Browsing by Author "Chou, Yang-Zhi"
Now showing 1 - 6 of 6
Results Per Page
Sort Options
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 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 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 Topological Solid State Materials with Quenched Disorder: Transport, Spectral Correlations, and Topological Protection(2016-06-13) Chou, Yang-Zhi; Foster, Matthew SOne of the defining characteristics of topological phases is the existence of edge and surface states at the boundaries of 2D and 3D topological materials. These edge states and surface states are ``topologically protected'', and evade Anderson localization. At the edge of a 2D topological insulator (TI), gapless edge states form a spin-momentum-locked 1D ``helical'' liquid. Rashba spin orbit coupling (RSOC) is often present as long as the inversion symmetry in the material is broken. RSOC enables unconventional impurity and inelastic electron-electron backscatterings. We derive the finite temperature conductivity correction from the most relevant inelastic interaction. At zero temperature, we show that the TI edge remains ballistic even with the combination of RSOC and non-magnetic impurities. In addition, strong inter-particle interactions are allowed for two proximate TI edges due to the RSOC. Such interactions are strictly forbidden for ideal quantum spin Hall insulator edges in the absence of RSOC. We identify a novel low-temperature transport regime which involves the interlocking of the two TI edges, which co-rotate as ``quantum gears.'' The Luttinger liquid parameter can be measured in the locking regime from a two-terminal conductance measurement. With respect to the 3D topological phases, we study the universal properties of the surfaces of the 3D topological superconductors (TSCs). We demonstrate the Chalker scaling and random matrix statistics in the surface states with weak and strong disorder. We also confirm numerically that the wavefunction multifractality and density of states in certain surface states follow the predictions of conformal field theory, rather than the strong disorder dominated Gade-Wegner fixed point. The multivalley surface state (spin or heat) transport is also investigated. We show that Altshuler-Aronov conductivity corrections always vanish on the multivalley TSC surfaces. We predict universal surface thermal and (if conserved) surface spin conductivities. The novel transport behaviors of the TIs and TSCs should provide new insights for characterizing new topological materials in the future experiments.