arXiv subjects

Liang Fu

Publications and source records attributed to Liang Fu.

At least 289 records · Page 16Linked to original sources

arXiv2014

Dirac mass generation from crystal symmetry breaking on the surfaces of topological crystalline insulators

The tunability of topological surface states (SS) and controllable opening of the Dirac gap are of fundamental and practical interest in the field of topological materials. In topological crystalline insulators (TCIs), a spontaneously generated Dirac gap was recently observed, which was ascribed to broken cubic crystal symmetry. However, this structural distortion has not been directly observed so far, and the microscopic mechanism of Dirac gap opening via crystal symmetry breaking remains elusive. In this work, we present scanning tunneling microscopy (STM) measurements of a TCI Pb$_{1-x}$Sn$_x$Se for a wide range of alloy compositions spanning the topological and non-topological regimes. STM topographies directly reveal a symmetry-breaking distortion on the surface, which imparts mass to the otherwise massless Dirac electrons - a mechanism analogous to the long sought-after Higgs mechanism in particle physics. Remarkably, our measurements show that the Dirac gap scales with alloy composition, while the magnitude of the distortion remains nearly constant. Based on theoretical calculations, we find the Dirac mass is controlled by the composition-dependent SS penetration depth, which determines the weight of SS in the distorted region that is confined to the surface. Finally, we discover the existence of SS in the non-topological regime, which have the characteristics of gapped, double-branched Dirac fermions.

cond-mat.mes-hall↗

arXiv2014

Topological Crystalline Insulators and Dirac Octets in Anti-perovskites

We predict a new class of topological crystalline insulators (TCI) in the anti-perovskite material family with the chemical formula A$_3$BX. Here the nontrivial topology arises from band inversion between two $J=3/2$ quartets, which is described by a generalized Dirac equation for a "Dirac octet". Our work suggests that anti-perovskites are a promising new venue for exploring the cooperative interplay between band topology, crystal symmetry and electron correlation.

cond-mat.str-el↗

arXiv2014

Strain-induced partially flat band, helical snake states, and interface superconductivity in topological crystalline insulators

Topological crystalline insulators in IV-VI compounds host novel topological surface states consisting of multi-valley massless Dirac fermions at low energy. Here we show that strain generically acts as an effective gauge field on these Dirac fermions and creates pseudo-Landau orbitals without breaking time-reversal symmetry. We predict the realization of this phenomenon in IV-VI semiconductor heterostructures, due to a naturally occurring misfit dislocation array at the interface that produces a periodically varying strain field. Remarkably, the zero-energy Landau orbitals form a flat band in the vicinity of the Dirac point, and coexist with a network of snake states at higher energy. We propose that the high density of states of this flat band gives rise to interface superconductivity observed in IV-VI semiconductor multilayers at unusually high temperatures, with non-BCS behavior. Our work demonstrates a new route to altering macroscopic electronic properties to achieve a partially flat band, and paves the way for realizing novel correlated states of matter.

cond-mat.supr-con↗

arXiv2014

Valley-selective optical Stark effect in monolayer WS2

Breaking space-time symmetries in two-dimensional crystals (2D) can dramatically influence their macroscopic electronic properties. Monolayer transition-metal dichalcogenides (TMDs) are prime examples where the intrinsically broken crystal inversion symmetry permits the generation of valley-selective electron populations, even though the two valleys are energetically degenerate, locked by time-reversal symmetry. Lifting the valley degeneracy in these materials is of great interest because it would allow for valley-specific band engineering and offer additional control in valleytronic applications. While applying a magnetic field should in principle accomplish this task, experiments to date have observed no valley-selective energy level shifts in fields accessible in the laboratory. Here we show the first direct evidence of lifted valley degeneracy in the monolayer TMD WS2. By applying intense circularly polarized light, which breaks time-reversal symmetry, we demonstrate that the exciton level in each valley can be selectively tuned by as much as 18 meV via the optical Stark effect. These results offer a novel way to control valley degree of freedom, and may provide a means to realize new valley-selective Floquet topological phases in 2D TMDs.

cond-mat.mes-hall↗

arXiv2014

Tensor Network Implementation of Bulk Entanglement Spectrum

Many topologically nontrivial states of matter possess gapless degrees of freedom on the boundary, and when these boundary states delocalize into the bulk, a phase transition occurs and the system becomes topologically trivial. We show that tensor networks provide a natural framework for analyzing such topological phase transitions in terms of the boundary degrees of freedom which mediate it. To do so, we make use of a correspondence between a topologically nontrivial ground state and its phase transition to a trivial phase established in [1]. This involved computing the bulk entanglement spectrum (BES) of the ground state, upon tracing out an extensive subsystem. This work implements BES via tensor network representations of ground states. In this framework, the universality class of the quantum critical entanglement Hamiltonian in d spatial dimensions is either derived analytically or mapped to a classical statistical model in d + 1 dimensions, which can be studied using Monte Carlo or tensor renormalization group methods. As an example, we analytically derive the universality classes of topological phase transitions from the spin-1 chain Haldane phase and demonstrate that the AKLT wavefunction (and its generalizations) remarkably contains critical six-vertex (and in general eight-vertex) models within it.

cond-mat.str-el↗

arXiv2014

Quantum Spin Hall Effect and Topological Field Effect Transistor in Two-Dimensional Transition Metal Dichalcogenides

We report a new class of large-gap quantum spin Hall insulators in two-dimensional transition metal dichalcogenides, namely, MX$_2$ with M=(Mo, W) and X=(S, Se, and Te), whose topological electronic properties are highly tunable by external electric field. We propose a novel topological field effect transistor made of these atomic layer materials and their van der Waals heterostructures. Our device exhibits parametrically enhanced charge-spin conductance through topologically protected transport channels, and can be rapidly switched off by electric field through topological phase transition instead of carrier depletion. Our work provides a practical material platform and device architecture for topological quantum electronics.

cond-mat.mes-hall↗

arXiv2014

Symmetry breaking and Landau quantization in topological crystalline insulators

In the recently discovered topological crystalline insulators SnTe and Pb_{1-x}Sn_{x}(Te,Se), crystal symmetry and electronic topology intertwine to create topological surface states with many interesting features including Lifshitz transition, Van-Hove singularity and fermion mass generation. These surface states are protected by mirror symmetry with respect to the (110) plane. In this work we present a comprehensive study of the effects of different mirror-symmetry-breaking perturbations on the (001) surface band structure. Pristine (001) surface states have four branches of Dirac fermions at low-energy. We show that ferroelectric-type structural distortion generates a mass and gaps out some or all of these Dirac points, while strain shifts Dirac points in the Brillouin zone. An in-plane magnetic field leaves surface state gapless, but introduces asymmetry between Dirac points. Finally, an out-of-plane magnetic field leads to discrete Landau levels. We show that the Landau level spectrum has an unusual pattern of degeneracy and interesting features due to the unique underlying band structure. This suggests that Landau level spectroscopy can detect and distinguish between different mechanisms of symmetry breaking in topological crystalline insulators.

cond-mat.mes-hall↗

arXiv2014

Bulk Entanglement Spectrum Reveals Quantum Criticality within a Topological State

A quantum phase transition is usually achieved by tuning physical parameters in a Hamiltonian at zero temperature. Here, we demonstrate that the ground state of a topological phase itself encodes critical properties of its transition to a trivial phase. To extract this information, we introduce a partition of the system into two subsystems both of which extend throughout the bulk in all directions. The resulting bulk entanglement spectrum has a low-lying part that resembles the excitation spectrum of a bulk Hamiltonian, which allows us to probe a topological phase transition from a single wavefunction by tuning either the geometry of the partition or the entanglement temperature. As an example, this remarkable correspondence between topological phase transition and entanglement criticality is rigorously established for integer quantum Hall states.

cond-mat.str-el↗

arXiv2014

Topological Crystalline Insulator Nanomembrane with Strain-Tunable Band Gap

The ability to fine-tune band gap and band inversion in topological materials is highly desirable for the development of novel functional devices. Here we propose that the electronic properties of a free-standing nanomembrane of topological crystalline insulator (TCI) SnTe and Pb$_{1-x}$Sn$_x$(Se,Te) are highly tunable by engineering elastic strain and controlling membrane thickness, resulting in tunable band gap and giant piezoconductivity. Membrane thickness governs the hybridization of topological electronic states on opposite surfaces, while elastic strain can further modulate the hybridization strength by controlling the penetration length of surface states. We propose a frequency-resolved infrared photodetector using force-concentration induced inhomogeneous elastic strain in TCI nanomembrane with spatially varying width. The predicted tunable band gap accompanied by strong spin-textured electronic states will open up new avenues for fabricating piezoresistive devices, thermoelectrics, infrared detectors and energy-efficient electronic and optoelectronic devices based on TCI nanomembrane.

cond-mat.mtrl-sci↗

arXiv2014

Loops, sign structures and emergent Fermi statistics in three-dimensional quantum dimer models

We introduce and study three-dimensional quantum dimer models with positive resonance terms. We demonstrate that their ground state wave functions exhibit a nonlocal sign structure that can be exactly formulated in terms of loops, and as a direct consequence, monomer excitations obey Fermi statistics. The sign structure and Fermi statistics in these "signful" quantum dimer models can be naturally described by a parton construction, which becomes exact at the solvable point.

cond-mat.str-el↗

arXiv2014

Experimental observation of Dirac-like surface states and topological phase transition in Pb$_{1-x}$Sn$_x$Te(111) films

The surface of a topological crystalline insulator (TCI) carries an even number of Dirac cones protected by crystalline symmetry. We epitaxially grew high quality Pb$_{1-x}$Sn$_x$Te(111) films and investigated the TCI phase by in-situ angle-resolved photoemission spectroscopy. Pb$_{1-x}$Sn$_x$Te(111) films undergo a topological phase transition from trivial insulator to TCI via increasing the Sn/Pb ratio, accompanied by a crossover from n-type to p-type doping. In addition, a hybridization gap is opened in the surface states when the thickness of film is reduced to the two-dimensional limit. The work demonstrates an approach to manipulating the topological properties of TCI, which is of importance for future fundamental research and applications based on TCI.

cond-mat.mtrl-sci↗

arXiv2013

Mapping the unconventional orbital texture in topological crystalline insulators

The newly discovered topological crystalline insulators (TCIs) harbor a complex band structure involving multiple Dirac cones. These materials are potentially highly tunable by external electric field, temperature or strain and could find future applications in field-effect transistors, photodetectors, and nano-mechanical systems. Theoretically, it has been predicted that different Dirac cones, offset in energy and momentum-space, might harbor vastly different orbital character, a unique property which if experimentally realized, would present an ideal platform for accomplishing new spintronic devices. However, the orbital texture of the Dirac cones, which is of immense importance in determining a variety of materials properties, still remains elusive in TCIs. Here, we unveil the orbital texture in a prototypical TCI Pb$_{1-x}$Sn$_x$Se. By using Fourier-transform (FT) scanning tunneling spectroscopy (STS) we measure the interference patterns produced by the scattering of surface state electrons. We discover that the intensity and energy dependences of FTs show distinct characteristics, which can directly be attributed to orbital effects. Our experiments reveal the complex band topology involving two Lifshitz transitions and establish the orbital nature of the Dirac bands in this new class of topological materials, which could provide a different pathway towards future quantum applications.

cond-mat.str-el↗

arXiv2013

Spin-filtered Edge States with an Electrically Tunable Gap in a Two-Dimensional Topological Crystalline Insulator

Three-dimensional topological crystalline insulators were recently predicted and observed in the SnTe class of IV-VI semiconductors, which host metallic surface states protected by crystal symmetries. In this work, we study thin films of these materials and expose their potential for device applications. We demonstrate that thin films of SnTe and Pb(1-x)Sn(x)Se(Te) grown along the (001) direction are topologically nontrivial in a wide range of film thickness and carry conducting spin-filtered edge states that are protected by the (001) mirror symmetry via a topological invariant. Application of an electric field perpendicular to the film will break the mirror symmetry and generate a band gap in these edge states. This functionality motivates us to propose a novel topological transistor device, in which charge and spin transport are maximally entangled and simultaneously controlled by an electric field. The high on/off operation speed and coupling of spin and charge in such a device may lead to electronic and spintronic applications for topological crystalline insulators.

cond-mat.mes-hall↗

arXiv2013

Weak Topological Insulators in PbTe/SnTe Superlattices

It is desirable to realize topological phases in artificial structures by engineering electronic band structures. In this paper, we investigate $(PbTe)_m(SnTe)_{2n-m}$ superlattices along [001] direction and find a robust weak topological insulator phase for a large variety of layer numbers m and 2n-m. We confirm this topologically non-trivial phase by calculating Z2 topological invariants and topological surface states based on the first-principles calculations. We show that the folding of Brillouin zone due to the superlattice structure plays an essential role in inducing topologically non-trivial phases in this system. This mechanism can be generalized to other systems in which band inversion occurs at multiple momenta, and gives us a brand-new way to engineer topological materials in artificial structures.

cond-mat.mtrl-sci↗

arXiv2013

Inducing time reversal invariant topological superconductivity and fermion parity pumping in quantum wires

We propose a setup to realize time-reversal invariant topological superconductors in quantum wires, proximity coupled to conventional superconductors. We consider a model of quantum wire with strong spin-orbit coupling and proximity coupling to two s-wave superconductors. When the relative phase between the two superconductors is $ϕ=π$ a Kramers' pair of Majorana zero modes appears at each edge of the wire. We study the robustness of the phase in presence of both time-reversal invariant and time-reversal breaking perturbations. In addition, we show that the system forms a natural realization of a fermion parity pump, switching the local fermion parity of both edges when the relative phase between the superconductors is changed adiabatically by $2π$.

cond-mat.str-el↗

arXiv2013

Observation of Dirac node formation and mass acquisition in a topological crystalline insulator

In the recently discovered topological crystalline insulators (TCIs), topology and crystal symmetry intertwine to create surface states with a unique set of characteristics. Among the theoretical predictions for TCIs is the possibility of imparting mass to the massless Dirac fermions by breaking crystal symmetry, as well as a Lifshitz transition with a change of Fermi surface topology. Here we report high resolution scanning tunneling microscopy studies of a TCI, Pb1-xSnxSe. We demonstrate the formation of zero mass Dirac fermions protected by crystal symmetry and the mechanism of mass generation via symmetry breaking, which constitute the defining characteristics of TCIs. In addition, we show two distinct regimes of fermiology separated by a Van-Hove singularity at the Lifshitz transition point. Our work paves the way for engineering the Dirac band gap and realizing interaction-driven topological quantum phenomena in TCIs.

cond-mat.mes-hall↗

arXiv2013

Surface States of Topological Crystalline Insulators in IV-VI Semiconductors

Topological crystalline insulators (TCI) are new topological phases of matter protected by crystal symmetry of solids. Recently, the first realization of TCI has been predicted and observed in IV-VI semiconductor SnTe and related alloys Pb_{1-x}Sn_{x}(Te, Se). By combining k.p theory and band structure calculation, we present a unified approach to study topological surface states on various crystal surfaces of TCI in IV-VI semiconductors. We explicitly derive k.p Hamiltonian for topological surface states from electronic structure of the bulk, thereby providing a microscopic understanding of bulk-boundary correspondence in TCI. Depending on the surface orientation, we find two types of surface states with qualitatively different properties. In particular, we predict that (111) surface states consist of four Dirac cones centered at time-reversal-invariant momenta Γ and M, while (110) surface states consist of Dirac cones at non-time-reversal-invariant momenta, similar to (001). Moreover, both (001) and (110) surface states exhibit a Lifshitz transition as a function of Fermi energy, which is accompanied by a Van-Hove singularity in density of states arising from saddle points in the band structure.

cond-mat.mtrl-sci↗

arXiv2013

Anomalous Supercurrent from Majorana States in Topological Insulator Josephson Junctions

We propose a Josephson junction setup based on a topological insulator (TI) thin film to detect Majorana states, which exploits the unique helical and extended nature of the TI surface state. When the magnetic flux through the junction is close to an integer number of flux quanta, Majorana states, present on both surfaces of the film, give rise to a narrow peak-dip structure in the current- phase relation by hybridizing at the edge of the junction. Moreover, the maximal Majorana-state contribution to Josephson current takes a (nearly) universal value, approximately equal to the supercurrent capacity of a single quantum-channel. These features provide a characteristic signature of Majorana states based entirely on supercurrent.

cond-mat.mes-hall↗