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Patrick A. Lee

Publications and source records attributed to Patrick A. Lee.

At least 37 records · Page 2Linked to original sources
arXiv2024

Observation of Cooper-pair density modulation state

Superconducting states that break space-group symmetries of the underlying crystal can exhibit nontrivial spatial modulation of the order parameter. Previously, such remarkable states were intimately associated with the breaking of translational symmetry, giving rise to the density-wave orders, with wavelengths spanning several unit cells. However, a related basic concept has been long overlooked: when only intra-unit-cell symmetries of the space group are broken, the superconducting states can display a distinct type of nontrivial modulation preserving long-range lattice translation. Here, we refer to this new concept as the pair density modulation (PDM), and report the first observation of a PDM state in exfoliated thin flakes of iron-based superconductor FeTe$_{\text{0.55}}$Se$_{\text{0.45}}$. Using scanning tunneling microscopy, we discover robust superconducting gap modulation with the wavelength corresponding to the lattice periodicity and the amplitude exceeding 30% of the gap average. Importantly, we find that the observed modulation originates from the large difference in superconducting gaps on the two nominally equivalent iron sublattices. The experimental findings, backed up by model calculations, suggest that in contrast to the density-wave orders, the PDM state is driven by the interplay of sublattice symmetry breaking and a peculiar nematic distortion specific to the thin flakes. Our results establish new frontiers for exploring the intertwined orders in strong-correlated electronic systems and open a new chapter for iron-based superconductors.

cond-mat.supr-con↗
arXiv2024

A model of non-Fermi liquid with power law resistivity: strange metal with a not-so-strange origin

We construct a model which exhibits resistivity going as a power law in temperature $T$, as $T^α$ down to the lowest temperature. There is no residual resistivity because we assume the absence of disorder and momentum relaxation is due to umklapp scattering. Our model consists of a quantum spin liquid state with spinon Fermi surface and a hole Fermi surface made out of doped holes. The key ingredient is a set of singular $2k_F$ modes living on a ring in momentum space. Depending on parameters, $α$ may be unity (strange metal) or even smaller. The model may be applicable to a doped organic compound, which has been found to exhibit linear T resistivity. We conclude that it is possible to obtain strange metal behavior starting with a model which is not so strange.

cond-mat.str-el↗
arXiv2024

Probing quantum spin liquids with a quantum twisting microscope

The experimental characterization of quantum spin liquids poses significant challenges due to the absence of long-range magnetic order, even at absolute zero temperature. The identification of these states of matter often relies on the analysis of their excitations. In this paper, we propose a method for detecting the signatures of the fractionalized excitations in quantum spin liquids using a tunneling spectroscopy setup. Inspired by the recent development of the quantum twisting microscope, we consider a planar tunneling junction, in which a candidate quantum spin liquid material is placed between two graphene layers. By tuning the relative twist angle and voltage bias between the leads, we can extract the dynamical spin structure factor of the tunneling barrier with momentum and energy resolution. Our proposal presents a promising tool for experimentally characterizing quantum spin liquids in two-dimensional materials.

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arXiv2024

Non-Analytic Magnetic Response and Intrinsic Ferromagnetic Clusters in a Dirac Spin Liquid Candidate

Finding distinct signatures of a quantum spin liquid (QSL) is an ongoing quest in condensed matter physics, invariably complicated by the presence of disorder in real materials. In this regard the 2D Kagome system YCu$_3$(OH)$_6$[(Cl$_x$Br$_{(1-x)}$)$_{3-y}$(OH)$_y$] (YCOB-Cl), where the vast mismatch in size of Y and Cu avoids subsitutional disorder, otherwise present in kagome materials, has emerged as a favorable candidate. In crystals of this system, with $x<$ 0.4 and no long range order, we report an unusual field dependent magnetization $M(B)$, where $M/B$ changes linearly with $|B|$, the absolute value of the field, in contrast to the expected quadratic behavior. Model calculations with a distribution of ferromagnetic (FM) clusters faithfully capture observed features suggesting such clusters to be intrinsic to real QSL materials. YCOB-Cl has a field enhanced $T^2$ heat capacity as expected for a Dirac QSL but lacks a linear $T$ behavior in the spin susceptibility. By demonstrating that FM clusters dominate the contribution to the susceptibility but not the heat capacity, our work paves the way towards reconciling the apparent inconsistency with a Dirac QSL.

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arXiv2024

Generation of gauge magnetic fields in a kagome spin liqud candidate using the Dzyaloshinskii-Moriya interaction

The recent discovery of magnetization oscillations in a kagome spin liquid candidate motivates us to examine the origin of the gauge magnetic field term that can give rise to quantum oscillations of fermionic spinons. We find that in the presence of the Dzyaloshinskii-Moriya interaction and an average spin polarization, the spin permutation operator around the unit cell acquires an imaginary part, and a net gauge flux is generated through the unit cell of the kagome lattice. This new mechanism of gauge field generation can account for the strength of the gauge magnetic field needed to explain the experiment.

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arXiv2023

Enhancement of Superconductivity in a Dirty Marginal Fermi Liquid

We study superconductivity in a two-dimensional, disordered marginal Fermi liquid. At the semiclassical level, the transition temperature $T_c$ is strongly suppressed because marginal Fermi liquid effects destroy well-defined quasiparticles. However, we show that interference between quantum-critical collective modes must be included, and these enhance $T_c$, violating Anderson's theorem. Our results suggest that phase coherence in a disordered, quantum-critical system can survive and manifest in the form of collective excitations, despite the absence of coherent quasiparticles.

cond-mat.supr-con↗
arXiv2023

Detection of collective modes in unconventional superconductors using tunneling spectroscopy

We propose using tunneling spectroscopy with a superconducting electrode to probe the collective modes of unconventional superconductors. The modes are predicted to appear as peaks in dI/dV at voltages given by eV = ωi/2 where ωi denotes the mode frequencies. This may prove to be a powerful tool to investigate the pairing symmetry of unconventional superconductors. The peaks associated with the collective modes appear at fourth order in the single particle tunneling matrix element. At the same fourth order, multiple Andreev reflection (MAR) leads to peaks at voltage equal to the energy gaps, which, in BCS superconductors, coincides with the expected position of the amplitude (Higgs) mode. The peaks stemming from the collective modes of unconventional superconductors do not suffer from this coincidence. For scanning tunneling microscopes (STM), we estimate that the magnitude of the collective mode contribution is smaller than the MAR contribution by the ratio of the energy gap to the Fermi energy. Moreover, there is no access to the mode dispersion. Conversely, for planar tunnel junctions the collective mode peak is expected to dominate over the MAR peak, and the mode dispersion can be measured. We discuss systems where the search for such collective modes is promising.

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arXiv2023

A mechanism for $π$ phase shifts in Little-Parks experiments: application to 4Hb-TaS$_2$ and to 2H-TaS$_2$ intercalated with chiral molecules

Recently, unusual $π$ phase shifts in Little-Parks experiments performed on two systems derived from the layered superconductor 2H-TaS$_2$ were reported. These systems share the common feature that additional layers have been inserted between the 1H-TaS$_2$ layers. In both cases, the $π$ phase shift has been interpreted as evidence for the emergence of exotic superconductivity in the 1H layers. Here, we propose an alternative explanation assuming that superconductivity in the individual 1H layers is of conventional $s$-wave nature derived from the parent 2H-TaS$_2$. We show that a negative Josephson coupling between otherwise decoupled neighboring 1H layers can explain the observations. Furthermore, we find that the negative coupling can arise naturally assuming a tunneling barrier containing paramagnetic impurities. An important ingredient is the suppression of non-spin-flip tunneling due to spin-momentum locking of Ising type in a single 1H layer together with the inversion symmetry of the double layer. In the exotic superconductivity scenario, it is challenging to explain why the critical temperature is almost the same as in the parent material and, in the 4Hb case, the superconductivity's robustness to disorder. Both are non-issues in our picture, which also exposes the common features that are special in these two systems.

cond-mat.supr-con↗
arXiv2023

Effective model for Pb$_9$Cu(PO$_4$)$_6$O

The copper substituted Pb-apatite has attracted a great deal of attention recently, due to the claim of the observation of room temperature superconductivity. Based on LDA calculations in the literature, we propose an effective model that describe the low energy physics. It consists of stacks of buckled honeycomb lattices, with Cu and O occupying the A and B sites respectively. In addition to the narrow Cu bands that have been emphasized, we call attention to the relatively small energy separation between the Cu and O orbitals. Thus despite the small hoping energies, the model may be in an interesting regime near the metal insulator transition driven by the charge transfer mechanism. Relationship with cuprates and the organic superconductors are discussed.

cond-mat.supr-con↗
arXiv2023

Electronic Density of States of a $U\left(1\right)$ Quantum Spin Liquid with Spinon Fermi Surface. II. Zeeman Magnetic Field Effects

The Zeeman effect lowers the energy of electrons with spin states which are anti-parallel to the applied magnetic field but lifts that of spin parallel states. In quantum spin liquids where the spin and charge degrees of freedom are fractionalized, anomalous Zeeman response may be expected. In the case of spin liquids with spinon Fermi surface, the threshold energy to excite an electronic state is found to exhibit no Zeeman shift. This is specific to the spinon Fermi surface case. In contrast, other gapped spin liquids are expected to exhibit the standard Zeeman shift at the band edge even though they also exhibit spin-charge fractionalization. When gauge field fluctuations are included, we find that the Zeeman shift of the electronic states gets affected by the gauge field induced binding. In the electronic density of states spectra, weak gauge binding induces band edge resonance peaks which exhibit the Zeeman shift in the same direction as that in the standard Zeeman effect, but the shift is reduced as the binding potential increases. With further increase in the binding potential the resonance becomes true in-gap bound states and eventually the shift direction reverses so it is opposite to the standard Zeeman effect. We propose that one can perform spin polarized scanning tunneling microscope measurements as a test of the spinon Fermi sea ground state in quantum spin liquid candidate materials.

cond-mat.str-el↗
arXiv2023

Signatures of Cooper pair dynamics and quantum-critical superconductivity in tunable carrier bands

Different superconducting pairing mechanisms are markedly distinct in the underlying Cooper pair kinematics. Pairing interactions mediated by quantum-critical soft modes are dominated by highly collinear processes, falling into two classes: forward scattering and backscattering. In contrast, phonon mechanisms have a generic non-collinear character. We show that the type of kinematics can be identified by examining the evolution of superconductivity when tuning the Fermi surface geometry. We illustrate our approach using recently measured phase diagrams of various graphene systems. Our analysis unambiguously connects the emergence of superconductivity at ``ghost crossings'' of Fermi surfaces in distinct valleys to the pair kinematics of a backscattering type. Together with the observed non-monotonic behavior of superconductivity near its onset (sharp rise followed by a drop), it provides strong support for a particular quantum-critical superconductivity scenario. These findings conclusively settle the long-standing debate on the origin of superconductivity in this system and demonstrate the essential role of quantum-critical modes in superconducting pairing. Moreover, our work highlights the potential of tuning bands via ghost crossings as a promising means of boosting superconductivity.

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arXiv2023

Proposal to detect emergent gauge field and its Meissner effect in spin liquids using NV Centers

We show that NV centers could provide distinct signatures of emergent gauge fields in certain phase transitions in spin liquids. We consider the relaxation rate $1/T_1$ of a diamond NV center placed a distance $z_0$ above a crystal consisting of two dimensional layers which hosts a $U(1)$ quantum spin liquid with spinon Fermi surface. We show that during a spinon pairing transition from a $U(1)$ to a $\mathbb{Z}_2$ spin liquid, the relaxation rate exhibits a rapid fall just below the pairing transition. The drop is much faster than what can be accounted for by the opening of the energy gap. Instead, the rapid fall with a unique $z_0$ dependence of its height and width, is the signature of the Meissner effect of the gauge field. We identify the organic ET compound which has a phase transition at 6K as a candidate for the experimental observation of this phenomenon.

cond-mat.str-el↗
arXiv2023

Ubiquitous Superconducting Diode Effect in Superconductor Thin Films

The macroscopic coherence in superconductors supports dissipationless supercurrents which could play a central role in emerging quantum technologies. Accomplishing unequal supercurrents in the forward and backward directions would enable unprecedented functionalities. This nonreciprocity of critical supercurrents is called superconducting (SC) diode effect. We demonstrate strong SC diode effect in conventional SC thin films, such as niobium and vanadium, employing external magnetic fields as small as 1 Oe. Interfacing the SC layer with a ferromagnetic semiconductor EuS, we further accomplish non-volatile SC diode effect reaching a giant efficiency of 65%. By careful control experiments and theoretical modeling, we demonstrate that the critical supercurrent nonreciprocity in SC thin films could be easily accomplished with asymmetrical vortex edge/surface barriers and the universal Meissner screening current governing the critical currents. Our engineering of the SC diode effect in simple systems opens door for novel technologies. Meanwhile, we reveal the ubiquity of Meissner screening effect induced SC diode effect in superconducting films, which should be eliminated with great care in the search of exotic superconducting states harboring finite-momentum Cooper pairing.

cond-mat.supr-con↗
arXiv2022

Understanding resistance oscillation in CsV$_3$Sb$_5$ superconductor

A recent demonstration of the periodic oscillation of resistance in the thin film of CsV$_3$Sb$_5$ superconductor with a hole in the film suggests that charge-$4e$ and charge-$6e$ Cooper pairs may have condensed in this compound. While exciting, such interpretation calls for a precise determination of the effective area for the passage of Cooper pairs from one end of the lead to the other. Unlike the traditional Little-Parks effect where the rim around the hole is thin, the effective hole area is not obviously defined for the "thick-rim geometry" adopted in [arxiv:2201.10352]. Here, we note that the experiment was conducted in a regime where the superconctivity is strongly fluctuating, which motivates an analysis based on the spacetime formulation of the time-dependent Ginzburg-Landau theory. We argue that under appropriate conditions, the optimal semi-classical path is not the geometrically shortest one, but the one that moves along the edge of the hole and takes advantage of the reduced fluctuations at the boundary of the hole. The condition for the cross-over from the geometrically shortest path to the path that sticks to the wall is clarified. In such a scenario, the geometric area of the hole indeed emerges as the effective area for the flux, providing a theoretical justification to the interpretation given in [arxiv:2201.10352]. The conclusion of our analysis may have implication for similar experiments in other superconductors where the geometry of the device is not obviously that of the Little-Parks experiment employing the thin wall, but of the thick-rim type such as used in [arxiv:2201.10352].

cond-mat.supr-con↗
arXiv2022

Probing the Quantum Noise of the Spinon Fermi Surface with NV Centers

We study the transverse electrical conductivity and the corresponding magnetic noise of a two-dimensional U(1) spin liquid state with a spinon Fermi surface. We show that in the quasi-static regime these responses have the same wave-vector dependence as that of a metal but are reduced by a dimensionless pre-factor controlled by the ratio of orbital diamagnetic susceptibilities of the spinons and chargons, correcting previous work. We estimate that this quasi-static regime is comfortably accessed by the typical NV center splittings of a few GHz and estimate that the expected T1 times for an NV center placed above candidate materials, such as the organic dmit and ET salts, monolayer 1T-TaS2/Se2, would range from several tens to a few hundred milliseconds.

cond-mat.str-el↗
arXiv2022

Evidence for a spinon Kondo effect in cobalt atoms on single-layer 1T-TaSe$_2$

Quantum spin liquids (QSLs) are highly entangled, disordered magnetic states that arise in frustrated Mott insulators and host exotic fractional excitations such as spinons and chargons. Despite being charge insulators some QSLs are predicted to exhibit gapless itinerant spinons that yield metallic behavior in the spin channel. We have deposited isolated magnetic atoms onto single-layer (SL) 1T-TaSe$_2$, a gapless QSL candidate, to experimentally probe how itinerant spinons couple to impurity spin centers. Using scanning tunneling spectroscopy we observe the emergence of new, impurity-induced resonance peaks at the 1T-TaSe$_2$ Hubbard band edges when cobalt adatoms are positioned to have maximal spatial overlap with the Hubbard band charge distribution. These resonance peaks disappear when the spatial overlap is reduced or when the magnetic impurities are replaced with non-magnetic impurities. Theoretical simulations using a modified Anderson impurity model integrated with a gapless quantum spin liquid show that these resonance peaks are consistent with a Kondo resonance induced by spinons combined with spinon-chargon binding effects that arise due to QSL gauge-field fluctuations.

cond-mat.str-el↗
arXiv2022

Interpreting Angle Dependent Magnetoresistance in Layered Materials: Application to Cuprates

The evolution of the low temperature electronic structure of the cuprate metals from the overdoped to the underdoped side has recently been addressed through Angle-Dependant Magneto-Resistance (ADMR) experiments in La$_{1.6-x}$Nd$_{0.4}$Sr$_x$CuO$_4$. The results show a striking difference between hole dopings $p = 0.24$ and $p = 0.21$ which lie on either side of a putative quantum critical point at intermediate $p$. Motivated by this, we here study the theory of ADMR in correlated layered materials, paying special attention to the role of angle dependent quasiparticle weights $Z_{\mathbf{k}}$. Such a $Z_{\mathbf{k}}$ is expected to characterize a number of popular models of the cuprate materials, particularly when underdoped. Further, in the limit of weak interlayer hopping the quasiparticle weight will affect the $c$-axis transport measured in ADMR experiments. We show that proper inclusion of the quasiparticle weight does not support an interpretation of the data in terms of a $(π, π)$ spin density wave ordered state, in agreement with the lack of direct evidence for such order. We show that a simple model of Fermi surface reconfiguring across a van Hove point captures many of the striking differences seen between $p = 0.21$ and $p = 0.24$. We comment on why such a model may be appropriate for interpreting the ADMR data, despite having a large Fermi surface at $p = 0.21$, seemingly in contradiction with other evidence for a small Fermi surafce at that doping level.

cond-mat.str-el↗
arXiv2021

Topological superconductivity in EuS/Au/superconductor heterostructures

In a recent work, signatures of a pair of Majorana bound states (MBS) were found in a new experimental platform formed by EuS islands deposited on top of a gold surface which was made superconducting through proximity coupling to a superconductor. In this work, we provide a theoretical understanding for how MBS can be formed in EuS/Au/superconductor heterostructures. We focus on the strip geometry where a narrow ferromagnetic strip is deposited on a planar structure. We first explicitly map out the topological phase diagram of the EuS/Au/superconductor heterostructure using the lattice Green's function method. Importantly, we find that the chemical potential step between the region with and without EuS covering is a crucial ingredient for the creation of MBS of this set-up. Next, we focus on the Bogoliugov quasi-particles that are bound to the region under the EuS by Andreev reflections from the surrounding superconductors. Moreover, we obtain the topological regimes analytically using the scattering matrix method. Notably, we confirm that the normal reflections induced by the chemical potential step are essential for creating finite topological regimes. Furthermore, the area of the topological regimes shows periodic oscillation as a function of chemical potential as well as the sample width.

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