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SUMMARY:Transmission and Topology in Disordered Networks of Coaxial Cables
  - David Whittaker (University of Sheffield)
DTSTART:20230324T120000Z
DTEND:20230324T123000Z
UID:TALK196693@talks.cam.ac.uk
DESCRIPTION:D.M.Whittaker and M.M. McCarthy\nWe show that disordered netwo
 rks of coaxial cables can exhibit very high electromagnetic transmission (
 theoretically 100%) at certainfrequencies. This high transmission is a sig
 nature that a network is at a boundary between two topological phases.\nWe
  make our networks by connecting together sections of coaxial cable\, all 
 with the same electrical length. They can be disordered either byrandomnes
 s in these connections\, or by randomly including cables with different el
 ectrical impedances. In this talk\, I focus on linearstructures\, made by 
 connecting\, end-to-end\, sections of cable with 50 and 93 ohm impedance. 
 Using a vector network analyser\, we can measuretransmission through the s
 tructure and the local density of states at any point. For certain sequenc
 es of impedance\, we find that that thetransmission at a particular freque
 ncy\, which we call the chiral frequency\, is close to 100%.\nOur key theo
 retical result is to show that a network can be represented by a tight-bin
 ding matrix Hamiltonian describing thevoltages at the cable junctions\, wi
 th the hopping matrix elements determined by the impedances of the corresp
 onding cables. As theseHamiltonians exhibit chiral (sublattice) symmetry\,
  one of the central symmetries of random matrix theory\, the networks are 
 an excellentsystem in which to investigate topological physics.\nOur rando
 m linear structures map onto the SSH (Su-Schrieffer-Heegler) model with di
 sordered hopping. The chiral frequency corresponds to thezero of energy in
  the model. Disordered SSH chains can exist in two topological phases\, de
 pending on the sequence of impedances. By &nbsp\; &nbsp\; &nbsp\; &nbsp\; 
 &nbsp\; &nbsp\; &nbsp\; &nbsp\; &nbsp\; &nbsp\; &nbsp\; &nbsp\; &nbsp\; &n
 bsp\; &nbsp\; &nbsp\; &nbsp\; &nbsp\;&nbsp\;swapping cables around\, we ca
 n quickly investigate the topological phase space\, using transmssion and 
 density of states measurements as aprobe.\nTo distinguish the phases\, we 
 introduce a topological invariant related to the eigenvalues of the transf
 er matrix describingtransmission through a structure. When there is a unit
  eigenvalue at the chiral frequency\, the structure is intermediate betwee
 n the twophases. However\, this is also the condition for perfect transmis
 sion\, which establishes the connection between a structure beingtopologic
 ally marginal and exhibiting high transmssion.\n&nbsp\;\n&nbsp\;\n&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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