1
|
Elenewski JE, Wójtowicz G, Rams MM, Zwolak M. Performance of reservoir discretizations in quantum transport simulations. J Chem Phys 2021; 155:124117. [PMID: 34598565 DOI: 10.1063/5.0065799] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
Quantum transport simulations often use explicit, yet finite, electronic reservoirs. These should converge to the correct continuum limit, albeit with a trade-off between discretization and computational cost. Here, we study this interplay for extended reservoir simulations, where relaxation maintains a bias or temperature drop across the system. Our analysis begins in the non-interacting limit, where we parameterize different discretizations to compare them on an even footing. For many-body systems, we develop a method to estimate the relaxation that best approximates the continuum by controlling virtual transitions in Kramers turnover for the current. While some discretizations are more efficient for calculating currents, there is little benefit with regard to the overall state of the system. Any gains become marginal for many-body, tensor network simulations, where the relative performance of discretizations varies when sweeping other numerical controls. These results indicate that typical reservoir discretizations have little impact on numerical costs for certain computational tools. The choice of a relaxation parameter is nonetheless crucial, and the method we develop provides a reliable estimate of the optimal relaxation for finite reservoirs.
Collapse
Affiliation(s)
- Justin E Elenewski
- Biophysical and Biomedical Measurement Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Gabriela Wójtowicz
- Jagiellonian University, Institute of Theoretical Physics, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Marek M Rams
- Jagiellonian University, Institute of Theoretical Physics, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Michael Zwolak
- Biophysical and Biomedical Measurement Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| |
Collapse
|
2
|
Zwolak M. Analytic expressions for the steady-state current with finite extended reservoirs. J Chem Phys 2020; 153:224107. [PMID: 33317280 PMCID: PMC8356363 DOI: 10.1063/5.0029223] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Open-system simulations of quantum transport provide a platform for the study of true steady states, Floquet states, and the role of temperature, time dynamics, and fluctuations, among other physical processes. They are rapidly gaining traction, especially techniques that revolve around "extended reservoirs," a collection of a finite number of degrees of freedom with relaxation that maintains a bias or temperature gradient, and have appeared under various guises (e.g., the extended or mesoscopic reservoir, auxiliary master equation, and driven Liouville-von Neumann approaches). Yet, there are still a number of open questions regarding the behavior and convergence of these techniques. Here, we derive general analytical solutions, and associated asymptotic analyses, for the steady-state current driven by finite reservoirs with proportional coupling to the system/junction. In doing so, we present a simplified and unified derivation of the non-interacting and many-body steady-state currents through arbitrary junctions, including outside of proportional coupling. We conjecture that the analytic solution for proportional coupling is the most general of its form for isomodal relaxation (i.e., relaxing proportional coupling will remove the ability to find compact, general analytical expressions for finite reservoirs). These results should be of broad utility in diagnosing the behavior and implementation of extended reservoir and related approaches, including the convergence to the Landauer limit (for non-interacting systems) and the Meir-Wingreen formula (for many-body systems).
Collapse
Affiliation(s)
- Michael Zwolak
- Biophysical and Biomedical Measurement Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| |
Collapse
|
3
|
Chiang TM, Hsu LY. Quantum transport with electronic relaxation in electrodes: Landauer-type formulas derived from the driven Liouville-von Neumann approach. J Chem Phys 2020; 153:044103. [PMID: 32752664 DOI: 10.1063/5.0007750] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We derive the exact steady-state solutions for the simplest model systems of resonant tunneling and tunneling with destructive quantum interference from the driven Liouville-von Neumann (DLvN) approach. Under the finite-state lead condition (the two electrodes have finite states), we analyze the asymptotic behavior of the steady-state current in the two limits of electronic relaxation. Under the infinite-state lead condition, the steady-state solutions of the two model systems can be cast as Landauer-type current formulas. According to the formulas, we show that the transmission functions near the resonant peak and the antiresonant dip can be significantly influenced by electronic relaxation in the electrodes. Moreover, under intermediate and strong electronic relaxation conditions, we analytically show that the steady-state current of the DLvN approach dramatically deviates from the Landauer current when destructive quantum interference occurs. In the regime of zero electronic relaxation, our results are reduced to the Landauer formula, indicating that the DLvN approach is equivalent to the Landauer approach when the leads have infinite states without any electronic relaxation.
Collapse
Affiliation(s)
- Tse-Min Chiang
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
| | - Liang-Yan Hsu
- Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei 10617, Taiwan
| |
Collapse
|
4
|
Rams MM, Zwolak M. Breaking the Entanglement Barrier: Tensor Network Simulation of Quantum Transport. PHYSICAL REVIEW LETTERS 2020; 124:137701. [PMID: 32302169 PMCID: PMC7654706 DOI: 10.1103/physrevlett.124.137701] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2019] [Revised: 10/08/2019] [Accepted: 02/21/2020] [Indexed: 06/11/2023]
Abstract
The recognition that large classes of quantum many-body systems have limited entanglement in the ground and low-lying excited states led to dramatic advances in their numerical simulation via so-called tensor networks. However, global dynamics elevates many particles into excited states, and can lead to macroscopic entanglement and the failure of tensor networks. Here, we show that for quantum transport-one of the most important cases of this failure-the fundamental issue is the canonical basis in which the scenario is cast: When particles flow through an interface, they scatter, generating a "bit" of entanglement between spatial regions with each event. The frequency basis naturally captures that-in the long-time limit and in the absence of inelastic scattering-particles tend to flow from a state with one frequency to a state of identical frequency. Recognizing this natural structure yields a striking-potentially exponential in some cases-increase in simulation efficiency, greatly extending the attainable spatial and time scales, and broadening the scope of tensor network simulation to hitherto inaccessible classes of nonequilibrium many-body problems.
Collapse
Affiliation(s)
- Marek M. Rams
- Jagiellonian University, Marian Smoluchowski Institute of Physics, Łojasiewicza 11, 30-348 Kraków, Poland
| | - Michael Zwolak
- Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| |
Collapse
|
5
|
Ochoa MA, Zwolak M. Optimal in situ electromechanical sensing of molecular species. J Chem Phys 2020; 152:034109. [PMID: 31968951 DOI: 10.1063/1.5132581] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We investigate protocols for optimal molecular detection with electromechanical nanoscale sensors under ambient conditions. Our models are representative of suspended graphene nanoribbons, which due to their piezoelectric and electronic properties provide responsive and versatile sensors. In particular, we analytically account for the corrections in the electronic transmission function and signal-to-noise ratio originating in environmental perturbations, such as thermal fluctuations and solvation effects. We also investigate the role of the sampling time in the current statistics. As a result, we formulate a protocol for optimal sensing based on the modulation of the Fermi level at a fixed bias and provide approximate forms for the current, linear susceptibility, and current fluctuations. We show how the algebraic tails in the thermally broadened transmission function affect the behavior of the signal-to-noise ratio and optimal sensing. These results provide further insights into the operation of graphene deflectometers and other techniques for electromechanical sensing.
Collapse
Affiliation(s)
- Maicol A Ochoa
- Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Michael Zwolak
- Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| |
Collapse
|
6
|
Wójtowicz G, Elenewski JE, Rams MM, Zwolak M. Open System Tensor Networks and Kramers' Crossover for Quantum Transport. PHYSICAL REVIEW. A 2020; 101:10.1103/PhysRevA.101.050301. [PMID: 33367191 PMCID: PMC7754794 DOI: 10.1103/physreva.101.050301] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Tensor networks are a powerful tool for many-body ground states with limited entanglement. These methods can nonetheless fail for certain time-dependent processes-such as quantum transport or quenches-where entanglement growth is linear in time. Matrix-product-state decompositions of the resulting out-of-equilibrium states require a bond dimension that grows exponentially, imposing a hard limit on simulation timescales. However, in the case of transport, if the reservoir modes of a closed system are arranged according to their scattering structure, the entanglement growth can be made logarithmic. Here, we apply this ansatz to open systems via extended reservoirs that have explicit relaxation. This enables transport calculations that can access steady states, time dynamics and noise, and periodic driving (e.g., Floquet states). We demonstrate the approach by calculating the transport characteristics of an open, interacting system. These results open a path to scalable and numerically systematic many-body transport calculations with tensor networks.
Collapse
Affiliation(s)
- Gabriela Wójtowicz
- Jagiellonian University, Institute of Theoretical Physics, Lojasiewicza 11, 30-348 Kraków, Poland
| | - Justin E. Elenewski
- Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, MD, USA
| | - Marek M. Rams
- Jagiellonian University, Institute of Theoretical Physics, Lojasiewicza 11, 30-348 Kraków, Poland
| | - Michael Zwolak
- Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD, USA
| |
Collapse
|
7
|
Ochoa MA, Zwolak M. Generalized Voigt broadening due to thermal fluctuations of electromechanical nanosensors and molecular electronic junctions. J Chem Phys 2019; 150:141102. [PMID: 30981273 PMCID: PMC6611703 DOI: 10.1063/1.5081140] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Graphene and other 2D materials give a platform for electromechanical sensing of biomolecules in aqueous, room temperature environments. The electronic current changes in response to mechanical deflection, indicating the presence of forces due to interactions with, e.g., molecular species. We develop illustrative models of these sensors in order to give explicit, compact expressions for the current and signal-to-noise ratio. Electromechanical structures have an electron transmission function that follows a generalized Voigt profile, with thermal fluctuations giving a Gaussian smearing analogous to thermal Doppler broadening in solution/gas-phase spectroscopic applications. The Lorentzian component of the profile comes from the contact to the electrodes. After providing an accurate approximate form of this profile, we calculate the mechanical susceptibility for a representative two-level bridge and the current fluctuations for electromechanical detection. These results give the underlying mechanics of electromechanical sensing in more complex scenarios, such as graphene deflectometry.
Collapse
Affiliation(s)
- Maicol A. Ochoa
- Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899
- Maryland Nanocenter, University of Maryland, College Park, MD 20742
| | - Michael Zwolak
- Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899
| |
Collapse
|
8
|
Sahu S, Zwolak M. Colloquium: Ionic phenomena in nanoscale pores through 2D materials. REVIEWS OF MODERN PHYSICS 2019; 91:10.1103/RevModPhys.91.021004. [PMID: 31579274 PMCID: PMC6774369 DOI: 10.1103/revmodphys.91.021004] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/12/2023]
Abstract
Ion transport through nanopores permeates through many areas of science and technology, from cell behavior to sensing and separation to catalysis and batteries. Two-dimensional materials, such as graphene, molybdenum disulfide (MoS2), and hexagonal boron nitride (hBN), are recent additions to these fields. Low-dimensional materials present new opportunities to develop filtration, sensing, and power technologies, encompassing ion exclusion membranes, DNA sequencing, single molecule detection, osmotic power generation, and beyond. Moreover, the physics of ionic transport through pores and constrictions within these materials is a distinct realm of competing many-particle interactions (e.g., solvation/dehydration, electrostatic blockade, hydrogen bond dynamics) and confinement. This opens up alternative routes to creating biomimetic pores and may even give analogues of quantum phenomena, such as quantized conductance, in the classical domain. These prospects make membranes of 2D materials - i.e., 2D membranes - fascinating. We will discuss the physics and applications of ionic transport through nanopores in 2D membranes.
Collapse
Affiliation(s)
- Subin Sahu
- Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
- Maryland NanoCenter, University of Maryland, College Park, Maryland 20742, USA
| | | |
Collapse
|
9
|
Zwolak M. Communication: Gibbs phenomenon and the emergence of the steady-state in quantum transport. J Chem Phys 2018; 149:241102. [PMID: 30599719 PMCID: PMC6602063 DOI: 10.1063/1.5061759] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Simulations are increasingly employing explicit reservoirs-internal, finite regions-to drive electronic or particle transport. This naturally occurs in simulations of transport via ultracold atomic gases. Whether the simulation is numerical or physical, these approaches rely on the rapid development of the steady state. We demonstrate that steady state formation is a manifestation of the Gibbs phenomenon well-known in signal processing and in truncated discrete Fourier expansions. Each particle separately develops into an individual steady state due to the spreading of its wave packet in energy. The rise to the steady state for an individual particle depends on the particle energy-and thus can be slow-and ringing oscillations appear due to filtering of the response through the electronic bandwidth. However, the rise to the total steady state-the one from all particles-is rapid, with time scale π/W, where W is the bandwidth. Ringing oscillations are now also filtered through the bias window, and they decay with a higher power. The Gibbs constant-the overshoot of the first ring-can appear in the simulation error. These results shed light on the formation of the steady state and support the practical use of explicit reservoirs to simulate transport at the nanoscale or using ultracold atomic lattices.
Collapse
Affiliation(s)
- Michael Zwolak
- Biophysics Group, Microsystems and Nanotechnology Division, Physical Measurement Laboratory, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| |
Collapse
|
10
|
Wertnik M, Chin A, Nori F, Lambert N. Optimizing co-operative multi-environment dynamics in a dark-state-enhanced photosynthetic heat engine. J Chem Phys 2018; 149:084112. [PMID: 30193490 DOI: 10.1063/1.5040898] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
We analyze the role of coherent, non-perturbative system-bath interactions in a photosynthetic heat engine. Using the reaction-coordinate formalism to describe the vibrational phonon-environment in the engine, we analyze the efficiency around an optimal parameter regime predicted in earlier studies. We show that, in the limit of high-temperature photon irradiation, the phonon-assisted population transfer between bright and dark states is suppressed due to dephasing from the photon environment, even in the Markov limit where we expect the influence of each bath to have an independent and additive effect on the dynamics. Manipulating the phonon bath properties via its spectral density enables us to identify both optimal low- and high-frequency regimes where the suppression can be removed. This suppression of transfer and its removal suggests that it is important to consider carefully the non-perturbative and cooperative effects of system-bath environments in designing artificial photosynthetic systems and also that manipulating inter-environmental interactions could provide a new multidimensional "lever" by which photocells and other types of quantum devices can be optimized.
Collapse
Affiliation(s)
- Melina Wertnik
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - Alex Chin
- Institut des NanoSciences de Paris, Sorbonne Université, 4 Place Jussieu, Bote Courrier 840, 75252 Paris Cedex 05, France
| | - Franco Nori
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - Neill Lambert
- Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| |
Collapse
|
11
|
Smolyanitsky A, Paulechka E, Kroenlein K. Aqueous Ion Trapping and Transport in Graphene-Embedded 18-Crown-6 Ether Pores. ACS NANO 2018; 12:6677-6684. [PMID: 29940107 DOI: 10.1021/acsnano.8b01692] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Using extensive room-temperature molecular dynamics simulations, we investigate selective aqueous cation trapping and permeation in graphene-embedded 18-crown-6 ether pores. We show that in the presence of suspended water-immersed crown-porous graphene, K+ ions rapidly organize and trap stably within the pores, in contrast with Na+ ions. As a result, significant qualitative differences in permeation between ionic species arise. The trapped ion occupancy and permeation behaviors are shown to be highly voltage-tunable. Interestingly, we demonstrate the possibility of performing conceptually straightforward ion-based logical operations resulting from controllable membrane charging by the trapped ions. In addition, we show that ionic transistors based on crown-porous graphene are possible, suggesting utility in cascaded ion-based logic circuitry. Our results indicate that in addition to numerous possible applications of graphene-embedded crown ether nanopores, including deionization, ion sensing/sieving, and energy storage, simple ion-based logical elements may prove promising as building blocks for reliable nanofluidic computational devices.
Collapse
Affiliation(s)
- Alex Smolyanitsky
- Applied Chemicals and Materials Division , National Institute of Standards and Technology Boulder , Colorado 80305 , United States
| | - Eugene Paulechka
- Applied Chemicals and Materials Division , National Institute of Standards and Technology Boulder , Colorado 80305 , United States
| | - Kenneth Kroenlein
- Applied Chemicals and Materials Division , National Institute of Standards and Technology Boulder , Colorado 80305 , United States
| |
Collapse
|
12
|
Elenewski JE, Gruss D, Zwolak M. Communication: Master equations for electron transport: The limits of the Markovian limit. J Chem Phys 2018; 147:151101. [PMID: 29055298 DOI: 10.1063/1.5000747] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Master equations are increasingly popular for the simulation of time-dependent electronic transport in nanoscale devices. Several recent Markovian approaches use "extended reservoirs"-explicit degrees of freedom associated with the electrodes-distinguishing them from many previous classes of master equations. Starting from a Lindblad equation, we develop a common foundation for these approaches. Due to the incorporation of explicit electrode states, these methods do not require a large bias or even "true Markovianity" of the reservoirs. Nonetheless, their predictions are only physically relevant when the Markovian relaxation is weaker than the thermal broadening and when the extended reservoirs are "sufficiently large," in a sense that we quantify. These considerations hold despite complete positivity and respect for Pauli exclusion at any relaxation strength.
Collapse
Affiliation(s)
- Justin E Elenewski
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Daniel Gruss
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| | - Michael Zwolak
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, Maryland 20899, USA
| |
Collapse
|
13
|
Prucker V, Bockstedte M, Thoss M, Coto PB. Dynamical simulation of electron transfer processes in self-assembled monolayers at metal surfaces using a density matrix approach. J Chem Phys 2018; 148:124705. [DOI: 10.1063/1.5020238] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- V. Prucker
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
| | - M. Bockstedte
- Department Chemistry and Physics of Materials, Universität Salzburg, Jakob-Haringer-Str. 2a, A-5020 Salzburg, Austria
- Lehrstuhl für Theoretische Festkörperphysik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
| | - M. Thoss
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany
| | - P. B. Coto
- Institut für Theoretische Physik und Interdisziplinäres Zentrum für Molekulare Materialien, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstr. 7/B2, D-91058 Erlangen, Germany
| |
Collapse
|
14
|
Chien CC, Velizhanin KA, Dubi Y, Ilic BR, Zwolak M. Topological quantization of energy transport in micro- and nano-mechanical lattices. PHYSICAL REVIEW. B 2018; 97:10.1103/PhysRevB.97.125425. [PMID: 30997441 PMCID: PMC6463522 DOI: 10.1103/physrevb.97.125425] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/09/2023]
Abstract
Topological effects typically discussed in the context of quantum physics are emerging as one of the central paradigms of physics. Here, we demonstrate the role of topology in energy transport through dimerized micro- and nano-mechanical lattices in the classical regime, i.e., essentially "masses and springs". We show that the thermal conductance factorizes into topological and nontopological components. The former takes on three discrete values and arises due to the appearance of edge modes that prevent good contact between the heat reservoirs and the bulk, giving a length-independent reduction of the conductance. In essence, energy input at the boundary mostly stays there, an effect robust against disorder and nonlinearity. These results bridge two seemingly disconnected disciplines of physics, namely topology and thermal transport, and suggest ways to engineer thermal contacts, opening a direction to explore the ramifications of topological properties on nanoscale technology.
Collapse
Affiliation(s)
- Chih-Chun Chien
- School of Natural Sciences, University of California, Merced, CA 95343, USA
| | | | - Yonatan Dubi
- Department of Chemistry and the Ilse Katz Institute for Nanoscale Science and Technology, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
| | - B. Robert Ilic
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| | - Michael Zwolak
- Center for Nanoscale Science and Technology, National Institute of Standards and Technology, Gaithersburg, MD 20899, USA
| |
Collapse
|