rangenano6

!
!
1"Tuning&the&Fano&Resonance&with&an&Intruder&Continuum&"J.
"Fransson1,"M.
-G.
"Kang2,"Y.
"Yoon2,"S.
"Xiao2,"Y.
"Ochiai3,"J.
"L.
"Reno4,"N.
"Aoki3"&"J.
"P.
"Bird2,3,*"1:"Department"of"Physics"and"Astronomy,"Uppsala"University,"Box"534,"SE-751"21,"Uppsala,"Sweden"2:"Department"of"Electrical"Engineering,"University"at"Buffalo,"the"State"University"of"New"York,"Buffalo,"NY"14260-1900,"USA"3.
"Graduate"School"of"Advanced"Integration"Science,"Chiba"University,"1-33"Yayoi-cho,"Inage-ku,"Chiba"263-8522,"Japan"4.
"CINT/Sandia"National"Laboratories,"Dept.
"1131,"MS"1303,"Albuquerque,"NM"87185,"USA"*"Corresponding"author:"jbird@buffalo.
edu,"+1-716-645-1015""Through"a"combination"of"experiment"and"theory"we"establish"the"possibility"of"achieving"strong"tuning"of"Fano"resonances"(FRs),"by"allowing"their"usual"two-path"geometry"to"interfere"with"an"additional,""in-truder","continuum.
"As"the"coupling"strength"to"this"intruder"is"varied,"we"predict"strong"modulations"of"the"resonance"lineshape"that,"in"principle"at"least,"may"exceed"the"amplitude"of"the"original"FR"itself.
"For"a"proof-of-concept"demonstration"of"this"phenomenon,"we"construct"a"nanoscale"interferometer"from"nonlocally-coupled"quantum"point"contacts"and"utilize"the"unique"features"of"their"density"of"states"to"realize"the"intruder.
"External"control"of"the"intruder"coupling"is"enabled"by"means"of"an"applied"mag-netic"field,"in"the"presence"of"which"we"demonstrate"the"predicted"distortions"of"the"FR.
"This"general"scheme"for"resonant"control"should"be"broadly"applicable"to"a"variety"of"wave-based"systems,"opening"up"the"possibility"of"new"applications"in"areas"such"as"chemical"and"biological"sensing,"and"secure"com-munications.
""Keywords:"Fano"resonance,"quantum"point"contacts,"nanoelectronics,"coherent-state"control"""!
!
2"&Arising"from"the"coupling"of"a"discrete"level"to"a"continuum,"the"Fano"resonance"(FR)"[1]"is"ubiq-uitous"to"atomic-,"molecular-,"and"condensed-matter"systems"[2-4].
"As"a"wave-interference"phenome-non,"it"is"also"of"increasing"importance"in"optics,"plasmonics,"and"metamaterials,"where"its"ability"to"cau-se"rapid"signal"modulations"under"variation"of"some"suitable"parameter"makes"it"desirable"for"a"variety"of"applications"[5].
"The"observation"of"this"resonance"in"plasmonic"nanostructures"[6-10],"for"example,"provides"a"sensitive"mechanism"for"chemical"and"biological"sensing.
"In"metamaterials,"in"contrast,"FRs"are"being"explored"for"use"in"slow-light"devices,"electromagnetically-induced"transparency"and"electro-optic"switching"[5,11-13].
"In"the"field"of"nanoelectronics,"FRs"have"been"widely"observed"in"semiconduc-tor"quantum"dots"[4],"and"have"motivated"a"number"of"proposals"for"electrical-"or"optical-signal"control"[4,14-22].
"One"possible"application"is"in"spintronics,"where"FRs"are"being"explored"as"a"means"to"filter"spins"in"an"initially-unpolarized"current"[4,21,22].
"Other"work"[20]"has"demonstrated"a"nonlinear"FR"in"optically-pumped"quantum"dots,"a"phenomenon"that"could"find"use"as"a"method"to"detect"weak"cou-plings"of"two-level"quantum"systems.
""A"surprising"feature"of"the"FR"is"that"its"rich"variations"are"obtained"from"a"simple"interference"geometry.
"As"first"formulated"by"Fano"[1],"this"involves"an"electron"that"is"excited"from"an"initial"atomic"level"(|i">)"to"a"final"state"(|f">)"in"a"continuum,"reaching"this"via"two"separate"paths.
"The"first"of"these"is"direct,"while"the"second"involves"an"intermediate"transition"through"a"discrete"level.
"Transmission"from"|i">"to"|f">"is"determined"by"the"phase"interference"of"these"two"paths,"dependent"upon"whose"relative"amplitudes"FRs"with"various"lineshapes"can"be"obtained.
"A"generalized"representation"of"this"scheme"is"presented"in"Fig.
"1(a),"in"which"the"direct"path"from"|i">"to"|f">"has"matrix"element"r,"while"transmission"via"the"discrete"level"(D)"is"described"by"matrix"elements"v.
"(It"should"be"noted"that"both"Figs.
"1(a)"&"1(b)"represent"transitions"between"quantum"states"in"some""configuration"space","and"that"the"various"states"involved"may"even"be"at"the"same"energy.
)"A"need"that"has"emerged"from"the"possible"technolog-ical"applications"of"FRs"is"to"tune"their"lineshape"to"achieve"signal"modulation.
"In"recent"studies"of"the"nonlinear"FR"mentioned"above,"this"was"achieved"by"using"optical"pumping"to"manipulate"the"coupling"between"quantum-dot"states"and"a"physically-separate"continuum,"thereby"allowing"the"FR"to"effective-ly"be"turned""on""or""off""[20].
"!
!
3""While"the"two-path"Fano"interferometer"provides"a"powerful"scheme"for"manipulating"wave"transmission,"in"this"Letter"we"demonstrate"the"possibility"of"achieving"even"stronger"resonant"control,"by"making"just"a"simple"modification"to"the"interference"geometry.
"The"essential"element"of"our"ap-proach"is"to"couple"an"additional"continuum"(C)"to"the"original"Fano"system,"thereby"forming"a"three-path"interferometer"(Fig.
"1(b)).
"By"varying"the"strength"of"the"coupling"(t)"to"this"continuum,"we"show"that"it"is"possible"to"induce"significant"lineshape"distortions,"which"may"even"exceed"the"amplitude"of"the"original"FR.
""Motivated"by"the"connection"of"this"phenomenon"to"that"of"q-reversal"in"Rydberg"atoms"[23]"–"in"which"the"FR"due"to"a"given"atomic"level"may"undergo"dramatic"phase"reversal"when"it"interacts"with"a"separate""intruder""level"–"we"refer"to"the"additional"continuum"as"an"intruder.
"For"a"proof-of-concept"demonstration"of"its"influence,"we"realize"the"intruder"in"a"nanoscale"interferometer"formed"by"a"pair"of"coupled"quantum"point"contacts"(QPCs)"[24,25].
"Exploiting"the"unique"aspects"of"the"density"of"states"in"these"structures,"we"configure"a"system"analogous"to"that"of"Fig.
"1(b)"by"forming"the"discrete"level"and"the"intruder"within"one"QPC.
"The"second"is"then"used"as"a"detector"whose"continuum"trans-port"is"affected"by"its"wavefunction"overlap"with"the"other"QPC.
"Through"suitable"control"of"the"relevant"gate"voltages,"a"FR"is"induced"in"the"detector"by"bringing"it"into"energetic"resonance"with"the"discrete"level"[26-29].
"The"resonance"develops"a"pronounced"and"systematic"distortion"in"a"magnetic"field,"be-havior"that"we"show"here"can"be"attributed"to"the"ability"of"this"parameter"to"tune"the"coupling"be-tween"the"intruder"and"the"two-path"interferometer.
""While"our"proof-of-concept"demonstration"of"the"intruder"focuses"on"a"solid-state"implementa-tion,"capable"only"of"operation"at"cryogenic"temperatures,"it"must"be"emphasized"that"the"general"scheme"presented"in"Fig.
"1(b)"should"be"broadly"applicable"to"a"variety"of"wave-based"systems.
"This"in"turn"should"open"up"the"possibility"of"new"applications,"including"those"in"chemical"and"biological"sens-ing"[5].
"Another"possibility"is"in"secure"communications,"where"the"role"of"the"intruder"could"be"played"by"an"undesirable"eavesdropper,"whose"attempts"to"intercept"secure"communications"could"be"sensi-tively"detected"as"an"associated"distortion"of"the"FR.
"Experiments"were"performed"on"coupled"QPCs"realized"in"epitaxially-grown"GaAs/AlGaAs"heter-ostructures"(Sandia"samples"EA750,"EA755"&"VA0284).
"Each"of"these"wafers"had"a"30-nm"thick"GaAs"!
!
4"quantum"well,"inside"of"which"a"high-quality"two-dimensional"electron"gas"was"formed.
"The"density"of"this"ranged"from"1.
8"—"2.
5"*"1011"cm2"at"4.
2"K,"with"corresponding"mobility"of"1.
4"—"3.
7"*"106"cm2/Vs.
"While"in"this"Letter"we"focus"on"new"results"obtained"from"measurements"of"the"device"of"Refs.
"28"&"29,"in"the"Supporting"Information"we"present"corroborating"results"from"a"second"device.
"Measurements"were"performed"by"placing"the"samples"in"the"vacuum"can"of"a"liquid-helium"cryostat,"and"subjecting"them"to"the"magnetic"field"generated"by"a"superconducting"solenoid.
"Our"investigations"were"per-formed"in"the"temperature"range"of"4.
2"–"40"K,"where"effects"arising"from"ballistic"carrier"transport"could"be"resolved.
""Our"experiments"make"use"of"the"peculiar"properties"of"QPCs"close"to"pinch-off,"where"strongly-"enhanced"carrier"interactions"can"spontaneously"distort"their"self-consistent"potential.
"The"distortion"is"associated"with"Friedel"oscillations"generated"by"scattering"from"the"QPC"barrier,"and"is"thought"to"lead"to"the"formation"of"a"narrow"well"that"may"support"a"quasi-localized"state"(LS)"near"the"center"of"the"QPC"[30-35].
"Several"studies"have"been"undertaken"to"explore"the"structure"of"this"unusual"microscopic"feature"[35-38],"and"we"have"revealed"its"presence"by"using"it"as"the"discrete"level"in"a"FR"geometry"[26-29].
"In"these"experiments"(see"the"Supporting"Information"for"further"details"on"the"measurement"pro-cedure),"two"QPCs"are"formed"in"close"proximity"and"are"allowed"to"interact"via"an"intervening"region"of"two-dimensional"electron"gas"(Fig.
"2(a)).
"By"suitable"variation"of"the"voltage"(Vs)"applied"to"the"gates"of"one"of"the"QPCs"(referred"to"hereafter"as"the""swept-QPC","and"denoted"by"the"subscript""s")"we"form"a"LS"inside"it"by"pinching"it"off.
"With"the"detector-QPC"(denoted"hereafter"by"the"subscript""d")"biased"at"fixed"gate"voltage"(Vd,"typically"chosen"to"ensure"that"this"device"operates"well"above"pinch-off),"a"reso-nance"is"then"observed"in"its"conductance"(Gd)"when"the"variation"of"Vs"drives"the"LS"through"the"Fermi"level.
"The"resonance"may"be"viewed"as"arising"in"the"process"indicated"in"the"upper"panel"of"Fig.
"2(b).
"Here,"an"electron"injected"from"an"initial"state"in"the"detector"reaches"a"final"state"in"the"drain,"either"di-rectly"(matrix"element"r)"or"in"a"process"in"which"it"tunnels"to"and"from"the"LS"(matrix"element"v"for"each"process)"before"reaching"the"drain.
"By"summing"over"initial"and"final"states"of"this"type,"the"result"is"a"FR"in"the"detector"conductance"[27]"that"corresponds"well"to"that"found"in"experiment.
"!
!
5"In"Figs.
"2(c)"&"3(a),"we"illustrate"the"evolution"of"the"detector"resonance"(at"4.
2"K)"when"a"mag-netic"field"(B)"is"applied"normal"to"the"plane"of"the"two-dimensional"electron"gas.
"In"each"of"the"four"panels"of"Fig.
"2(c),"we"show"the"detector"FR"and"the"associated"variation"of"the"swept-QPC"conductance"(Gs).
"Consistent"with"our"prior"work"[29],"at"zero"field"we"find"that"the"detector"resonance"is"only"weakly"asymmetric.
"With"increasing"magnetic"field,"however,"this"feature"undergoes"a"dramatic"evolution,"de-veloping"a"pronounced"dip"that"evolves"systematically"on"its"less-negative"gate-voltage"side.
"Importantly"(see"Supporting"Information),"the"shape"of"this"new"resonance"cannot"be"described"by"the"universal"form"[1]"typical"of"FRs.
"These"lineshape"distortions"are"far"too"strong"to"arise"from"Zeeman"splitting"[28],"and"also"cannot"be"attributed"to"magneto-dispersion"of"the"detector"states.
"While"the"magnetic"field"does"depopulate"[24,25]"the"subbands"of"the"detector,"resulting"in"an"overall"decrease"of"its"conduct-ance"(see"Fig.
"S6"of"the"Supporting"Information),"our"experiments"are"configured"in"a"manner"such"that"the"influence"of"this"is"never"strong"enough"to"pinch"the"detector"off.
"Under"such"operation,"prior"work"has"shown"that"the"detector"resonance"remains"essentially"unaffected"by"even"large"changes"in"back-ground"conductance"[28].
"In"Fig.
"4(a),"we"demonstrate"that"the"high-field"resonance"has"an"extremely"unusual"tempera-ture"dependence.
"With"increase"of"temperature"above"4.
2"K"its"peak"is"quickly"suppressed"while"the"dip"grows"more"pronounced.
"The"overall"effect"is"therefore"of"a"transition"to"an"anti-resonance,"whose"structure"becomes"more"clearly"resolved"with"increasing"temperature.
""Key"to"understanding"the"results"described"above"is"the"expected"form"of"the"density"of"states"in"the"swept-QPC"at"pinch-off.
"This"form"is"sketched"in"the"schematics"of"Fig.
"2(b),"in"which"we"indicate"two"distinct"components;"a"narrow"peak"corresponding"to"the"LS"and"a"quasi-continuous"spectrum.
"The"lat-ter"feature"corresponds"to"the"one-dimensional"(1D)"subbands"that"govern"transport"when"the"swept-QPC"is"open,"but"which"should"be"driven"above"the"Fermi"level"once"it"is"pinched-off.
"Both"schematics"indicate"the"situation"for"which"the"LS"is"aligned"with"the"reservoir"Fermi"level,"and"so"is"in"resonance"with"the"detector.
"At"zero"magnetic"field"(upper"schematic)"the"1D"subbands"lie"well"above"the"LS"and"so"have"little"influence"on"this"resonance.
"This"situation"changes"in"a"magnetic"field,"however,"due"to"its"tendency"to"induce"compression"of"the"various"electronic"levels"[39,40].
"This"is"shown"in"Fig.
"2(d)"where"!
!
6"we"plot,"for"a"non-interacting"model,"the"magneto-dispersion"of"the"LS"and"the"edge"of"the"lowest"1D"subband.
"These"calculations"were"performed"by"assuming"that"the"potential"of"the"swept-QPC"at"pinch-off"consists"of"a"narrow"well,"embedded"at"the"saddle"point"of"the"two-dimensional"barrier"more"nor-mally"associated"with"QPCs"(see"the"Supporting"Information).
"The"LS"is"therefore"modeled"with"a"two-dimensional"harmonic"confinement"(!
ωLS"="1"meV),"while"the"1D"subbands"are"attributed"to"the"more"common"transverse"confinement"(!
ω1D"="3"meV),"allowing"their"magneto-dispersions"to"be"analytically"calculated"[39,40].
"Figure"2(d)"shows"a"clear"trend"for"the"LS"to"approach"the"lowest"1D"subband"with"in-creasing"magnetic"field,"a"result"suggesting"that"the"latter"may"function"as"an"intruder"and"influence"the"FR"due"to"the"LS.
"As"sketched"In"the"lower"schematic"of"Fig.
"2(b),"the"detector"resonance"observed"in"such"a"situation"will"arise"from"a"three-path"interference"phenomenon,"whose"direct"path"once"again"in-volves"transmission"from"an"initial"state"in"the"detector"to"a"final"one"in"the"drain"(path"r).
"Interfering"with"this"channel"are"two"further"pathways:"one"in"which"the"electron"tunnels"to"and"from"the"LS"(char-acterized"by"matrix"elements"v)"before"reaching"the"drain,"and;"a"second"in"which"the"tunneling"instead"takes"the"electron"to"the"lowest"1D"subband"and"back.
"It"is"this"last"process"that"represents"the"contri-bution"of"the"intruder,"and"the"magnetic"field"should"serve"as"the"control"parameter"that"allows"its"cou-pling"to"be"varied.
"Note"here"that"while"this"mechanism"may"not"immediately"appear"to"resemble"that"in"Fig.
"1(b),"it"does"nonetheless"have"the"essential"feature"of"three"separate"paths"with"different"interme-diate"steps"(|i">"→"|f">,"|i">"→"D"→"|f">"&"|i">"→"C6→"|f">).
""For"a"more"detailed"analysis"of"our"experiment,"we"have"formulated"(Supporting"Information)"a"generalized"theoretical"description"of"the"three-path"interferometer"of"our"experiment.
"In"Fig.
"1(c),"we"demonstrate"the"possibility"of"using"this"scheme"to"induce"produced"signal"modulations,"whose"ampli-tude"can"even"exceed"that"of"the"original"FR.
"Specifically"shown"in"this"figure"is"the"energy-dependent"conductance"(δGd,"related"to"the"transmission)"from"|i">"to"|f">,"for"various"values"of"the"intruder"cou-pling.
"A"general"result"which"follows"from"our"analysis"is"that"the"full"resonance"lineshape"in"this"system"may"be"interpreted"as"arising"from"two"contributions;"the"first"being"the"usual"Fano"mechanism,"while"the"second"involves"interference"of"the"intruder"with"the"original"continuum.
"Although"the"former"pro-cess"(δGLS,"inset"to"Fig.
"1(c))"yields"a"nearly-symmetric"resonance"(i.
e.
"q">>"0)"for"the"set"of"parameters"!
!
7"considered"here,"the"contribution"from"the"intruder"(δGs,"Fig.
"1(d))"shows"a"pronounced"anti-resonance.
"The"location"of"this"feature"is"determined"by"the"energy"separation"assumed"between"the"discrete"level"and"the"intruder,"whose"density"of"states"is"taken"to"be"of"1D"character.
"From"a"comparison"of"Figs.
"1(c)"&"1(d),"it"is"clear"that"the"overall"resonance"is"strongly"affected"by"the"intruder,"which"distorts"its"line-shape"dramatically;"while"the"peak"now"arises"from"the"usual"Fano"mechanism,"the"minimum"is"due"to"the"two-continuum"interference"and"the"separate"control"of"these"two"processes,"as"enabled"by"the"coupling"t,6provides"an"effective"means"for"resonant"control.
""In"Fig.
"3(b),"we"show"how"the"evolution"of"the"detector"resonance"in"the"magnetic"field"may"be"reproduced"within"our"model,"by"direct"variation"of"the"intruder"coupling"t.
"For"simplicity"in"these"calcu-lations,"we"have"assumed"a"fixed"detuning"of"0.
1"meV"between"the"LS"and"the"intruder,"motivated"by"our"expectation"that"the"separation"between"these"states"should"vary"only"slowly"at"high"fields"(see"Fig.
"2(d)).
"In"this"way,"we"are"able"to"compute"resonance"curves"that"compare"very"well"with"those"obtained"experimentally.
"The"implication,"therefore,"is"that"the"magnetic-field"induced"distortion"of"the"detector"resonance"does"indeed"result"from"increased"coupling"to"an"intruder,"in"this"case"one"that"is"formed"by"the"lowest"1D"subband"of"the"swept-QPC.
"In"support"of"this"scenario,"we"note"that"the"most"pronounced"change"in"the"detector"resonance"occurs"between"0-"and"2-T,"beyond"which"little"further"change"is"ob-served"(compare"the"2-"and"4-T"plots"in"Fig.
"2(c)).
"Such"behavior"is"consistent"with"the"results"of"Fig.
"2(d),"in"which"the"intruder"quickly"approaches"the"LS"with"initial"increase"of"the"magnetic"field,"but"thereafter"advances"on"it"much"more"slowly.
"A"further"point"that"can"be"made"here"follows"by"comparing"the"varia-tions"of"Gs"and"Gd"(Fig.
"2(c)),"which"shows"that"the"peak"in"the"detector"resonance"always"occurs"once"the"swept"QPC"is"fully"pinched-off"(where"Gs"~"0).
"The"dip,"on"the"other"hand,"occurs"at"less-negative"Vs,"where"the"QPC"is"beginning"to"open.
"This"sequence"is"consistent"with"the"form"of"the"density"of"states"suggested"in"Fig.
"2(b),"in"which"the"LS"lies"at"lower"energy"than"the"1D"subbands"and"so"should"require"stronger"gate"biasing"to"align"it"with"the"Fermi"level"in"the"drain.
"At"the"same"time,"the"correlation"of"the"dip"to"the"onset"of"Gs"is"fully"consistent"with"the"idea"that"the"dip"occurs"on"achieving"alignment"be-tween"the"edge"of"the"1D"continuum"and"this"Fermi"level.
"!
!
8""Turning"to"the"temperature-dependent"evolution"of"the"detector"resonance"in"Fig.
"4(a),"this"be-havior"cannot"be"reproduced"by"adopting"the"usual"thermal"smearing"of"the"Fermi"function.
"Instead,"in"Fig.
"4(b)"we"demonstrate"that"that"the"essential"features"of"experiment"can"be"captured"by"mimicking"the"increase"of"temperature"by"simultaneously"decreasing"the"coupling"(v)"to"the"LS"while"increasing"that"(t)"to"the"intruder.
"In"terms"of"justifying"this"ad-hoc"approach,"we"note"that"the"confinement"of"the"LS"should"weaken"with"increasing"temperature,"and"previous"experiment"[28]"suggests"that"the"charac-teristic"temperature"scale"on"which"this"occurs"corresponds"well"to"that"for"which"the"peak"is"sup-pressed"in"Fig.
"4(a).
"At"the"same"time,"since"the"intruder"lies"at"higher"energy"than"the"LS,"activation"into"this"component"should"increase"with"increasing"temperature.
"In"the"Supporting"Information,"we"show"that"reasonable"agreement"with"experiment"can"be"obtained"by"varying"the"coupling"to"the"LS"alone.
"Although"the"quality"of"the"resulting"fits"is"not"as"good"as"in"Fig.
"4(b),"this"provides"confidence"that"we"capture"the"essential"physics"of"the"intruder.
"Most"importantly,"the"essential"conclusion"reached"from"our"calculations"is"that"the"unusual"temperature"dependence"of"Fig.
"4(a)"directly"reflects"the"fact"that"the"peak"and"dip"of"the"high-field"resonance"are"due"to"physically"distinct"states"(LS"vs.
"1D"intruder,"re-spectively).
"Indeed,"it"is"interesting"that"at"40"K,"where"all"evidence"of"the"peak"is"suppressed,"the"high-energy"tail"of"the"anti-resonance"in"Fig.
"4(a)"is"suggestive"of"the"1D"form"of"the"intruder"density"of"states.
""Concluding"with"some"general"comments,"while"we"have"focused"here"on"providing"a"solid-state"implementation"of"the"intruder-modified"FR,"it"must"be"emphasized"that"the"interference"scheme"we"have"proposed"is"a"completely"general"one.
"As"such,"it"should"be"broadly"applicable"across"a"variety"of"different"wave-based"systems,"including"those"in"both"photonics"and"electronics.
"The"intruder"provides"an"effective"means"to"tune"the"FR,"and"this"characteristic"could"enable"sensitive"schemes"for"chemical"or"biological"sensing,"and"for"the"modulation"of"photonic"or"electronic"signals.
"In"the"field"of"secure"com-munications,"for"example,"the"intruder"could"represent"an"undesirable"eavesdropper"whose"attempts"to"intercept"a"secure"transmission"channel"could"be"detected"directly"as"a"sensitive"distortion"of"its"FR.
"Perhaps"most"importantly,"however,"our"study"suggests"the"value"of"pursuing"extended"geometries"for"interference,"in"which"the"two-path"Fano"interferometer"serves"merely"as"the"basic"building"block.
"&!
!
9"ASSOCIATED&CONTENT"&SUPPORTING&INFORMATION&Supporting&Information&Available:"Detailed"theoretical"derivation"of"the"influence"of"the"intruder"on"the"Fano"resonance,"as"well"as"a"simple"analytical"model"for"the"magneto-dispersion"of"the"QPC"localized"state"and"the"edge"of"the"1D"subbands.
"Experimental"details"include"a"description"of"measurement"techniques,"and"a"demonstration"of"the"intruder"in"an"alternative"gate"configuration.
"This"material"is"available"free"of"charge"via"the"Internet"at"http://pubs.
acs.
org.
""AUTHOR&INFORMATION&Corresponding&Author:&Jonathan"Bird,"jbird@buffalo.
edu,"phone:"+1"(716)"645-1015&Author&Contributions:&The"authors"contributed"equally"to"this"work.
&Notes:&The"authors"declare"no"competing"financial"interest.
""ACKNOWLEDGEMENTS&The"experimental"research"was"supported"by"the"U.
S.
"Department"of"Energy,"Office"of"Basic"Energy"Sci-ences,"Division"of"Materials"Sciences"and"Engineering"under"Award"DE-FG02-04ER46180.
"The"work"was"performed,"in"part,"at"the"Center"for"Integrated"Nanotechnologies,"a"U.
S.
"Department"of"Energy,"Office"of"Basic"Energy"Sciences"user"facility.
"Sandia"National"Laboratories"is"a"multi-program"laboratory"man-aged"and"operated"by"Sandia"Corporation,"a"wholly"owned"subsidiary"of"Lockheed"Martin"Corporation,"for"the"U.
S.
"Department"of"Energy's"National"Nuclear"Security"Administration"under"contract"DE-AC04-94AL85000.
"JF"acknowledges"support"from"the"Swedish"Research"Council.
"""!
!
10"REFERENCES&1.
Fano,"U.
"Phys.
6Rev.
"1961,"124,"1866"–"1878.
"2.
Smith,"K.
"Rep.
6Prog.
6Phys.
61966,"29,"373"–"443.
"3.
Fano,"U.
"&"Rau,"A.
"R.
"P.
"Atomic6Collisions6and6Spectra;"Academic"Press:"Orlando,"FL,"1986.
"4.
Miroshnichenko,"A.
"E.
;"Flach,"S.
;"Kivshar,"Yu.
"S.
"Rev.
6Mod.
6Phys.
"2010,"82,"2257"–"2298.
"5.
Luk'yanchuk,"B.
;"Zheludev,"N.
"I.
;"Maier,"S.
"A.
;"Halas,"N.
"J.
;"Nordlander,"P.
;"Giessen,"H.
;"Chong,"C.
"T.
"Nature6Mater.
!
2010,"9,"707"–"715.
"6.
Hao,"F.
;"Sonnefraud,"Y.
;"Van"Dorpe,"P.
;"Maier,"S.
"A.
;"Halas,"N.
"J.
;"Nordlander,"P.
"Nano6Lett.
"2008,"8,"3983""–"3988.
"7.
Hao,"F.
;"Nordlander,"P.
;"Sonnefraud,"Y.
;"Van"Dorpe,"P.
;"Maier,"S.
"A.
"ACS"Nano"2009,"3,"643–652.
"8.
Verellen,"N.
;"Sonnefraud,"Y.
;"Sobhani,"H.
;"Hao","F.
;"Moshchalkov,"V.
"V.
;"Dorpe,"P.
"V.
;"Nordlander,"P.
;"Maier,"S.
"A.
"Nano6Lett.
"2009,"9,"1663"–"1667.
"9.
Pakizeh,"T.
;"Langhammer,"C.
;"Zoric,"I.
;"Apell,"P.
;"Kll,"M.
"Nano"Lett.
"2009,"9,"882"–"886.
"10.
Liu,"N.
;"Weiss,"T.
;"Mesch,"M.
;"Langguth,"L.
;"Eigenthaler,"U.
;"Hirscher,"M.
;"Snnichsen,"C.
;"Giessen,"H.
"Nano6Lett.
"2010,"10,"1103"–"1107.
"11.
Papasimakis,"N.
;"Zheludev,"N.
"I.
"Opt.
6Phot.
6News"2009,"20,"22"–"27.
"12.
Plum,"E.
;"Liu,"X.
-X.
;"Fedotov,"V.
"A.
;"Chen,"Y.
;"Tsai,"D.
"P.
;"Zheludev,"N.
"I.
"Phys.
6Rev.
6Lett.
"2009,"102,"113902.
"13.
Papasimakis,"N.
;"Fu,"Y.
"H.
;"Fedotov,"V.
"A.
;"Prosvirnin,"S.
"L.
;"Tsai,"D.
"P.
;"Zheludev,"N.
"I.
"Appl.
6Phys.
6Lett.
62009,"94,"211902.
"14.
Goldhaber-Gordon,"D.
;"Shtrikman,"H.
;"Mahalu,"D.
;"Abusch-Magder,"D.
;"Meirav,"U.
;"Kastner,"M.
"A.
"Nature"1998,"391,"156"–"159.
"15.
Zacharia,"I.
"G.
;"Goldhaber-Gordon,"D.
;"Granger,"G.
;"Kastner,"M.
"A.
;"Khavin,"Yu.
"B.
;"Shtrikman,"H.
;"Mahalu,"D.
;"Meirav,"U.
"Phys.
6Rev.
6B"2001,"64,"155311.
"16.
Kobayashi,"K.
;"Aikawa,"H.
;"Katsumoto,"S.
;"Iye,"Y.
"Phys.
6Rev.
6Lett.
62002,"88,"256806.
"17.
Kobayashi,"K.
;"Aikawa,"H.
;"Katsumoto,"S.
;"Iye,"Y.
"Phys.
6Rev.
6B.
62003,"68,"235304.
"!
!
11"18.
Kim,"J.
;"Kim,"J.
-R.
;"Lee,"J.
-O.
;"Park,"J.
"W.
;"So,"H.
"M.
;"Kim,"N.
;"Kang,"K.
;"Yoo,"K.
-H.
;"Kim,"J.
-J.
"Phys.
6Rev.
6Lett.
62003,"90,"166403.
"19.
Johnson,"A.
"C.
;"Marcus,"C.
"M.
;"Hanson,"M.
"P.
;"Gossard,"A.
"C.
"Phys.
6Rev.
6Lett.
"2004,"93,"106803.
"20.
Kroner,"M.
;"Govorov,"A.
"O.
;"Remi,"S.
;"Biedermann,"B.
;"Seidl,"S.
;"Badolato,"A.
;"Petroff,"P.
"M.
;"Zhang,"W.
;"Barbour,"R.
;"Gerardot,"B.
"D.
;"Warburton,"R.
"J.
;"Karrai,"K.
"Nature62008,"451,"311"–"314.
"21.
Song,"J.
"F.
;"Ochiai,"Y.
;"Bird,"J.
"P.
"Appl.
6Phys.
6Lett.
62003,"82,"4561"–"4563.
"22.
Lee,"M.
;"Bruder,"C.
;"Phys.
6Rev.
6B"2006,"73,"085315.
"23.
Connerade,"J.
-P.
;"Lane,"A.
"M.
"Rep.
6Prog.
6Phys.
"1988,"51,"1439"–"1478.
"24.
See"Ch.
"5"of:"Ferry,"D.
"K.
;"Goodnick,"S.
"M.
;"Bird,"J.
"P.
"Transport6in6Nanostructures,"Cambridge"Uni-versity"Press;"Cambridge,"U.
"K.
,"2009.
"25.
Micolich,"A.
"P.
"J.
6Phys.
:6Condens.
6Matt.
"2011,"23,"443201.
"26.
Bird,"J.
"P.
;"Ochiai,"Science"2004,"303,"1621"–"1622.
"27.
Puller,"V.
"I.
;"Mourokh,"L.
"G.
;"Shailos,"A.
;"Bird,"J.
"P.
"Phys.
6Rev.
6Lett.
62004,"92,"096802.
"28.
Yoon,"Y.
;"Mourokh,"L.
;"Morimoto,"T.
;"Aoki,"N.
;"Ochiai,"Y.
;"Reno,"J.
"L.
;"Bird,"J.
"P.
!
Phys.
6Rev.
6Lett.
62007,"99,"136805.
"29.
Yoon,"Y.
;"Kang,"M.
-G.
;"Morimoto,"T.
;"Mourokh,"L.
;"Aoki,"N.
;"Reno,"J.
"L.
;"Bird,"J.
"P.
;"Ochiai,"Y.
"Phys.
6Rev.
6B"2009,"79,"121304(R).
"30.
Hirose,"K.
;"Meir,"Y.
;"Wingreen,"N.
"S.
"Phys.
6Rev.
6Lett.
"2003,"90,"026804.
"31.
Rejec,"T.
;"Meir,"Y.
"Nature"2006,"442,"900"–"903.
"32.
Guclu,"A.
"D.
;"Umrigar,"C.
"J.
;"Jiang,"H.
;"Baranger,"H.
"U.
"Phys.
6Rev.
6B"2009,"80,"201302(R).
"33.
Song,"T.
;"Ahn,"K.
-H.
"Phys.
6Rev.
6Lett.
"2011,"106,"057203.
"34.
Yakimenko,"I.
"I.
;"Tsykunov,"V.
"S.
;"Berggren,"K.
-F.
"J.
6Phys.
:6Cond.
6Matt.
"2013,"25,"072201.
"35.
Iqbal,"M.
"J.
;"Levy,"R.
;"Koop,"E.
"J.
;"Dekker,"J.
"B.
;"de"Jong,"J.
"P.
;"van"der"Velde,"J.
"H.
"M.
;"Reuter,"D.
;"Wieck,"A.
"D.
;"Aguado,"R.
;"Meir,"Y.
;"van"der"Wal,"C.
"H.
"Nature"2013,"501,"79"–"83.
"36.
Ren,"Y.
;"Yu,"W.
"W.
;"Frolov,"S.
"M.
;"Folk,"J.
"A.
;"Wegscheider,"W.
"Phys.
"Rev.
"B"2010,"82,"045313.
"37.
Klochan,"O.
;"Micolich,"A.
"P.
;"Hamilton,"A.
"R.
;"Trunov,"K.
;"Reuter,"D.
;"Wieck,"A.
"D.
"Phys.
6Rev.
6Lett.
"2011,"107,"076805.
"!
!
12"38.
Wu,"P.
"M.
;"Li,"P.
;"Zhang,"H.
;"Chang,"A.
"M.
"Phys.
6Rev.
6B"2012,"85,"085305.
"39.
Berggren,"K.
-F.
;"Roos,"G.
;"van"Houten,"H.
"Phys.
6Rev.
6B"1988,"37,"10118"–"10124.
"40.
Kouwenhoven,"L.
"P.
;"Austing,"D.
"G.
;"Tarucha,"S.
"Rep.
6Prog.
6Phys.
"2001,"64,"701"–"736.
"""!
!
13"FIGURE&CAPTIONS&"Figure&1.
&(a)&Schematic"illustration"of"the"interference"geometry"involved"in"the"conventional"Fano"reso-nance.
"(b)"Modified"Fano"geometry"with"the""intruder""continuum"(C).
"(c)&Influence"of"the"intruder"on"the"Fano-resonance"lineshape.
"The"main"panel"shows"the"variation"of"the"overall"resonance"lineshape"(δGd)"as"a"function"of"t,"while"the"inset"shows"the"original"resonance"(δGLS)"due"to"the"two-path"geome-try"when"t"="0.
"For"the"specific"values"of"r"(="0.
1)"and"v"(="4)"chosen"here,"this"resonance"is"only"weakly"asymmetric.
"(d)"The"contribution"to"the"resonance"in"(c)"from"continuum-continuum"interference"alone"(δGs),"for"various"values"of"t.
"In"both"(c)"and"(d),"the"zero"of"energy"corresponds"to"that"of"the"discrete"level"(D)"and"the"detuning"between"C"and"D"is"held"fixed"at"~0.
1"meV.
""Figure&2.
&(a)&Electron-microscope"image"of"the"coupled-QPC"device"studied"here,"showing"the"biasing"scheme"for"the"various"gates.
"The"upper-left"pair"of"gates"define"the"detector-QPC"while"the"lower-left"pair"form"the"swept-QPC"(circled).
"The"interference"pathways"(r,"v"&"t)"for"the"detector"resonance"are"also"indicated.
"Gates"denoted""Gnd""are"held"at"ground"potential"and"so"have"no"influence"on"the"exper-iment.
"For"this"reason"these"structures"have"been"artificially"lightened"in"the"image.
&(b)&Schematics"illus-trating"how"the"coupled-QPCs"provide"a"realization"of"two-"(top)"and"three-"(bottom)"path"interferome-ters.
"Top"and"bottom"panels"are"for"B"="0"and"B">"0,"respectively,"and"the"corresponding"form"of"the"density"of"states"(DoS)"in"the"swept-QPC"is"also"indicated.
"Red"denotes"the"LS,"while"the"blue"curve"cor-responds"to"the"continuum"arising"from"the"1D"subbands.
"(c)&Evolution"of"the"detector"resonance"at"4.
2"K"in"a"perpendicular"magnetic"field.
"Blue"data"are"the"resonant"contribution"to"the"detector-QPC"con-ductance"(δGd),"while"the"red"curves"show"the"corresponding"variation"of"Gs.
"δGd"was"obtained"by"sub-tracting"a"monotonic"background"from"Gd(Vs),"as"described"in"Ref.
"29.
"The"dotted"red"line"in"each"panel"denotes"pinch-off"of"the"swept-QPC,"identified"as"the"vanishing"of"Gs.
"(d)&Calculated"(non-interacting)"dispersion"of"the"LS"and"the"bottom"of"the"lowest"1D"subband"as"a"function"of"B.
"The"inset"shows"the"corresponding"separation"of"the"two"levels"as"a"function"of"the"field,"and"the"dotted"line"denotes"the"as-ymptotic"variation"of"the"level"spacing.
"See"Supporting"Information"for"further"details"of"the"calculation.
"!
!
14"&Figure&3.
&(a)&Experimental"variation"of"the"detector"resonance"at"4.
2"K"for"several"magnetic"fields"(indi-cated).
"(b)&Corresponding"theoretical"curves,"using"t"as"the"control"parameter"(values"indicated).
"The"calculations"consider"fixed"detuning"(~0.
1"meV)"between"the"LS"and"the"intruder,"and"the"curves"have"their"amplitudes"normalized"to"match"experiment.
"Successive"curves"in"both"(a)"and"(b)"are"shifted"up-wards"in"increments"of"0.
025"*"2e2/h.
""Figure&4.
&(a)&Detector"resonance"measured"at"B"="8"T"and"various"temperatures"(indicated).
"The"insets"highlight"the"behavior"at"the"highest"and"lowest"temperature.
&(b)&Calculated"resonance"obtained"by"simultaneously"increasing"transmission"via"the"intruder"(t"="1.
10"–"1.
60)"while"decreasing"that"via"the"discrete"level"(v"="6.
80"–"2.
80).
"The"insets"highlight"the"behavior"obtained"at"the"two"ends"of"this"series"(coupling"parameters"indicated"in"each"plot).
""|f>|i>rvvttCDab|f>|i>rvvDδGd(arb.
units)cE(meV)E(meV)δGs(arb.
units)t=00.
140.
290.
430.
570.
710.
861.
00dδGLS(arb.
units)t=00.
140.
290.
430.
570.
710.
861.
00aVdVdVsVsGndGndGndGnd150nmSOURCErv,tDRAINcGs,δGd(2e2/h)Vs(V)Vs(V)Vs(V)Vs(V)0T1T2T4Td!
ω1D=3meV!
ωLS=1meVbDoSESwept-QPCDetector-QPCrvDoSESwept-QPCDetector-QPCrvt|i>|f>|i>|f>Vs(V)Vs(V)abδGd(2e2/h)B=0T0.
4T1.
2T1.
6T2.
4T2.
8Tt=01.
181.
251.
281.
321.
35abVdVdVsVsGndGndGndGnd12348765SOURCEDRAINLOCALIZEDSTATEDoSE5.
01.
80.
4-1.
6-1.
4-1.
2-18T2T0T0.
050.
0250.
010Vs(V)DETECTORCONDUCTANCE.
(2e2/h)Table&of&Contents&Graphic