arXiv subjects

Patrick A. Lee

Publications and source records attributed to Patrick A. Lee.

At least 73 records · Page 4Linked to original sources

arXiv2018

Kekulé valence bond order in an extended Hubbard model on the honeycomb lattice, with possible applications to twisted bilayer graphene

Using large-scale quantum Monte Carlo simulations, we exactly solve a model of Fermions hopping on the honeycomb lattice with cluster charge interactions, which has been proposed as an effective model with possible application to twisted bilayer graphene near half-filling. We find an interaction driven semimetal to insulator transition to an insulating phase consisting of a valence bond solid with Kekulé pattern. Finite size scaling reveals that the phase transition of the semimetal to Kekulé valence bond solid phase is continuous and belongs to chiral XY universality class.

cond-mat.str-el↗

arXiv2018

Effect of magnetization on the tunneling anomaly in compressible quantum Hall states

Tunneling of electrons into a two-dimensional electron system is known to exhibit an anomaly at low bias, in which the tunneling conductance vanishes due to a many-body interaction effect. Recent experiments have measured this anomaly between two copies of the half-filled Landau level as a function of in-plane magnetic field, and they suggest that increasing spin polarization drives a deeper suppression of tunneling. Here we present a theory of the tunneling anomaly between two copies of the partially spin-polarized Halperin-Lee-Read state, and we show that the conventional description of the tunneling anomaly, based on the Coulomb self-energy of the injected charge packet, is inconsistent with the experimental observation. We propose that the experiment is operating in a different regime, not previously considered, in which the charge-spreading action is determined by the compressibility of the composite fermions.

cond-mat.str-el↗

arXiv2018

Semiclassical theory of the tunneling anomaly in partially spin-polarized compressible quantum Hall states

Electron tunneling into a system with strong interactions is known to exhibit an anomaly, in which the tunneling conductance vanishes continuously at low energy due to many-body interactions. Recent measurements have probed this anomaly in a quantum Hall bilayer of the half-filled Landau level, and shown that the anomaly apparently gets stronger as the half-filled Landau level is increasingly spin polarized. Motivated by this result, we construct a semiclassical hydrodynamic theory of the tunneling anomaly in terms of the charge-spreading action associated with tunneling between two copies of the Halperin-Lee-Read state with partial spin polarization. This theory is complementary to our recent work (arXiv:1709.06091) where the electron spectral function was computed directly using an instanton-based approach. Our results show that the experimental observation cannot be understood within conventional theories of the tunneling anomaly, in which the spreading of the injected charge is driven by the mean-field Coulomb energy. However, we identify a qualitatively new regime, in which the mean-field Coulomb energy is effectively quenched and the tunneling anomaly is dominated by the finite compressibility of the composite Fermion liquid.

cond-mat.str-el↗

arXiv2018

Spinon Fermi surface in a cluster Mott insulator model on a triangular lattice and possible application to 1T-TaS$_2$

1T-TaS$_2$ is a cluster Mott insulator on the triangular lattice with 13 Ta atoms forming a star of David cluster as the unit cell. We derive a two dimensional XXZ spin-1/2 model with four-spin ring exchange term to describe the effective low energy physics of a monolayer 1T-TaS$_2$, where the effective spin-1/2 degrees of freedom arises from the Kramers degenerate spin-orbital states on each star of David. A large scale density matrix renormalization group simulation is further performed on this effective model and we find a gapless spin liquid phase with spinon Fermi surface at moderate to large strength region of four-spin ring exchange term. All peaks in the static spin structure factor are found to be located on the "$2k_F$" surface of half-filled spinon on the triangular lattice. Experiments to detect the spinon Fermi surface phase in 1T-TaS$_2$ are discussed.

cond-mat.str-el↗

arXiv2018

Pairing states of spin-3/2 fermions: Symmetry-enforced topological gap functions

We study the topological properties of superconductors with paired $j=\frac{3}{2}$ quasiparticles. Higher spin Fermi surfaces can arise, for instance, in strongly spin-orbit coupled band-inverted semimetals. Examples include the Bi-based half-Heusler materials, which have recently been established as low-temperature and low-carrier density superconductors. Motivated by this experimental observation, we obtain a comprehensive symmetry-based classification of topological pairing states in systems with higher angular momentum Cooper pairing. Our study consists of two main parts. First, we develop the phenomenological theory of multicomponent (i.e., higher angular momentum) pairing by classifying the stationary points of the free energy within a Ginzburg-Landau framework. Based on the symmetry classification of stationary pairing states, we then derive the symmetry-imposed constraints on their gap structures. We find that, depending on the symmetry quantum numbers of the Cooper pairs, different types of topological pairing states can occur: fully gapped topological superconductors in class DIII, Dirac superconductors and superconductors hosting Majorana fermions. Notably, we find a series of nematic fully gapped topological superconductors, as well as double-Dirac superconductors with quadratic dispersion. Our approach, applied here to the case of $j=\frac{3}{2}$ Cooper pairing, is rooted in the symmetry properties of pairing states, and can therefore also be applied to other systems with higher angular momentum and high-spin pairing. We conclude by relating our results to experimentally accessible signatures in thermodynamic and dynamic probes.

cond-mat.supr-con↗

arXiv2017

Emergence of Gapped Bulk and Metallic Side Walls in the Zeroth Landau level in Dirac and Weyl semimetals

Recent transport experiments have revealed the activation of longitudinal magnetoresistance of Weyl semimetals in the quantum limit, suggesting the breakdown of chiral anomaly in a strong magnetic field. Here we provide a general mechanism for gapping the zeroth chiral Landau levels applicable for both Dirac and Weyl semimetals. Our result shows that the zeroth Landau levels anticross when the magnetic axis is perpendicular to the Dirac/Weyl node separation and when the inverse magnetic length $l_B^{-1}$ is comparable to the node separation scale $Δk$. The induced bulk gap increases rapidly beyond a threshold field in Weyl semimetals, but has no threshold and is non-monotonic in Dirac systems due to the crossover between $l_B^{-1}>Δk$ and $l_B^{-1}<Δk$ regions. We also find that the Dirac and possibly Weyl systems host counterpropagating edge states between the zeroth Landau levels, leading to a state with metallic side walls and zero Hall conductance.

cond-mat.mes-hall↗

arXiv2017

Pairing from dynamically screened Coulomb repulsion in bismuth

Recently, Prakash et. al. have discovered bulk superconductivity in single crystals of bismuth, which is a semi metal with extremely low carrier density. At such low density, we argue that conventional electron-phonon coupling is too weak to be responsible for the binding of electrons into Cooper pairs. We study a dynamically screened Coulomb interaction with effective attraction generated on the scale of the collective plasma modes. We model the electronic states in bismuth to include three Dirac pockets with high velocity and one hole pocket with a significantly smaller velocity. We find a weak coupling instability, which is greatly enhanced by the presence of the hole pocket. Therefore, we argue that bismuth is the first material to exhibit superconductivity driven by retardation effects of Coulomb repulsion alone. By using realistic parameters for bismuth we find that the acoustic plasma mode does not play the central role in pairing. We also discuss a matrix element effect, resulting from the Dirac nature of the conduction band, which may affect $T_c$ in the $s$-wave channel without breaking time-reversal symmetry.

cond-mat.supr-con↗

arXiv2017

Emergent orbitals in the cluster Mott insulator on a breathing Kagome lattice

Motivated by the recent developments on cluster Mott insulating materials such as the cluster magnet LiZn$_2$Mo$_3$O$_8$, we consider the strong plaquette charge ordered regime of the extended Hubbard model on a breathing Kagome lattice and reveal the properties of the cluster Mottness. The plaquette charge order arises from the inter-site charge interaction and the collective motion of three localized electrons on the hexagon plaquettes. This model leads naturally to a reduction of the local moments by 2/3 as observed in LiZn$_2$Mo$_3$O$_8$. Furthermore, at low temperatures each hexagon plaquette contains an extra orbital-like degree of freedom in addition to the remaining spin 1/2. We explore the consequence of this emergent orbital degree of freedom. We point out the interaction between the local moments is naturally described by a Kugel-Khomskii spin-orbital model. We develop a parton approach and suggest a spin liquid ground state with spinon Fermi surfaces for this model. We further predict an emergent orbital order when the system is under a strong magnetic field. Various experimental consequences for LiZn$_2$Mo$_3$O$_8$ are discussed, including an argument that the charge ordering much be short ranged if the charge per Mo is slightly off stoichiometry.

cond-mat.str-el↗

arXiv2017

Superconductivity in three-dimensional spin-orbit coupled semimetals

Motivated by the experimental detection of superconductivity in the low-carrier density half-Heusler compound YPtBi, we study the pairing instabilities of three-dimensional strongly spin-orbit coupled semimetals with a quadratic band touching point. In these semimetals the electronic structure at the Fermi energy is described by spin j=3/2 quasiparticles, which are fundamentally different from those in ordinary metals with spin j=1/2. We develop a general approach to analyzing pairing instabilities in j=3/2 materials by decomposing the pair scattering interaction into irreducible channels, projecting them to the Fermi surface and deriving the corresponding Eliashberg theory. Applying our method to a generic density-density interaction in YPtBi we establish the following results: (i) The pairing strength in each channel uniquely encodes the j=3/2 nature of the Fermi surface band structure--a manifestation of the fundamental difference with ordinary metals. In particular, this implies that Anderson's theorem, which addresses the effect of spin-orbit coupling and disorder on pairing states of spin-1/2 electrons, cannot be applied in this case. (ii) The leading pairing instabilities are different for electron and hole doping. This implies that superconductivity depends on carrier type. (iii) In the case of hole doping--relevant to YPtBi, we find two odd-parity channels in close competition with s-wave pairing. One of these two channels is a multicomponent pairing channel, allowing for the possibility of time-reversal symmetry breaking. (iv) In the case of Coulomb interactions mediated by the long-ranged electric polarization of optical phonon modes, a significant coupling strength is generated in spite of the extremely low density of carriers. Furthermore, non-linear response and Fermi liquid corrections can favor non-s-wave pairing and potentially account for the experimentally-observed Tc.

cond-mat.supr-con↗

arXiv2017

Is 1T-TaS$_2$ a 40 year old quantum spin liquid?

1T-TaS$_2$ is unique among transition metal dichalcogenides in that it is understood to be a correlation driven insulator, where the unpaired electron in a 13 site cluster experiences enough correlation to form a Mott insulator. We argue based on existing data that this well-known material should be considered as a quantum spin liquid, either a fully gapped $Z2$ spin liquid or a Dirac spin liquid. We discuss the exotic states that emerge upon doping and propose further experimental probes.

cond-mat.str-el↗

arXiv2017

Direct optical detection of Weyl fermion chirality in a topological semimetal

A Weyl semimetal (WSM) is a novel topological phase of matter, in which Weyl fermions (WFs) arise as pseudo-magnetic monopoles in its momentum space. The chirality of the WFs, given by the sign of the monopole charge, is central to the Weyl physics, since it directly serves as the sign of the topological number and gives rise to exotic properties such as Fermi arcs and the chiral anomaly. Despite being the defining property of a WSM, the chirality of the WFs has never been experimentally measured. Here, we directly detect the chirality of the WFs by measuring the photocurrent in response to circularly polarized mid-infrared light. The resulting photocurrent is determined by both the chirality of WFs and that of the photons. Our results pave the way for realizing a wide range of theoretical proposals for studying and controlling the WFs and their associated quantum anomalies by optical and electrical means. More broadly, the two chiralities, analogous to the two valleys in 2D materials, lead to a new degree of freedom in a 3D crystal with potential novel pathways to store and carry information.

cond-mat.mtrl-sci↗

arXiv2017

Photocurrents in Weyl semimetals

The generation of photocurrent in an ideal two-dimensional Dirac spectrum is symmetry-forbidden. In sharp contrast, we show that three-dimensional Weyl semimetals can generically support significant photocurrent generations due to the combination of inversion symmetry breaking and finite tilts of the Weyl spectra. Symmetry properties, chirality relations and various dependences on the system and light sources are explored in details. Our results suggest that noncentrosymmetric Weyl materials can be advantageously applied to room temperature detections of mid- and far-infrared radiations.

cond-mat.mes-hall↗

arXiv2016

Type-II Weyl cone transitions in driven semimetals

Periodically driven systems provide tunable platforms to realize interesting Floquet topological phases and phase transitions. In electronic systems with Weyl dispersions, the band crossings are topologically protected even in the presence of time-periodic perturbations. This robustness permits various routes to shift and tilt the Weyl spectra in the momentum and energy space using circularly polarized light of sufficient intensity. We show that type-II Weyl fermions, in which the Weyl dispersions are tilted with the appearance of pocket-like Fermi surfaces, can be induced in driven Dirac semimetals and line node semimetals. Under a circularly polarized drive, both semimemtal systems immediately generate Weyl node pairs whose types can be further controlled by the driving amplitude and direction. The resultant phase diagrams demonstrate experimental feasibilities.

cond-mat.mes-hall↗

arXiv2016

Observation of two distinct pairs fluctuation lifetimes and supercurrents in the pseudogap regime of cuprate junctions

Pairs fluctuation supercurrents and inverse lifetimes were measured on epitaxial c-axis junctions of the cuprates in the pseudogap regime, with a $PrBa_2Cu_3O_{7-δ}$ barrier sandwiched in between two $YBa_2Cu_3O_{7-δ}$ or doped $YBa_2Cu_3O_y$ electrodes, with or without magnetic fields parallel to the a-b planes. All junctions had a $\rm T_c(high)\approx 85-90$ K and a $\rm T_c(low)\approx 50-55$ K electrodes, allowing us to study pairs fluctuation supercurrents and inverse life times in between these two temperatures. In junctions with a pseudogap electrode under zero field, an excesss current due to pair fluctuations was observed which persisted at temperatures above $\rm T_c(low)$, in the pseudogap regime, and up to about $\rm T_c(high)$. No such excess current was observed in junctions without a pseudo-gap in the electrode. The measured conductance spectra at temperatures above $\rm T_c(low)$ were fitted using a modified fluctuations model by Scalapino [Phys. Rev. Lett. \textbf{24}, 1052(1970)] of a junction with a serial resistance. We found that in the pseudo-gap regime, the conductance vs voltage consists of a narrow peak sitting on top of a very broad peak. This yielded two distinct pairs fluctuation lifetimes in the pseudogap electrode which differ by an order of magnitude up to about $\rm T_c(high)$. Under in-plane fields, these two lifetime values remain separated in two distinct groups, which varied with increasing field moderately. We also found that detection of Amperian pairing [Phys. Rev. X \textbf{4}, 031017 (2014)] in our cuprate junctions is not feasible, due to Josephson vortices penetration into the superconducting electrodes which drove the necessary field above the depairing field.

cond-mat.supr-con↗

arXiv2016

Optical Conductivity From Pair Density Waves

We present a theory of optical conductivity in systems with finite-momentum Cooper pairs. In contrast to the BCS pairing where AC conductivity is purely imaginary in the clean limit, there is nonzero AC absorption across the superconducting gap for finite-momentum pairing if we break the Galilean symmetry explicitly in the electronic Hamiltonian. Vertex correction is crucial for maintaining the gauge invariance in the mean-field formalism and dramatically changes the optical conductivity in the direction of the pairing momentum. We carried out a self-consistent calculation and gave an explicit formula for optical conductivity in a simple case. This result applies to the Fulde-Ferrell-Larkin-Ovchinnikov state and candidates with pair density waves proposed for High- Tc cuprates. It may help detect PDW and determine the pairing gap as well as the direction of the pairing momentum in experiments.

cond-mat.supr-con↗

arXiv2016

Superconductivity at very low density: the case of strontium titanate

Doped strontium titanate becomes superconducting at a density as low as n = 5 x 10^17 cm^-3, where the Fermi energy is orders of magnitude smaller than the longitudinal-optical-phonon frequencies. In this limit the only optical mode with a frequency which is smaller than the Fermi energy is the plasmon. In contrast to metals, the interaction strength is weak due to screening by the crystal, which allows the construction of a controllable theory of plasmon superconductivity. We show that plasma mediated pairing alone can account for the observed transition temperatures if the screening by the crystal is reduced in the slightly doped samples compared with the insulating ones. This mechanism can also explain the pairing in the two-dimensional superconducting states observed at surfaces and interfaces with other oxides. We also discuss unique features of the plasmon mechanism, which appear in the tunneling density of states above the gap.

cond-mat.supr-con↗

arXiv2015

When chiral photons meet chiral fermions - Photoinduced anomalous Hall effects in Weyl semimetals

The Weyl semimetal is characterized by three-dimensional linear band touching points called Weyl nodes. These nodes come in pairs with opposite chiralities. We show that the coupling of circularly polarized photons with these chiral electrons generates a Hall conductivity without any applied magnetic field in the plane orthogonal to the light propagation. This phenomenon comes about because with all three Pauli matrices exhausted to form the three-dimensional linear dispersion, the Weyl nodes cannot be gapped. Rather, the net influence of chiral photons is to shift the positions of the Weyl nodes. Interestingly, the momentum shift is tightly correlated with the chirality of the node to produce a net anomalous Hall signal. Application of our proposal to the recently discovered TaAs family of Weyl semimetals leads to an order-of-magnitude estimate of the photoinduced Hall conductivity which is within the experimentally accessible range.

cond-mat.mes-hall↗

arXiv2015

Selective scattering between Floquet-Bloch and Volkov states in a topological insulator

The coherent optical manipulation of solids is emerging as a promising way to engineer novel quantum states of matter. The strong time periodic potential of intense laser light can be used to generate hybrid photon-electron states. Interaction of light with Bloch states leads to Floquet-Bloch states which are essential in realizing new photo-induced quantum phases. Similarly, dressing of free electron states near the surface of a solid generates Volkov states which are used to study non-linear optics in atoms and semiconductors. The interaction of these two dynamic states with each other remains an open experimental problem. Here we use Time and Angle Resolved Photoemission Spectroscopy (Tr-ARPES) to selectively study the transition between these two states on the surface of the topological insulator Bi2Se3. We find that the coupling between the two strongly depends on the electron momentum, providing a route to enhance or inhibit it. Moreover, by controlling the light polarization we can negate Volkov states in order to generate pure Floquet-Bloch states. This work establishes a systematic path for the coherent manipulation of solids via light-matter interaction.

cond-mat.mes-hall↗