Confining two dimensional Dirac fermions on the surface of topological insulators has remained an outstanding conceptual challenge. Here we show that Dirac fermion confinement is achievable in topological crystalline insulators (TCI), which host mult
iple surface Dirac cones depending on the surface termination and the symmetries it preserves. This confinement is most dramatically reflected in the flux dependence of these Dirac states in the nanowire geometry, where different facets connect to form a closed surface. Using SnTe as a case study, we show how wires with all four facets of the <100> type display pronounced and unique Aharonov-Bohm oscillations, while nanowires with the four facets of the <110> type such oscillations are absent due to a strong confinement of the Dirac states to each facet separately. Our results place TCI nanowires as versatile platform for confining and manipulating Dirac surface states.
While nondissipative hydrodynamics in two-dimensional electron systems has been extensively studied, the role of nondissipative viscosity in three-dimensional transport has remained elusive. In this work, we address this question by studying the nond
issipative viscoelastic response of three dimensional crystals. We show that for systems with tetrahedral symmetries, there exist new, intrinsically three-dimensional Hall viscosity coefficients that cannot be obtained via a reduction to a quasi-two-dimensional system. To study these coefficients, we specialize to a theoretically and experimentally motivated tight binding model for a chiral magentic metal in (magnetic) space group [(M)SG] $P2_13$ (No.~198$.$9), a nonpolar group of recent experimental interest which hosts both chiral magnets and topological semimetals. Using the Kubo formula for viscosity, we compute the nondissipative Hall viscosity for the spin-1 fermion in two ways. First we use an electron-phonon coupling ansatz to derive the phonon strain coupling and associated phonon Hall viscosity. Second we use a momentum continuity equation to derive the viscosity corresponding to the conserved momentum density. We conclude by discussing the implication of our results for hydrodynamic transport in three-dimensional magnetic metals, and discuss some candidate materials in which these effects may be observed.
Calculating the observables of a Hamiltonian requires taking matrix elements of operators in the eigenstate basis. Since eigenstates are only defined up to arbitrary phases that depend on Hamiltonian parameters, analytical expressions for observables
are often difficult to simplify. In this work, we show how for small Hilbert space dimension N all observables can be expressed in terms of the Hamiltonian and its eigenvalues using the properties of the SU(N) algebra, and we derive explicit expressions for N=2,3,4. Then we present multiple applications specializing to the case of Bloch electrons in crystals, including the computation of Berry curvature, quantum metric and orbital moment, as well as a more complex observable in non-linear response, the linear photogalvanic effect (LPGE). As a physical example we consider multiband Hamiltonians with nodal degeneracies to show first how constraints between these observables are relaxed when going from two to three-band models, and second how quadratic dispersion can lead to constant LPGE at small frequencies.
The quantum Hall effect in curved space has been the subject of many theoretical investigations in the past, but devising a physical system to observe this effect is hard. Many works have indicated that electronic excitations in strained graphene rea
lize Dirac fermions in curved space in the presence of a background pseudo-gauge field, providing an ideal playground for this. However, the absence of a direct matching between a numerical, strained tight-binding calculation of an observable and the corresponding curved space prediction has hindered realistic predictions. In this work, we provide this matching by deriving the low-energy Hamiltonian from the tight-binding model analytically to second order in the strain and mapping it to the curved-space Dirac equation. Using a strain profile that produces a constant pseudo-magnetic field and a constant curvature, we compute the Landau level spectrum with real-space numerical tight-binding calculations and find excellent agreement with the prediction of the quantum Hall effect in curved space. We conclude discussing experimental schemes for measuring this effect.
We appraise the importance of position matrix elements in tight-binding calculations of linear and nonlinear optical properties of acentric materials. A common approximation consists of discarding off-diagonal matrix elements of the position operator
$hat{boldsymbol{r}}$. Such matrix elements can be naturally incorporated into the tight-binding formalism through the so-called Wannier-interpolation scheme, which we adopt in this work. Using monolayer BC$_2$N as case study, we find that the shift photocurrent is very sensitive to off-diagonal position matrix elements, which is confirmed in two separate ways: by explicitly evaluating their contribution in textit{ab initio} calculations, and by means of a $boldsymbol{k}cdotboldsymbol{p}$ model that implicitly assumes the $hat{boldsymbol{r}}$-diagonal approximation. Our results indicate that the error incurred by truncating the position matrix is particularly severe for two-band models, where even the linear dielectric function is strongly affected.
Structurally chiral materials hosting multifold fermions with large topological number have attracted considerable attention because of their naturally long surface Fermi arcs and bulk quantized circular photogalvanic effect (CPGE). Multifold fermion
s only appear in metallic states, and therefore, most studies so far have only focused on the semimetals in compounds with chiral crystal structures. In this work, we show that the structurally chiral topological trivial insulators are also exotic states, which is interesting from the application point of view, owing to their natural advantage to host a large bulk photovoltaic effect in the visible wavelength region. In the last decades, the shift current in the visible wavelength region was limited to be 10 uA/V2 . By scanning the insulators with chiral structure, we found a class of compounds with photoconductivity ranging from 20 to 80 uA/V2 , which is approximately one order of magnitude larger than that reported in other real materials. This work illustrates that the compounds with chiral structure can host both quantum CPGE and a strong shift current in the second order optical response. Moreover, this work offers a good platform for the study of the shift current and its future application by putting the focus on insulator with chiral lattices, so far overlooked in photovoltaic technologies.
When two lasers are applied to a non-centrosymmetric material, light can be generated at the difference of the incoming frequencies $Deltaomega$, a phenomenon known as difference frequency generation (DFG), well characterized in semiconductors. In th
is work, we derive a general expression for DFG in metals, which we use to show that the DFG in chiral topological semimetals under circular polarized light is quantized in units of $e^3/h^2$ and independent of material parameters, including the scattering time $tau$, when $Deltaomega gg tau^{-1}$. In this regime, DFG provides a simpler alternative to measure a quantized response in metals compared to previous proposals based on single frequency experiments. Our general derivation unmasks, in addition, a free-carrier contribution to the circular DFG beyond the semiclassical one. This contribution can be written as a Fermi surface integral, features strong frequency dependence, and oscillates with a $pi/2$ shift with respect to the quantized contribution. We make predictions for the circular DFG of chiral and non-chiral materials using generic effective models, and ab-initio calculations for TaAs and RhSi. Our work provides a complete picture of the DFG in the length gauge approach, in the clean, non-interacting limit, and highlights a plausible experiment to measure topologically quantizated photocurrents in metals.
Among the different platforms to engineer Majorana fermions in one-dimensional topological superconductors, topological insulator nanowires remain a promising option. Threading an odd number of flux quanta through these wires induces an odd number of
surface channels, which can then be gapped with proximity induced pairing. Because of the flux and depending on energetics, the phase of this surface pairing may or may not wind around the wire in the form of a vortex. Here we show that for wires with discrete rotational symmetry, this vortex is necessary to produce a fully gapped topological superconductor with localized Majorana end states. Without a vortex the proximitized wire remains gapless, and it is only if the symmetry is broken by disorder that a gap develops, which is much smaller than the one obtained with a vortex. These results are explained with the help of a continuum model and validated numerically with a tight binding model, and highlight the benefit of a vortex for reliable use of Majorana fermions in this platform.
Lattice translation symmetry gives rise to a large class of weak topological insulators (TIs), characterized by translation-protected gapless surface states and dislocation bound states. In this work we show that space group symmetries lead to constr
aints on the weak topological indices that define these phases. In particular we show that screw rotation symmetry enforces the Hall conductivity along the screw axis to be quantized in multiples of the screw rank, which generally applies to interacting systems. We further show that certain 3D weak indices associated with quantum spin Hall effects (class AII) are forbidden by the Bravais-lattice and by glide or even-fold screw symmetries. These results put a strong constraints on candidates of weak TIs in the experimental and numerical search for topological materials, based on the crystal structure alone.
While the basic principles and limitations of conventional solar cells are well understood, relatively little attention has gone toward maximizing the potential efficiency of photovoltaic devices based on shift currents. In this work, we outline simp
le design principles for the optimization of shift currents for frequencies near the band gap, derived from the analysis of a general effective model. The use of a novel sum rule allows us to express the band edge shift current in terms of a few model parameters and to show it depends explicitly on wavefunctions via Berry connections in addition to standard band structure. We use our approach to identify two new classes of shift current photovoltaics, ferroelectric polymer films and single-layer orthorhombic monochalcogenides such as GeS. We introduce tight-binding models for these systems, and show that they exhibit the largest shift current responsivities at the band edge reported so far. Moreover, exploring the parameter space of these models we find photoresponsivities that can exceed $100$ mA/W. Our results show how the study of the shift current via effective models allows one to improve the possible efficiency of devices based on this mechanism and better grasp their potential to compete with conventional solar cells.
