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The geometric characteristics of Bloch wave functions play a crucial role in electronic transport properties. We show that the thermoelectric performance of materials is governed by the geometric structure of Bloch wave functions within the framework of the Boltzmann equation. The essential geometric notion is the Hilbert-Schmidt quantum distance, measuring the resemblance between two quantum states. We establish a geometric characterization of the scattering rate by extending the concept of quantum distance between two states in momentum space at a distance.Employing isotropic quadratic band touching semimetals, where one can concentrate on the role of quantum geometric effects other than the Berry curvature, we find that the response functions for electrical quantum transport and, therefore, the thermoelectric power factor can be succinctly expressed in terms of the maximum quantum distance, $d_\mathrm{max}$. Specifically, when $d_\mathrm{max}$ reaches one, the power factor doubles compared to the case with trivial geometry ($d_\mathrm{max}=0$). Our finding highlights the significance of quantum geometry in improving the performance of thermoelectric devices.

Quantum conductors attached to metallic reservoirs have been demonstrated to overcome the thermodynamic uncertainty relation (TUR), a trade-off relation between the amount of dissipation and the absence of charge and heat current fluctuations. Here, we report large TUR violations when superconducting reservoirs replace metallic ones. The coexistence of different transport processes, namely (multiple) Andreev reflection, where electrons and their retro-reflected holes create Cooper pairs, in addition to the normal quasiparticle transport is identified as the source for such TUR breakdowns. The large TUR violation is a remarkable advantage for building low dissipative and highly stable quantum thermal machines., Comment: 6 pages, 2 figures

Optimal engine performances are accomplished by quantum effects. Here we explore two routes towards ideal engines, namely (1) quantum systems that operate as hybrid machines being able to perform more than one useful task and (2) the suppression of fluctuations in doing such tasks. For classical devices, the absence of fluctuations is conditioned by a high entropy production as dictate the thermodynamic uncertainty relations. Here we generalize such relations for multiterminal conductors that operate as hybrid thermal machines. These relations are overcome in quantum conductors as we demonstrate for a double quantum dot contacted to normal metals and a reservoir being a generator of entangled Cooper pairs., Comment: 5 pages, 3 figures + Supplemental material

We propose dynamical protocols allowing for the engineered realization of topological surface states in isolation. Our approach builds on the concept of synthetic dimensions generated by driving systems with incommensurate frequencies. As a concrete example, we consider 3d topological surface states of a 4d quantum Hall insulator via a $(1+2_\mathrm{syn})$-dimensional protocol. We present first principle analytical calculations demonstrating that no supporting 4d bulk phase is required for a 3d topological surface phase. We back the analytical approach by numerical simulations and present a detailed blueprint for the realization of the synthetic surface phase with existing quantum linear optical network device technology. We then discuss generalizations, including a proposal for a quantum simulator of the $(1+1_\mathrm{syn})$ dimensional surface of the common 3d topological insulator., Comment: 17 pages (main text) + 10 pages (supplemental materials)

A dc (e.g. electric) field with commensurate lattice direction turns a single particle band structure in $d=3$ dimensions into an infinite set of equally spaced irreducible $(d-1)=2$-dimensional Wannier-Stark (WS) band structures that are spatially localized along the field direction. Particle transport is expected to be suppressed once the WS bands are gapped in energy. The topological character of the irreducible band structure leads to one-dimensional sets of boundary states which fill the energy gaps. As a result, eigenmodes are smoothly connected in energy and space and yield anomalous particle transport throughout the ladder. The number of chiral boundary modes can be tuned by the dc field strength and manifests through the distribution of dissipated energy and spatial motion, and the temperature dependence of angular momentum carried by particles., Comment: 10 pages, 6 figures

The anomalous Floquet Anderson insulator (AFAI) is a two dimensional periodically driven system in which static disorder stabilizes two topologically distinct phases in the thermodynamic limit. The presence of a unit-conducting chiral edge mode and the essential role of disorder induced localization are reminiscent of the integer quantum Hall (IQH) effect. At the same time, chirality in the AFAI is introduced via an orchestrated driving protocol, there is no magnetic field, no energy conservation, and no (Landau level) band structure. In this paper we show that in spite of these differences the AFAI topological phase transition is in the IQH universality class. We do so by mapping the system onto an effective theory describing phase coherent transport in the system at large length scales. Unlike with other disordered systems, the form of this theory is almost fully determined by symmetry and topological consistency criteria, and can even be guessed without calculation. (However, we back this expectation by a first principle derivation.) Its equivalence to the Pruisken theory of the IQH demonstrates the above equivalence. At the same time it makes predictions on the emergent quantization of transport coefficients, and the delocalization of bulk states at quantum criticality which we test against numerical simulations., Comment: 15 pages, 5 figures

The discovery of two-dimensional gapless Dirac fermions in graphene and topological insulators (TI) has sparked extensive ongoing research toward applications of their unique electronic properties. The gapless surface states in three-dimensional insulators indicate a distinct topological phase of matter with a non-trivial Z2 invariant that can be verified by angle-resolved photoemission spectroscopy or magnetoresistance quantum oscillation. In TI nanowires, the gapless surface states exhibit Aharonov-Bohm (AB) oscillations in conductance, with this quantum interference effect accompanying a change in the number of transverse one-dimensional modes in transport. Thus, while the density of states (DOS) of such nanowires is expected to show such AB oscillation, this effect has yet to be observed. Here, we adopt nanomechanical measurements that reveal AB oscillations in the DOS of a topological insulator. The TI nanowire under study is an electromechanical resonator embedded in an electrical circuit, and quantum capacitance effects from DOS oscillation modulate the circuit capacitance thereby altering the spring constant to generate mechanical resonant frequency shifts. Detection of the quantum capacitance effects from surface-state DOS is facilitated by the small effective capacitances and high quality factors of nanomechanical resonators, and as such the present technique could be extended to study diverse quantum materials at nanoscale., Comment: 15+16 pages, 4+11 figures

Spin current plays a central role in spintronics. In particular, finding more efficient ways to generate spin current has been an important issue and studied actively. For example, representative methods of spin current generation include spin polarized current injections from ferromagnetic metals, spin Hall effect, and spin battery. Here we theoretically propose a new mechanism of spin current generation based on nonlinear phenomena. By using Boltzmann transport theory, we show that a simple application of the electric field $\bf{E}$ induces spin current proportional to $\bf{E^2}$ in noncentrosymmetric spin-orbit coupled systems. We demonstrate that the nonlinear spin current of the proposed mechanism is supported in the surface state of three-dimensional topological insulators and two-dimensional semiconductors with the Rashba and/or Dresselhaus interaction. In the latter case, the angular dependence of the nonlinear spin current can be manipulated by the direction of the electric field and by the ratio of the Rashba and Dresselhaus interactions. We find that the magnitude of the spin current largely exceeds those in the previous methods for a reasonable magnitude of the electric field. Furthermore, we show that application of AC electric fields (e.g. terahertz light) leads to the rectifying effect of the spin current where DC spin current is generated. These findings will pave a new route to manipulate the spin current in noncentrosymmetric crystals., Comment: 10 pages, 4 figures

We investigate the quantum phase transition of the Su-Schrieffer-Heeger (SSH) model by inspecting the two-site entanglements in the ground state. It is shown that the topological phase transition of the SSH model is signified by a nonanalyticity of local entanglement, which becomes discontinuous for finite even system sizes, and that this nonanalyticity has a topological origin. Such a peculiar singularity has a universal nature in one-dimensional topological phase transitions of noninteracting fermions. We make this clearer by pointing out that an analogous quantity in the Kitaev chain exhibiting the identical nonanalyticity is the local electron density. As a byproduct, we show that there exists a different type of phase transition, whereby the pattern of the two-site entanglements undergoes a sudden change. This transition is characterised solely by quantum information theory and does not accompany the closure of the spectral gap. We analyse the scaling behaviours of the entanglement in the vicinities of the transition points.

The generation of photocurrent in condensed matter is of main interest for photovoltaic and optoelectronic applications. Shift current, a nonlinear photoresponse, has attracted recent intensive attention as a dominant player of bulk photovoltaic effect in ferroelectric materials. In three dimensional topological insulators $\text{Bi}_2\text{X}_3$ (X: Te, Se), we find that Dirac surface states with a hexagonal warping term carry shift current by linearly polarized light. In addition, shift spin-current is introduced with the time-reversal symmetry breaking perturbation. The estimate for the magnitudes of the shift charge- and spin-currents are 0.13$I_0$ and 0.21$I_0$(nA/m) with the intensity of light $I_0$ measured in $(\text{W}/\text{m}^2)$, respectively, which can offer a useful method to generate these currents efficiently., Comment: 12 pages including supplementary information, 2 figures

The effect of surface disorder on electronic systems is particularly interesting for topological phases with surface and edge states. Using exact diagonalization, it has been demonstrated that the surface states of a 3D topological insulator survive strong surface disorder, and simply get pushed to a clean part of the bulk. Here we explore a new method which analytically eliminates the clean bulk, and reduces a $D$-dimensional problem to a Hamiltonian-diagonalization problem within the $(D-1)$-dimensional disordered surface. This dramatic reduction in complexity allows the analysis of significantly bigger systems than is possible with exact diagonalization. We use our method to analyze a 2D topological spin-Hall insulator with non-magnetic and magnetic edge impurities, and we calculate the probability density (or local density of states) of the zero-energy eigenstates as a function of edge-parallel momentum and layer index. Our analysis reveals that the system size needed to reach behavior in the thermodynamic limit increases with disorder. We also compute the edge conductance as a function of disorder strength, and chart a lower bound for the length scale marking the crossover to the thermodynamic limit., Comment: 12 pages, 9 figures