state of high-Tc superconductors is studied in the U(1) mean field theory of the t-J model. Our findings are the following. 1) In the absence of antiferromagnetism a robust staggered current pattern exists in the core of vortices if the doping is not too high. 2) At a fixed doping and with increasing magnetic field, the size of the staggered current core expands, and eventually percolates. 3) The polarity of the staggered current is pinned by the direction of the magnetic field. 4) Vortex cores locally modify the hole density-in a staggered (non-staggered) core, the excess charge is slightly negative (positive). 5) Gutzwiller projection does not wash out the staggered current. Finally we present two experimental predictions concerning neutron scattering and STM spectra that capture the signature of the staggered current induced by the vortices.
The surface of a topological insulator is a closed two dimensional manifold. The surface states a... more The surface of a topological insulator is a closed two dimensional manifold. The surface states are described by the Dirac Hamiltonian in curved two dimensional spaces. For a slab-like sample with a magnetic field perpendicular to its top and bottom surfaces, there are chiral states delocalized on the four side faces. These "chiral sheets" carry both charge and spin currents. In strong magnetic fields, the quantized charge Hall effect (σxy = (2n + 1)e 2 /h) will coexist with spin Hall effect.
We discuss how the braiding properties of Laughlin quasi-particles in quantum Hall states can be ... more We discuss how the braiding properties of Laughlin quasi-particles in quantum Hall states can be understood within a one-dimensional formalism we proposed earlier. In this formalism the twodimensional space of the Hall liquid is identified with the phase space of a one-dimensional lattice system, and localized Laughlin quasi-holes can be understood as coherent states of lattice solitons. The formalism makes comparatively little use of the detailed structure of Laughlin wavefunctions, and may offer ways to be generalized to non-abelian states.
We report the first variational Monte Carlo (VMC) study of the iron-based superconductors. We use... more We report the first variational Monte Carlo (VMC) study of the iron-based superconductors. We use realistic band structures, and the ordering instabilities/variational ansatzs are suggested by previous functional renormalization group calculations. We examine antiferromagnetism, superconducting pairing, normal state fermi surface distortion and orbital order in the antiferromagnetic state.
We address two important issues that arise in recent studies of iron-based superconductivity. (1)... more We address two important issues that arise in recent studies of iron-based superconductivity. (1) Why are the Tc of AxFe2−ySe2 and the single unit cell FeSe on SrTiO3 so high despite both only have electron pockets? (2) What (if any) are the effects of orbital order and orbital fluctuation on the Cooper pairing. Our conclusions are summarized in the third paragraph of the paper. The discovery of A x Fe 2−y Se 2 [1] (T max c = 48K, under pressure[2]) and single unit cell FeSe on SrTiO 3 (FeSe/STO)[3] (T max c =65K, determined by angle-resolved photoemission spectroscopy (ARPES)[4]), stirred up a new wave of excitement in iron-based superconductors (FeSCs) research. In ARPES studies it is found, at ambient pressure, both systems have no hole pocket[4, 5]. Because it is often perceived that the scattering between the electron and hole pockets are important for both antiferromagnetism and Cooper pairing[6], this becomes an issue.
We introduce and solve a semi-classical random walk (RW) model that describes the dynamics of spi... more We introduce and solve a semi-classical random walk (RW) model that describes the dynamics of spin polarization waves in zinc-blende semiconductor quantum wells. We derive the dispersion relations for these waves, including the Rashba, linear and cubic Dresselhaus spin-orbit interactions, as well as the effects of an electric field applied parallel to the spin polarization wave vector. In agreement with calculations based on quantum kinetic theory [P. Kleinert and V. V. Bryksin, Phys. Rev. B 76, 205326 (2007)], the RW approach predicts that spin waves acquire a phase velocity in the presence of the field that crosses zero at a nonzero wave vector, q 0. In addition, we show that the spin-wave decay rate is independent of field at q 0 but increases as (q − q 0) 2 for q = q 0. These predictions can be tested experimentally by suitable transient spin grating experiments.
We study the dependence of the ground state energy on an applied Aharonov-Bohm flux Φ for the Lut... more We study the dependence of the ground state energy on an applied Aharonov-Bohm flux Φ for the Luttinger model with large momentum scattering. Employing the method of finite size bosonization, we show that for systems with a spin gap but with gapless charge degrees of freedom, the ground state energy has an exact period of hc/2e, i. e. half a flux quantum, in the limit of large system size L. Finite size corrections are found to vanish exponentially in L. This behavior is contrasted to that of the spin gapless case, for both even and odd particle number. Generalizations to finite temperature are also discussed.
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Papers by Dung-Hai LEE