Browsing by Author "Foster, Matthew S."
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Item Chalker scaling, level repulsion, and conformal invariance in critically delocalized quantum matter: Disordered topological superconductors and artificial graphene(American Physical Society, 2014) Chou, Yang-Zhi; Foster, Matthew S.We numerically investigate critically delocalized wave functions in models of two-dimensional Dirac fermions, subject to vector potential disorder. These describe the surface states of three-dimensional topological superconductors, and can also be realized through long-range correlated bond randomness in artificial materials like molecular graphene. A “frozen” regime can occur for strong disorder in these systems, wherein a single wave function presents a few localized peaks separated by macroscopic distances. Despite this rarefied spatial structure, we find robust correlations between eigenstates at different energies, at both weak and strong disorder. The associated level statistics are always approximately Wigner-Dyson. The system shows generalized Chalker (quantum critical) scaling, even when individual states are quasilocalized in space. We confirm analytical predictions for the density of states and multifractal spectra. For a single Dirac valley, we establish that finite energy states show universal multifractal spectra consistent with the integer quantum Hall plateau transition. A single Dirac fermion at finite energy can therefore behave as a “Quantum Hall critical metal.” For the case of two valleys and non-Abelian disorder, we verify predictions of conformal field theory. Our results for the non-Abelian case imply that both delocalization and conformal invariance are topologically protected for multivalley topological superconductor surface states.Item Critical Percolation without Fine-Tuning on the Surface of a Topological Superconductor(American Physical Society, 2018) Ghorashi, Sayed Ali Akbar; Liao, Yunxiang; Foster, Matthew S.We present numerical evidence that most two-dimensional surface states of a bulk topological superconductor (TSC) sit at an integer quantum Hall plateau transition. We study TSC surface states in class CI with quenched disorder. Low-energy (finite-energy) surface states were expected to be critically delocalized (Anderson localized). We confirm the low-energy picture, but find instead that finite-energy states are also delocalized, with universal statistics that are independent of the TSC winding number, and consistent with the spin quantum Hall plateau transition (percolation).Item Criticality across the energy spectrum from random artificial gravitational lensing in two-dimensional Dirac superconductors(American Physical Society, 2020) Ghorashi, Sayed Ali Akbar; Karcher, Jonas F.; Davis, Seth M.; Foster, Matthew S.; Rice Center for Quantum MaterialsWe numerically study weak, random, spatial velocity modulation [quenched gravitational disorder (QGD)] in two-dimensional massless Dirac materials. QGD couples to the spatial components of the stress tensor; the gauge-invariant disorder strength is encoded in the quenched curvature. Although it is expected to produce negligible effects, wave interference due to QGD transforms all but the lowest-energy states into a quantum-critical “stack” with universal, energy-independent spatial fluctuations. We study five variants of velocity disorder, incorporating three different local deformations of the Dirac cone: flattening or steepening of the cone, pseudospin rotations, and nematic deformation (squishing) of the cone. QGD should arise for nodal excitations in the d-wave cuprate superconductors (SCs) due to gap inhomogeneity. Our results may explain the division between low-energy “coherent” (plane-wave-like) and finite-energy “incoherent” (spatially inhomogeneous) excitations in the SC and pseudogap regimes. The model variant that best matches the cuprate phenomenology possesses quenched random pseudospin rotations and nematic fluctuations. This model variant and another with pure nematic randomness exhibit a robust energy swath of stacked critical states, the width of which increases with increasing disorder strength. By contrast, quenched fluctuations that isotropically flatten or steepen the Dirac cone tend to produce strong disorder effects, with more rarefied wave functions at low and high energies. Our models also describe the surface states of class DIII topological SCs.Item Dephasing Catastrophe in 4−ε Dimensions: A Possible Instability of the Ergodic (Many-Body-Delocalized) Phase(American Physical Society, 2018) Liao, Yunxiang; Foster, Matthew S.; Rice Center for Quantum MaterialsIn two dimensions, dephasing by a bath cuts off Anderson localization that would otherwise occur at any energy density for fermions with disorder. For an isolated system with short-range interactions, the system can be its own bath, exhibiting diffusive (non-Markovian) thermal density fluctuations. We recast the dephasing of weak localization due to a diffusive bath as a self-interacting polymer loop. We investigate the critical behavior of the loop in d=4−ε dimensions, and find a nontrivial fixed point corresponding to a temperature T∗∼ε>0 where the dephasing time diverges. Assuming that this fixed point survives to ε=2, we associate it with a possible instability of the ergodic phase. Our approach may open a new line of attack against the problem of the ergodic to many-body-localized phase transition in d>1 spatial dimensions.Item Dynamics, disorder, and interactions in low-dimensional quantum matter: Fractionalization waves, non-Markovian dephasing, and quenched gravity(2021-08-11) Davis, Seth M; Foster, Matthew S.We consider three topics, all concerning the confluence of dynamics, disorder, and interactions in low-dimensional quantum many-body systems of interest for the potential manipulation of quantum matter. Particle fractionalization is believed to orchestrate the physics of many strongly correlated systems, yet its direct experimental detection remains a challenge. We propose a measurement for an ultracold matter system, in which correlations in initially decoupled 1D chains are imprinted via quantum quench upon two-dimensional Dirac fermions. Coupling fractionalized initial states launches relativistic "fractionalization waves'' along the chains, while coupling noninteracting chains induces perpendicular dispersion. These could be easily distinguished in an ultracold gas experiment. As a potential window on transitions out of the ergodic phase of weakly disordered, quasi-one-dimensional fermion systems, we study dephasing due to a diffusive noise bath generated by inelastic scattering due to short-ranged interactions. We calculate the dephasing of weak localization perturbatively through second order in the bath coupling and discover a failure of the self-consistent Born approximation. We also consider a many-channel quantum wire where short-ranged, spin-exchange interactions coexist with screened Coulomb interactions. We calculate the dephasing rate, treating the short-ranged interaction perturbatively and the Coulomb interaction exactly, giving the first controlled calculation of quasi-1D dephasing due to diffusive noise. Our results are relevant to the search for precursors to the many-body localization transition. They also link dephasing to the enhancement of the spin-triplet interaction near a metal-insulator transition, providing for the amplification of dephasing at low temperatures in spin SU(2)-symmetric quantum wires. The physics of massless, 2D Dirac fermions with a spatially modulated Dirac cone could have important applications in low-dimensional superconductivity and other Dirac materials. This is mathematically identical to a theory of massless fermions on a certain class of curved spacetime manifolds. We study these manifolds, which are dominated by curvature singularities, and find that isotropic and nematic fluctuations have profound yet different effects on the spacetime geometry. We present analytical results on geodesic geometry, give some exact solutions for some highly-symmetric toy models, and speculate about the role of induced one-dimensionality for such bound orbits in the physics of 2D dirty d-wave superconductivity.Item Electromagnetic Responses in Topological Superconductors, and Transport and Superconductivity in Dirty Quantum Critical Systems(2023-08-03) Wu, Tsz Chun; Foster, Matthew S.This thesis is devoted to two frontier research topics in condensed matter physics: (i) novel probes for topological superconductors, and (ii) transport and superconductivity in disordered quantum critical systems. In the first part, we present new electromagnetic probes to detect Majorana surface states in three dimensional topological superconductors (TSCs). We start by studying the temperature dependence of the magnetic penetration depth by incorporating the paramagnetic current due to the surface states. In addition to the bulk-dominated London response, we identify a $T^3$ power-law-in-temperature contribution from the surface, valid in the low-temperature limit. Our system is fully gapped in the bulk, and should be compared to bulk nodal superconductivity, which also exhibits power-law behavior. Power-law temperature dependence of the penetration depth can be one indicator of topological superconductivity. We then explore the optical absorption in a topological Weyl superconductor due to a novel surface-to-bulk mechanism, which we dub the topological anomalous skin effect. This occurs even in the absence of disorder for a single-band superconductor, and is facilitated by the topological splitting of the Hilbert space into bulk and chiral surface Majorana states. In the clean limit, the effect manifests as a characteristic absorption peak due to surface-bulk transitions. We also consider the effects of bulk disorder, using the Keldysh response theory. For weak disorder, the bulk response is reminiscent of the Mattis-Bardeen result for $s$-wave superconductors, with strongly suppressed spectral weight below twice the pairing energy, despite the presence of gapless Weyl points. For stronger disorder, the bulk response becomes more Drude-like and the $p$-wave features disappear. We show that the surface-bulk signal survives when combined with the bulk in the presence of weak disorder. The topological anomalous skin effect can therefore serve as a fingerprint for Weyl superconductivity. We also compute the Meissner response in the slab geometry, incorporating the effect of the surface states. In the second part, we explore the electric transport and superconductivity in a dirty quantum critical system. We first study the electrical transport of a two-dimensional non-Fermi liquid with disorder, and we determine the first quantum correction to the semiclassical dc conductivity due to quantum interference. We consider a system with $N$ flavors of fermions coupled to SU($N$) critical matrix bosons. %Motivated by the Sachdev–Ye–Kitaev (SYK) model, we employ the bilocal field formalism and derive a set of finite-temperature saddle-point equations governing the fermionic and bosonic self-energies in the large-$N$ limit. Interestingly, disorder smearing induces a marginal Fermi liquid (MFL) self-energy for the fermions. We next consider fluctuations around the saddle points and derive a MFL-Finkel'stein nonlinear sigma model. We find that the Altshuler-Aronov quantum conductance correction gives linear-$T$ resistivity that can dominate over the Drude result at low temperature. The strong temperature dependence of the quantum correction arises due to rapid relaxation of the mediating quantum-critical bosons. We verify that our calculations explicitly satisfy the Ward identity at the semiclassical and quantum levels. We then move on to study superconductivity of the disordered MFL. 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 \emph{enhance} $T_c$, violating Anderson's theorem. Both of our results establish that quantum interference persists in two-particle hydrodynamic modes, even when quasiparticles are subject to strong (Planckian) dissipation.Item Enhanced Thermoelectric Power in Graphene: Violation of the Mott Relation by Inelastic Scattering(American Physical Society, 2016) Ghahari, Fereshte; Xie, Hong-Yi; Taniguchi, Takashi; Watanabe, Kenji; Foster, Matthew S.; Kim, Philip; Rice Center for Quantum MaterialsWe report the enhancement of the thermoelectric power (TEP) in graphene with extremely low disorder. At high temperature we observe that the TEP is substantially larger than the prediction of the Mott relation, approaching to the hydrodynamic limit due to strong inelastic scattering among the charge carriers. However, closer to room temperature the inelastic carrierヨoptical-phonon scattering becomes more significant and limits the TEP below the hydrodynamic prediction. We support our observation by employing a Boltzmann theory incorporating disorder, electron interactions, and optical phonons.Item Helical Quantum Edge Gears in 2D Topological Insulators(American Physical Society, 2015) Chou, Yang-Zhi; Levchenko, Alex; Foster, Matthew S.; Rice Center for Quantum MaterialsWe show that two-terminal transport can measure the Luttinger liquid (LL) parameter K, in helical LLs at the edges of two-dimensional topological insulators (TIs) with Rashba spin-orbit coupling. We consider a Coulomb drag geometry with two coplanar TIs and short-ranged spin-flip interedge scattering. Current injected into one edge loop induces circulation in the second, which floats without leads. In the low-temperature (T→0) perfect drag regime, the conductance is (e2/h)(2K+1)/(K+1). At higher T, we predict a conductivity ∼T−4K+3. The conductivity for a single edge is also computed.Item Interaction-Mediated Surface-State Instability in Disordered Three-Dimensional Topological Superconductors with Spin SU(2) Symmetry(American Physical Society, 2012-12) Foster, Matthew S.; Yuzbashyan, Emil A.We show that arbitrarily weak interparticle interactions destabilize the surface states of 3D topological superconductors with spin SU(2) invariance (symmetry class CI) in the presence of nonmagnetic disorder. The conduit for the instability is disorder-induced wave function multifractality. We argue that timereversal symmetry breaks spontaneously at the surface, so that topologically protected states do not exist for this class. The interaction-stabilized surface phase is expected to exhibit ferromagnetic order, or to reside in an insulating plateau of the spin quantum Hall effect.Item Non-Markovian dephasing of disordered quasi-one-dimensional fermion systems(American Physical Society, 2020) Davis, Seth M.; Foster, Matthew S.; Rice Center for Quantum MaterialsAs a potential window on transitions out of the ergodic, many-body-delocalized phase, we study the dephasing of weakly disordered, quasi-one-dimensional fermion systems due to a diffusive, non-Markovian noise bath. Such a bath is self-generated by the fermions, via inelastic scattering mediated by short-ranged interactions. The ergodic phase can be defined by the nonzero dephasing rate, which makes transport incoherent and classical on long length scales. We calculate the dephasing of weak localization perturbatively through second order in the bath coupling, obtaining a short-time expansion. However, no well-defined dephasing rate can be identified, and the expansion breaks down at long times. This perturbative expansion is not stabilized by including a mean-field cooperon “mass” (decay rate), signaling a failure of the self-consistent Born approximation. We also consider a many-channel quantum wire where short-ranged, spin-exchange interactions coexist with screened Coulomb interactions. We calculate the dephasing rate, treating the short-ranged interactions perturbatively and the Coulomb interaction exactly. The latter provides a physical infrared regularization that stabilizes perturbation theory at long times, giving the first controlled calculation of quasi-1D dephasing due to diffusive noise. At first order in the diffusive bath coupling, we find an enhancement of the dephasing rate, but at second order, we find a rephasing contribution. Our results differ qualitatively from those obtained via self-consistent calculations commonly employed in higher dimensions. Our results are relevant in two different contexts: first, in the search for precursors to many-body localization in the ergodic phase of an isolated many-fermion system. Second, our results provide a mechanism for the enhancement of dephasing at low temperatures in spin SU(2)-symmetric quantum wires, beyond the Altshuler-Aronov-Khmelnitsky result. The enhancement is possible due to the amplification of the triplet-channel interaction strength and provides an additional physical mechanism that could contribute to the experimentally observed low-temperature saturation of the dephasing time.Item Quantum Dynamics, Localization, and Fractal-mediated Superconductivity and Magnetism(2023-04-18) Zhang, Xinghai; Foster, Matthew S.In this thesis, we consider two topics that involve strong spatial or temporal fluctuations in interacting quantum many-body systems. We first consider far-from equilibrium quantum hydrodynamics in light-driven helical edge states of a 2D topological insulator. We then consider the enhancement of superconducting and magnetic instabilities in fermion systems with random or structured inhomogeneity, driven by the nesting of fractal wave functions. In the first part, we study quantum quenches of helical edge liquids with spin-flip inelastic scattering. Counterpropagating charge packets in helical edges can be created by an ultrashort electric pulse applied across a 2D topological insulator. Localized “hot spots” that form due to scattering enable two types of strongly nonlinear wave dynamics. First, propagating packets develop self-focusing shock fronts. Second, colliding packets with opposite charge can exhibit near-perfect retroreflection, despite strong dissipation. This leads to an interaction-mediated frequency doubling that could be detected experimentally from emitted terahertz radiation. In the second part, we study the enhanced correlation effects in many-fermion systems induced by structured or random inhomogeneities. We consider the interplay of superconductivity and a wide spectrum of critical (multifractal) wave functions (“spectrum-wide quantum criticality,” SWQC) in the one-dimensional Aubry-Andr ́e and power-law random-banded matrix models (PRBMs) with attractive interactions, using self-consistent BCS theory. We find that SWQC survives the incorporation of attractive interactions at the Anderson localization transition, whereas the pairing amplitude is maximized near this transition in both models. Although increasing inhomogeneity always depletes the superfluid stiffness, we find that superconductivity is still controlled by the fractal-enhanced amplitude near the Anderson transition. Our results suggest that SWQC, recently discovered in two-dimensional topological surface-state and nodal superconductor models, can robustly enhance superconductivity. We also study the interplay of magnetic ordering and the spectrum-wide quantum critical wave functions in PRBMs with repulsive Hubbard interaction. We employ self-consistent Hartree-Fock numerics and analytical field theory calculations using a Keldysh Finkel’stein nonlinear sigma model. We find that weak interactions delocalize the system, while strong interaction localizes the system. Ferromagnetism sets in near the Anderson transition, where the ferromagnetic spin susceptibility is also shown to peak. This indicates that ferromagnetic ordering is enhanced by the fractal wave functions. Using the sigma model, we calculate the quantum corrections to the conductance and spin susceptibility. We find that the analytical and numerical results are mutually consistent.Item Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension(American Physical Society, 2018) Roy, Bitan; Foster, Matthew S.We compute the effects of generic short-range interactions on gapless electrons residing at the quantum critical point separating a two-dimensional Dirac semimetal and a symmetry-preserving band insulator. The electronic dispersion at this critical point is anisotropic (Ek=±√v2k2x+b2k2ny with n=2), which results in unconventional scaling of thermodynamic and transport quantities. Because of the vanishing density of states [ϱ(E)∼|E|1/n], this anisotropic semimetal (ASM) is stable against weak short-range interactions. However, for stronger interactions, the direct Dirac-semimetal to band-insulator transition can either (i) become a fluctuation-driven first-order transition (although unlikely in a particular microscopic model considered here, the anisotropic honeycomb lattice extended Hubbard model) or (ii) get avoided by an intervening broken-symmetry phase. We perform a controlled renormalization group analysis with the small parameter ε=1/n, augmented with a 1/n expansion (parametrically suppressing quantum fluctuations in the higher dimension) by perturbing away from the one-dimensional limit, realized by setting ε=0 and n→∞. We identify charge density wave (CDW), antiferromagnet (AFM), and singlet s-wave superconductivity as the three dominant candidates for broken symmetry. The onset of any such order at strong coupling (∼ε) takes place through a continuous quantum phase transition across an interacting multicritical point, where the ordered phase, band insulator, Dirac, and anisotropic semimetals meet. We also present the phase diagram of an extended Hubbard model for the ASM, obtained via the controlled deformation of its counterpart in one dimension. The latter displays spin-charge separation and instabilities to CDW, spin density wave, and Luther-Emery liquid phases at arbitrarily weak coupling. The spin density wave and Luther-Emery liquid phases deform into pseudospin SU(2)-symmetric quantum critical points separating the ASM from the AFM and superconducting orders, respectively. Our phase diagram shows an intriguing interplay among CDW, AFM, and s-wave paired states that can be germane for a uniaxially strained optical honeycomb lattice for ultracold fermion atoms, or the organic compound α−(BEDT−TTF)2I3.Item Quench-Induced Floquet Topologicalᅠp-Wave Superfluids(American Physical Society, 2014) Foster, Matthew S.; Gurarie, Victor; Dzero, Maxim; Yuzbashyan, Emil A.Ultracold atomic gases in two dimensions tuned close to a p-wave Feshbach resonance were expected to exhibit topological superfluidity, but these were found to be experimentally unstable. We show that one can induce a topological Floquet superfluid if weakly interacting atoms are brought suddenly close (“quenched”) to such a resonance, in the time before the instability kicks in. The resulting superfluid possesses Majorana edge modes, yet differs from a conventional Floquet system as it is not driven externally. Instead, the periodic modulation is self-generated by the dynamics.Item Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way(Elsevier, 2017) Liao, Yunxiang; Levchenko, Alex; Foster, Matthew S.; Rice Center for Quantum MaterialsWe derive the finite temperature Keldysh response theory for interacting fermions in the presence of quenched short-ranged disorder, as applicable to any of the 10 Altland–Zirnbauer classes in an Anderson delocalized phase with at least a U(1) continuous symmetry. In this formulation of the interacting Finkel’stein nonlinear sigma model, the statistics of one-body wave functions are encoded by the constrained matrix field, while physical correlations follow from the hydrodynamic density or spin response field, which decouples the interactions. Integrating out the matrix field first, we obtain weak (anti) localization and Altshuler–Aronov quantum conductance corrections from the hydrodynamic response function. This procedure automatically incorporates the correct infrared cutoff physics, and in particular gives the Altshuler–Aronov–Khmelnitsky (AAK) equations for dephasing of weak (anti)localization due to electron–electron collisions. We explicate the method by deriving known quantumcorrections in two dimensions for the symplectic metal class AII, as well as the spin-SU(2) invariant superconductor classes C and CI. We show that quantum conductance corrections due to the special modes at zero energy in nonstandard classes are automatically cut off by temperature, as previously expected, while the Wigner–Dyson class Cooperon modes that persist to all energies are cut by dephasing. We also show that for short-ranged interactions, the standard self-consistent solution for the dephasing rate is equivalent to a particular summation of diagrams via the self-consistent Born approximation. This should be compared to the corresponding AAK solution for long-ranged Coulomb interactions, which exploits the Markovian noise correlations induced by thermal fluctuations of the electromagnetic field. We discuss prospects for exploring the many-body localization transition as a dephasing catastrophe in short-range interacting models, as encountered by approaching from the ergodic side.Item Spectroscopic probes of isolated nonequilibrium quantum matter: Quantum quenches, Floquet states, and distribution functions(American Physical Society, 2015) Liao, Yunxiang; Foster, Matthew S.We investigate radio-frequency (rf) spectroscopy, metal-to-superconductor tunneling, and angle-resolved photoemission spectroscopy (ARPES) as probes of isolated out-of-equilibrium quantum systems, and examine the crucial role played by the nonequilibrium distribution function. As an example, we focus on the induced topological time-periodic (Floquet) phase in a two-dimensional p+ip superfluid, following an instantaneous quench of the coupling strength. The post-quench Cooper pairs occupy a linear combination of “ground” and “excited” Floquet states, with coefficients determined by the distribution function. While the Floquet band structure exhibits a single avoided crossing relative to the equilibrium case, the distribution function shows a population inversion of the Floquet bands at low energies. For a realization in ultracold atoms, these two features compensate, producing a bulk average rf signal that is well captured by a quasiequilibrium approximation. In particular, the rf spectrum shows a robust gap. The single crossing occurs because the quench-induced Floquet phase belongs to a particular class of soliton dynamics for the BCS equation. The population inversion is a consequence of this, and ensures the conservation of the pseudospin winding number. As a comparison, we compute the rf signal when only the lower Floquet band is occupied; in this case, the gap disappears for strong quenches. The tunneling signal in a solid-state realization is ignorant of the distribution function, and can show wildly different behaviors. We also examine rf, tunneling, and ARPES for weak quenches, such that the resulting topological steady state is characterized by a constant nonequilibrium order parameter. In a system with a boundary, tunneling reveals the Majorana edge states. However, the local rf signal due to the edge states is suppressed by a factor of the inverse system size, and is spatially deconfined throughout the bulk of the sample.Item Surface transport coefficients for three-dimensional topological superconductors(American Physical Society, 2015) Xie, Hong-Yi; Chou, Yang-Zhi; Foster, Matthew S.We argue that surface spin and thermal conductivities of three-dimensional topological superconductors are universal and topologically quantized at low temperature. For a bulk winding number ν, there are |ν| “colors” of surface Majorana fermions. Localization corrections to surface transport coefficients vanish due to time-reversal symmetry (TRS). We argue that Altshuler-Aronov interaction corrections vanish because TRS forbids color or spin Friedel oscillations. We confirm this within a perturbative expansion in the interactions, and to lowest order in a large-|ν| expansion. In both cases, we employ an asymptotically exact treatment of quenched disorder effects that exploits the chiral character unique to two-dimensional, time-reversal-invariant Majorana surface states.Item Topological Protection from Random Rashba Spin-Orbit Backscattering: Ballistic Transport in a Helical Luttinger Liquid(American Physical Society, 2016) Xie, Hong-Yi; Li, Heqiu; Chou, Yang-Zhi; Foster, Matthew S.; Rice Center for Quantum MaterialsThe combination of Rashba spin-orbit coupling and potential disorder induces a random current operator for the edge states of a 2D topological insulator. We prove that charge transport through such an edge is ballistic at any temperature, with or without Luttinger liquid interactions. The solution exploits a mapping to a spin 1/2 in a time-dependent field that preserves the projection along one randomly undulating component (integrable dynamics). Our result is exact and rules out random Rashba backscattering as a source of temperature-dependent transport, absent integrability-breaking terms.Item Topological protection, disorder, and interactions: Survival at the surface of three-dimensional topological superconductors(American Physical Society, 2014) Foster, Matthew S.; Xie, Hong-Yi; Chou, Yang-ZhiWe consider the interplay of disorder and interactions upon the gapless surface states of 3D topological superconductors. The combination of topology and superconducting order inverts the action of time-reversal symmetry, so that extrinsic time-reversal invariant surface perturbations appear only as “pseudomagnetic” fields (Abelian and non-Abelian vector potentials, which couple to spin and valley currents). The main effect of disorder is to induce multifractal scaling in surface state wave functions. These critically delocalized, yet strongly inhomogeneous states renormalize interaction matrix elements relative to the clean system. We compute the enhancement or suppression of interaction scaling dimensions due to the disorder exactly, using conformal field theory. We determine the conditions under which interactions remain irrelevant in the presence of disorder for symmetry classes AIII and DIII. In the limit of large topological winding numbers (many surface valleys), we show that the effective field theory takes the form of a Finkel’stein nonlinear sigma model, augmented by the Wess-Zumino-Novikov-Witten term. The sigma model incorporates interaction effects to all orders and provides a framework for a controlled perturbative expansion; the inverse spin or thermal conductance is the small parameter. For class DIII, we show that interactions are always irrelevant, while in class AIII, there is a finite window of stability, controlled by the disorder. Outside of this window, we identify new interaction-stabilized fixed points.Item Transport coefficients of graphene: Interplay of impurity scattering, Coulomb interaction, and optical phonons(American Physical Society, 2016) Xie, Hong-Yi; Foster, Matthew S.; Rice Center for Quantum MaterialsWe study the electric and thermal transport of the Dirac carriers in monolayer graphene using the Boltzmann-equation approach. Motivated by recent thermopower measurements [F. Ghahari, H.-Y. Xie, T. Taniguchi, K. Watanabe, M. S. Foster, and P. Kim, Phys. Rev. Lett. 116, 136802 (2016)], we consider the effects of quenched disorder, Coulomb interactions, and electron–optical-phonon scattering. Via an unbiased numerical solution to the Boltzmann equation we calculate the electrical conductivity, thermopower, and electronic component of the thermal conductivity, and discuss the validity of Mott's formula and of the Wiedemann-Franz law. An analytical solution for the disorder-only case shows that screened Coulomb impurity scattering, although elastic, violates the Wiedemann-Franz law even at low temperature. For the combination of carrier-carrier Coulomb and short-ranged impurity scattering, we observe the crossover from the interaction-limited (hydrodynamic) regime to the disorder-limited (Fermi-liquid) regime. In the former, the thermopower and the thermal conductivity follow the results anticipated by the relativistic hydrodynamic theory. On the other hand, we find that optical phonons become non-negligible at relatively low temperatures and that the induced electron thermopower violates Mott's formula. Combining all of these scattering mechanisms, we obtain the thermopower that quantitatively coincides with the experimental data.Item Tunneling spectroscopy of c-axis epitaxial cuprate junctions(American Physical Society, 2020) Zhou, Panpan; Chen, Liyang; Sochnikov, Ilya; Wu, Tsz Chun; Foster, Matthew S.; Bollinger, Anthony T.; He, Xi; Božović, Ivan; Natelson, DouglasAtomically precise epitaxial structures are unique systems for tunneling spectroscopy that minimize extrinsic effects of disorder. We present a systematic tunneling spectroscopy study, over a broad doping, temperature, and bias range, in epitaxial c-axis La2−xSrxCuO4/La2CuO4/La2−xSrxCuO4 heterostructures. The behavior of these superconductor/insulator/superconductor (SIS) devices is unusual. Down to 20 mK there is complete suppression of c-axis Josephson critical current with a barrier of only 2 nm of La2CuO4, and the zero-bias conductance remains at 20–30% of the normal-state conductance, implying a substantial population of in-gap states. Tunneling spectra show greatly suppressed coherence peaks. As the temperature is raised, the superconducting gap fills in rather than closing at Tc. For all doping levels, the spectra show an inelastic tunneling feature at ∼80 meV, suppressed as T exceeds Tc. These nominally simple epitaxial cuprate junctions deviate markedly from expectations based on the standard Bardeen-Cooper-Schrieffer theory.